Biomedical Signal Processing and Modeling Complexity of Living Systems 2013

Biomedical Signal Processing and Modeling Complexity of Living Systems 2013Guest Editors Carlo Cattani Radu Badea Sheng-yong Chen and Maria Crisan

Computational and Mathematical Methods in Medicine

Biomedical Signal Processing and ModelingComplexity of Living Systems 2013



Guest Editors CarloCattani RaduBadea Sheng-yongChenand Maria Crisan

Copyright copy 2013 Hindawi Publishing Corporation All rights reserved

This is a special issue published in ldquoComputational and Mathematical Methods in Medicinerdquo All articles are open access articles dis-tributed under theCreativeCommonsAttributionLicensewhich permits unrestricted use distribution and reproduction in anymediumprovided the original work is properly cited

Editorial Board

Emil Alexov USAGeorgios Archontis CyprusDimos Baltas GermanyChris Bauch CanadaMaxim Bazhenov USAThierry Busso FranceCarlo Cattani ItalySheng-yong Chen ChinaWilliam Crum UKRicardo Femat MexicoAlfonso T Garcıa-Sosa EstoniaDamien Hall Australia

Volkhard Helms GermanySeiya Imoto JapanLev Klebanov Czech RepublicQuan Long UKC-M Charlie Ma USAReinoud Maex FranceSimeone Marino USAMichele Migliore ItalyKarol Miller AustraliaErnst Niebur USAKazuhisa Nishizawa JapanHugo Palmans UK

David James Sherman FranceSivabal Sivaloganathan CanadaNestor V Torres SpainNelson J Trujillo-Barreto CubaGabriel Turinici FranceKutlu O Ulgen TurkeyEdelmira Valero SpainJacek Waniewski PolandGuang Wu ChinaHenggui Zhang UK

Contents

Biomedical Signal Processing and Modeling Complexity of Living Systems 2013 Carlo CattaniRadu Badea Sheng-yong Chen and Maria CrisanVolume 2013 Article ID 173469 2 pages

Complexity Analysis and Parameter Estimation of Dynamic Metabolic Systems Li-Ping TianZhong-Ke Shi and Fang-Xiang WuVolume 2013 Article ID 698341 8 pages

Wavelet-Based Artifact Identification and Separation Technique for EEG Signals during GalvanicVestibular Stimulation Mani Adib and Edmond CretuVolume 2013 Article ID 167069 13 pages

Multiscale Cross-Approximate Entropy Analysis as a Measure of Complexity among the Aged andDiabetic Hsien-Tsai Wu Cyuan-Cin Liu Men-Tzung Lo Po-Chun Hsu An-Bang Liu Kai-Yu Changand Chieh-Ju TangVolume 2013 Article ID 324325 7 pages

Constructing Benchmark Databases and Protocols for Medical Image Analysis Diabetic RetinopathyTomi Kauppi Joni-Kristian Kamarainen Lasse Lensu Valentina Kalesnykiene Iiris Sorri Hannu Uusitaloand Heikki KalviainenVolume 2013 Article ID 368514 15 pages

Comparative Evaluation of Osseointegrated Dental Implants Based on Platform-Switching ConceptInfluence of Diameter LengthThread Shape and In-Bone Positioning Depth on Stress-BasedPerformance Giuseppe Vairo and Gianpaolo SanninoVolume 2013 Article ID 250929 15 pages

Effect of Pilates Training on Alpha Rhythm Zhijie Bian Hongmin Sun Chengbiao Lu Li YaoShengyong Chen and Xiaoli LiVolume 2013 Article ID 295986 7 pages

Fast Discriminative Stochastic Neighbor Embedding Analysis Jianwei Zheng Hong Qiu Xinli XuWanliang Wang and Qiongfang HuangVolume 2013 Article ID 106867 14 pages

Fractal Analysis of Elastographic Images for Automatic Detection of Diffuse Diseases of SalivaryGlands Preliminary Results Alexandru Florin Badea Monica Lupsor Platon Maria Crisan Carlo CattaniIulia Badea Gaetano Pierro Gianpaolo Sannino and Grigore BaciutVolume 2013 Article ID 347238 6 pages

Nonlinear Radon Transform Using Zernike Moment for Shape Analysis Ziping Ma Baosheng KangKe Lv and Mingzhu ZhaoVolume 2013 Article ID 208402 9 pages

ANovel Automatic Detection System for ECG Arrhythmias Using MaximumMargin Clustering withImmune Evolutionary Algorithm Bohui Zhu Yongsheng Ding and Kuangrong HaoVolume 2013 Article ID 453402 8 pages

Structural Complexity of DNA Sequence Cheng-Yuan Liou Shen-Han Tseng Wei-Chen Chengand Huai-Ying TsaiVolume 2013 Article ID 628036 11 pages

Improving Spatial Adaptivity of Nonlocal Means in Low-Dosed CT Imaging Using Pointwise FractalDimension Xiuqing Zheng Zhiwu Liao Shaoxiang Hu Ming Li and Jiliu ZhouVolume 2013 Article ID 902143 8 pages

Three-Dimensional Identification of Microorganisms Using a Digital Holographic MicroscopeNing Wu Xiang Wu and Tiancai LiangVolume 2013 Article ID 162105 6 pages

Thresholded Two-Phase Test Sample Representation for Outlier Rejection in Biological RecognitionXiang Wu and Ning WuVolume 2013 Article ID 248380 10 pages

Computational Approach to Seasonal Changes of Living Leaves Ying Tang Dong-Yan Wu and Jing FanVolume 2013 Article ID 619385 8 pages

Reliable RANSAC Using a Novel Preprocessing Model Xiaoyan Wang Hui Zhang and Sheng LiuVolume 2013 Article ID 672509 5 pages

Plane-Based Sampling for Ray Casting Algorithm in Sequential Medical Images Lili LinShengyong Chen Yan Shao and Zichun GuVolume 2013 Article ID 874517 5 pages

Self-Adaptive Image Reconstruction Inspired by Insect Compound Eye Mechanism Jiahua ZhangAiye Shi Xin Wang Linjie Bian Fengchen Huang and Lizhong XuVolume 2012 Article ID 125321 7 pages

Bayes Clustering and Structural Support Vector Machines for Segmentation of Carotid Artery Plaquesin Multicontrast MRI Qiu Guan Bin Du Zhongzhao Teng Jonathan Gillard and Shengyong ChenVolume 2012 Article ID 549102 6 pages

Heavy-Tailed Prediction Error A Difficulty in Predicting Biomedical Signals of 1119891Noise TypeMing Li Wei Zhao and Biao ChenVolume 2012 Article ID 291510 5 pages

In Vitro Evaluation of Ferrule Effect and Depth of Post Insertion on Fracture Resistance of Fiber PostsR Schiavetti and G SanninoVolume 2012 Article ID 816481 6 pages

Optimization and Implementation of Scaling-Free CORDIC-Based Direct Digital FrequencySynthesizer for Body Care Area Network Systems Ying-Shen Juang Lu-Ting Ko Jwu-E ChenTze-Yun Sung and Hsi-Chin HsinVolume 2012 Article ID 651564 9 pages

A Rate-Distortion-Based Merging Algorithm for Compressed Image Segmentation Ying-Shen JuangHsi-Chin Hsin Tze-Yun Sung Yaw-Shih Shieh and Carlo CattaniVolume 2012 Article ID 648320 7 pages

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2013 Article ID 173469 2 pageshttpdxdoiorg1011552013173469

EditorialBiomedical Signal Processing and Modeling Complexity ofLiving Systems 2013

Carlo Cattani1 Radu Badea2 Sheng-Yong Chen3 and Maria Crisan4

1 Department of Mathematics University of Salerno Via Ponte Don Melillo 84084 Fisciano (SA) Italy2 Department of Clinical Imaging Ultrasound ldquoIuliuHatieganurdquoUniversity ofMedicine and Pharmacy 400000 Cluj-Napoca Romania3 College of Computer Science amp Technology Zhejiang University of Technology Hangzhou 310023 China4Department of Histology ldquoIuliu Hatieganurdquo University of Medicine and Pharmacy 400000 Cluj-Napoca Romania

Correspondence should be addressed to Carlo Cattani ccattaniunisait

Received 7 November 2013 Accepted 7 November 2013

Copyright copy 2013 Carlo Cattani et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Biomedical signal processing aims to provide significantinsights into the analysis of the information flows fromphysiological signals As such it can be understood as a spe-cific interdisciplinary scientific discipline In fact biomedicalsignals extract information from complex biological modelsthus proposing challenging mathematical problems whosesolution has to be interpreted from a biological point of viewThe focus of this special issue is the mathematical analysisand modeling of time series in living systems and biomedicalsignals The main steps of the biomedical signals processingare as follows

(1) Signal processing of biological data implies manydifferent interesting problems dealing with signalacquisition sampling and quantization The noisereduction and similar problems as image enhance-ment are a fundamental step in order to avoid signif-icant errors in the analysis of data Feature extractionis themost important part of the analysis of biologicalsignals because of the importance which is clinicallygiven to even the smallest singularity of the image(signal)

(2) Information flows from signals imply the modelingand analysis of spatial structures self-organizationenvironmental interaction behavior and develop-ment Usually this is related to the complexity analysisin the sense that the information flows come fromcomplex systems so that signals show typical featuressuch as randomness nowhere differentiability fractal

behavior and self-similarity which characterize com-plex systems As a consequence typical parametersof complexity such as entropy power spectrumrandomness and multifractality play a fundamentalrole because their values can be used to detect theemergence of clinical pathologies

(3) Physiological signals usually come as 1D time series or2D images The most known biosignals are based onsounds (ultrasounds) electromagnetic pulses (ECGEEG and MRI) radiation (X-ray and CT) images(microscopy) and many others The clinical signalunderstanding of them follows from the correct froma mathematical point of view interpretation of thesignal

(4) Physiological signals are detected and measured bymodern biomedical devices Amongothers one of themain problems is to optimize both the investigationmethods and the device performances

The papers selected for this special issue represent agood panel in recent challenges They represent some of themost recent advances inmany different clinical investigationsdevoted to the analysis of complexity in living systems likefor example network science dynamical systems theorydynamical complexity pattern analysis implementation andalgorithms They cannot be exhaustive because of the rapidgrowing both ofmathematical methods of signal analysis andof the technical performances of devices However they aim

2 Computational and Mathematical Methods in Medicine

to offer a wide introduction on a multidisciplinary disciplineand to give some of themore interesting and original solutionof challenging problems Among them themost fascinating isto understanding of the biological structure and organizationthe intracellular exchange of information the localization ofinformation in cell nuclei and in particular the unrevealing ofthe mathematical information (functionally related) contentin DNA

This special issue contains 23 papers In the category ofmodeling dynamical complexity L-P Tian et al make com-plex analysis and parameter estimation of dynamicmetabolicsystems M Adib and E Cretu present wavelet-based artifactidentification and separation technique for EEG signalsduring galvanic vestibular stimulation X Wu and N Wuuse thresholded two-phase test sample representation foroutlier rejection in biological recognition ZMa et al proposenonlinear Radon transform using Zernike moment for shapeanalysis C-Y Liou et al study structural complexity of DNAsequenceM Li et al investigate heavy-tailed prediction errorin predicting biomedical signals of 1f noise type X Wanget al propose reliable RANSAC using a novel preprocessingmodel J Zheng et al give fast discriminative stochasticneighbor embedding analysis

In the category of methods for analysis of dynamicalcomplexity R Schiavetti and G Sannino give in vitro evalu-ation of ferrule effect and depth of post insertion on fractureresistance of fiber posts G Sannino and G Vairo makecomparative evaluation of osseointegrated dental implantsbased on platform-switching concept and find influenceof diameter length thread shape and in-bone positioningdepth on stress-based performance H-T Wu et al usemultiscale cross-approximate entropy analysis as a measureof complexity among the aged and diabetic T Kauppi et alconstruct benchmark databases and protocols for medicalimage analysis with diabetic retinopathy B Zhu et al presenta novel automatic detection system for ECG arrhythmiasusing maximum margin clustering with an immune evolu-tionary algorithm Y-S Juang et al study optimization andimplementation of scaling-free CORDIC-based direct digitalfrequency synthesizer for body care area network systems ZBian et al find the effect of Pilates training on alpha rhythm

In the category of biomedical signal analysis A FBadea et al give fractal analysis of elastographic images forautomatic detection of diffuse diseases of salivary glands QGuan et al present Bayes clustering and structural supportvectormachines for segmentation of carotid artery plaques inmulticontrastMRI J Zhang et al present self-adaptive imagereconstruction inspired by insect compound eye mechanismX Zheng et al improve spatial adaptivity of nonlocal meansin low-dosed CT imaging using pointwise fractal dimen-sion N Wu et al study three-dimensional identification ofmicroorganisms using a digital holographic microscope YTang et al propose a computational approach to seasonalchanges of living leaves L Lin et al study plane-basedsampling for a ray casting algorithm in sequential medicalimages Y-S Juang et al propose a rate-distortion-basedmerging algorithm for compressed image segmentation

As already mentioned the topics and papers are not anexhaustive representation of the area of biomedical signal

processing and modeling complexity of living systems How-ever we believe that we have succeeded to collect some ofthe most significant papers in this area aiming to improvethe scientific debate in the modern interdisciplinary field ofbiomedical signal processing

Acknowledgments

We thank the authors for their excellent contributions anddiscussions onmodern topicsThe reviewers also deserve ourspecial thanks for their useful comments on the papers thathelped the authors to clarify some crucial points

Carlo CattaniRadu Badea

Sheng-Yong ChenMaria Crisan


Research ArticleComplexity Analysis and Parameter Estimation ofDynamic Metabolic Systems

Li-Ping Tian1 Zhong-Ke Shi2 and Fang-Xiang Wu34

1 School of Information Beijing Wuzi University Beijing 101149 China2 School of Atuomation Northwestern Polytechnical University Xirsquoan Shaanxi 710072 China3Department of Mechanical Engineering University of Saskatchewan 57 Campus Drive Saskatoon SK Canada S7N 5A94Division of Biomedical Engineering University of Saskatchewan 57 Campus Drive Saskatoon SK Canada S7N 5A9

Correspondence should be addressed to Fang-Xiang Wu faw341mailusaskca

Received 24 April 2013 Revised 18 August 2013 Accepted 5 September 2013

Academic Editor Shengyong Chen

Copyright copy 2013 Li-Ping Tian et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A metabolic system consists of a number of reactions transforming molecules of one kind into another to provide the energy thatliving cells need Based on the biochemical reaction principles dynamic metabolic systems can be modeled by a group of coupleddifferential equations which consists of parameters states (concentration of molecules involved) and reaction rates Reaction ratesare typically either polynomials or rational functions in states and constant parameters As a result dynamic metabolic systemsare a group of differential equations nonlinear and coupled in both parameters and states Therefore it is challenging to estimateparameters in complex dynamic metabolic systems In this paper we propose a method to analyze the complexity of dynamicmetabolic systems for parameter estimation As a result the estimation of parameters in dynamic metabolic systems is reducedto the estimation of parameters in a group of decoupled rational functions plus polynomials (which we call improper rationalfunctions) or in polynomials Furthermore by taking its special structure of improper rational functions we develop an efficientalgorithm to estimate parameters in improper rational functions The proposed method is applied to the estimation of parametersin a dynamic metabolic system The simulation results show the superior performance of the proposed method

1 Introduction

Living cells require energy andmaterial for maintaining theiressential biological processes through metabolism which isa highly organized process Metabolic systems are defined bythe enzymes dynamically converting molecules of one typeinto molecules of another type in a reversible or irreversiblemanner Modeling and parameter estimation in dynamicmetabolic systems provide new approaches towards theanalysis of experimental data and properties of the systemsultimately leading to a great understanding of the language ofliving cells and organisms Moreover these approaches canalso provide systematic strategies for key issues in medicinepharmaceutical and biotechnological industries [1] Theformulation and identification ofmetabolic systems generallyincludes the building of themathematical model of biologicalprocess and the estimating of system parameters Because thecomponents of a pathway interact not only with each other

in the same pathway but also with those in different path-ways most (if not all) of mathematical models of metabolicsystems are highly complex and nonlinear The widely usedapproaches for modeling inter- and intracellular dynamicprocesses are based on mass action law [1ndash4] By mass actionlaw the reaction rates are generally polynomials in concen-trations of metabolites with reaction constants or rationalfunctions which are a fraction and whose denominator andnumerators are polynomials in concentrations of metaboliteswith reaction constants [1ndash4] As a result the mathematicalmodel is nonlinear not only in the states but also in theparameters Estimation of these parameters is crucial toconstruct a whole metabolic system [5ndash7]

In general all algorithms for nonlinear parameter esti-mation can be used to estimate parameters in metabolic sys-tems for example Gauss-Newton iteration method and itsvariants such as Box-Kanemasu interpolation method Lev-enberg damped least squares methods and Marquardtrsquos


ATP ATP ATP

ATP ATP

ADP

ADP

ADP

ADP ADP

Glucose Gluc6P Fruc6P

ATP + AMP 2ADP

v1

v2

v3

v4 v

5

v6

v7

v8

Fruc16P2

Figure 1 Schematic representation of the upper part of glycolysis [4]

method [8 9] However these iteration methods are initial-sensitive Another main shortcoming is that these methodsmay converge to the local minimum of the least squares costfunction and thus cannot find the real values of parame-ters Furthermore because of their highly complexity andnonlinearity Gauss-Newton iterationmethod and its variantscannot efficiently and accurately estimate the parameters inmetabolic systems [5ndash7 10 11]

In this paper we propose a systematic method for esti-mating parameters in dynamic metabolic systems Typicallymathematical model of dynamic metabolic systems consistsof a group of nonlinear differential equations some of whichcontains several rational functions in which parameters arenonlinear In Section 2 we propose a method for modelcomplexity analysis via the stoichiometric matrix As a resultwe obtain a group of equations each of which contains onlyone-rational function plus polynomial functions which wecalled an improper rational function Then based on theobservation that in the improper rational functions both thedenominator and numerator are linear in parameters whilepolynomials are also linear in parameters we develop an iter-ative linear least squares method for estimating parametersin dynamic metabolic systems in Section 3 The basic ideais to transfer optimizing a nonlinear least squares objectivefunction into iteratively solving a sequence of linear leastsquares problems In Section 4 we apply our developedmethod to estimate parameters in a metabolism systemFinally we give conclusions and some directions of futurework along with this study in Section 5

2 Model Complexity Analysis forParameter Estimation

A dynamic metabolic system consists of 119896 substances(molecules) and 119898 reactions can be described by a systemof differential equations as follows

119889119909119894

119889119905=

119898

sum

119895=1

119888119894119895119903119895 for 119894 = 1 119896 (1)

where 119909119894represents the concentrations of molecule 119894 119903

119895

represents the reaction rate 119895 and 119888119894119895represents the stoi-

chiometric coefficient of molecule 119894 in reaction 119895 The massaction law in biochemical kinetics [2ndash4 12] states that thereaction rate is proportional to the probability of a collisionof the reactants This probability is in turn proportional tothe concentration of reactants Therefore reaction rate 119903

119895is

a function of the concentrations of molecules involved inreaction 119895 and proportion constants

The stoichiometric coefficient 119888119894119895assigned to molecule 119894

and reaction 119895 can be put into a so-called stoichiometricmatrix C = [119888

119894119895]119896times119898

Let 119883 = [1199091 1199092 119909

119896]119879 and r =

[1199031 1199032 119903

119898]119879 and let 120573 = [120573

1 1205732 120573

119901]119879 represent the

vector consisting of all independent proportion constantsand then (1) can be rewritten in the following vector-matrixformat

119889119883

119889119905= Cr (119883120573) (2)

In principle the stoichiometric coefficient 119888119894119895in matrix C

is a constant integer and can be decided according to howmolecule 119894 is involved in reaction 119895 According to mass actionlaw the expression of reaction rates can be determined to bepolynomials or rational functions with reaction constants [2ndash4 12] The challenge to build up the mathematic model ofdynamic metabolic system (2) is to estimate the parametervector 120573 especially when some reaction rates are in the formof rational functions in which parameters are nonlinear

If each differential equation in (2) contains one-rationalfunction without or with polynomial functions the parame-ters in model (2) can be estimated by algorithms in [13 14]or a new algorithm proposed in the next section of thispaper Unfortunately each differential equation contains alinear combination of several rational functionswhichmakesthe parameter estimation in those coupled differential equa-tions more difficult The stoichiometric matrix contains veryimportant information about the structure of the metabolicsystems and is widely used to analyze the steady state andflux balance of metabolic systems [2ndash4] In this paper viathe stoichiometric matrix we propose a systematic methodto transfer a system of differential equations (2) into anothersystem of differential equations in which each differentialequation contains at most one-rational function

Running Example To illustrate the proposed method we usethe upper part of glycolysis system as a running exampleshowing how the method is applied to this system step afterstep The schematic representation of this system is shown inFigure 1 The model for this metabolic system is described bythe system of differential equations (2) as follows

119889

119889119905Gluc6P = 119903

1minus 1199032minus 1199033

119889

119889119905Fruc6P = 119903

3minus 1199034

119889

119889119905Fruc1 6P

2= 1199034minus 1199035

Computational and Mathematical Methods in Medicine 3

119889

119889119905ATP = minus119903

1minus 1199032minus 1199034+ 1199036minus 1199037minus 1199038

119889

119889119905ADP = 119903

1+ 1199032+ 1199034minus 1199036+ 1199037+ 21199038

119889

119889119905AMP = minus119903

8

(3)

Based on the mass action law the individual reaction ratescan be expressed as

1199031=

119881max2ATP (119905)

119870ATP1 + ATP (119905)

1199032= 1198962ATP (119905) sdot Gluc6P (119905)

1199033= (

119881119891

max3

119870Gluc6P3Gluc6P (119905)

minus119881119903

max3

119870Fruc6P3Fruc6P (119905))

times (1 + (Gluc6P (119905)

119870Gluc6P3)

+Fruc6P (119905)

119870Fruc6P3)

minus1

1199034=

119881max4(Fruc6P (119905))2

119870Fruc6P4 (1 + 120581(ATP (119905) AMP (119905))2) + (Fruc6P (119905))

2

1199035= 1198965Fruc1 6P

2 (119905)

1199036= 1198966ADP (119905)

1199037= 1198967ATP (119905)

1199038= 1198968119891ATP (119905) sdot AMP (119905) minus 119896

8119903(ADP (119905))2

(4)

Model (3) has six ordinary differential equations (ODEs) and15 parameters contained in eight reaction rates three out ofwhich are rational functions Some ODEs contain more thanone rational reaction rates which makes the parameter moredifficult

Comparing (3) to (2) we have the state vector X =[Gluc6P Fruc6P Fruc16P

2 ATP ADP AMP] and stoichio-

metric matrix

C =

[[[[[[[

[

1 minus1 minus1 0 0 0 0 0

0 0 1 minus1 0 0 0 0

0 0 0 1 minus1 0 0 0

minus1 minus1 0 minus1 0 1 minus1 minus1

1 1 0 1 0 minus1 1 2

0 0 0 0 0 0 0 minus1

]]]]]]]

]

(5)

In the following we describe our proposedmethod to analyzethe complexity of model (2) through the running example

Step 1 Collect the columns in the stoichiometric matrixcorresponding to the rational reaction rates in model (2) toconstruct a submatrix C

119903and collect other columns (cor-

responding to polynomial reaction rates) to construct asubmatrix C

119901 Therefore we have

119889119883

119889119905= Cr (119883120573) = C

119903r119903(119883120573) + C

119901r119901(119883120573) (6)

where r119903is the subvector of r and consists of all rational

reaction rates while r119901is another subvector of r and consists

of all polynomial reaction rates In this step we shouldmake sure that the rank of matrix C

119903equals the number of

rational reaction rates If the rank of matrixC119903does not equal

the number of rational reaction rates it means that somerational reaction rates are not independentThenwe combinedependent rational reaction rates together to create a newreaction rate such that all resulted rational reaction ratesshould be linearly independent [14] As a result the rank ofmatrix C

119903will equal the number of rational reaction rates

For the running example we have

C119903= [1198881 1198883 1198884] =

[[[[[[[

[

1 minus1 0

0 1 minus1

0 0 1

minus1 0 minus1

1 0 1

0 0 0

]]]]]]]

]

C119901

= [1198882 1198885 1198886 1198887 1198888] =

[[[[[[[

[

minus1 0 0 0 0

0 0 0 0 0

0 minus1 0 0 0

minus1 0 1 minus1 minus1

1 0 minus1 1 2

0 0 0 0 minus1

]]]]]]]

]

(7)

and r119903

= [1199031 1199033 1199034] and r

119901= [1199032 1199035 1199036 1199037 1199038] The rank of

matrix C119903equals 3 which is the number of rational reaction

rates

Step 2 Calculate the left inverse matrix of C119903 That is cal-

culate Cminus119903such that

Cminus119903C119903= 119868 (8)

As matrix C119903has the column full rank matrix Cminus

119903satisfying

(8) exists although it is typically not unique For a givenmatrix C

119903 Cminus119903can be easily found by solving (8) which is

a linear algebraic system If it is not unique any matrixsatisfying (8) works for our proposed method

For the running example we can have

Cminus119903

= [

[

1 1 1 0 0 0

0 1 1 0 0 0

0 0 1 0 0 0

]

]

(9)

Step 3 Multiply (6) by matrix Cminus119903from the left to obtain

Cminus119903

119889119883

119889119905= Cminus119903C119903r119903(119883120573) + Cminus

119903C119901r119901(119883120573)

= r119903(119883120573) + Cminus

119903C119901r119901(119883120573)

(10)


or

r119903(119883120573) + Cminus

119903C119901r119901(119883120573) = Cminus

119903

119889119883

119889119905 (11)

From its expression each differential equation in the system(11) contains only one-rational reaction rates plus a linearcombination of polynomial reaction rates


1199031minus 1199032minus 1199035=

119889

119889119905(Gluc6P + Fruc6P + Fruc1 6P

2)

1199033minus 1199035=

119889

119889119905(Fruc6P + Fruc1 6P

2)

1199034minus 1199035=

119889

119889119905Fruc1 6119875

2

(12)

Step 4 Calculate matrix Cperp119903such that

Cperp119903C119903= 0 (13)

where Cperp119903has the full row rank and rank(Cperp

119903) + rank(Cminus

119903) =

the number of rows in C119903 Note that Cperp

119903can be easily found

by solving (13) which is a homogenous linear algebraicsystem Again if it is not unique any matrix satisfying (13)works for our proposed method

Then multiply (6) by matrix Cperp119903from the left to obtain

Cperp119903

119889119883

119889119905= Cperp119903C119903r119903(119883120573) + Cperp

119903C119901r119901(119883120573) = Cperp

119903C119901r119901(119883120573)

(14)or

Cperp119903C119901r119901(119883120573) = Cperp

119903

119889119883

119889119905 (15)


Cperp119903

= [

[

1 1 2 1 0 0

0 0 0 1 1 0

0 0 0 0 0 1

]

]

Cperp119903C119901

= [

[

minus2 minus2 1 minus1 minus1

0 0 0 0 1

0 0 0 0 minus1

]

]

(16)

Step 5 Let119863 = Cperp119903C119901 If rank(119863) ge the number of columns

then solving (15) yields

r119901(119883120573) = (119863

119879119863)minus1

119863119879Cperp119903

119889119883

119889119905 (17)

If rank(119863) lt the number of columns it means that somepolynomial reaction rates in (15) are linearly dependentThencombine the linearly dependent rates and construct a newreaction rate vector r

119901(119883120573) and full column rank matrix 119863

such that

119863r119901(119883120573) = 119863r

119901(119883120573) = Cperp

119903C119901r119901(119883120573) = Cperp

119903

119889119883

119889119905 (18)

and then solving (18) yields

r119901(119883120573) = (119863

119879

119863)119863119879Cperp119903

119889119883

119889119905 (19)

For the running example we have rank(119863) lt the numberof columns As the first four columns are linearly dependentwe can have a new reaction ratesminus2119903

2minus21199035+1199036minus1199037Therefore

we have

119863 = [

[

1 minus1

0 1

0 minus1

]

]

119863119879Cperp119903

= [1 1 2 1 0 0

minus1 minus1 minus2 0 1 minus1]

(20)

and furthermore noting that (119889119889119905)(ATP+ADP+AMP) = 0from (19) we have

1199036minus 1199037minus 21199032minus 21199035

=119889

119889119905(Gluc6P + Fruc6P

+ 2Fruc1 6P2+ ATP minus AMP)

1199038= minus

119889

119889119905AMP

(21)

After these five steps dynamic metabolic system (2) istransferred into a system of differential equations in whicheach differential equation contains one-rational functionplus polynomial functions ((11) or (12)) or only polynomialfunction ((19) or (21)) Parameters in (19) can be analyticallyestimated by well-known least squares methods In the nextsection we describe an algorithm to estimate parameters in(11)

3 Parameter Estimation Algorithm

After its complexity analysis estimating parameters indynamic metabolic system is reduced to mainly estimatingparameters in a rational function plus polynomial whichwe call the improper rational function These functions arenonlinear in both parameters and state variables Thereforeestimation of parameters in these models is a nonlinearestimation problem In general all algorithms for nonlinearparameter estimation can be used to estimate parametersin the improper rational functions for example Gauss-Newton iteration method and its variants such as Box-Kanemasu interpolation method Levenberg damped leastsquares methods Marquardtrsquos method [9ndash12 15] and moresophisticatedmethods [16]However these iterationmethodsare initial sensitive Another main shortcoming is that mostof these methods may converge to the local minimum ofthe least squares cost function and thus cannot find thereal values of parameters In the following we describe aniterative linear least squaresmethod to estimate parameters inthe improper rational functions The basic idea is to transferoptimizing a nonlinear least squares objective function intoiteratively solving a sequence of linear least squares problems

Consider the general form of the following improperrational functions

120578 (X120573) =1198730 (X) + sum

119901119873

119894=1119873119894 (X) 120573119873119894

1198630 (X) + sum

119901119863

119895=1119863119895 (X) 120573119863119895

+

119901119875

sum

119896=1

119875119896 (X) 120573119875119896

(22)


where the vector X consists of the state variables and the119901-dimensional vector 120573 consists of all parameters in theimproper rational function (22) which can naturally bedivided into three groups those in the numerator of the ratio-nal functions 120573

119873119894(119894 = 1 119901

119873) those in the denominator

of the rational function 120573119863119895

(119895 = 1 119901119863) and those in the

polynomial 120573119875119896

(119896 = 1 119901119875) where we have that 119901

119863+119901119873+

119901119875

= 119901 119873119894(X) (119894 = 0 1 119901

119873) 119863119895(X) (119895 = 0 1 119901

119863)

and 119875119896(X) (119896 = 1 119901

119875) are the known functions nonlinear

in the state variable X and do not contain any unknownparameters Either 119873

0(X) or 119863

0(X) must be nonzero and

otherwise from sensitivity analysis [9 16] the parameters inmodel (22) cannot be uniquely identified

If there is no polynomial part model (22) is reducedto a rational function Recently several methods have beenproposed for estimating parameters in rational functions[5 6 13 14] The authors in [5 6] have employed generalnonlinear parameter estimation methods to estimate param-eters in rational functions As shown in their results theestimation error is fairly large We have observed that inrational functions both the denominator and numerator arelinear in the parameters Based on this observation we havedeveloped iterative linear least squares methods in [13 14] forestimating parameters in rational functions Mathematicallyimproper rational function (22) can be rewritten as thefollowing rational function

120578 (X120573) = (1198730 (X) +

119901119873

sum

119894=1

119873119894 (X) 120573119873119894

+ (

119901119875

sum

119896=1

119875119896 (X) 120573119875119896

)

times(1198630 (X) +

119901119863

sum

119895=1

119863119895 (X) 120573119863119895

))

times (1198630(X) +

119901119863

sum

119895=1

119863119895(X)120573119863119895

)

minus1

(23)

However in the numerator of the model above there are119901119863119901119875

+ 119901119873

+ 119901119875coefficients while there are 119901

119863+ 119901119873

+

119901119875unknown parameters When 119901

119875= 1 the number of

parameters is equal to the numbers of coefficients and themethods developed in [13 14] can be applied However when119901119875

gt 1 those methods are not applicable as the numberof parameters is less than the number of coefficients in thenumerator

In order to describe an algorithm to estimate parametersin the improper rational function (22) for 119899 given groups ofobservation data 119910

119905and X

119905(119905 = 1 2 119899) we introduce the

following notation

120573119873

= [1205731198731

1205731198732

120573119873119901119873

]119879

isin 119877119901119873

120573119863

= [1205731198631

1205731198632

120573119863119901119863

]119879

isin 119877119901119863

120573119875

= [1205731198751

1205731198752

120573119875119901119863

]119879

isin 119877119901119875

120573 = [ 120573119879119875120573119879119873120573119879119863]119879

120593119873

(X119905) = [119873

1(X119905) 1198732(X119905) 119873

119901119873(X119905)] isin 119877

119901119873

120593119863

(X119905) = [119863

1(X119905) 1198632(X119905) 119863

119901119863(X119905)] isin 119877

119901119863

120593119875(X119905) = [119875

1(X119905) 1198752(X119905) 119875

119901119875(X119905)] isin 119877

119901119875

Y = [119910(1) 119910(2) 119910(119899)]119879

isin 119877119899

Φ1198730

= [1198730(X1) 1198730(X2) 119873

0(X119899)]119879

isin 119877119899

Φ1198630

= [1198630(X1) 1198630(X2) 119863

0(X119899)]119879

isin 119877119899

Φ119873

=

[[[[[

[

120593119873

(X1)

120593119873

(X2)

120593119873

(X119899)

]]]]]

]

isin 119877119899times119901119873

Φ119863

=

[[[[[

[

120593119863

(X1)

120593119863

(X2)

120593119863

(X119899)

]]]]]

]

isin 119877119899times119901119863

Φ119875

=

[[[[[

[

120593119875(X1)

120593119875(X2)

120593119875(X119899)

]]]]]

]

isin 119877119899times119901119875

Ψ (120573119863) = diag

[[[[[

[

1198630(X1) + 120593119863

(X1)120573119863

1198630(X2) + 120593119863

(X2)120573119863

1198630(X119899) + 120593119863

(X119899)120573119863

]]]]]

]

isin 119877119899times119899

(24)

To estimate parameters in the improper rational function(22) as in [11] we form a sum of the weighted squared errors(the cost function) with the notions above as follows

119869 (120573) = 119869 (120573119875120573119873120573119863)

= sum(1198630(X119905) + 120593119863

(X119905)120573119863)2

times (1198730(X119905) + 120593119873

(X119905)120573119873

1198630(X119905) + 120593119863

(X119905)120573119863

+ Φ119875120573119875minus 119910119905)

2

(25)

Minimizing 119869(120573) with respect to 120573 = [120573119879119875120573119879119873120573119879119863]119879

cangive the nonlinear least squares estimation of parameters 120573

119875

120573119873 and120573

119863We rewrite the objective function (22) as follows

119869 (120573) = sum[(1198630(X119905) + 120593119863

(X119905)120573119863)Φ119875120573119875+ 120593119873

(X119905)120573119873

minus120593119863

(X119905) 119910119905120573119863

minus 1198630(X119905) 119910119905+ 1198730(X119905)]2

(26)


Table 1 The true value (from [4]) estimated value and relative estimation errors

Parameter name True value Estimated value REE ()119881max2 (mMsdotminminus1) 502747 502447 00001119870ATP1 (mM) 010 010000 003991198962(mMminus1sdotminminus1) 226 22599 00049

119881119891

max3 (mMsdotminminus1) 140282 1394917 05633119881119903

max3 (mMsdotminminus1) 140282 1413623 07701119870Gluc6P3 (mM) 080 07999 13884119870Fruc6P3 (mM) 015 01499 00930119881max4 (mMsdotminminus1) 447287 446664 01372119870Fruc6P4 (mM2) 0021 00206 18457119896 015 01526 174471198965(minminus1) 604662 60466 00007

1198966(minminus1) 6848 684837 00054

1198967(minminus1) 321 320797 00078

1198968119891

(minminus1) 4329 4328408 001371198968119903(minminus1) 13333 133314 00120

In the objective function (26) for a given parameters 120573119863in

the first term we have

119869 (120573) = 119869 (120573119875120573119873120573119863120573119863)

= [A (120573119863)120573 minus b]

119879

[A (120573119863)120573 minus b]

(27)

where

119860(120573119863) =

[[[

[

Ψ(120573119863)Φ119879

119875

Φ119879

119873

minus diag (119884)Φ119879

119863

]]]

]

isin 119877119899times119901

(28)

b = (Φ1198630

diag (119884) minus Φ1198730

) isin 119877119899 (29)

Then for given parameters 120573119863 we can estimate the param-

eters 120573 = [120573119879119875120573119879119873120573119879119863]119879

by linear least squares method asfollows

120573 = [A119879 (120573119863)A (120573

119863)]minus1

A119879 (120573119863) b (30)

Based on the above discussion we propose the followingiterative linear least squares method

Step 1 Choose the initial guess for 1205730119863

Step 2 Iteratively construct matrix A(120573119904119863) and vector b by

(28) and (29) respectively and then solve the linear leastsquares problem

119869 (120573119904+1

) = [A (120573119904

119863)120573119904+1

minus b]119879

[A (120573119904

119863)120573119904+1

minus b] (31)

which gives the solution

120573119904+1

= [A119879 (120573119904119863)A (120573

119904

119863)]minus1

A119879 (120573119904119863) b (32)

until the stopping criterion is met where 120573119904 = [120573119904119879119875

120573119904119879119873

120573119904119879119863

]119879 is the estimation of parameters 120573 at step 119904

From (31) if the estimation sequence 12057311205732 is con-verged to120573lowast the objective function (26) reaches itsminimumvalue at 120573lowast That is 120573lowastis the estimation of parameters inmodel (22)

There are several ways to set up a stopping criterion Inthis paper the stopping criteria are chosen as

10038171003817100381710038171003817120573119896 minus 120573119896minus1

1003817100381710038171003817100381710038171003817100381710038171003817120573119896minus1

10038171003817100381710038171003817+ 1

le 120576 (33)

where sdot is the Euclidean norm of the vector and 120576 is a presetsmall positive number for example 10minus5

4 Application

To investigate the method developed in previous sec-tions this study generates artificial data from the dynamicmetabolic system in the running example with the biochem-ically plausible parameter values [4] listed in column 2 ofTable 1 and initial values Gluc6P(0) = 1mM Fruc6P(0) =0mM Fruc16P

2(0) = 0mM ATP(0) = 21mM ADP(0) =

14mM and AMP (0) = 01mMThe trajectory of this systemis depicted in Figure 2 From Figure 2 the concentrations ofall molecules except for Frucose-16-biphosphate reach theirits steady states after about 01 minutes while Frucose-16-biphosphate after 05 minutes Therefore we do not use thedata simulated after 05 minutes

Although no noise is added to the artificial data in thesimulation noises are introduced in numerically calculatingthe derivatives by finite difference formulas In general thehigher the sampling frequency and more data points areused the more accurate the numerical derivatives are On theother hand we may not obtain data with the high frequencybecause of experimental limitations in practice In this studythe sampling frequency is 100 data points per minute Innumerically calculating the concentration change rate at each


0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6

Time (min)

Gluc6PFruc6P

ATPADPAMP

Con

cent

ratio

ns

Fruc16P2

Figure 2 Trajectory of system (3)

time point from concentration 119909 we adopt the five-pointcentral finite difference formula as follows

119909(119905119899) =

1

12Δ119905[119909 (119905119899minus2

) minus 8119909 (119905119899minus1

) + 8119909 (119905119899+1

) minus 119909 (119905119899+2

)]

(34)

The estimation accuracy of the proposed method isinvestigated in terms of relative estimation error which isdefined as

REE =estimate value minus true value

true value (35)

As all parameters to be estimated are nonnegative initialvalues are chosen as 0 or 1 in this study The experimentalresults are listed in columns 3 and 4 in Table 1 From column 3in Table 1 the estimated parameter values are very close to thecorresponding true values Actually the relative estimationerrors calculated from (29) for all estimated parametersexcept for two are less than 1 This indicates that theproposed method can accurately estimate the parameters inthis system

5 Conclusions and Future Work

In this study we have first described a method to analyze thecomplexity of metabolic systems for parameter estimationbased on the stoichiometric matrix of the metabolic systemsAs a result the estimation of parameters in the metabolicsystems has been reduced to the estimation of parametersin the improper rational functions or polynomial functionsThen we have developed an iterative linear least squaresmethod for estimating parameters in the improper rationalmodels The results from its application to a metabolismsystem have shown that the proposed method can accuratelyestimate the parameters in metabolic systems

We do not consider the noises in the data except thoseintroduced by numerical derivatives in this study One direc-tion of future work is to investigate the influence of noises inthe data to the estimation accuracy In addition low samplingfrequency is expected particularly for molecular biologicalsystems as in practice measurements from them may bevery expensive or it is impossible to sample measurementswith high frequencies Another direction of future work isto improve the estimation accuracy of the proposed methodwith low sampling frequencies

Acknowledgments

This work was supported by the Special Fund of Ministry ofEducation of Beijing for Distinguishing Professors and Sci-ence and Technology Funds of Beijing Ministry of Education(SQKM201210037001) to Li-Ping Tian by National NaturalScience Foundation of China (NSFC 61134004) to Zhong-Ke Shi and by Natural Sciences and Engineering ResearchCouncil of Canada (NSERC) to Fang-Xiang Wu

References

[1] M Fussenegger J E Bailey and J Varner ldquoA mathematicalmodel of caspase function in apoptosisrdquo Nature Biotechnologyvol 18 no 7 pp 768ndash774 2000

[2] J Nielsen J Villadsen and G Liden Bioreaction EngineeringPrinciples Kluwer Academic Publishers New York NY USA2nd edition 2003

[3] G N Stephanopoulos A A Aritidou and J NielsenMetabolicEngineering Principles and Methodologies Academic Press SanDiego Calif USA 1998

[4] E Klipp R Herwig A Kowald C Wierling and H LehrachSystems Biology in Practice Concepts Implementation andApplicationWiley-VCHandKGaAWeinheimGermany 2005

[5] K G Gadkar J Varner and F J Doyle III ldquoModel identificationof signal transduction networks from data using a state regula-tor problemrdquo Systems Biology vol 2 no 1 pp 17ndash29 2005

[6] K G Gadkar R Gunawan and F J Doyle III ldquoIterativeapproach to model identification of biological networksrdquo BMCBioinformatics vol 6 article 155 2005

[7] I-C Chou and E O Voit ldquoRecent developments in parameterestimation and structure identification of biochemical andgenomic systemsrdquoMathematical Biosciences vol 219 no 2 pp57ndash83 2009

[8] J V Beck and K J Arnold Parameter Estimation in Engineeringand Science John Wiley amp Sons New York NY USA 1977

[9] A van den Bos Parameter Estimation for Scientists and Engi-neers John Wiley amp Sons Hoboken NJ USA 2007

[10] P Mendes and D B Kell ldquoNon-linear optimization of bio-chemical pathways applications to metabolic engineering andparameter estimationrdquo Bioinformatics vol 14 no 10 pp 869ndash883 1998

[11] C G Moles P Mendes and J R Banga ldquoParameter estimationin biochemical pathways a comparison of global optimizationmethodsrdquoGenome Research vol 13 no 11 pp 2467ndash2474 2003

[12] E Klipp W Liebermeister C Wierling A Kowald H Lehracjand R Herwing Systems Biology A Textbook Wiley-VCH andKGaA Weiheim Germany 2009


[13] F X Wu L Mu and Z K Shi ldquoEstimation of parametersin rational reaction rates of molecular biological systems viaweighted least squaresrdquo International Journal of Systems Sciencevol 41 no 1 pp 73ndash80 2010

[14] F X Wu Z K Shi and L Mu ldquoEstimating parameters inthe caspase activated apoptosis systemrdquo Journal of BiomedicalEngineering and Technology vol 4 no 4 pp 338ndash354

[15] L Marucci S Santini M di Bernardo and D di BernardoldquoDerivation identification and validation of a computationalmodel of a novel synthetic regulatory network in yeastrdquo Journalof Mathematical Biology vol 62 no 5 pp 685ndash706 2011

[16] L Cheng Z G Hou Y Lin M Tan W C Zhang and F-X Wu ldquoRecurrent neural network for non-smooth convexoptimization problems with application to the identificationof genetic regulatory networksrdquo IEEE Transactions on NeuralNetworks vol 22 no 5 pp 714ndash726 2011


Research ArticleWavelet-Based Artifact Identification and Separation Techniquefor EEG Signals during Galvanic Vestibular Stimulation

Mani Adib and Edmond Cretu

Department of Electrical and Computer Engineering The University of British Columbia Vancouver BC Canada V6T 1Z4

Correspondence should be addressed to Mani Adib maniadibgmailcom

Received 22 March 2013 Accepted 5 June 2013

Academic Editor Carlo Cattani

Copyright copy 2013 M Adib and E Cretu This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

We present a newmethod for removing artifacts in electroencephalography (EEG) records during Galvanic Vestibular Stimulation(GVS)Themain challenge in exploiting GVS is to understand how the stimulus acts as an input to brain We used EEG to monitorthe brain and elicit the GVS reflexes However GVS current distribution throughout the scalp generates an artifact on EEG signalsWe need to eliminate this artifact to be able to analyze the EEG signals during GVS We propose a novel method to estimate thecontribution of the GVS current in the EEG signals at each electrode by combining time-series regression methods with waveletdecomposition methods We use wavelet transform to project the recorded EEG signal into various frequency bands and thenestimate the GVS current distribution in each frequency bandThe proposedmethodwas optimized using simulated signals and itsperformance was compared to well-accepted artifact removal methods such as ICA-based methods and adaptive filtersThe resultsshow that the proposed method has better performance in removing GVS artifacts compared to the others Using the proposedmethod a higher signal to artifact ratio ofminus1625 dBwas achieved which outperformed othermethods such as ICA-basedmethodsregression methods and adaptive filters

1 Introduction

Brain stimulation by means of electrical currents has beenemployed in neurological studies for therapy purposes formany years [1ndash5] However the ability to analyze the ongoingneural activities during the stimulation is limited due to theartifact generated by GVS The leakage of the stimulationcurrent through the scalp generates an additional electricalpotential with a much higher amplitude than that of theneural activities As a result higher artifactual potentials arecollected by the EEG electrodes especially in the neighbour-hood of stimulation areasThe stimulation artifacts which aresuperimposed on the EEG signals are the main obstacle inunderstanding the effects of the GVS interactions with neuralcircuitries in different brain regions Analyzing the EEG sig-nals during GVS stimulation is of high importance as it pro-vides information on how it affects the neural activities Forinstance in suppressing the symptoms of some neurologicaldisorders using GVS researchers are interested in elicitingGVS responses in different brain regions Furthermore to be

able to perform GVS studies in closed-loop mode where thedelivered GVS stimuli are adjusted in response to ongoingneural activities it is necessary to remove the stimulationartifacts from neural activities signals An experimentallymeasured example of EEG signals contaminated with theGVS artifacts is illustrated in Figure 1

Considering that the frequency spectra of the neuralsignals and GVS artifacts overlap filtering the frequencycomponents of GVS artifacts results in the loss of the originalneural signalsThe fourmajor EEG frequency bands areDelta(the lowest frequency band up to 4Hz)Theta (4Hz to 8Hz)Alpha (8Hz to 12Hz) and Beta (12Hz to 30Hz) In order toanalyze and understand the effect of GVS on EEG patterns itis essential to be able to remove the artifact signals from thefrequency band of interest before establishing any GVS-EEGinteraction models

There are various methods to remove different types ofartifacts such as myogenic artifacts [6ndash9] ocular artifacts[10ndash15] extrinsic artifacts such as MRI induced artifacts insimultaneous EEGfMRI studies [16] stimulation artifacts


02 04 06 08 1 12 14 16 18 2

0500

1000150020002500

Time (ms) times105

minus500

minus1000

minus1500

minus2000

minus2500

EEG

vol

tage

(120583V

)

Figure 1Measured EEG data during 72 seconds of GVS stimulationand 60 seconds before and after applying the GVS

[17ndash20] and general artifacts and signals that have noncere-bral origin [21 22] One of themost commonly usedmethodsto remove artifacts from EEG signals is the IndependentComponent Analysis (ICA) Generally in the component-basedmethods such as ICA the EEG signals are decomposedinto statistically independent and uncorrelated terms theartifact components are then identified and filtered out andthe EEG signals can be reconstructed from the neural compo-nents without artifacts However applying ICA to remove theGVS stimulation artifacts is challenging particularly whenwe increase the amplitude of the GVS over 1mAwith a signalto artifact ratio less than minus35 dB We will discuss this in moredetail later in the section ldquoComparison of the performance ofdifferent artifact removal methodsrdquo

We propose a novel method for GVS artifacts removalby combining time-series regression methods and waveletdecompositionmethods To enhance the precision of the arti-fact estimation using regression models the models shouldaccount for the complex behavior of the GVS interactionsin the frequency domain So we decomposed the recordedEEG and GVS signals into different frequency bands andthen used regression models to estimate the GVS artifactsin each frequency band We used multiresolution waveletanalysis to decompose nonstationary EEG signals in the time-frequency plane Both the discrete wavelet transform (DWT)and the stationary wavelet transform (SWT) algorithms wereemployed and the results were compared To estimate theGVS current distribution through the scalp using time-series regression methods based on biophysical models weused and compared the performance of different parametricregression models such as discrete-time polynomials non-linear Hammerstein-Wiener and state-space models

In this study we firstly used simulated data to assess andoptimize the performance of the proposed method usingvarious regression models and different wavelet algorithmsThe resulting optimizedmethodwas then applied to real dataWe compared the results of the proposed method and othermethods such as ICA using both simulated and real dataThis paper is organized as follows Section 2 provides adetailed description of the equipment and set-up the datasimulation the signal processing methods and the compar-ison of their performances Section 3 shows the results of

Table 1 EEG channels

ch1 ch2 ch3 ch4 ch5 ch6 ch7 ch8 ch9 ch10FP1 FP2 F7 F3 Fz F4 F8 T7 C3 Czch11 ch12 ch13 ch14 ch15 ch16 ch17 ch18 ch19 ch20C4 T8 P7 P3 Pz P4 P8 O1 O2 Ref

the proposed artifact removal method and in Section 4 wediscuss the proposedmethod its results and suggestedworksfor the future

2 Materials and Methods

21 Equipment and Setup The EEG recording was carriedout with a NeuroScan SynAmps2 system with 20 electrodeslocated according to the international 10ndash20 EEG system(Table 1) and with a sampling frequency set to 1 kHz

The GVS signal was applied using a Digitimer DS5 iso-lated bipolar current stimulator This stimulator can generatea stimulation current with a waveform proportional to thecontrolling voltage applied to its input The waveform wasgenerated using LabVIEWand sent to the stimulator througha National Instrument (NI) Data Acquisition (DAQ) boardIn this study we applied a zero-mean pink noise current witha 1119891-type power spectrum within a frequency range of 01 to10Hz and duration of 72 seconds We kept the amplitude ofthe delivered stimuli lower than the feeling threshold in therange of 100 120583A to 800120583A with the root mean square valuesbetween 60120583A and 450 120583A The stimulator is equipped witha data acquisition device to record the delivered stimuluswhich allows us to make a continuous record of the deliveredstimulation current and voltageWe recorded the EEG signalsduring the stimulation 60 seconds before and 60 secondsafter the stimulation The EEG data for these experimentswere acquired by our collaborator in the Pacific ParkinsonrsquosResearch Centre Nine healthy subjects (6 males 3 females)between the ages of 21 and 53 yr with no known history ofneurological disease or injury participated in this study Allsubjects were asked to relax remain still and concentrateon a focal point on the screen in front of them so thatless myogenic and ocular artifacts occur Also under restingconditions there are less variations in the head impedance[23] which is important for data acquisition in this study

22 Simulated Data To quantitatively assess and optimizethe performance of the proposed method and compare theaccuracy of different methods in removing the GVS artifactsfrom the EEG recordings we used simulated data The simu-lation study was carried out by combining the clean (artifactfree) EEG recordings with the simulatedGVS contaminationTo simulate the actual process of the GVS contamination wepaid attention to the physical structure of the electrode-skininterface and the electrical impedance of the head betweenthe points that the EEG and the GVS electrodes are placedAs the skull impedance is much higher than scalp impedance[23] we can assume that the GVS current mainly distributesthrough the scalp The skin and the electrode-skin interface


Sweat glandsand ducts

Skin

Epidermis Dermis andsubcutaneous layer

Elec

trode

Elec

trode

gel

Rp

Ep

Cp

RuR

e

Ese

Rs

Rd

Ehe

Cd

Ce

Figure 2 Electrical equivalent circuit for the electrode-skin inter-face and the underlying skin [24]

can be modeled using a resistive-capacitive circuit [24] asshown in Figure 2

In this electrical equivalent circuit 119864ℎ119890

is the half cellpotential of the electrodegel interface and the parallel com-bination of resistive 119877

119889and capacitive 119862

119889components repre-

sents the impedance associated with the electrode-gel inter-face 119877

119904is the series impedance associated with the resistance

of the electrode gel 119864119904119890is the potential difference across the

epidermis whose impedance is represented by the resistance119877119890and capacitance 119862

119890 In general the dermis and the subcu-

taneous layer under it behave as an equivalent pure resistance119877119906Thedeeper layers of the skin containing vascular nervous

components and hair follicles contribute very less to theelectrical skin impedance but sweat glands and ducts add anequivalent parallel RC network (represented by broken linesin Figure 2) and a potential difference between sweat glandsducts dermis and subcutaneous layers [24] If we neglect thepure resistance of the deeper layers of skin and the resistanceof the electrode gel we can simplify the impedance structureas follows

119885 (119904) asymp (119877119889

119904119877119889119862119889+ 1

+119877119890

119904119877119890119862119890+ 1

119877119901

119904119877119901119862119901+ 1

) (1)

This equation can be rewritten as

119885 (119904) asymp1199041198611+ 1198610

11990421198602+ 1199041198601+ 1

(2)

where 119904 is the complex frequency variable11986021198601 1198612 and 119861

1

represent specific combinations of 119877119889 119877119890 119877119901 119862119889 119862119890 and 119862

119901

for each electrode This model-based identification approachsuggests the following relation between the injected GVScurrent and the collected EEG voltage at a given electrode

119864119898= 119883in

1199041198611+ 1198610

11990421198602+ 1199041198601+ 1

+ 119864 +119882noise (3)

0 5 10 15 200

10

20

30

40

50

60

70

80

90

100

EEG channels

Fit p

erce

ntag

e

Figure 3 Fit percentage between the simulation output and themeasured EEG at each channel

where 119864119898

is the measured EEG 119883in is the injected GVScurrent 119864 is the original neural signals or EEG without arti-fact and119882noise is the measurement noise We simulated thisimpedance structure to be able to compute the GVS contri-bution at each EEG channel output

119864lowast

119898= 119883in

1199041198611+ 1198610

11990421198602+ 1199041198601+ 1

(4)

where 119864lowast119898represents the GVS artifacts in the measured EEG

signals The simulated impedance structure between GVSelectrodes and all 19 EEG electrodes was used to calculate theoutput voltage due to the GVS current (the GVS artifact) ateach EEG electrode (Figure 3)

The fit percentage is a measure of the relative energyfraction in the simulated GVS artifact calculated as given by

fit = 100(1 minussum (119864119898 (119905) minus 119864

lowast

119898(119905))2

(sum (119864119898 (119905) minusmean(119864

119898 (119905))2))

) (5)

The results show that the fitness of simulated GVS artifactis higher at the EEG electrodes which are closer to the GVSelectrodes and it is lower at further channels like channel15 (Pz) channel 10 (Cz) channel 5 (Fz) channel 1 (FP1)and channel 2 (FP2) According to (2) we can assume thatthe skin impedance model is a low-order continuous-timetransfer function with one zero and two poles To simulatethe skin impedance structure we used an iterative nonlinearleast-squares algorithm to minimize a selected cost functiontaken as the weighted sum of the squares of the errorsThis algorithm has been applied to real measured data andthe parameters of the impedance model were identified foreach EEG electrode For instance the simulated electricalequivalent impedance for channel 18 (O1 occipital) has beencalculated as

119885 (119904) = 119870119901

1 + 119904119879119911

11990421198792119908+ 2119904120577 sdot 119879

119908+ 1

(6)

with 119870119901

= minus40921 119879119908

= 010848 120577 = 47863 and119879119911= minus23726 We used this modeled impedance to simulate


0 10 20 30 40 50 60 700

102030405060708090

100

Number of time intervals

Fit p

erce

ntag

e

(a)

0 5 10 15 20 25 30 350

102030405060708090

100


Fit p

erce

ntag

e

(b)

1 2 3 4 5 6 7 8 9 10 11 12 13 140

102030405060708090

100


Fit p

erce

ntag

e

(c)

1 2 3 4 5 6 7 8 9 100

102030405060708090

100


Fit p

erce

ntag

e

(d)

1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

90

100


Fit p

erce

ntag

e

(e)

1 2 3 4 50

10

20

30

40

50

60

70

80

90

100


Fit p

erce

ntag

e

(f)

Figure 4 The fit percentage for the simulated GVS artifact at channel 18 for time intervals (a) 1 sec (b) 2 sec (c) 5 sec (d) 7 sec (e) 10 secand (f) 14 sec

the output signal due to scalp propagation between channel18 and the GVS electrodes (the simulated GVS artifact) whichis the dominant term of the total measured EEG signals witha high fit percentage of about 87

We calculated the impedance models using the entireEEG data collected in each trial (70 seconds) To addressthe concern about the time-variant properties of the scalpimpedance we computed the impedance models for shorter

time intervals (eg 1s 2s 5s 7s 10s and 14s) and analyzed thefitness of the simulated GVS artifact with the measured EEGdata (Figure 4)

The results show that the fitness of the models does notvary for different lengths of time intervals and for differenttime intervals it is very close to the fitness of the outputmodelusing the entire 70 seconds EEG data which is around 87The above results indicate that the impedance of the scalp can


be represented by one transfer function for the entire trial Tosimulate the measured EEG data during the GVS we com-bined the simulated GVS artifacts with the clean EEG datacollected right before the GVS is applied in order to get aglobal data set with known EEG and GVS artifact compo-nents This facilitates a quantitative comparison of the effec-tiveness of the method in removing the undesirable artifactsignals

23 Regression-Based Methods for Artifact Removal Theinjected GVS current and the EEG signals are recorded con-currently by the measurement system while the GVS currentdistribution through the scalp contaminates the recordedEEG signals We can use the recorded GVS current as a refer-ence to identify the GVS artifacts in the measured EEG sig-nals To identify the GVS artifacts in the contaminated EEGsignals we applied time-series regression methods using dif-ferent model structures One class of model structures is thediscrete-time polynomial models described by the followinggeneral equation

119860 (119902) 119910 (119905) =119861 (119902)

119865 (119902)119906 (119905) +

119862 (119902)

119863 (119902)119890 (119905) (7)

Here 119906(119905) is the recorded GVS current 119910(119905) is the esti-mated GVS artifact and 119890(119905) is a white noise (mean = 0 vari-ance = 120590

2) which represents the stochastic part of the model119860(119902) 119861(119902) 119862(119902) 119863(119902) and 119865(119902) are polynomials in termsof the time-shift operator q which describe the influence ofthe GVS current and measurement noise on the EEG dataModel structures such as ARMAX Box-Jenkins andOutput-Error (OE) are the subsets of the above general polynomialequation In ARMAX model 119865(119902) and 119863(119902) are equal to 1 inBox-Jenkins 119860(119902) is equal to 1 and in Output-Error model119860(119902) 119862(119902) and119863(119902) are equal to 1

Another class of model structures is Hammerstein-Wiener model which uses one or two static nonlinear blocksin series with a linear block This model structure can beemployed to capture some of the nonlinear behavior ofthe system The linear block is a discrete transfer functionrepresents the dynamic component of the model and will beparameterized using an Output-Error model similar to theprevious model The nonlinear block can be a nonlinearfunction such as dead-zone saturation or piecewise-linearfunctions As we have not observed any dead-zone or satura-tion type of nonlinearity in our data we chose the piecewise-linear function by which we can break down a nonlinear sys-tem into a number of linear systems between the breakpoints

We also used state-space models in which the relationbetween the GVS signals noise and the GVS artifacts aredescribed by a system of first-order differential equationsrelating functions of the state variables noise and the GVSsignal to the first derivatives of the state variables and Outputequations relating the state variables and the GVS signal tothe GVS artifact

24 Adaptive Filtering Methods for Artifact Removal Adap-tive filtering is another approach to remove artifacts Thismethod is specifically suitable for real time applications

The adaptive filter uses the received input data point to refineits properties (eg transfer function or filter coefficients) andmatch the changing parameters at every time instant Thesefilters have been employed to remove different EEG artifacts[25]

In our application the primary input to the adaptive filtersystem is the measured contaminated EEG signal 119864

119898(119899) as a

mixture of a true EEG 119864119905(119899) and an artifact component 119911(119899)

The adaptive filter block takes the GVS current 119894GVS(119899) as thereference input and estimates the artifact componentThe fil-ter coefficients ℎ

119898are adjusted recursively in an optimization

algorithm driven by an error signal

119890 (119899) = 119864119898 (119899) minus 119864GVS (119899) = 119864

119905 (119899) minus [119911 (119899) minus 119864GVS (119899)] (8)

where

119864GVS (119899) =119872

sum

119898=1

ℎ119898sdot 119894GVS (119899 + 1 minus 119898) (9)

Because of the function of vestibular systemwhichmodulatesthe stimulation signals [26] there is no direct linear correla-tion between the true EEG 119864(119899) and the GVS current 119894GVS(119899)On the other hand there is a strong correlation betweenthe GVS artifact 119911(119899) and 119894GVS(119899) so we can calculate theexpected value of 1198902 as follows

119864 [1198902(119899)] = 119864 [(119864

119898 (119899) minus 119864GVS (119899))2

] (10)

or

119864 [1198902(119899)] = 119864 [119864

2

119905(119899)] minus 119864 [(119911 (119899) minus 119864GVS (119899))

2

] (11)

And as the adjustment of the filter coefficients does notaffect the 119864[1198642

119905(119899)] therefore minimizing the term 119864[(119911(119899) minus

119864GVS(119899))2] is equivalent to minimizing 119864[1198902(119899)]

Among the various optimization techniques we chose theRecursive Least-Squares (RLS) and the Least Mean Squares(LMS) for our application In the section ldquoComparison ofthe performance of different artifact removal methodsrdquo wecompared the results of adaptive filters with those of the othermethods

25 Wavelet Decomposition Methods In this section weexplain how we employ the wavelet methods to enhance theperformance of our artifact removal method The appliedGVS current in this study is a pink noise with frequency bandof 01ndash10Hz Both the GVS current and the EEG data areacquired at the sampling rate of 1000Hz After antialiasingfiltering the signals are in a frequency range of 0ndash500HzThe following is the power spectrumof theGVS current usingWelchrsquos method (Figure 5)

As shown above the main GVS frequency componentsare in the range of 01 to 10Hz To achieve the best fit betweenthe estimated GVS contribution and the measured EEG ateach EEG channel we broke down the recorded GVS currentand the contaminated EEG data into various frequencybands by means of wavelet analysis and estimated the GVSartifacts in each frequency bandWavelet transform is able to


Table 2 Frequency bands for approximation and details components

L1 L2 L3 L4 L5 L6Approximation 0ndash250 0ndash125 0ndash625 0ndash3125 0ndash1575 0ndash787Details 250ndash500 125ndash250 625ndash125 3125ndash625 1575ndash3125 787ndash1575


0 50 100 150 200 250 300 350 400 450 500Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

Welch power spectral density estimateminus50

minus55

minus60

minus65

minus70

minus75

minus80

minus85

2 4 6 8 10 12 14Frequency (Hz)

minus52

minus53

minus54

minus55

minus56

minus57

Pow

erfr

eque

ncy

(dB

Hz)

Figure 5 The GVS current power spectrum

construct a high resolution time-frequency representation ofnonstationary signals like EEG signals In wavelet transformthe signal is decomposed into a set of basis functionsobtained by dilations and shifts of a unique function 120595 calledthemother or the prototypewavelet as opposed to a sine wavewhich is used as the basis function in the Fourier TransformWhen the signals are discrete the discrete wavelet transform(DWT) algorithm can be applied and the set of basis func-tions are defined on a ldquodyadicrdquo grid in the time-scale plane as

120595119895119896 (119905) = 2

minus(1198952)120595 (2minus119895119905 minus 119896) (12)

where 2119895 governs the amount of scaling and 1198962

119895 governsthe amount of translation or time shifting The wavelettransform is the inner product of the basis wavelet functionsand the signal in the time domain In the DWT algorithmthe discrete time-domain signal is decomposed into highfrequency or details components and low frequency orapproximation components through successive low pass andhigh pass filters For multi resolution analysis the originalsignal is decomposed into an approximation and details partsThe approximation part is decomposed again by iteratingthis process thus one signal can be decomposed into manycomponents The basic DWT algorithm does not preservetranslation invariance Consequently a translation of waveletcoefficients does not necessarily correspond to the sametranslation of the original signalThis nonstationary propertyoriginates from the downsampling operations in the pyram-idal algorithm The algorithm can be modified by inserting2119895minus 1 zeros between filters coefficients of the layer 119895 instead

of down-sampling This modified version of the DWTalgorithm is called stationary wavelet transform (SWT) and itcan preserve the translation invariance property In this studywe applied both DWT and SWT to decompose the EEGsignals using different mother wavelets such as Symlet andDaubechies of different orders Both the GVS current and thesimulated EEG signals were decomposed into 12 levels andthus we have the frequency bands for approximation anddetail components shown in Table 2

26 ICA-Based Methods for Artifact Removal IndependentComponent Analysis (ICA) is a statistical method used toextract independent components from a set of measuredsignals This method is a special case of the Blind Source Sep-arationmethods where the 119870 channels of the recorded EEGsignals (119864(119905) = 119890

1(119905) 119890

119870(119905)) are assumed to be a linear

combination of 119873(119873 le 119870) unknown independent sources(119878(119905) = 119904

1(119905) 119904

119873(119905))

119864 (119905) = 119872119878 (119905) (13)

where 119872 is the unknown mixing matrix defining weightsfor each source contributions to the EEG signals recorded ateach channel In ICA the measured 119870 channel EEG signalsare taken into an 119873 dimensional space and projected onto acoordinate frame where the data projections are minimallyoverlapped and maximally independent of each other Thereare various algorithms with different approaches to find theindependent components such as minimizing the mutualinformation or maximizing the joint entropy among the data


0 02 04 06 08 1 12 14 16 18 2

0

5

10

15

Time (ms)

minus5

minus10

minus15

ICA

com

pone

nt (120583

V)

times105

Figure 6The ICA component attributed to the stimulus artifact 72seconds in the middle

projections The ICA algorithm we used in this study isthe extended Infomax algorithm [27] which is a modifiedversion of the Infomax algorithm proposed by Bell andSejnowski [28] It uses a learning rule that switches betweendifferent types of distributions such as Sub-gaussian andSuper-gaussian sources The extended Infomax algorithm isimplemented in EEGLABMATLAB toolbox [29] and widelyused to analyze EEG studies The ICA was applied to themeasured EEG set to find the GVS artifacts componentsTo remove the GVS artifact we need to find all componentsthat are attributed to the GVS applied to the subject Thesecomponents can be identified by calculating the correlationcoefficient between the ICA components and the GVS signalThe temporal structure of the GVS artifact components isalso different from the other components as during the timethat the GVS is applied a large amplitude artifact appears(Figure 6)

We tried two approaches to remove the artifact Thefirst approach is to zero out the artifact signals from thecomponents that account for the GVS parasitic influenceand obtain a new cleaned-up source matrix 119878(119905) The secondapproach is to apply a threshold on the artifact componentsin order to extract the artifact spikes and set them to zeroThethresholdwas set at three standard deviations above themeanof the EEG signal without the artifact (eg the signal beforeapplying the GVS) and all data points with amplitude overthe threshold were set to zeroThus we obtained a new sourcematrix 119878(119905) with the modified componentsThe threshold at3 standard deviations of the original neural signals enablesus to keep a major part of the original neural activitiesuntouched as much as possible (Figure 7)

Eventually we reconstruct ICA-corrected EEG signals as

119864 (119905) = 119872119878 (119905) (14)

where 119864(119905) is the new data set which represents the estimatedartifact-free data

27 The Proposed Artifact Removal Method In the proposedmethod we decomposed the EEG andGVS current signals in12 frequency bands (Table 2) and then using the regression

0 02 04 06 08 1 12 14 16 18 2

00102030405

Time (ms) times105

ICA

com

pone

nt (120583

V)

minus01

minus02

minus03

minus04

minus05

Figure 7 The ICA component attributed to the stimulus artifactafter applying the threshold

methods we estimated the GVS artifact components in eachfrequency band Figure 8 shows the process for detectingGVS artifacts As shown in this flowchart in each frequencyband the GVS artifacts are detected through a regressionanalysis where the GVS signals are taken as the referencesignals

The estimated GVS artifact frequency components aresubtracted from the contaminated EEG frequency compo-nents The wavelet decomposition enables us to focus onthe frequency bands of interest and calculate the estimatedGVS artifacts in each frequency band independently thusthe regression method can deal better with some nonlinearbehaviors of the skin in the frequency domain This wavelet-based time-frequency analysis approach enhances the perfor-mance of the artifact removal methodThe cleaned-up signalis reconstructed from the proper frequency components ofthe estimated GVS signal components in the frequency rangeof interest (eg 1 Hz to 32Hz) We calculated the correlationcoefficients between the GVS signals and the estimated GVSartifacts reconstructed from different frequency bands andwe observed that the regression results improve when wereconstruct the estimated GVS artifact components fromcorresponding frequency bands separately

The result of the correlation analysis is tabulated inTable 3 In this analysis the real data from channel O1occipital EEG was decomposed into 12 frequency bandsusing the SWT algorithm with the mother wavelet db3 andthe GVS current was estimated using OE regression model oforder 2We calculated Pearsonrsquos correlation for the correlationanalysis as

Corr (119906 119910) =Cov (119906 119910)120590119906sdot 120590119910

(15)

where 119906(119905) is the recorded GVS current and 119910119894(119905) is the esti-

mated GVS artifact reconstructed from different frequencycomponents

The result shows that the correlation between the GVSsignal and the estimated GVS artifact significantly increasesby using wavelet decomposition method We applied thewavelet transform to remove frequency components lower


Table 3 Correlation between the GVS signal and the estimated GVS artifact reconstructed from different frequency components

Estimated GVS artifact withoutwavelet decomposition

Estimated GVS artifactfrom 012Hz to 250Hz



Correlation 06960 08463 09168 09725Estimated GVS artifact from049Hz to 3125Hz




Correlation 09776 09769 09899 09899

GVS current

EEG signal during GVS

Wavelet decomposition

L1

L2

L3

L4

L5

L6

L7

L8

L9

L10

L12

L11

GVSEEG Regression analysisGVS

Regression analysisGVSEEG Regression analysisGVSEEGGVSEEG Regression analysisGVSEEG Regression analysisGVSEEG Regression analysisGVSEEG Regression analysisGVSEEG Regression analysisGVSEEG Regression analysisGVSEEG Regression analysisGVSEEG Regression analysis

Estimated GVS artifact L1

Regression analysis

Estimated GVS artifact L2Estimated GVS artifact L3Estimated GVS artifact L4Estimated GVS artifact L5Estimated GVS artifact L6Estimated GVS artifact L7Estimated GVS artifact L8Estimated GVS artifact L9Estimated GVS artifact L10Estimated GVS artifact L11Estimated GVS artifact L12

EEG

Figure 8 Flowchart of the process for detecting GVS artifacts in the proposed method

than 098Hz and higher than 3125Hz which are not of themain interest and the correlation between theGVS signal andestimated GVS artifact was increased up to 09899

We employed both SWT andDWTalgorithms in the pro-posed artifact removal methodThe difference between SWTand DWT algorithms was briefly explained in the waveletanalysis section We also used various regression models toestimate the GVS artifact To assess the performance of theproposed method using different algorithms and models weapplied our method to the simulated data and examinedthe cleaned-up EEG signals in comparison with the originalartifact-free EEG signals For this assessment not only did wecalculate the correlation between the artifact-removed EEGsignals and the original artifact-free EEG signals but also wemeasured the fitness of the artifact-removed signals basedon the normalized residual sum of squares which is sometimeintroduced as the normalized quadratic error defined by

RSS119873=

sum (119864119900 (119905) minus 119864

119900 (119905))2

sum(119864119900 (119905) minusmean (119864

119900 (119905)))2 (16)

where 119864119900(119905) represents the original artifact-free signal and

119864119900(119905) is the artifact-removed signal

We measured the performance of the proposed methodbased on the correlation (15) and the normalized residualsum of squares (16)The choice for the wavelet algorithm andmother wavelet was made such that the performance of theartifact removal method is maximized To compare differentwavelet algorithms and mother wavelets we employed anumber of mother wavelets from two different waveletfamilies which have been commonly used in EEG signal pro-cessing Daubechies (1198891198873 1198891198874 and 1198891198875) and Symlets (11990411991011989831199041199101198984 and 1199041199101198985) Both SWT and DWTwere used with thesemotherwavelets in the proposed artifact removalmethod andapplied to the simulated data We tabulated the normalizedresidual sum of squares and the correlation between theartifact-removed signals and the original artifact-free signalsin the frequency range lower than 3125Hz (Table 4)

The results show that SWT algorithm has a superiorperformance compared to DWT algorithm and between dif-ferent mother wavelets both Daubechies and Symlet waveletswith order of 4 performed better than the others

Another step to improve the performance of the methodis finding an optimum regression method to calculate theestimated GVS artifacts as accurate as possible We usedthree different classes of model structure Output-Error (OE)


Table 4 Correlation and normalized residual sum of squares between the artifact-removed signals and the original artifact-free EEG signalsfor simulated data using different wavelet decomposition algorithms

DWT db3 DWT db4 DWT db5 DWT db6 DWT sym3 DWT sym4 DWT sym5 DWT sym6Corr 08781 09023 09155 09242 08781 09023 09156 09242RSS119873

05517 04870 04503 04255 05517 04870 04503 04255SWT db3 SWT db4 SWT db5 SWT db6 SWT sym3 SWT sym4 SWT sym5 SWT sym6

Corr 09932 09933 09933 09932 09932 09933 09933 09932RSS119873

01710 01700 01705 01714 01710 01700 01705 01714

Table 5 Correlation and normalized residual sum of squaresbetween the artifact-removed signals and the original artifact-freeEEG signals for simulated data using different models for estimatingthe GVS artifacts

OE2 OE3 OE4 OE5 NLHW2Corr 09933 09933 09933 09822 09934RSS119873

01700 01701 01704 02267 01711SS2 SS3 SS4 NLHW3 NLHW4

Corr 09933 08105 07466 09926 09851RSS119873

01704 07628 09174 01230 01725

as a simple special case of the general polynomial modelHammerstein-Wiener with the piecewise-linear functionand Space-State models which were all introduced in theldquoRegression-based approachrdquo section We employed thesemodels with different orders in the proposed artifact removalmethod and applied the proposed method using each ofthese models to the simulated data In order to compare theperformance we used SWTwith Daubechies 4 to decomposethe contaminated signals estimated the GVS artifact usingdifferent models and then assessed the performance in termsof the correlation and the normalized residual sum of squaresbetween the original artifact-free signal and the artifact-removed signal reconstructed in the frequency range lowerthan 3125Hz The results are tabulated in Table 5

For nonlinear Hammerstein-Wiener models we used thepiecewise-linear function and broke down the EEG signalinto a number of intervals We tried a various number ofintervals and observed that with 4 intervals (or less) wecould get the highest correlation and the least residual

The results show that between all those models bothOutput-Error and nonlinear Hammerstein-Wiener have bet-ter performance We employed these regression models tomaximize the performance of the proposed method then weapplied the proposed method to the real data

We also used two ICA-based methods for removing theartifact filtering out the artifact components and applying athreshold on the artifact components amplitude to removethe artifact spikes beyond the threshold

To assess the performances of the ICA methods on thesimulated data we calculated both the correlation and thenormalized residual sum of squares between the artifact-removed EEG signals and the original artifact-free EEGsignals

We compared the ICA-based methods with the pro-posed methods using the Output-Error and nonlinear

Table 6 Correlation and normalized residual sum of squaresbetween the artifact-removed signals and the original artifact-freeEEG signals for simulated data using the proposedmethod and ICA-based methods

Removingthe ICAartifact

component

Applyingthreshold tothe ICAartifact

component

SWT decom-position withDB4 modeledwith OE2

SWT decom-position withDB4 modeledwith NLHW2

Corr 06445 06171 09933 09934RSS119873

09567 10241 01700 01711

Table 7 Correlation between the GVS signals and the estimatedGVS artifact extracted from EEG signals for real data using theproposed method and ICA-based methods


component


component



Corr 06859 06858 08743 08743

Hammerstein-Wiener models order 2 along with 12-levelSTW decomposition with DB4 mother wavelet (Tables 6 and7)

28 Comparison of Different Artifact Removal Methods Weapplied different artifact removal methods on real EEG dataacquired during application of GVS We used the data fromchannel O1 (occipital EEG) of different subjects in EEGGVSstudies We applied stimulation signals of different ampli-tudes in our experiments and observed consistent resultsfrom these experiments By calculating the correlation coef-ficients between the GVS signals and the estimated GVS arti-facts we compared the performance of these methods Firstwe compare ICA-based regression-based and adaptive filterswithout using the wavelet analysisThen we use the proposedmethod where the wavelet analysis was employed to improvethe performance of our artifact removal method

The best algorithms for ICA-based methods best modelsfor regression-based methods and best filters for adaptivefiltering methods were selected Between different ICA algo-rithms (as mentioned in the section ldquoICA-based artifactremoval methodsrdquo) the extended Infomax showed betterresults Between regression-based methods (as previouslyintroduced in the section ldquoRegression-based artifact removal


Table 8 Correlation between the GVS signals and the estimatedGVS artifact extracted from EEG signals for real data using differentmethods

Method CorrelationICA-Infomax method (remove the artifactcomponent) 06859

ICA-Infomax method (threshold the artifactcomponent) 06858

Regression method with OE2 07673RLS Adaptive filter (forgetting factor 099997length 2) 07615

LMS Adaptive filter (adaptation gain 05 length 3) 07010

Table 9 Correlation between theGVS signal and the estimatedGVSartifact reconstructed from different frequency components for realdata

Frequency band CorrelationEstimated GVS artifact without waveletdecomposition 07673

Estimated GVS artifact from 012Hz to 250Hz 08463Estimated GVS artifact from 024Hz to 125Hz 09168Estimated GVS artifact from 049Hz to 625Hz 09725Estimated GVS artifact from 049Hz to 3125Hz 09776Estimated GVS artifact from 049Hz to 1575Hz 09769Estimated GVS artifact from 098Hz to 3125Hz 09899Estimated GVS artifact from 098Hz to 1575Hz 09899

methodsrdquo) OE order 2 showed better performance andbetween adaptive filters (as previously introduced in thesection ldquoAdaptive filtering methods for artifact removalrdquo)RLS filterwith the forgetting factor of 099997 the filter lengthof 2 LMS filter with the adaptation gain of 05 and the filterlength of 3 had better performance We tabulated (Table 8)the correlation between the GVS signals and the estimatedGVS artifacts

The results show that between all the above methodsthe regression-based methods are able to estimate the GVSartifacts with higher correlation with the original GVS sig-nals Thus we employed the regression-based method alongwith the wavelet analysis in our proposed method to achievethe best performance in removing GVS artifact The waveletdecomposition method improves the estimation of the GVSartifacts in both correlation performance and robustnessThis is due to the separate transfer function estimations foreach frequency band aspect that makes it less prone to non-linear skin behavior or to other noise sources Furthermorewith wavelet decomposition we can filter out the frequencycomponents that are not of interest Removing those fre-quency components can improve the results of the regressionanalysis as well The cleaned EEG data is reconstructed fromthe frequency range of interest (eg 1 Hz to 32Hz)

Using a correlation analysis we show how the wavelet-based time-frequency analysis approach enhances the per-formance of the artifact removal method We calculatedthe correlation coefficients between the GVS signals and

0 05 1 15 2 25 3 35

065

07

075

08

085

09

095

1

GVS (mA)

Cor

rela

tion

Figure 9 Correlation between the GVS signal and the estimatedGVS artifact using the proposed method (red) and the ICA method(blue) for different GVS amplitudes

the estimated GVS artifacts reconstructed from differentfrequency bands (tabulated in Table 9) We observed that byfocusing on the frequency components of interest for exam-ple between 1Hz to 32Hz we could achieve much highercorrelation between the estimated and original GVS signals

As shown in Table 9 after removing the frequency bandslower than 098Hz and larger than 3125Hz which were out-side our interest at the present time the correlation betweenthe GVS signal and the estimated GVS artifact significantlyincreases from 07673 to 09899 by using wavelet decomposi-tion method

So far we showed the proposedmethod has superior per-formance than the other methods when it is applied to low-amplitude stochastic GVS signals up to 1mAWe also appliedour artifact removal method to EEGGVS data sets collectedby our other collaborator in the Sensorimotor PhysiologyLaboratory where higher amplitude pink noise GVS up to3100 120583Awas applied in the EEGGVS studies In one data setspink noise GVS in a wide range of amplitudes from 100 120583Ato 3100 120583A (each 300 120583A) was applied and the EEGGVSdata were collected We compared the performance of theproposed method and the extended Infomax ICA methodThe results show that while the performance of the ICAmethod deteriorates as the GVS amplitude is increased theproposed method provides a robust performance (Figure 9)

3 Results

In the section ldquoThe proposed artifact removal methodrdquo weoptimized the proposed method using the simulated dataTo find the optimum algorithms for signal decompositionwe compared the SWT and DWT decomposition algo-rithms using different mother wavelets (the results shown inTable 4) and to achieve better estimation of theGVS artifactswe employed different model structures (results shown inTable 5)

In the optimized algorithm we employed the SWTdecomposition algorithm using DB4 mother wavelet anddecomposed the signals into 12 frequency bandsThis enabledus to separate the GVS artifact into different frequency bands


1 2 3 4 5 6 7 8 9 10 11 120

10

20

30

40

50

60

70

80

90

100

Frequency bands

Fit p

erce

ntag

e

Figure 10 The fit percentage of the detail components of theestimated GVS artifacts using the OE model order 2 in eachfrequency band

1 2 3 4 5 6 7 8 9 10 11 120

01

02

03

04

05

06

07

08

09

1

Frequency bands

Cor

relat

ion

coeffi

cien

t

Figure 11 The correlation between the detail components of theestimated GVS signals and the GVS signals for the simulated datausing the OE model order 2 in each frequency bands

and estimate the artifact using a time-domain regressionmodel The comparison of the different model structuresshows that the Output-Error (OE) and the nonlinear Ham-merstein-Wiener order 2 have similar performances betterthan the other models

In the previous section we compared the performance ofdifferent methods and observed that how the combining ofwavelet decomposition and regression analysis (Table 9) canimprove the performance of the artifact removal method forGVSEEG studies

Using the proposed method we can focus on specificfrequency bands and remove the GVS artifact with betterperformance in each frequency band separately Figures 10and 11 show the fit percentage (5) and the correlation (15)between the detail components of the estimated GVS signals

0 02 04 06 08 1 12 14 16 18 2

0

100

200

300

Time (ms)

minus100

minus200

minus300

minus400

EEG

vol

tage

(120583V

)

times105

Figure 12 The occipital EEG channel data after applying theproposed artifact removal method using the frequency componentslower than 64Hz

0 02 04 06 08 1 12 14 16 18 2

050

100150200250

Time (ms)

minus50

minus100

minus150

minus200

minus250

EEG

vol

tage

(120583V

)

times105

Figure 13 The occipital EEG channel data after applying theproposed artifact removal method using the frequency componentsbetween 1Hz to 32Hz

and the GVS signals for the simulated data in the frequencybands introduced in Table 2

The results show that for frequency components L6 toL10 which correspond approximately to 8ndash16Hz 4ndash8Hz2ndash4Hz 1-2Hz and 05ndash1Hz bands we can achieve higherperformance in rejecting the GVS artifacts separately Oneof the reasons of the robustness of the method is buildingseparate equivalent transfer functions for the GVS signals foreach frequency band which helps in maintaining the perfor-mance of the algorithms for a large range of GVS intensitylevels and frequency ranges To illustrate the importance ofthe wavelet analysis we depicted the artifact-removed signalsusing different frequency components (Figures 12 13 and 14)

Figure 14 shows that whenwe use specific frequency com-ponents to estimate the GVS artifacts we can significantlysuppress the GVS artifact and achieve high signal to artifactratio (SAR) SAR is defined as the ratio of the signal amplitudeto the artifact amplitude in decibels (dB) We can achieve anSARofminus1625 dB in the frequency range of 1Hzndash16Hzwhileusing the frequency components in the range of 1Hzndash32Hz


0

50

100

150

minus50

minus100

minus150

0 02 04 06 08 1 12 14 16 18 2Time (ms)

EEG

vol

tage

(120583V

)

times105


(Figure 13) we can obtain a SAR of minus10498 dB using the fre-quency components in the range of 1Hzndash64Hz (Figure 12)we have an SAR of minus13863 dB In the original contaminatedEEG signals without removing the GVS artifact (Figure 1)the SAR is minus32189 dB

4 Discussion

In the section ldquoSimulated datardquo we showed that by simulatingthe skin impedance and estimating the transfer function ofthe skin (one function for the whole frequency range) wecould reconstruct a major portion of the GVS artifact As anexample for channel 18 around 87 of the GVS artifact wasreconstructed (Figure 3) thus we could simulate the contam-inated EEG signals to assess the performance of the proposedmethod

Using the wavelet decomposition we were able to recon-struct up to 96 of the GVS artifact components in somefrequency bands especially in the frequency range of theGVSsignals (Figure 10)

We showed that the use of the wavelet decomposition canimprove the time domain regression approach to estimate theGVS artifacts By means of the combination of the regressionandwavelet analysis in the proposed artifact removalmethodwe were able to focus on different frequency bands andsignificantly improve the SAR of the contaminated EEG datain specific frequency bands

The proposed method and the ICA-based methodsbehave differently in rejecting the GVS artifact We observeda high correlation between the estimated GVS artifacts andthe original GVS signals using the proposed method but wecould not obtain a good correlation using the ICA-basedmethods

As illustrated earlier we cannot completely remove theGVS contamination in all frequency ranges (eg over 16Hz)Removing the whole GVS artifacts remains a problem for thefuture approaches

In this study we also observed that nonlinear Ham-merstein-Wienermodel of the second order using piecewise-linear blocks with 4 breakpoints (or less) provided the same

performance as the Output-Error model of the second orderThis implies that the relationships between the GVS artifactsat the EEG electrodes and the injected GVS current are linearand remain constant over the entire epoch Our simulationstudy results also showed that the impedancemodels betweenthe EEG electrodes and the GVS electrodes remain constantover the entire epoch (Figure 4) and using short epochswould not improve the fitness of the impedance models andthe estimation of the GVS artifacts As a matter of fact it mayeven worsen the estimation of time-domain characteristics

We also showed that when we apply the proposedmethod to remove the GVS artifacts less distortion is intro-duced in the cleaned EEG signals compared to the distortionthat the other methods (eg ICA-based methods) introduceFurthermore using the proposed method we do not needto collect and process all EEG channels as in the ICA-based analysis therefore it is much faster than the ICA-basedmethods This allows us to have a simple experimental setupfor collecting EEG signals with less EEG channels for theGVSstudies which makes the preparation for the data acquisitionsession take less time before the subject gets tired and moremyogenic and ocular artifacts are introduced Comparedto the ICA methods the proposed method is easier to beimplemented in a real time system for future applications

Acknowledgments

The authors would like to thank the research team of Pro-fessor Martin J McKeown from Pacific Parkinsonrsquos ResearchCentre and also the research team of Professor Jean-Sebastien Blouin from the Sensorimotor Physiology Labora-tory University of British Columbia for the collection of theexperimental data and for the useful dialogs during ourwork

References

[1] Y Yamamoto Z R Struzik R Soma K Ohashi and S KwakldquoNoisy vestibular stimulation improves autonomic and motorresponsiveness in central neurodegenerative disordersrdquo Annalsof Neurology vol 58 no 2 pp 175ndash181 2005

[2] W Pan R Soma S Kwak and Y Yamamoto ldquoImprovementof motor functions by noisy vestibular stimulation in centralneurodegenerative disordersrdquo Journal of Neurology vol 255 pp1657ndash1661 2008

[3] S Pal SM Rosengren and J G Colebatch ldquoStochastic galvanicvestibular stimulation produces a small reduction in sway inparkinsonrsquos diseaserdquo Journal of Vestibular Research vol 19 pp137ndash142 2009

[4] Y Yamamoto R Soma Z R Struzik and S Kwak ldquoCanelectrical vestibular noise be used for the treatment of braindiseasesrdquo in Proceedings of the 4th International Conference onUnsolved Problems of Noise and Fluctuations in Physics Biologyand High Technology (UPoN rsquo05) pp 279ndash286 Gallipoli ItalyJune 2005

[5] K S Utz V Dimova K Oppenlander and G Kerkhoff ldquoElec-trified minds transcranial direct current stimulation (tdcs)and galvanic vestibular stimulation (gvs) as methods of non-invasive brain stimulation in neuropsychologymdasha review ofcurrent data and future implicationsrdquoNeuropsychologia vol 48no 10 pp 2789ndash2810 2010


[6] A J Shackman B W McMenamin H A Slagter J S MaxwellL L Greischar and R J Davidson ldquoElectromyogenic artifactsand electroencephalographic inferencesrdquo Brain Topographyvol 22 no 1 pp 7ndash12 2009

[7] B W McMenamin A J Shackman J S Maxwell et alldquoValidation of ica-based myogenic artifact correction for scalpand source-localized EEGrdquoNeuroImage vol 49 no 3 pp 2416ndash2432 2010

[8] M Crespo-Garcia M Atienza and J L Cantero ldquoMuscleartifact removal from human sleep EEG by using independentcomponent analysisrdquo Annals of Biomedical Engineering vol 36no 3 pp 467ndash475 2008

[9] B W McMenamin A J Shackman J S Maxwell L LGreischar and R J Davidson ldquoValidation of regression-basedmyogenic correction techniques for scalp and source-localizedEEGrdquo Psychophysiology vol 46 no 3 pp 578ndash592 2009

[10] J Gao Y Yang P Lin P Wang and C Zheng ldquoAutomaticremoval of eye-movement and blink artifacts from EEG sig-nalsrdquo Brain Topography vol 23 no 3 pp 105ndash114 2010

[11] A Schlogl C Keinrath D Zimmermann R Scherer R Leeband G Pfurtscheller ldquoA fully automated correction method ofeog artifacts in eeg recordingsrdquo Clinical Neurophysiology vol118 no 1 pp 98ndash104 2007

[12] R Magjarevic M A Klados C Papadelis C D Lithariand P D Bamidis ldquoThe removal of ocular artifacts from eegsignals a comparison of performances for differentmethodsrdquo inProceedings of the 4th European Conference of the InternationalFederation for Medical and Biological Engineering (IFMBE rsquo09)J Sloten P Verdonck M Nyssen and J Haueisen Eds vol 22pp 1259ndash1263 Springer Berlin Germany 2009

[13] P He G Wilson C Russell and M Gerschutz ldquoRemoval ofocular artifacts from the EEG a comparison between time-domain regression method and adaptive filtering method usingsimulated datardquo Medical and Biological Engineering and Com-puting vol 45 no 5 pp 495ndash503 2007

[14] A Schloegl A Ziehe and K R Muller ldquoAutomated ocularartifact removal comparing regression and component-basedmethodsrdquo Nature Precedings 2009

[15] G L Wallstrom R E Kass A Miller J F Cohn and N AFox ldquoAutomatic correction of ocular artifacts in the eeg a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[16] F Grouiller L Vercueil A Krainik C Segebarth P KahaneandODavid ldquoA comparative study of different artefact removalalgorithms for eeg signals acquired during functional MRIrdquoNeuroImage vol 38 no 1 pp 124ndash137 2007

[17] Y Erez H Tischler A Moran and I Bar-Gad ldquoGeneralizedframework for stimulus artifact removalrdquo Journal of Neuro-science Methods vol 191 no 1 pp 45ndash59 2010

[18] F Morbidi A Garulli D Prattichizzo C Rizzo and S RossildquoApplication of Kalman filter to remove TMS-induced artifactsfrom EEG recordingsrdquo IEEE Transactions on Control SystemsTechnology vol 16 no 6 pp 1360ndash1366 2008

[19] T I Aksenova D V Nowicki and A-L Benabid ldquoFiltering outdeep brain stimulation artifacts using a nonlinear oscillatorymodelrdquoNeural Computation vol 21 no 9 pp 2648ndash2666 2009

[20] T Hashimoto C M Elder and J L Vitek ldquoA template sub-traction method for stimulus artifact removal in highfrequencydeep brain stimulationrdquo Journal of Neuroscience Methods vol113 no 2 pp 181ndash186 2002

[21] G Inuso F La ForestaNMammone andFCMorabito ldquoBrainactivity investigation by EEG processing wavelet analysis kur-tosis and Renyirsquos entropy for artifact detectionrdquo in Proceedingsof the International Conference on InformationAcquisition (ICIArsquo07) pp 195ndash200 Seogwipo-si South Korea July 2007

[22] G Inuso F La Foresta N Mammone and F C MorabitoldquoWavelet-ICA methodology for efficient artifact removal fromElectroencephalographic recordingsrdquo in Proceedings of theInternational Joint Conference on Neural Networks (IJCNN rsquo07)pp 1524ndash1529 Orlando Fla USA August 2007

[23] A T Tidswell A Gibson R H Bayford and D S HolderldquoElectrical impedance tomography of human brain activitywith a two-dimensional ring of scalp electrodesrdquo PhysiologicalMeasurement vol 22 no 1 pp 167ndash175 2001

[24] J G WebsterMedical Instrumentation-Application and DesignWiley New York NY USA 4th edition 2009

[25] A Garces Correa E Laciar H D Patıo andM E ValentinuzzildquoArtifact removal from EEG signals using adaptive filters incascaderdquo Journal of Physics vol 90 Article ID 012081 2007

[26] R C Fitzpatrick and B L Day ldquoProbing the human vestibularsystemwith galvanic stimulationrdquo Journal of Applied Physiologyvol 96 no 6 pp 2301ndash2316 2004

[27] T-W Lee M Girolami and T J Sejnowski ldquoIndependent com-ponent analysis using an extended infomax algorithm formixedsubgaussian and supergaussian sourcesrdquo Neural Computationvol 11 no 2 pp 417ndash441 1999

[28] A J Bell and T J Sejnowski ldquoAn information-maximizationapproach to blind separation and blind deconvolutionrdquo NeuralComputation vol 7 no 6 pp 1129ndash1159 1995

[29] A Delorme and S Makeig ldquoEeglab an open source toolbox foranalysis of single-trial EEG dynamics including independentcomponent analysisrdquo Journal of Neuroscience Methods vol 134no 1 pp 9ndash21 2004


Research ArticleMultiscale Cross-Approximate Entropy Analysis as a Measure ofComplexity among the Aged and Diabetic

Hsien-Tsai Wu1 Cyuan-Cin Liu1 Men-Tzung Lo2 Po-Chun Hsu1 An-Bang Liu3

Kai-Yu Chang1 and Chieh-Ju Tang4

1 Department of Electrical Engineering National Dong Hwa University No 1 Section 2 Da Hsueh Road ShoufengHualien 97401 Taiwan

2 Research Center for Adaptive Data Analysis amp Center for Dynamical Biomarkers and Translational MedicineNational Central University Chungli 32001 Taiwan

3Department of Neurology Buddhist Tzu Chi General Hospital and Buddhist Tzu Chi University Hualien 97002 Taiwan4Department of Internal Medicine Hualien Hospital Health Executive Yuan Hualien 97061 Taiwan

Correspondence should be addressed to Hsien-Tsai Wu dsphansmailndhuedutw

Received 22 March 2013 Revised 27 May 2013 Accepted 1 June 2013


Copyright copy 2013 Hsien-Tsai Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Complex fluctuations within physiological signals can be used to evaluate the health of the human body This study recruited fourgroups of subjects young healthy subjects (Group 1 119899 = 32) healthy upper middle-aged subjects (Group 2 119899 = 36) subjects withwell-controlled type 2 diabetes (Group 3 119899 = 31) and subjects with poorly controlled type 2 diabetes (Group 4 119899 = 24) Dataacquisition for each participant lasted 30 minutes We obtained data related to consecutive time series with R-R interval (RRI) andpulse transit time (PTT) Using multiscale cross-approximate entropy (MCE) we quantified the complexity between the two seriesand thereby differentiated the influence of age and diabetes on the complexity of physiological signals This study used MCE in thequantification of complexity between RRI and PTT time series We observed changes in the influences of age and disease on thecoupling effects between the heart and blood vessels in the cardiovascular system which reduced the complexity between RRI andPTT series

1 Introduction

Multiple temporal and spatial scales produce complex fluctu-ations within the output signals of physiological systems [1]In recent studies on translational medicine [1ndash5] researchershave found that implicit information within the complexfluctuations of physiological signals can be used to evaluatehealth conditions

Many recent studies [2 3] have employed nonlineardynamical analysis to quantify the complexity of physiolog-ical signals in the cardiovascular system Costa et al [2]were the first to propose multiscale entropy (MSE) as anapproach to analyze the R-R interval (RRI) series of healthyindividuals and discovered that the RRI series of youngindividuals were more complex than that of elderly peopleWu et al [3] adopted the same method in an examination ofpulse wave velocity (PWV) and found that the complexity of

these series decreased with aging andor the progression ofdiabetes In addition to time and space ldquocoupling behaviorrdquoin the physiological system also affects the complexity ofindividual physiological signals such as RRI or PWV [6]Drinnan et al [7] indicated that pulse transit time (PTT)is influenced by RRI and other cardiovascular variablesand used cross-correlation functions to quantify the phaserelationship between the two time series signals in thecardiovascular system They established that there was astrong correlation betweenPTT andRRI variations in healthysubjects However Pincus [8] claimed that cross-approximateentropy (Co ApEn) is more effective than cross-correlationfunctions in the evaluation of complexity between the twoseries

Despite the fact that Co ApEn has been widely appliedto evaluate the complexity between two time series [9ndash12] single-scale entropy values are not necessarily able to


identify the dynamic complexity of physiological signalsTherefore this study was an attempt to use a multiscaleCo ApEn (MCE) [13] to quantify the complexity betweenthe synchronous time series of cardiac functions and thedegree of atherosclerosisWe assumed that complexity wouldexist in RRI and PTT series of the cardiovascular systemdue to the mutual interaction between the heart and bloodvessels Moreover we assumed that complexity reduces withaging and the influence of disease We used MCE to developan index for the quantification of complexity between thetwo time series capable of distinguishing between healthyindividuals and those with diabetes

2 Methods

21 Study Design This study evaluated the influences of ageand diabetes on RRI and PTT Considering that RRI and PTTare nonlinear cardiovascular variables we tested the applica-bility of MCE in the study subjects and investigated whetherthis dynamic parameter could provide further informationrelated to the clinical control of diabetes

22 Subject Populations and Experiment Procedure BetweenJuly 2009 and March 2012 four groups of subjects wererecruited for this study young healthy subjects (Group 1 agerange 18ndash40 119899 = 32) healthy upper middle-aged subjects(Group 2 age range 41ndash80 119899 = 36) subjects with well-controlled type 2 diabetes (Group 3 age range 41ndash80 119899 =

31 65 ≦ glycosylated hemoglobin (HbA1c) lt 8) andsubjects with poorly controlled type 2 diabetes (Group 4 agerange 41ndash80 119899 = 24 HbA1c ≧ 8) [3] The other 22 subjectswere excluded due to incomplete or unstable waveform dataacquisition All diabetic subjects were recruited from theHualienHospital DiabeticOutpatient Clinic healthy controlswere recruited from a health examination program at thesame hospital None of the healthy subjects had personalor family history of cardiovascular disease Type 2 diabeteswas diagnosed as either fasting sugar higher than 126mgdLor HbA1c ≧ 65 All diabetic subjects had been receivingregular treatment and follow-up care in the clinic for morethan two years Regarding the use of medications there wasno significant difference in the type (ie antihypertensivelipid-lowering and hypoglycemic medications) dosage andfrequency among the well-controlled and poorly controlleddiabetic subjectsThis studywas approved by the InstitutionalReview Board (IRB) of Hualien Hospital and National DongHwa University All subjects refrained from caffeinated bev-erages and theophylline-containing medications for 8 hoursprior to each hospital visit Each subject gave informedconsent completed questionnaires on demographic data andmedical history and underwent blood sampling prior to dataacquisition Blood pressure was obtained once from the leftarm of supine subjects using an automated oscillometricdevice (BP3AG1Microlife Taiwan) with a cuff of appropriatesize followed by the acquisition of waveform data fromthe second toe using a six-channel ECG-PWV [14 15] aspreviously described

23 Data Collection and Calculation of RRI and PTT SeriesAll subjects were permitted to rest in a supine position in aquiet temperature-controlled room at 25 plusmn 1∘C for 5 minutesprior to subsequent 30-minute measurements Again a goodreproducibility of six-channel ECG-PWV system [14 15]was used for waveform measurement from the second toeInfrared sensors were simultaneously applied to points of ref-erence for the acquisition of data Electrocardiogram (ECG)measurementswere obtained using the conventionalmethodAfter being processed through an analog-to-digital converter(USB-6009 DAQ National Instruments Austin TX USA) ata sampling frequency of 500Hz the digitized signals werestored on a computer Because of its conspicuousness the Rwave in Lead II was selected as a reference point the timeinterval between the R-wave peak of the jth cardiac cycle tothe footpoint of the toe pulse from the left foot was defined asPTT(j) the time difference between the two continues peakof ECG R wave was defined as RRI(i) as shown as Figure 1

Using ECG and photoplethysmography (PPG) weobtained the RRI series RRI(119894) = RRI(1)RRI(2) RRI(1000) and PTT series PTT(119895) = PTT(1)PTT(2) PTT(1000) from each subject All series were retrieved from1000 consecutive stable ECG tracings and PPG toe pulsesignals synchronous with the cardiac cycle [14]

Due to a trend within physiological signals [6 16]nonzeromeansmay be included therefore we used empiricalmode decomposition (EMD) [17] to deconstruct the RRI(119894)and PTT(119895) series thereby eliminating the trend fromthe original series We then normalized the RRI(119894) andPTT(119895) series as shown in (1) In these equations SD

119909and

SD119910represent the standard deviations of series RRI(119894) and

PTT(119895) respectively Complexity analysis was performedon the normalized results RRI1015840(119894) and PTT1015840(119895) Consider

RRI1015840 (119894) =RRI (119894)SD119909

PTT1015840 (119895) =PTT (119895)

SD119910

(1)

24 Multiscale Cross-Approximate Entropy (MCE) Using Nor-malized RRI and PTT Series Together Previous studies [1ndash318] have employed MSE to overcome comparison difficultiesat a scale factor of 1 when physiological complexity isreduced due to age or disease However other research [7]has indicated a strong relationship between variations in PTTseries and RRI series therefore we used MCE to investigatethe interactions between PTT and RRI

241 Coarse-Grained Process and Cross-Approximate Entropy(Co ApEn) MSE involves the use of a scale factor 120591 (120591 =

1 2 3 119899) which is selected according to a 1D series ofconsecutive cycles This factor enables the application ofa coarse-graining process capable of deriving a new seriesprior to the calculation of entropy in each new individ-ual series [1ndash3 18] Using this approach we performedcoarse-graining on the normalized 1D consecutive cycles ofthe RRI1015840(119894) and PTT1015840(119895) series based on scale factor 120591


ECG

PPG

RRI(1) RRI(2) RRI(1000)

PTT(1) PTT(2)PTT(1000)

middot middot middot


Figure 1 1000 consecutive data points from ECG signals and PPG signals PTT(j) refers to the time interval between the R-wave peak of thejth cardiac cycle to the footpoint of the toe pulse from the left foot

thereby obtaining the series RRI1015840(120591) and PTT1015840(120591) as shownin (2) We then calculated entropy as follows

RRI1015840(119906)(120591) = 1

120591

119906120591

sum

119894=(119906minus1)120591+1

RRI1015840 (119894) 1 le 119906 le1000

120591

PTT1015840(119906)(120591) = 1

120591

119906120591

sum

119895=(119906minus1)120591+1

PTT1015840 (119895) 1 le 119906 le1000

120591

(2)

Previous studies [19 20] have used Co ApEn animproved analysis method of approximate entropy to ana-lyze two synchronous physiological time series define theirrelationship and calculate the complexity within that rela-tionship [8 21] This method utilizes the dynamic changesbetween the two series to evaluate the physiological systemSimilarities between changes in the two series can be usedto observe the regulatory mechanisms in the physiologicalsystem However many studies [8 19ndash21] presented theirresults at a scale factor of 1 To obtain a deeper understandingof the complexity of the physiological system we utilizedcoarse-grained RRI1015840(120591) and PTT1015840(120591) series to calculate theCo ApEn at each scale using (7) We refer to this approachas multiscale cross-approximate entropy (MCE) The detailsof the algorithm are as follows [22]

(1) For given119898 for two sets of119898-vectors

x (119894) equiv [RRI1015840(120591) (119894) RRI1015840(120591) (119894 + 1) sdot sdot sdot RRI1015840(120591) (119894 + 119898 minus 1)]

119894 = 1 119873 minus 119898 + 1

y (119895)

equiv [PTT1015840(120591) (119895) PTT1015840(120591) (119895 + 1) sdot sdot sdot PTT1015840(120591) (119895 + 119898 minus 1)]

119895 = 1 119873 minus 119898 + 1

(3)

(2) Define the distance between the vectors x(119894) y(119895)as the maximum absolute difference between theircorresponding elements as follows

119889 [x (119894) y (119895)]

=119898max119896=1

[10038161003816100381610038161003816RRI1015840(120591) (119894 + 119896 minus 1) minus PTT1015840(120591) (119895 + 119896 minus 1)

10038161003816100381610038161003816]

(4)

(3) With the given x(119894) find the value of 119889[x(119894)y(119895)](where 119895 = 1 to119873 ndash119898 + 1) that is smaller than or equalto r and the ratio of this number to the total numberof119898-vectors (119873 ndash119898 + 1) That is

let119873119898RRI1015840(120591)PTT1015840(120591)(119894) = the number of y(119895) satisfy-ing the requirement 119889[x(119894)y(119895)] ≦ 119903 then

119862119898

RRI1015840(120591)PTT1015840(120591) (119894) =119873119898

RRI1015840(120591)PTT1015840(120591) (119894)

119873 minus 119898 + 1 (5)

C119898RRI1015840(120591)PTT1015840(120591)(119894) measures the frequency of them-point PTT1015840(120591) pattern being similar (within atolerance of plusmn119903) to the 119898-point RRI1015840(120591) patternformed by x(119894)

(4) Average the logarithm of 119862119898

RRI1015840(120591)PTT1015840(120591)(119894) over 119894 toobtain 120601

119898

RRI1015840(120591)PTT1015840(120591)(119903) as follows

120601119898

RRI1015840(120591)PTT1015840(120591) (119903) =1

119873 minus 119898 + 1

119873minus119898+1

sum

119894=1

ln119862119898RRI1015840(120591)PTT1015840(120591) (119894) (6)

(5) Increase 119898 by 1 and repeat steps 1sim 4 to obtain119862119898+1

RRI1015840(120591)PTT1015840(120591)(119894) 120601119898+1

RRI1015840(120591)PTT1015840(120591)(119903)(6) Finally take Co ApEnRRI1015840(120591)PTT1015840(120591)(119898 119903) = lim

119873rarrinfin

[120601119898

RRI1015840(120591)PTT1015840(120591)(119903) minus 120601119898+1

RRI1015840(120591)PTT1015840(120591)(119903)] and for 119873-pointdata the estimate is

Co ApEnRRI1015840(120591)PTT1015840(120591) (119898 119903119873) = 120601119898

RRI1015840(120591)PTT1015840(120591) (119903)

minus 120601119898+1

RRI1015840(120591)PTT1015840(120591) (119903) (7)


where 119898 represents the chosen vector dimension 119903represents a tolerance range and119873 is the data lengthTo ensure efficiency and accuracy of calculation theparameters of this study were set at 119898 = 3 119903 = 015and119873 = 1000

242 RRI and PTT-Based Multiscale Cross-ApproximateEntropy Index (MCEI) for Small and Large Scales The valuesof Co ApEnRRI1015840(120591)PTT1015840(120591)(120591)were obtained from a range of scalefactors between 1 and 20 using theMCEdata analysismethodThe values of Co ApEnRRI1015840(120591)PTT1015840(120591)(120591) between scale factors1 and 5 were defined as small scale those between scalefactors 6 and 20 were defined as large scale [23] The sumof MCE between scale factors 1 and 5 was MCEISS in (8)while the sum of MCE between scale factors 6 and 20 wasMCEILS in (9) Defining and calculating these two indices ofmultiscale cross-approximate entropy enables the assessmentand quantification of complexity in RRI and PTT betweendifferent scale factors Consider

MCEISS =5

sum

120591=1

Co ApEnRRI1015840(120591)PTT1015840(120591) (120591) (8)

MCEILS =20

sum

120591=6

Co ApEnRRI1015840(120591)PTT1015840(120591) (120591) (9)

25 Multiscale Entropy Index (MEI) Using RRI or PTT OnlySample entropy (119878

119864) was used to quantify the complexity of

RRI or PTT series in twenty scales The values of 119878119864between

scale factors 1 and 5were defined as small scale whereas thosebetween scale factors 6 and 20 were defined as large scaleThesum of MSE in small scale was defined as MEISS while thesum of MSE in large scale was MEILS [3]

26 Statistical Analysis Average values were expressed asmean plusmn SD Significant differences in anthropometric hemo-dynamic and computational parameters (ie RRI PTTMCEISS and MCEILS) between different groups were deter-mined using an independent sample 119905-test Statistical Packagefor the Social Science (SPSS version 140 for Windows) wasused for all statistical analysis A 119875 value less than 005 wasconsidered statistically significant

3 Results

31 Comparison of Basic Demographic and CardiovascularParameters in Different Groups Table 1 presents the basicdemographic parameters of Group 1 and Group 2 showingno significant difference in major demographic parametersexcept for age HbA1c levels and body height Significantdifferences were observed in body mass index (BMI) waistcircumference systolic blood pressure (SBP) pulse pressure(PP) HbA1c levels and fasting blood sugar level betweenGroup 2 and Group 3 (Group 3 gt Group 2) In additionsignificant differences were also observed in HbA1c levelstriglycerides and fasting blood sugar level between Group 3and Group 4

32 MCEI119871119878

as Parameters Indicative of Age and DiabeticControl There were no significant differences in the val-ues of 119878

119864(RRI) and 119878

119864(PTT) at any scale (Figure 2) or

in MEISS(RRI) MEILS(RRI) MEISS(PTT) and MEILS(PTT)among the 4 groups (Table 1)

Figure 3 summarizes the results of the MCE analysisfor the values of RRI and PTT time series over 1000identical cardiac cycles obtained from the four groups ofparticipants At a scale factor of 1 (120591 = 1) the magnitudesof Co ApEnRRI1015840(1)PTT1015840(1)(1) ranked as follows Group 1Group3Group 4Group 2 The value of Co ApEnRRI1015840(120591)PTT1015840(120591)(120591)began dropping in all groups at a scale factor of 2 (120591 = 2)

Beginning at a scale factor of 3 (120591 = 3) the reduction inCo ApEnRRI1015840(120591)PTT1015840(120591)(120591) in Group 1 slowed However in theother groups the values continued decreasing rapidly Begin-ning at a scale factor of 5 (120591 = 5) the Co ApEnRRI1015840(120591)PTT1015840(120591)(120591)of Group 2 achieved stability with only minor fluctuationsThe decline in Co ApEnRRI1015840(120591)PTT1015840(120591)(120591) in Group 4 remainedgreater than that in Group 3When plotted against large scalefactors (ie 6ndash20) the magnitudes of Co ApEnRRI1015840(120591)PTT1015840(120591)(120591)ranked as follows Group 1 Group 2 Group 3 and Group 4

MCEISS only presented a significant difference betweenGroups 1 and 2 (1018 plusmn 052 versus 942 plusmn 070 119875 lt 001)Thedifferences among Groups 2 3 and 4 did not reach statisticalsignificance In comparison MCEILS presented significantdifferences among all four of the groups (Group 1 versusGroup 2 2830 plusmn 126 versus 2596 plusmn 199 119875 lt 001 Group2 versus Group 3 2596 plusmn 199 versus 2314 plusmn 185 119875 lt 001Group 3 versus Group 4 2314 plusmn 185 versus 2013 plusmn 173119875 lt 001) (Table 1)

4 Discussion

Since Pincus and Singerrsquos study [19] Co ApEn has generallybeen used to reveal similarities between two synchronousconsecutive variables within a single network This approachhas also been used to research the complexity of physio-logical signals [12 19] however the influence of multipletemporal and spatial scales creates complexity Thus thisstudy employed multiscale Co ApEn (MCE) to evaluate thecomplexity between the cardiac function-related parameterRRI and the atherosclerosis-related parameter PTT in thecardiovascular systems of various subject groups

Previous studies [1 2 18] have also indicated that physio-logical signals are generally nonlinear and exist in nonstation-ary states The use of MSE to quantify complexity within thetimes series of a single type of physiological signal (ie RRIor PWV) demonstrated that the complexity of physiologicalsignals decreases with aging [2] or with the influence ofdiabetes [3] In this study although we used MSE to quantifycomplexity of RRI or PTT series there were no significantdifferences in MEISS(RRI) MEILS(RRI) MEISS(PTT) andMEILS(PTT) between well-controlled and poor-controlleddiabetic subjects Therefore the influence of the degree ofglycemic control on complexity of physiological signalsmightnot be evaluated efficiently according to the use ofMSE whenanalyzing single time series (ie RRI or PTT)

Drinnan et alrsquos study [7] stated that cardiovascularvariables such as RRI and PTT are regulated by complex


Table 1 Comparisons of demographic anthropometric and serum biochemical parameters MCEISS and MCEILS among different subjectpopulations

Parameters Group 1 Group 2 Group 3 Group 4Age year 2656 plusmn 960 5819 plusmn 829

lowastlowast6274 plusmn 055 6058 plusmn 768

Body height cm 16938 plusmn 792 16283 plusmn 685lowastlowast

16156 plusmn 897 16117 plusmn 728

Body weight kg 6638 plusmn 1221 6522 plusmn 1155 6940 plusmn 1137 7375 plusmn 1486

BMI kgm22302 plusmn 327 2455 plusmn 390 2652 plusmn 321

dagger2842 plusmn 547

Waist circumference cm 8120 plusmn 1109 8294 plusmn 1100 9333 plusmn 937daggerdagger

9746 plusmn 377

SBP mmHg 11650 plusmn 1289 11567 plusmn 1412 12832 plusmn 1608daggerdagger

12846 plusmn 1636

DBP mmHg 7144 plusmn 670 7475 plusmn 993 7558 plusmn 963 7821 plusmn 989

PP mmHg 4297 plusmn 096 4092 plusmn 929 5274 plusmn 1434daggerdagger

5025 plusmn 1312

HbA1c 543 plusmn 032 584 plusmn 034lowastlowast

674 plusmn 062daggerdagger

936 plusmn 159DaggerDagger

Triglyceride mgdL 8888 plusmn 6254 11406 plusmn 8815 12087 plusmn 4774 16804 plusmn 9843Dagger

Fasting blood sugar mgdL 9313 plusmn 696 9778 plusmn 1469 12727 plusmn 2475daggerdagger


MEISS(RRI) 931 plusmn 054 854 plusmn 078 800 plusmn 108dagger

764 plusmn 081

MEILS(RRI) 2711 plusmn 216 2638 plusmn 207 2559 plusmn 289 2545 plusmn 325

MEISS(PTT) 997 plusmn 038 990 plusmn 040 985 plusmn 056 950 plusmn 141

MEILS(PTT) 2673 plusmn 240 2386 plusmn 371lowastlowast

2165 plusmn 255dagger

2106 plusmn 492

MCEISS 1018 plusmn 052 942 plusmn 070lowastlowast

941 plusmn 062 925 plusmn 039

MCEILS 2830 plusmn 126 2596 plusmn 199lowastlowast



Group 1 healthy young subjects Group 2 healthy uppermiddle-aged subjects Group 3 type 2 diabetic well-controlled patients Group 4 type 2 diabetic poorlycontrolled patients Values are expressed as mean plusmn SD BMI body mass index SBP systolic blood pressure DBP diastolic blood pressure PP pulse pressureHbA1c glycosylated hemoglobin MEISS(RRI) R-R interval-based multiscale entropy index with small scale MEILS(RRI) R-R interval-based multiscaleentropy index with large scale MEISS(PTT) pulse transit time-based multiscale entropy index with small scale MEILS(PTT) pulse transit time-basedmultiscale entropy index with large scale MCEISS multiscale Co ApEnRRI1015840(120591)PTT1015840(120591) (120591) index with small scale MCEILS multiscale Co ApEnRRI1015840(120591)PTT1015840(120591) (120591)index with large scaledagger119875 lt 005 Group 2 versus Group 3 Dagger119875 lt 005 Group 3 versus Group 4 lowastlowast119875 lt 001 Group 1 versus Group 2 daggerdagger119875 lt 001 Group 2 versus Group 3 and DaggerDagger119875 lt001 Group 3 versus Group 4

0 5 10 15 2008

1

12

14

16

18

2

Scale

Sam

ple e

ntro

py (R

RI)

Group 1Group 2

Group 3Group 4

(a)

Scale

Group 1Group 2

Group 3Group 4

0 5 10 15 201

12

14

16

18

2

22

24

Sam

ple e

ntro

py (P

TT)

(b)

Figure 2Multiscale entropy (MSE) analysis of (a) RRI and (b) PTT time series showing changes in sample entropy 119878119864 among the four groups

of study subjects for different scale factors Symbols represent the mean values of entropy for each group and bars represent the standarderror (given by SE = SDradic119899 where 119899 is the number of subjects)


0 2 4 6 8 10 12 14 16 18 20

12

14

16

18

2

22

Group 1Group 2

Group 3Group 4

120591

Co

ApEn

RRI998400(120591)PT

T998400(120591)(120591)

Figure 3 Co ApEnRRI1015840(120591)PTT1015840(120591) (120591) curve of the four groups was cal-culated using the MCE calculation (120591 = 1sim20) on 1000 consecutiveRRI and PTT times series Symbols represent the mean values ofentropy for each group and bars represent the standard error (givenby SE = SDradic119899 where n is the number of subjects)

physiological systems and that a strong relationship existsbetween variations in PTT and those in RRI We there-fore employed the Co ApEn integrated with preprocessingcoarse-graining to calculate MCEI values as well as thecomplexity between the synchronous time series RRI andPTT Figure 3 shows that at small-scale factors (from 1 to 5)it is difficult to determine the influence of age diabetes orglycemic control based on the complexity between the timeseries RRI and PTT using Co ApEnRRI1015840(120591)PTT1015840(120591)(120591) SimilarlyMCEISS indicates only that aging reduces the complexitybetween the two time series This finding is similar to thatof previous studies [3] As the scale factor increased (from6 to 20) Co ApEnRRI1015840(120591)PTT1015840(120591)(120591) began revealing significantdifferences between the four study groups (Figure 3) Table 1shows that the MCEILS values of the young healthy subjectswere the highest whereas subjects with poorly controlledtype 2 diabetes were the lowest This may be due to the factthat the coupling effect between the heart and the bloodvessels in the cardiovascular system varies according to ageand the influence of disease [24 25] In other words thecomplexity between the time series RRI and PTT decreasesdue to age and disease

Although the MCEILS can be used to quantify the com-plexity of RRI and PTT and have been shown to effectivelyidentify significant difference among study groups limita-tions still exist First a lengthy process of data acquisition andconsiderable calculation and off-line processing is neededMCE analysis involves a 30-minutemeasurement as opposedto the relatively shorter duration measurement of only RRIand PTT making the process tiring for participants Thenature of analysis postmeasurement further prevented sub-jects from receiving their MCEI test results immediatelySecond the medications that the diabetic patients used suchas hypoglycemic antihyperlipidemic and antihypertensivedrugs may also affect autonomic nervous activity Theseeffects however were difficult to assess The potential effect

ofmedications therefore was not considered in the statisticalanalysis of this study

5 Conclusions

This study integrates cross-approximate entropy with multi-ple scales to analyze the complexity between two synchronousphysiological signals (RRI and PTT) in the cardiovascularsystem According to our results MCEILS clearly revealsa reduction in the complexity of two physiological signalscaused by aging and diabetes

Authorsrsquo Contribution

M-T Lo and A-B Liu equally contributed in this studycompared with the corresponding author

Conflict of Interests

The authors declare no conflict of interests

Acknowledgments

The authors would like to thank the volunteers involved inthis study for allowing them to collect and analyze their dataThe authors are grateful for the support of Texas Instru-ments Taiwan in sponsoring the low power instrumentationamplifiers and ADC tools The authors would also liketo thank Miss Crystal J McRae who is a native Englishspeaker to go over the whole paper This research was partlysupported by National Science Council under Grants NSC100-2221-E-259-030-MY2 and NSC 101-2221-E-259-012 andNational Dong Hwa University on campus interdisciplinaryintegration Projects no 101T924-3 and 102T931-3 M-T Lowas supported by NSC (Taiwan ROC) Grant no 100-2221-E-008-008-MY2 joint foundation of CGH and NCUGrant no CNJRF-101CGH-NCU-A4 VGHUST102-G1-2-3and NSC support for the Center for Dynamical Biomarkersand Translational Medicine National Central UniversityTaiwan (NSC 101-2911-I-008-001)

References

[1] M Costa A L Goldberger and C K Peng ldquoMultiscale entropyanalysis of biological signalsrdquo Physical Review E vol 71 no 2part 1 2005

[2] M Costa A L Goldberger and C K Peng ldquoMultiscale entropyto distinguish physiologic and synthetic RR time seriesrdquo Com-puting in Cardiology vol 29 pp 137ndash140 2002

[3] H-TWu P-C Hsu C-F Lin et al ldquoMultiscale entropy analysisof pulse wave velocity for assessing atherosclerosis in the agedand diabeticrdquo IEEE Transactions on Biomedical Engineering vol58 no 10 pp 2978ndash2981 2011

[4] R T Vieira N Brunet S C Costa S Correia B G A Netoand J M Fechine ldquoCombining entropy measures and cepstralanalysis for pathological voices assessmentrdquo Journal of Medicaland Biological Engineering vol 32 no 6 pp 429ndash435 2012


[5] J Y Lan M F Abbod R G Yeh S Z Fan and J S ShiehldquoReview intelligent modeling and control in anesthesiardquo Jour-nal of Medical and Biological Engineering vol 32 no 5 pp 293ndash307 2012

[6] C-K Peng M Costa and A L Goldberger ldquoAdaptive dataanalysis of complex fluctuations in physiologic time seriesrdquoAdvances in Adaptive Data Analysis vol 1 no 1 pp 61ndash70 2009

[7] M J Drinnan J Allen and A Murray ldquoRelation betweenheart rate and pulse transit time during paced respirationrdquoPhysiological Measurement vol 22 no 3 pp 425ndash432 2001

[8] S M Pincus ldquoApproximate entropy in cardiologyrdquo Herz-schrittmachertherapie und Elektrophysiologie vol 11 no 3 pp139ndash150 2000

[9] S M Pincus T Mulligan A Iranmanesh S Gheorghiu MGodschalk and J D Veldhuis ldquoOlder males secrete luteiniz-ing hormone and testosterone more irregularly and jointlymore asynchronously than younger malesrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 93 no 24 pp 14100ndash14105 1996

[10] F Roelfsema S M Pincus and J D Veldhuis ldquoPatients withCushingrsquos disease secrete adrenocorticotropin and cortisoljointly more asynchronously than healthy subjectsrdquo Journal ofClinical Endocrinology and Metabolism vol 83 no 2 pp 688ndash692 1998

[11] J D Veldhuis A Iranmanesh T Mulligan and S M PincusldquoDisruption of the young-adult synchrony between luteiniz-ing hormone release and oscillations in follicle-stimulatinghormone prolactin and nocturnal penile tumescence (NPT)in healthy older menrdquo Journal of Clinical Endocrinology andMetabolism vol 84 no 10 pp 3498ndash3505 1999

[12] D-Y Wu G Cai Y Yuan et al ldquoApplication of nonlineardynamics analysis in assessing unconsciousness a preliminarystudyrdquo Clinical Neurophysiology vol 122 no 3 pp 490ndash4982011

[13] M U Ahmed and D P Mandic ldquoMultivariate multiscaleentropy a tool for complexity analysis of multichannel datardquoPhysical Review E vol 84 no 6 Article ID 061918 2011

[14] A-B Liu P-C Hsu Z-L Chen and H-T Wu ldquoMeasuringpulse wave velocity using ECG and photoplethysmographyrdquoJournal of Medical Systems vol 35 no 5 pp 771ndash777 2011

[15] H T Wu P C Hsu A B Liu Z L Chen R M Huang CP Chen et al ldquoSix-channel ECG-based pulse wave velocity forassessing whole-body arterial stiffnessrdquo Blood Press vol 21 no3 pp 167ndash176 2012

[16] Z Wu N E Huang S R Long and C-K Peng ldquoOn the trenddetrending and variability of nonlinear and nonstationary timeseriesrdquo Proceedings of the National Academy of Sciences of theUnited States of America vol 104 no 38 pp 14889ndash14894 2007

[17] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hubert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety A vol 454 no 1971 pp 903ndash995 1998

[18] M D Costa C-K Peng and A L Goldberger ldquoMultiscaleanalysis of heart rate dynamics entropy and time irreversibilitymeasuresrdquo Cardiovascular Engineering vol 8 no 2 pp 88ndash932008

[19] S Pincus and B H Singer ldquoRandomness and degrees ofirregularityrdquo Proceedings of the National Academy of Sciences ofthe United States of America vol 93 no 5 pp 2083ndash2088 1996

[20] M Kreuzer H Hentschke B Antkowiak C Schwarz E FKochs and G Schneider ldquoCross-approximate entropy of corti-cal local field potentials quantifies effects of anesthesiamdasha pilotstudy in ratsrdquo BMC Neuroscience vol 11 article 122 2010

[21] S M Pincus ldquoIrregularity and asynchrony in biologic networksignalsrdquoMethods in Enzymology vol 321 pp 149ndash182 2000

[22] F Yang B Hong and Q Tang ldquoApproximate entropy andits application to biosignal analysisrdquo in Nonlinear BiomedicalSignal Processing DynamicAnalysis andModelingMAkay Edvol 2 John Wiley amp Sons Hoboken NJ USA 2000

[23] D Cheng S-J Tsai C-J Hong and A C Yang ldquoReducedphysiological complexity in robust elderly adults with theAPOE1205764 allelerdquo PLoS ONE vol 4 no 11 Article ID e7733 2009

[24] D E Vaillancourt and K M Newell ldquoChanging complexity inhuman behavior and physiology through aging and diseaserdquoNeurobiology of Aging vol 23 no 1 pp 1ndash11 2002

[25] D T Kaplan M I Furman S M Pincus S M Ryan L ALipsitz and A L Goldberger ldquoAging and the complexity ofcardiovascular dynamicsrdquo Biophysical Journal vol 59 no 4 pp945ndash949 1991


Research ArticleConstructing Benchmark Databases and Protocols forMedical Image Analysis Diabetic Retinopathy

Tomi Kauppi1 Joni-Kristian Kaumlmaumlraumlinen2 Lasse Lensu1 Valentina Kalesnykiene3

Iiris Sorri3 Hannu Uusitalo4 and Heikki Kaumllviaumlinen1

1 Machine Vision and Pattern Recognition Laboratory Department of Mathematics and Physics Lappeenranta University ofTechnology (LUT) Skinnarilankatu 34 FI-53850 Lappeenranta Finland

2Department of Signal Processing Tampere University of Technology Korkeakoulunkatu 10 FI-33720 Tampere Finland3Department of Ophthalmology University of Eastern Finland Yliopistonranta 1 FI-70211 Kuopio Finland4Department of Ophthalmology University of Tampere Biokatu 14 FI-33520 Tampere Finland

Correspondence should be addressed to Lasse Lensu lasselensulutfi

Received 25 January 2013 Accepted 26 May 2013


Copyright copy 2013 Tomi Kauppi et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We address the performance evaluation practices for developing medical image analysis methods in particular how to establishand share databases of medical images with verified ground truth and solid evaluation protocols Such databases support thedevelopment of better algorithms execution of profound method comparisons and consequently technology transfer fromresearch laboratories to clinical practice For this purpose we propose a framework consisting of reusablemethods and tools for thelaborious task of constructing a benchmark database We provide a software tool for medical image annotation helping to collectclass label spatial span and expertrsquos confidence on lesions and a method to appropriately combine the manual segmentations frommultiple experts The tool and all necessary functionality for method evaluation are provided as public software packages As acase study we utilized the framework and tools to establish the DiaRetDB1 V21 database for benchmarking diabetic retinopathydetection algorithms The database contains a set of retinal images ground truth based on information from multiple experts anda baseline algorithm for the detection of retinopathy lesions

1 Introduction

Image databases and expert ground truth are regularlyused in medical image processing However it is relativelycommon that the data is not public and therefore reliablecomparisons and state-of-the-art surveys are difficult toconduct In contrast to for example biometrics includingface iris and fingerprint recognition the research has beendriven by public databases and solid evaluation protocolsThese databases have been extended and revised resulting incontinuous pressure for the development of better methodsFor every medical application it should be an acknowledgedscientific contribution to provide a set of images collectaccurate and reliable ground truth for the images and devisea meaningful evaluation protocol Once this pioneering work

has been done it sets an evaluation standard for a selectedproblem

We have set our primary goal to the automatic detectionof diabetic retinopathy [1] which is very well motivated sincediabetes has become one of the most rapidly increasinghealth threats worldwide [2 3] Since the retina is vul-nerable to microvascular changes of diabetes and diabeticretinopathy is the most common complication of diabetesretinal imaging is considered a noninvasive and painlessmean to screen and monitor the progress of the disease[4] Since these diagnostic procedures as well as regularmonitoring of state of diabetes require the attention ofmedical personnel for example GP and ophthalmologiststhe workload and shortage of personnel will eventuallyexceed the current resources for screening To cope with


these challenges digital imaging of the eye fundus andautomatic or semiautomatic image analysis algorithms basedon image processing and computer vision techniques providea great potential For this suitable retinal image databasescontaining well-defined and annotated ground truth areneeded

In this work our main contributions are (1) an imageannotation tool for medical experts (2) a public retinalimage databasewith expert annotations (3) a solid evaluationframework for the image analysis system development andcomparison (Figure 1) and (4) image-based and pixel-basedevaluation methods We particularly focus on constructingbenchmark databases and protocols We have experiencedthat developing databases from scratch is demanding labo-rious and time consuming However certain tasks occurrepeatedly and are reusable as such Here we discuss therelated practical issues point out and solve repeated occur-ring subtasks and provide the solutions as open-sourcetools on our website In the experimental part we utilizethe proposed framework and construct a revised versionof the diabetic retinopathy database DiaRetDB1 originallypublished in [5 6] and later discussed in [7]

The paper is organized as follows in Section 2 we discussmedical benchmarking in general provide relevant guide-lines and briefly survey the related works In Section 3 wediscuss collecting patient images and the spatial ground truthWe propose a portable data format for the ground truth andrepresent and solve the problem of fusing multiple expertannotations In Section 4 we discuss evaluation practicesin general and provide an evaluation approach based onthe standard ROC analysis We evaluate our color-cue-based detection method (baseline) by using the constructeddatabase In Section 5 we utilize the given results andtools to establish the diabetic retinopathy evaluation andbenchmarking database DiaRetDB1 V21 and we draw theconclusions in Section 6

2 Benchmarking in General andPrevious Work

Public image databases for benchmarking purposes areessential resources in the development of image analysisalgorithms and help medical imaging researchers evaluateand compare state-of-the-art methods Eventually this leadsto the development of better algorithms and consequentlywill support technology transfer from research laborato-ries to clinical practice However the public availability ofimage databases is limited because of the amount of workneeded to make internal data publicly available includingthe ground truth annotation and the privacy protectionof the patient information Therefore reliable comparisonsand state-of-the-art surveys are difficult to perform In thissection a benchmarking framework is described that pro-vides guidelines on how to construct benchmarking imagedatabases with a particular emphasis on retinal image analy-sisThe benchmarking framework comprises three importantrequirements (1) patient images (2) the ground truth and(3) an evaluation protocol

21 Key Questions in Constructing Benchmarks Thacker et al[10] studied the performance characterization of computervisionmethodsThey provide good examples which are easilytransferable to applications of medical image processingThe results in [10] can be utilized in every step of themethod development but we set special attention to the finaldiagnosis that is the subject-wise decision making directlyserving the clinical work In other words the frameworkomits the development and research phase evaluations andconstructs the good practices to evaluate the performance ofretinal image analysis algorithms For that purpose the eightgeneral considerations adopted from [10] are addressed andreferred to as the key questions

C1 ldquoHow is testing currently performedrdquo If a commonlyused database and protocol are available their validityfor the development and evaluation needs to beexamined In the worst case a new database needsto be constructed for which the proposed frameworkcan be useful

C2 ldquoIs there a data set for which the correct answers areknownrdquo Such a data set can be used to report theresults in accordance to other studies This enablesmethod comparison

C3 ldquoAre there data sets in common userdquo See C1 and C2Common data sets facilitate fair method comparison

C4 ldquoAre there experiments which show that algorithmsare stable and work as expectedrdquo These experimentscan be realized if representative data and expertground truth are available

C5 ldquoAre there any strawman algorithmsrdquo If a strawmanalgorithm is included in the database it definesthe baseline performance for other methods In thispaper we call these kinds of baseline methods asstrawman algorithms

C6 ldquoWhat code and data are availablerdquo By publishing themethodrsquos code or at least executable version of it otherresearch groups can avoid laborious reimplementa-tion

C7 ldquoIs there a quantitative methodology for the design ofalgorithmsrdquo This depends on the medical problembut the methodology can be typically devised byfollowing corresponding clinical work and practicesUnderstanding of the medical practitionersrsquo taskwhich should be assisted or automated provides aconceptual guideline If the database is correctly builtto reflect the real-world conditions then the databaseimplicitly reflects the applicability of the algorithmrsquosdesign to the problem

C8 ldquoWhat should we be measuring to quantify perfor-mance which metrics are usedrdquo At least in theimage-wise (subject-wise) experiments the receiveroperating characteristic (ROC) curve is in accordancewith the medical practice where the sensitivity andspecificity values are in common useThe ROC curvealso known as ROC analysis is a widely used toolin medical community for visualizing and comparing


GMM-FJ

Lesion detection

lesions

testingBenchmarking framework PDF lesions

Train images

Test image

Likelihood lesions

RGB lesions

Overall score

Multiple expert

Baseline

trainingBaseline

Score

Pixel-based evaluation

Image-based evaluation

RGB image

RGB imagesannotation

fusion

annotationfusion

annotationsExpert

Multiple expertannotations

Expert

Figure 1 A framework for constructing benchmark databases and protocols [1]

methods based on their performance [11] It is agraphical representation that describes the trade-offbetween the sensitivity and specificity (eg correctlyclassified normal images versus correctly classifiedabnormal images) In the curve the 119909-axis is definedas 1 minus specificity and the 119910-axis is directly thesensitivity [12]

In general C1 isin C2 isin C3 which means that if there is acommonly used data set in the form of for example abenchmark database the answers to C1 and C2 are knownSimilarly C4 isin C5 isin C6 defines the maturity of the existingsolutions In the case where the data and code are bothavailable and have been shown to work by achieving therequired sensitivity and specificity rates the solution is at amature level and true clinical experiments can be started C7

is a general guideline for the design to find an acceptable workflow for a specific problem and C8 sets the quantitative andmeaningful performance measures

22 Requirements for Benchmarking Benchmarking imagedatabases in retinal imaging require threemandatory compo-nents (1) patient images (2) ground truth by domain expertsand (3) an evaluation protocol Additional components suchas a baseline algorithm provide notable additional valuebut in the following the three mandatory components arediscussed

221 True Patient Images True patient images carry infor-mation which is meaningful for solving a given problem thatis algorithms which work with these images are expected toperform well also in practice The images can be recordedusing alternative subjects such as animals that are physio-logically close to humans and disease-related lesions can beproduced artificially by using various substances These arestandard practices in medical research but before drawingany general conclusions their relevance and accuracy tothe real world must be carefully verified With true patientimages the results are biased by the distribution of database

images with respect to the specific real population Thecollection and selection of images are further discussed inSection 3 The true patient image requirement concerns thekey questions C2C3C4 and C6

222 Ground Truth Given by Experts Ground truth must beaccurate and reliable in the sense that it is statistically repre-sentative over experts In the field of retinal image processingit is advisable that the tools for ground truth annotationare provided by computer vision scientists but the imagesare selected and annotated by medical experts specializedin the field It is also clear that the ground truth must beindependently collected from multiple experts This can belaborious and expensive but it enables statistical studies ofreliability In the case of multiple experts disambiguation ofthe data is often necessary prior to the application of machinelearning methods Collecting the ground truth from expertsconcerns the key questions C2C3C4 and C6

223 Evaluation Protocol A valid evaluation protocol pro-viding quantitative and comparable information is essentialfor reliable performance evaluations Most articles related toretinal image analysis report the sensitivity and specificityseparately but they are meaningless metrics unless a methodcan produce superior values for both The golden standardin similar problems is the ROC analysis The approach isessentially the same as reporting the sensitivity and specificitybut provides the evaluation result over all possible combi-nations of these values It turns out that in benchmarkingthe comparison of ROC curves is problematic and thereforespecific well-justified operation points or the area undercurve (AUC) can be used as a single measure This issue isfurther discussed in Section 4 In addition to the evaluationprotocol a baseline method (C5) or at least the results withthe baseline method are helpful since they set the perfor-mance level which new methods should clearly outperformFrom another viewpoint the best reported results by usinga commonly accepted database set the state of the art


Table 1 Summary of the current state of the reference image databases in terms of the key questions addressed in Section 21

Key questions STARE(vessel)

STARE(disc) DRIVE MESSIDOR CMIF ROC REVIEW

C2 ldquoIs there a data set for which the correct answers are knownrdquo x x x x xC3 ldquoAre there data sets in common userdquo x x x x x x xC4 ldquoAre there experiments which show algorithms are stable and workas expectedrdquo x x x

C5 ldquoAre there any strawman algorithmsrdquo x x xC61 ldquoWhat code is availablerdquo xC62 ldquoWhat data is availablerdquo x x x x x x xC7 ldquoIs there a quantitative methodology for the design of algorithmsrdquoC81 ldquoWhat should we be measuring to quantify performancerdquo x x x x xC82 ldquoWhat metrics are usedrdquo x x x xsum 6 5 7 3 2 7 5

The evaluation protocol requirement concerns the key ques-tions C1C4C7 and C8

23 Eye Disease Databases This section describes the mostimportant public benchmarking databases in retinal imageanalysisThe database review provides a short description foreach database where the key questions C1ndashC8 addressed inSection 21 are used to highlight the main properties Sinceeach database is publicly available they are expected to be incommon use (C3) See Table 1 for a short summary

STARE (structured analysis of the retina) [17] is one ofthe most used reference image database in the literature(C3C4) for comparing blood vessel detection and optic disclocalization algorithms The STARE website [17] provides 20images with pixel-wise hand-labeled ground truth for bloodvessel detection (C2) and 81 images for optic disc localizationwithout ground truth The performance of blood vesseldetection is measured using the ROC curve analysis wherethe sensitivity is the proportion of correctly classified bloodvessel pixels and the specificity is the proportion of correctlyclassified normal pixels (C81) [18] In the evaluation of opticdisc localization the proportion of correctly localized opticdiscs indicates that the performance and the localizationare successful if the center of optic disc generated by thealgorithm is within 60 pixels from the ground truth (C8) [19]The evaluation procedures for both data sets are publishedwith vessel detection algorithm and baseline results (C5)[18 19]

DRIVE (digital retinal images for vessel extraction) [2021] is another well-known reference database for blood vesseldetection (C3) which contains 40 retinal images (C62) withmanually segmented pixel-wise ground truth (C2C62) Themanual segmentation task was divided between three medi-cal experts and the database was published along with vesseldetection algorithm (C5) [21] The detection performanceis measured similarly as in the STARE database that iscomparing the sensitivity to the specificity (C81) fromwhichthe area under curve (AUC) is computed to produce the finalmeasure for the algorithm comparison (C82) [20 21] In

addition the authors implemented and internally evaluateda number of blood vessel detection algorithms from variousresearch groups and the results were published in [22] and onthe DRIVE database website (C4) [20]

MESSIDOR (methods to evaluate segmentation andindexing techniques in the field of retinal ophthalmology)[23] is a reference image database collected to facilitatecomputer-assisted image analysis of diabetic retinopathy Itsprimary objectives are to enable evaluation and compar-ison of algorithms for analyzing the severity of diabeticretinopathy prediction of the risk of macular oedema andindexing and managing image databases that is supportimage retrieval For the evaluation the MESSIDOR databasewebsite [23] provides 1200 images (C62) with image-wise severity grading (C2C62) from three ophthalmologicdepartments including descriptions for the severity gradingIt is noteworthy to mention that the severity grading is basedon the existence and number of diabetic lesions and theirdistance from the macula

CMIF (collection of multispectral images of the fundus)[24 25] is a public multispectral retinal image databaseThe spectral images were obtained by implementing a ldquofilterwheelrdquo into a fundus camera containing a set of narrow-bandfilters corresponding to the set of desired wavelengths [25]The database itself consists of normal and abnormal images(C62) spanning a variety of ethnic backgrounds covering35 subjects in total [25] As such the database is not readyfor benchmarking but it provides a new insight into retinalpathologies

ROC (retinopathy online challenge) [26 27] follows theidea of asynchronous online algorithm comparison proposedby Scharstein and Szeliski [28] for stereo correspondencealgorithms (Middlebury Stereo Vision Page) where a webevaluation interface with public evaluation data sets ensuresthat the submitted results are comparable The researchgroups download the data set they submit their results inthe required format and the results are evaluated by the webevaluation system Since the evaluation is fully automatic theresearch groups can submit and update their results contin-uously In the current state the ROC database website [26]


Table 2 Summary of the DiaRetDB1 V21 database in terms of the key questions addressed in Section 21

Key questions DiaRetDB1 V21C2 ldquoIs there a data set for which the correct answers areknownrdquo Yes

C3 ldquoAre there data sets in common userdquo Yes (publicly available at [13])C4 ldquoAre there experiments which show algorithms are stableand work as expectedrdquo Experimental results reported in Section 44

C5 ldquoAre there any strawman algorithmsrdquo No but the baseline algorithm sets the baseline results for theDiaRetDB1 database

C61 ldquoWhat code is availablerdquoFunctionality for readingwriting images and ground truthstrawman algorithm and annotation software (publiclyavailable at [13 14])

C62 ldquoWhat data is availablerdquo Images and ground truth (XML) (publicly available at [13])C7 ldquoIs there a quantitative methodology for the design ofalgorithmsrdquo

No but medical practice is used as a guideline at eachdevelopment step

C81 ldquoWhat should we be measuring to quantify performancerdquo Image- and pixel-based ROC analysis (description in Section 4)C82 ldquoWhat metrics are usedrdquo Equal error rate (EER) defined in Section 4

provides 100 retinal images (C62) a ground truth (C2C62)and an online evaluation system for microaneurysms andthe evaluation results for a number of detection algorithms(C4) The algorithm performance is measured by comparingthe sensitivity (the proportion of correctly classified lesions)against the average number of false positives in the imagethat is free-response receiver operating characteristic curve(FROC) (C81) [27] The sensitivities of predefined falsepositive points are averaged to generate the final measurefor algorithm comparison (C82) [27] The annotations weregathered from 4 medical experts by marking the locationapproximate size and confidence of the annotation Consen-sus of two medical experts was required for a lesion to beselected to the ground truth

REVIEW (retinal vessel image set for estimation ofwidths) [29 30] is a new reference image database toassess the performance of blood vessel width measurementalgorithms To characterize the different vessel propertiesencountered in the retinal images the database consists offour image sets (1) high-resolution image set (4 images)(2) vascular disease image set (8 images) (3) central lightreflex image set (2 images) and (4) kick point image set(2 images) (C62) The REVIEW database concentrates onhigh-precision annotations and therefore it provides onlysegments of blood vessels and not the whole networkTo achieve high precision the human observers used asemiautomatic tool to annotate a series of image locationsfrom which the vessel widths were automatically determined[30] The annotations were gathered from three medicalexperts and the mean vessel width was defined as theground truth (C2C62) In the evaluation the performance ismeasured using an unbiased standard deviation of the widthdifference between the algorithm-estimated vessel widths andthe ground truth (C8) [30]

In general most of the reference databases reach theminimal requirements for benchmarking image analysisalgorithms that is they provide true patient images groundtruth from experts and an evaluation protocol (Table 1)

In some cases the usability is already at a mature levelfor example in the case of the web evaluation system inthe ROC database The primary shortcomings appear tobe related to the availability of software (C61) and howthe algorithmrsquos design for the medical problem is observed(C7) By publishing source codes or an executable otherresearchers can avoid laborious reimplementation and if thedatabase is correctly built to reflect real-world conditionsthen the database implicitly reflects the applicability of thealgorithmrsquos design to the problem The database propertiesin terms of the key questions are summarized in Table 1 andfor comparison the proposed DiaRetDB1 database propertiesare summarized in Table 2 The framework for constructingbenchmark databases and protocols has been summarized inFigure 1 The details of the framework are discussed in thenext sections

3 Patient Images and Ground Truth

31 Collecting Patient Images The task of capturing andselecting patient images should be conducted by medicaldoctors or others specifically trained for photographing theeye fundus With the images there are two issues whichshould be justified (1) distribution correspondence with thedesired population and (2) privacy protection of patient data

InDiaRetDB1 the ophthalmologistswanted to investigatethe accuracy of automatic methods analyzing retinal imagesof patients who are diagnosed with having diabetes Conse-quently the images do not correspond to the actual severity orprevalence of diabetic retinopathy in the Finnish populationbut provide clear findings for automated detection methodsThe data is however clinically relevant since the studiedsubpopulation is routinely screened by Finnish primaryhealth care

The privacy protection of patient data is a task related tothe ethics of clinical practice medical research and also datasecurity A permission for collecting and publishing the datamust be acquired from a corresponding national organization


(eg national or institutional ethical committee) and fromthe patients themselves Moreover all data must be securelystored that is all patient information such as identifyingmetadata must be explicitly removed from images which areto be used in a public database In DiaRetDB1 the retinalimages were acquired using a standard fundus camera and itsaccompanying softwareThe acquired images were convertedto raw bitmaps and then saved to portable network graphics(PNG) format using lossless compression The raw bitmapscontained nothing but the pixel data which guaranteed theremoval of hidden metadata

32 Image Annotations as the Ground Truth In generalthe image annotations are essential for training supervisedalgorithms as well as for their evaluation and comparisonSuch information is typically collected by manually anno-tating a set of images In face recognition for example aground truth contains identifiers of persons in the imagesand often also the locations of facial landmarks such as eyecenters which can be very useful in training the methodsCommonly simple tailored tools are used to collect thedata but also generic applications are available for problemswhich require an exhaustive amount of image data forexample LabelMe [31] Web tool for annotating visual objectcategories Annotating medical images is not an exceptionbut two essential considerations apply (1) annotations mustbe performed by clinically qualified persons (specialized orspecializing medical doctors or other trained professionalsfor specific tasks) denoted as ldquoexpertsrdquo and (2) the groundtruth should include annotations from multiple experts

A more technical problem is to develop a reusable toolfor the annotation task To avoid biasing the results theexperts should be given minimal guidance for their actualannotation work Basic image manipulation such as zoomand brightness control for viewing the images is needed anda set of geometric primitives are provided for making thespatial annotations In LabelMe [31] the only primitive ispolygon region defined by an ordered set of points A polygoncan represent an arbitrarily complex spatial structure butophthalmologists found also the following primitives usefulsmall circle which can be quickly put on a small lesionand circle area and ellipse area which are described by theircentroid radiusradii and orientation (ellipse) The systemalso requires at least one representative point for each lesionThis point should represent themost salient cue such as coloror texture that describes the specific lesion Furthermorea confidence selection from the set of three discrete valueslow moderate or high is required for every annotation Theexperts are allowed to freely define the types of annotationsthat is the class labels for the lesion types but typically itis preferable to agree with the labels beforehand (eg inDiaRetDB1 hard exudates soft exudates microaneurysmsand haemorrhages) An important design choice is relatedto the usability of the tool with respect to its graphical userinterface (GUI) For example the GUI should not use colorswhich distract the annotators from image content

The development of an annotation tool may take unde-sirable amount of research time and resources To help other

Figure 2 Graphical user interface of the image annotation tool [1]

researchers in this task the tool is available upon request asMatlab M-files and as a Windows executable Users have fullaccess to the source code which enables tailoring of the toolfor their specific needs The default graphical user interface(GUI) is shown in Figure 2

33 Data Format forMedical Annotations To store the anno-tations and to be able to restore their graphical layout the dataformat must be definedThe data is naturally structured andtherefore structural data description languages are preferredSeveral protocols for describing medical data exist such asHL7 based on the extensible markup language (XML) [32]but these are complex protocols designed for patient infor-mation exchange between organizations and informationsystems Since the requirements for benchmarking databasesin general are considerably less comprehensive a light-weightdata format based on the XML data description language isadopted Instead of the XML Schema document descriptionamore compact and consequently more interpretable Docu-ment Type Definition (DTD) description is appliedThe usedformat is given in Listing 1

34 Fusion of Manual Segmentations from Multiple ExpertsA desired characteristic of collecting the ground truth formedical images is that one or several experts provide infor-mation on the image contents such as the disease-relatedlesions Since there can exist inconsistencies in the case of asingle expert (eg due to changing criteria while performingthe annotation work) and nobody can be considered as theunparalleled expert the use of several experts is preferredOnly in clear cases however the experts fully agree on theinterpretation of the visible information Since the early signsof retinopathy are very subtle changes in the images it isnecessary to develop a method to appropriately combinethe expert information which is only partially coherent Todesign such a method the important questions relevantto training evaluating and benchmarking by using thedatabase are as follows (1) how to resolve inconsistencies


ltELEMENT imgannotooldata (header markinglist)gtltELEMENT header (creator software

affiliation copyrightnotice)gtltELEMENT creator (PCDATA)gtltELEMENT software (PCDATA)gtltATTLIST software version CDATA REQUIREDgt

ltELEMENT affiliation (PCDATA)gtltELEMENT copyrightnotice (PCDATA)gtltELEMENT imagename (PCDATA)gtltELEMENT imagesize (width height)gtltELEMENT width (PCDATA)gtltELEMENT height (PCDATA)gtltELEMENTmarkinglist (markinglowast)gtltELEMENTmarking ((polygonregion |

circleregion | ellipseregion)representativepoint+ confidencelevel markingtype)gt

ltELEMENT centroid (coords2d)gtltELEMENT polygonregion (centroid coords2d

coords2d coords2d+)gtltELEMENT circleregion (centroid radius)gtltELEMENT ellipseregion (centroid radius radius rotangle)gtltELEMENT representativepoint (coords2d)gtltELEMENT coords2d (PCDATA)gtltELEMENT radius (PCDATA)gtltATTLIST radius direction CDATA REQUIREDgt

ltELEMENT rotangle (PCDATA)gtltELEMENTmarkingtype (PCDATA)gtltELEMENT confidencelevel (PCDATA)gt]gt

Listing 1 DTD definition

Representative point

Spatial coverage polygon

True finding area

Figure 3 The available expert information in the DiaRetDB1database The expertrsquos subjective confidence for the annotation isdefined as follows 100 gt50 and lt50 [1]

in the annotations from a single expert and (2) how to fuseequally trustworthy (no prior information on the superiorityof the experts related to the task) information from multipleexperts

In our data format the available expert information isthe following (Figure 3) (1) spatial coverage (polygon area)(2) representative point(s) (small circle areas) and (3) the

subjective confidence level The representative points aredistinctive ldquocue locationsrdquo that attracted the expertrsquos attentionto the specific lesion The confidence level with a three-value scale describes the expertrsquos subjective confidence for thelesion to represent a specific class (lesion type) as shown inFigure 4

Combining the manual segmentations from multipleexperts was originally studied in [9] In the study the areaintersection provided the best fusion results in all experimen-tal setups and is computed in a straightforward manner asthe sum of expert-annotated confidence images divided bythe number of experts For DiaRetDB1 the fused confidencewith the threshold 075 yielded the best results [1] resolvingthe inconsistencies of annotations either from a single expertor multiple expert cofusion problems

The area intersection is intuitive and the result is based onprocessing the whole image ensemble However the thresh-old was selected with the baselinemethod which undesirablytied the training and evaluation together Therefore thecombination problem was revised in [8]

Themost straightforward combination procedure is aver-aging where the expert segmentations are spatially averagedfor each image and lesion type In this procedure the givenconfidence levels are used and the only requirement for theconfidence scale is that it is monotonically increasing Theaverage confidence image corresponds to the mean expertopinion but it has two disadvantages (1) it does not take


Figure 4 Four independent sets of spatial annotations (contours and representative points) for the same lesion type (hard exudates) Therepresentative point markers denote the confidence level (119904119902119906119886119903119890 = 100 119905119903119894119886119899119892119897119890 gt 50 and 119888119894119903119888119897119890 lt 50) [1]

(a) (b) (c)

Figure 5 1st row DiaRetDB1 expert spatial annotations for the lesionHard exudate (red high confidence yellow moderate green low) 2ndrow the ground truth (white) produced by the original method and (a) minimal and (b) maximal confidence The disambiguated groundtruth by (c) the revised method [8]

into account the possible differences of the experts in theiruse of the scale and (2) it does not produce binary values forthe foreground (lesion of specific type) and background As asolution a binary mask can be generated by thresholding theaverage expert segmentation imageThe threshold parameter120591 isin [0 1] adjusts expertsrsquo joint agreement for 120591 rarr 0 thebinary mask approaches set union and for 120591 rarr 1 approachesset intersection (see Figure 5)

The revised combining method is based on the followingprinciple The ground truth should optimally represent themutual agreement of all experts To evaluate the degree ofmutual agreement a performance measure is needed Theperformance depends only on two factors expertsrsquo markingsand the ground truth and without loss of generality themeasure is expected to output a real number

perf 119868exp119894119895119899

119892119905119894119895

997888rarr R (1)

where expert segmentation masks 119868exp119894119895119899

represents theexpert segmentation mask for the input image 119894 lesion type119895 and expert 119899 119892

119905is the ground truth and sdot is used

to denote that the performance is computed for a set of

rated images Generation of the image-wise ground truth isstraightforward if any of the pixels in the produced 119868mask119894119895for the lesion 119895 is nonzero the image is labeled to containthat lesion A detection ROC curve can be automaticallycomputed from the image-wise ground truth and imagescores computed from the expert images For the image-wise expert scores we adopted the summax rule described inSection 4 pixel confidences of 119868exp

119894119895119899

are sorted and 1 of thehighest values are summedThe average equal error rate (EERpoint on the ROC curve) was chosen as the performancemeasure in (1) which can be given in an explicit form

perf (119868exp119894119895119899

119892119905119894119895

)

=1

119873sum

119899

EER (summax1 (119868exp

119894119895119899

) 119868mask119894119895 (119909 119910 120591))

(2)

A single EER value is computed for each expert 119899 and overall images (119894) and then the expert-specific EER values aresummed for the lesion type 119895


(a) (b)

Figure 6 Pixel-wise likelihoods for Hard exudates produced by the strawman algorithm (a) original image (hard exudates are the smallyellow spots in the right part of the image) (b) ldquolikelihood maprdquo for hard exudates [9]

The utilization of the summax rule is justified as a robustmaximum rule by the multiple classifier theory [33] Alsothe EER measure can be replaced with any other measureif for example prior information on the decision-relatedcosts is available The only factor affecting the performancein (2) is the threshold 120591 which is used to produce the groundtruth To maximize the mutual agreement it is necessary toseek the most appropriate threshold 120591 providing the highestaverage performance (EER) over all experts Instead of asingle threshold lesion-specific thresholds 120591

119895are determined

since different lesions may significantly differ by their visualdetectability The optimal ground truth is equivalent tosearching the optimal threshold

120591119895larr997888 argmin

120591119895

1

119873sum

119899

EER (sdot sdot) (3)

A straightforward approach to implement the optimization isto iteratively test all possible values of 120591 from 0 to 1 Equation(3) maximizes the performance for each lesion type over allexperts (119873) The optimal thresholds 120591

119895are guaranteed to

produce the maximal mutual expert agreement according tothe performance measure perf

The revised combining method was shown to producebetter results when compared to the original method andeven to simultaneous truth and performance level estimation(STAPLE) [34] The full description of the method andcomparisons is presented in [8]

4 Algorithm Evaluation

41 Evaluation Methodology The ROC-based analysis per-fectly suits to medical decision making being the acknowl-edged methodology in medical research [35] An evaluationprotocol based on the ROC analysis was proposed in [6] forimage-based (patient-wise) evaluation and benchmarkingand the protocol was further studied in [9] In clinicalmedicine the terms sensitivity and specificity defined in the

range [0 100] or [0 1] are used to compare methods andlaboratory assessments The sensitivity

SN =TP

TP + FN(4)

depends on the diseased population whereas the specificity

SP =TN

TN + FP(5)

on the healthy population defined by true positive (TP) truenegative (TN) false positive (FP) and false negative (FN)The 119909-axis of an ROC curve is 1 minus specificity whereas the119910-axis represents directly the sensitivity [12]

It is useful to form an ROC-based quality measure thequality measures preferred are as followsThe equal error rate(EER) [36] defined as when (SN = SP)

SN = SP = 1 minus EER (6)

or weighted error rate (WER) [37]

WER () =FPR + sdot FNR

1 + =

(1 minus SP) + sdot (1 minus SN)

1 + (7)

where = 119862FNR119862FPR is the cost ratio between the falsenegative rate FNR = 1 minus SN = FN(TP + FN) and falsepositive rate FPR = 1 minus SP = FP(FP + TN) The maindifference between the two measures is that EER assumesequal penalties for both false positives and negatives whereasin the WER the penalties are adjustable

In the image-based evaluation a single likelihood valuefor each lesion should be produced for all test images Usingthe likelihood values an ROC curve can be automaticallycomputed [9] If a method provides multiple values fora single image such as the full-image likelihood map inFigure 6(b) the values must be fused to produce a singlescore

42 Image-Based Evaluation The automatic image-basedevaluation follows the medical practice where the decisions


(1) for each test image do(2) TN larr 0 TP larr 0 FN larr 0 FP larr 0

(3) curr score larr image score(4) for each test image do(5) if curr score ge image score then(6) if ground truth assignment = ldquonormalrdquo then(7) TN = TN + 1

(8) else(9) FN = FN + 1

(10) end if(11) else(12) if ground truth assignment = ldquoabnormalrdquo then(13) TP = TP + 1

(14) else(15) FP = FP + 1

(16) end if(17) end if(18) end for(19) SN =

TPTP + FN

(Sensitivity)

(20) SP =TN

TN + FP(Specificity)

(21) Add new ROC point (119909 119910) = (1minus SP SN)(22) end for(23) Return the final ROC curve (all points)

Algorithm 1 Image-wise evaluation based on image scores

are ldquosubject-wiserdquo An image analysis system is treated asa black-box which takes an image as the input If the imagesare assumed to be either normal or abnormal the systemproduces a score that corresponds to the probability of theimage being abnormal and a high score corresponds withhigh probabilityThe objective of the image-based evaluationprotocol is to generate an ROC curve by manipulating thescore values of the test images The practices were adoptedfrom [38]

Let the image analysis algorithm produced score valuesfor 119899 test images be 120577im = 120577

im1

120577im119899

and let the corre-sponding image-wise ground truths be 120596im = 120596

im1

120596im119899

where each 120596

im119894

is either ldquonormalrdquo or ldquoabnormalrdquo Thenby selecting a threshold for the score values (120577im) the testimages can be classified as either normal or abnormal andthe performance expressed in the form of sensitivity andspecificity can be determined by comparing the outcomewith the corresponding image-wise ground truth (120596im) If thesame procedure is repeated using each test image score as thethreshold the ROC curve can be automatically determinedsince each threshold generates a (sensitivity specificity)pair that is a point on the ROC curve Consequently theprocedure requires that the test images include samples fromboth populations normal and abnormal The image score-based evaluation method is presented in Algorithm 1

43 Pixel-Based Evaluation To validate a design choice inmethod development it can be useful to measure also

the spatial accuracy that is whether the detected lesionsare found in correct locations Therefore a pixel-basedevaluation protocol which is analogous to the image-basedevaluation is proposed In this case the image analysis systemtakes an image as the input and outputs a similar score foreach pixel The objective of the pixel-based evaluation isto generate an ROC curve which describes the pixel-levelsuccess

Let the image analysis algorithm-produced pixel scorevalues for all 119899 pixels in test set be 120577pix = 120577

pix1

120577pix119899

and let the corresponding pixel-wise ground truth be120596pix = 120596

pix1

120596pix119899

where the 120596pix is either ldquonormalrdquo orldquoabnormalrdquo Then by selecting a global pixel-wise thresholdfor the pixel score values (120577pix) the pixels in all images can beclassified to either normal or abnormal Now the sensitivityand specificity can be computed by comparing the outcometo the pixel-wise ground truth (120596pix) If the procedure isrepeated using each unique pixel score as the threshold theROC curve can be automatically determined The pixel-wiseevaluation procedure is given in Algorithm 2 Note that theabnormal test image pixels contribute to both sensitivity andspecificity whereas the normal images only contribute to thespecificity

The evaluation forms a list of global pixel-wise scoresfrom the test image pixel scores which determines the scorethresholdsTheuse of all unique pixel scores in the test imagesis time consuming if the number of images in the test setis large or high-resolution images are used The problemcan be overcome by sampling the test image pixel scores


(1) Form a list of tested pixel scores(2) for each tested pixel score (curr pix score) do(3) TN larr 0 TP larr 0 FN larr 0 FP larr 0

(4) for each test image do(5) for each test image pixel score do(6) if curr pix score ge pixel score then(7) if ground truth pixel assignment = ldquonormalrdquo then(8) TN = TN + 1(9) else(10) FN = FN + 1(11) end if(12) else(13) if ground truth pixel assignment = ldquoabnormalrdquo then(14) TP = TP + 1(15) else(16) FP = FP + 1(17) end if(18) end if(19) end for(20) end for(21) SN =

TPTP + FN

(Sensitivity)

(22) SP =TN



Algorithm 2 Pixel-wise evaluation based on pixel scores

(1) Extract colour information (119903 119892 119887) of the lesion from the train set images (Section 34)(2) Estimate 119901(119903 119892 119887 | lesion) from the extracted color information using a Gaussian

mixture model determined by using the Figueiredo-Jain method [15 16](3) Compute 119901(119903 119892 119887 | lesion) for every pixel in the test image (repeat step for every

test image in the test set)(4) Evaluate the performance (Section 4)

Algorithm 3 Strawman algorithm

To preserve the test setrsquos pixel score distribution the globalthreshold scores can be devised as follows (1) sort all theunique pixel scores in an ascending order to form an orderedsequence 119871 and (2) compose the new reduced sequenceof pixel scores 119871 sampled by selecting every 119895th likelihood in119871

44The Strawman Algorithm We provide a baseline methodin the form of a strawman algorithm The algorithm is basedon the use of photometric cue as described in Algorithm 3[9]

The score fusion in the strawman algorithm is based onthe following reasoning if we consider 119872 medical evidence(features) extracted from the image x

1 x

119872 where each

evidence is a vector then we can denote the score value of theimage as 119901(x

1 x

119872| abnormal) The joint probability is

approximated from the classification results (likelihoods) interms of decision rules using the combined classifier theory(classifier ensembles) [33]The decision rules for deriving thescore were compared in the study [9] where the rules weredevised based on Kittler et al [33] and an intuitive rank-order-based rule ldquosummaxrdquo The rule defines the image score119901(x1 x

119872| abnormal) using the compared decision rules

when the prior values of the population characteristics areequal (119875(normal) = 119875(abnormal)) as follows

SCOREsummax = sum

119898isin119873119884

119901 (x119898

| abnormal) (8)

where 119873119884 are the indices of 119884 top-scoring pixel scores

Experimenting also with the max mean and productrules strong empirical evidence supports the rank-order-based sum of maxima (summax proportion fixed to 1)[9]


0 10

02

04

06

08

1Se

nsiti

vity

05

HaemorrhagesMicroaneurysms

Hard exudatesSoft exudates

1minus specificity

(a)

0 05 10

02

04

06

08

1

Sens

itivi

ty



1minus specificity

(b)

Figure 7The ROC curves for the DiaRetDB1 strawman algorithm using the original ground truth (squares denote the EER points) (a) imagebased (b) pixel based Note the clear difference with microaneurysms as compared to the revised ground truth in Figure 8

Table 3 The minimum maximum and average EER (5 random iterations) for the baseline method and evaluation protocol when usingDiaRetDB1 The results include the original and the revised ground truth [8]

Haemorrhage (HA) Hard exud (HE) Microaneurysm (MA) Soft exud (SE) OverallMin Max Avg Min Max Avg Min Max Avg Min Max Avg

In [9] 0233 0333 0273 0200 0220 0216 0476 0625 0593 0250 0333 0317 0349In [8] (min) 0263 0476 0322 0250 0250 0250 0286 0574 0338 0333 0333 0333 0311In [8] ( max) 0263 0476 0322 0250 0250 0250 0386 0574 0338 0200 0268 0241 0288

The achieved results for DiaRetDB1 are shown in Figure 7(ROC curves) and in Table 3 (EER values) The performanceis reported by using the EER which is justified since EERrepresents a ldquobalanced error pointrdquo on the ROC curve andallows comparison to the previous works

To quantify the effect of the revised method for combin-ing the expert information results from a comparison areshown in Table 3 It should be noted that the experimentis independent of the one presented above The originalconfidence threshold (075) in [9] was not optimal for any ofthe lesion types and was clearly incorrect for haemorrhages(HA 060) and microaneurysms (MA 010) The underlinedvalues in the table are the best achieved performances Theaverage performance for all lesion types significantly variesdepending on the threshold

The minimum and maximum thresholds for the revisedcombining method produce equal results except in the caseof soft exudates for which the maximum in the equallyperforming interval (10) is clearly betterThemain differencefrom the original DiaRetDB1 method occurs with microa-neurysms since the optimal threshold (01) significantly dif-fers from the original (075) For haemorrhages the original

result was too optimistic since the optimal confidence yieldsworse minimum and average EER On average the revisedmethod provided 11ndash17 better performance The relatedROC curves are shown in Figure 8

5 Case Study DiaRetDB1 DiabeticRetinopathy Database and Protocol V21

The authors have published two medical image databaseswith the accompanied ground truth DiaRetDB0 andDiaRetDB1 The work on DiaRetDB0 provided us withessential information on how diabetic retinopathy datashould be collected stored annotated and distributedDiaRetDB1 was a continuation to establish a better databasefor algorithm evaluation DiaRetDB1 contains retinal imagesselected by experienced ophthalmologistsThe lesion types ofinterest were selected by the medical doctors (see Figure 9)microaneurysms (distensions in the capillary) haemorrhages(caused by ruptured or permeable capillaries) hard exudates(leaking lipid formations) soft exudates (microinfarcts) andneovascularisation (new fragile blood vessels) These lesions


1

09

08

07

06

05

04

03

02

01

010908070605040302010

HAHA-orig

(a) Haemorrhage

1

09

08

07

06

05

04

03

02

01

010908070605040302010

HEHE-orig

(b) Hard exudate

1

09

08

07

06

05

04

03

02

01

010908070605040302010

MAMA-orig

(c) Microaneurysm

1

09

08

07

06

05

04

03

02

01

010908070605040302010

SESE-orig

(d) Soft exudate

Figure 8 ROC curves for the DiaRetDB1 baseline method using the original and revised (max) method to generate the training and testingdata [8]

are signs of mild moderate and severe diabetic retinopathyand they provide evidence also for the early diagnosis Theimages were annotated by four independent and experiencedmedical doctors inspecting similar images in their regularwork

The images and ground truth are publicly available on theInternet [13] The images are in PNG format and the groundtruth annotations follow the XML format Moreover weprovide a DiaRetDB1 kit containing full Matlab functionality(M-files) for reading and writing the images and groundtruth fusing expert annotations and generating image-based evaluation scores The whole pipeline from images toevaluation results (including the strawman algorithm) can

be tested using the provided functionality The annotationsoftware (Matlab files and executables) is also available uponrequest

6 Conclusions

We have discussed the problem of establishing benchmarkdatabases for the development of medical image analysisWe have pointed out the importance of commonly acceptedand used databases We have proposed the framework forconstructing benchmark databases and protocols for diabeticretinopathy inmedical image analysisWe have built reusabletools needed to solve the important subtasks including


(a) (b)

(c) (d)

Figure 9 Abnormal retinal findings caused by the diabetes (best viewed in colour) (a) haemorrhages (b) microaneurysms (marked with anarrow) (c) hard exudates (d) soft exudate (marked with an arrow) [6]

the annotation tool for collecting the expert knowledgemade our implementations publicly available and establishedthe diabetic retinopathy database DiaRetDB1 to promoteand help other researchers collect and publish their dataWe believe that public databases and common evalua-tion procedures support development of better methodsand promote the best methods to be adopted in clinicalpractice

Acknowledgments

The authors thank the Finnish Funding Agency for Tech-nology and Innovation (TEKES Project nos 4043005and 4003907) and the partners of the ImageRet project(httpwww2itlutfiprojectimageret) for their support

References

[1] T Kauppi Eye fundus image analysis for automatic detection ofdiabetic retinopathy [PhD thesis] Lappeenranta University ofTechnology 2010

[2] World Health Organization ldquoDefinition diagnosis and classi-fication of diabetes mellitus and its complications part 1 diag-nosis and classification of diabetes mellitusrdquo Tech Rep WorldHealth Organization Noncommunicable Geneva Switzerland1999

[3] World Health Organization and The International DiabetesFederation Diabetes Action Now An Initiative of the WorldHealth Organization and the International Diabetes Federation2004

[4] G von Wendt Screening for diabetic retinopathy aspects ofphotographic methods [PhD thesis] Karolinska Institutet 2005

[5] T Kauppi V Kalesnykiene J-K Kamarainen et al ldquoThediaretdb1 diabetic retinopathy database and evaluation proto-colrdquo in Proceedings of the British Machine Vision Conference(BMVC rsquo07) pp 252ndash261 University of Warwick 2007

[6] T Kauppi V Kalesnykiene J K Kamarainen et al ldquoDiaretdb1diabetic retinopathy database and evaluation protocolrdquo inProceedings of the Medical Image Understanding and Analysis(MIUA rsquo07) pp 61ndash65 2007

[7] T Kauppi J-K Kamarainen L Lensu et al ldquoA framework forconstructing benchmark databases and protocols for retinopa-thy in medical image analysisrdquo in Intelligent Science and Intel-ligent Data Engineering J Yang F Fang and C Sun Edsvol 7751 of Lecture Notes in Computer Science pp 832ndash843Springer Berlin Germany 2012

[8] J-K Kamarainen L L Lensu and T Kauppi ldquoCombiningmul-tiple image segmentations bymaximizing expert agreementrdquo inMachine Learning in Medical Imaging F Wang D Shen P Yanand K Suzuki Eds Lecture Notes in Computer Science pp193ndash200 Springer Berlin Germany 2012

[9] T Kauppi J-K Kamarainen L Lensu et al ldquoFusion of multipleexpert annotations and overall score selection for medical


image diagnosisrdquo in Proceedings of the 16th ScandinavianConference on Image Analysis (SCIA rsquo09) pp 760ndash769 Springer2009

[10] N A Thacker A F Clark J L Barron et al ldquoPerformancecharacterization in computer vision a guide to best practicesrdquoComputer Vision and Image Understanding vol 109 no 3 pp305ndash334 2008

[11] K H Zou ldquoReceiver operating characteristic (roc) litera-ture researchrdquo 2002 httpwwwsplharvardeduarchivespl-pre2007pagespplzourochtml

[12] T Fawcett ldquoAn introduction to roc analysisrdquo Pattern Recogni-tion Letters vol 27 no 8 pp 861ndash874 2006

[13] ldquoDiabetic retinopathy database and evaluation protocol(DIARETDB1)rdquo Electronic material (Online) httpwww2itlutfiprojectimageretdiaretdb1 v2 1

[14] ldquoImage annotation tool (IMGANNOTOOL)rdquo Electronic mate-rial (Online) httpwww2itlutfiprojectimageret

[15] M A T Figueiredo and A K Jain ldquoUnsupervised learning offinite mixture modelsrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 24 no 3 pp 381ndash396 2002

[16] P Paalanen J-K Kamarainen J Ilonen and H KalviainenldquoFeature representation and discrimination based on Gaus-sian mixture model probability densitiesmdashpractices and algo-rithmsrdquo Pattern Recognition vol 39 no 7 pp 1346ndash1358 2006

[17] ldquoStructured analysis of the retina (STARE)rdquo Electronic material(Online) httpwwwclemsoneduces

[18] A Hoover V Kouznetsova andM Goldbaum ldquoLocating bloodvessels in retinal images by piece-wise threhsold probing of amatched filter responserdquo IEEETransactions onMedical Imagingvol 19 no 3 pp 203ndash210 2000

[19] A Hoover and M Goldbaum ldquoLocating the optic nerve in aretinal image using the fuzzy convergence of the blood vesselsrdquoIEEE Transactions on Medical Imaging vol 22 no 8 pp 951ndash958 2003

[20] ldquoDigital retinal images for vessel extraction (DRIVE)rdquo Elec-tronic material (Online) httpwwwisiuunlResearchData-basesDRIVE

[21] J J Staal M D Abramoff M Niemeijer M A Viergever andB van Ginneken ldquoRidge-based vessel segmentation in colorimages of the retinardquo IEEETransactions onMedical Imaging vol23 no 4 pp 501ndash509 2004

[22] M Niemeijer J Staal B van Ginneken M Loog and M DAbramoff ldquoComparative study of retinal vessel segmentationa new publicly available databaserdquo in Medical Imaging ImageProcessing pp 648ndash656 2004

[23] ldquoMethods to evaluate segmentation and indexing techniquesin the field of retinal ophthalmology (MESSIDOR)rdquo Electronicmaterial (Online) httpmessidorcrihanfr

[24] ldquoCollection of multispectral images of the fundus (CMIF)rdquoElectronic material (Online) httpwwwcsbhamacukresearchprojectsfundus-multispectral

[25] I B Styles A Calcagni E Claridge F Orihuela-Espina andJ M Gibson ldquoQuantitative analysis of multi-spectral fundusimagesrdquo Medical Image Analysis vol 10 no 4 pp 578ndash5972006

[26] ldquoRetinopathy online challenge (ROC)rdquo Electronic material(Online) httprochealthcareuiowaedu

[27] M Niemeijer B van Ginneken M J Cree et al ldquoRetinopathyonline challenge automatic of microaneurysms in digital pho-tographsrdquo IEEE Transactions on Medical Imaging vol 29 no 1pp 185ndash195 2010

[28] D Scharstein and R Szeliski ldquoA taxonomy and evaluation ofdense two-frame stereo correspondence algorithmsrdquo Interna-tional Journal of ComputerVision vol 47 no 1ndash3 pp 7ndash42 2002

[29] ldquoReview retinal vessel image set for estimation of widths(REVIEW)rdquo Electronic material (Online) httpreviewdblincolnacuk

[30] B Al-Diri A Hunter D Steel M Habib T Hudaib and SBerry ldquoReviewmdasha reference data set for retinal vessel profilesrdquoin Proceedings of the 30th Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society pp 2262ndash2265 Vancouver BC Canada August 2008

[31] B C Russell A Torralba K P Murphy and W T FreemanldquoLabelme a database andweb-based tool for image annotationrdquoInternational Journal of Computer Vision vol 77 no 1ndash3 pp157ndash173 2008

[32] ldquoApplication protocol for electronic data exchange in healthcareenvironments versionrdquo 251 ANSI Standard httpwwwhl7org

[33] J Kittler M Hatef R P W Duin and J Matas ldquoOn combiningclassfiersrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 20 no 3 pp 226ndash239 1998

[34] S KWarfield K H Zou andWMWells ldquoSimultaneous truthand performance level estimation (STAPLE) an algorithm forthe validation of image segmentationrdquo IEEE Transactions onMedical Imaging vol 23 no 7 pp 903ndash921 2004

[35] T A Lasko J G Bhagwat K H Zou and L Ohno-MachadoldquoThe use of receiver operating characteristic curves in biomed-ical informaticsrdquo Journal of Biomedical Informatics vol 38 no5 pp 404ndash415 2005

[36] P J Phillips H Moon S A Rizvi and P J Rauss ldquoThe FERETevaluation methodology for face-recognition algorithmsrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol22 no 10 pp 1090ndash11104 2000

[37] E Bailliere S Bengio F Bimbot et al ldquoThe BANCA databaseand evaluation protocolrdquo in Proceedings of the InternationalConference on Audio- and Video-based Biometric PersonAuthentication (AVBPA rsquo03) pp 625ndash638 2003

[38] M Everingham and A Zisserman ldquoThe pascal visual objectclasses challenge VOC2006 resultsrdquo in Proceedings of the ECCVWorkshop of VOC 2006


Research ArticleComparative Evaluation of Osseointegrated Dental ImplantsBased on Platform-Switching Concept Influence of DiameterLength Thread Shape and In-Bone Positioning Depth onStress-Based Performance

Giuseppe Vairo1 and Gianpaolo Sannino2

1 Department of Civil Engineering and Computer Science University of Rome ldquoTor Vergatardquo Via del Politecnico 1 00133 Rome Italy2 Department of Oral Health University of Rome ldquoTor Vergatardquo Viale Oxford 00133 Rome Italy

Correspondence should be addressed to Gianpaolo Sannino gianpaolosanninouniroma2it

Received 31 March 2013 Accepted 19 May 2013


Copyright copy 2013 G Vairo and G Sannino This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This study aimed to investigate the influence of implant design (in terms of diameter length and thread shape) in-bonepositioning depth and bone posthealing crestal morphology on load transfer mechanisms of osseointegrated dental implantsbased on platform-switching concept In order to perform an effective multiparametric comparative analysis 11 implants differentin dimensions and in thread features were analyzed by a linearly elastic 3-dimensional finite element approach under a staticload Implant models were integrated with the detailed model of a maxillary premolar bone segment Different implant in-bonepositioning levels were modeled considering also different posthealing crestal bone morphologies Bone overloading risk wasquantified by introducing proper local stress measures highlighting that implant diameter is a more effective design parameterthan the implant length as well as that thread shape and thread details can significantly affect stresses at peri-implant boneespecially for short implants Numerical simulations revealed that the optimal in-bone positioning depth results from the balanceof 2 counteracting effects cratering phenomena and bone apposition induced by platform-switching configuration Proposedresults contribute to identify the mutual influence of a number of factors affecting the bone-implant loading transfer mechanismsfurnishing useful insights and indications for choosing andor designing threaded osseointegrated implants

1 Introduction

In the last three decades and in the field of the prostheticdentistry features of dental implants and surgical procedureshave been developed and enhanced aiming to ensure pre-dictable results and to improve function and aesthetics incompletely or partially edentulous patients [1]

A dental implant is a biocompatible device surgicallyplaced into mandibular or maxillary bone for supporting aprosthetic tooth crown and thus allowing the replace of theteeth lost due to caries periodontal disease injuries or otherreasons Worldwide statistics show that a high success rate ofdental implants (over 95) occurs if implants are properlydesigned andmanufactured and if they are inserted in a bonesegment characterized by good quality and quantity (eg

[2ndash4]) Nevertheless success of the prosthetic treatment iswidely affected by a number of factors that can change thebiomechanichal coupling between implant and bone such asimplant location mechanical and morphological propertiesof bone mechanical and geometrical features of implant andtype and magnitude of the load transferred by the implant tothe bone as well as by host factors such as smoking andbacterial environment [5ndash7]

A crucial aspect that determines the effectiveness of adental implantation is identified by the proper developmentof the osseointegration process at the bone-implant interfaceThis process is similar to the healing process in bone fracture[7ndash9] and arises from remodeling mechanisms that involve anumber of cellular and extracellular coupled biomechanicalfeatures After the implantation the gap between the implant


and the host bone is rapidly filled by blood clots that areafterwards substituted by a trabecular network The lattergenerally evolves towards the formation of lamellar bone thatin turn undergoes amaturation process thatmodifies densityand mechanical properties of the tissue [8ndash11] At the end ofthe healing process the mature bone is directly in contactwith the implant surface leading to an interfacial bindingthat allows to enhance loading transfer mechanisms fromprosthetic crown to the bone [12 13]

Nevertheless a proper osseointegration process may becounteracted by the activation of histological resorptionmechanisms [9 14ndash16] that can induce bone weakening orloss at the peri-implant region Bone resorptionmainly affectsthe bone region around the implant neck producing a crater-ing morphology and it may be activated by surgical traumaor bacterial infection as well as by overloading states [4 5 14ndash22] Under functional or pathological (eg induced by brux-ism) loads overloading at the peri-implant bone may occurby a shortcoming in load transfer mechanisms mainly dueto bad occlusion improper implant use wrong prosthesisandor implant design and improper implant placement Inthese cases high stress concentrations are induced at thebone-implant interfaces leading to possible physiologicallyinadmissible strains that activate bone resorption [23 24]Clinical trials and follow-up analyses [2ndash4 17 18] have shownthat the implant failure may generally occur if the boneresorption process significantly evolves from a crestal initi-ation Depending on implant features positioning and loadsthis process may become instable leading to a progressiveincrease in stress intensity at the peri-implant interface [19]that in turn further contributes to the progressive overload-induced bone loss

Recent clinical evidence [25ndash29] suggests that crateringphenomenamay be significantly limitedwhen the connectiondiameter of the abutment is narrower than the implantcollar and when an implant subcrestal positioning is appliedIn this case probably due to the different position of theimplantabutment microgap and to the different stress pat-tern induced at the peri-implant regions with respect toa crestal positioning remodeling process generally evolvesallowing bone apposition on the horizontal implant surfaceand thus transferring the biological width from the verticalto the horizontal level (platform switching) [30ndash34]

In order to improve durability and clinical effectivenessof rehabilitations based on such an approach mechanicaland biological factors mainly affecting loading transfer fromimplant to bone have to be properly identified and quantifiedThereby optimized implant designing strategies and surgicalprotocols could be traced allowing us to minimize overload-ing risks and marginal bone loss as well as contributing toensure predictable clinical results

In the recent specialized literature many authors haveproposed results based on well-established in vivo in vitroand in silico approaches aiming to investigate main biome-chanical factors influencing the preservation of the peri-implant marginal bone as well as the stressstrain patternsinduced by osseointegrated implants [4 26ndash29 35 36] In thiscontext finite-element method has been widely used in thelast years to analyze the influence of implant and prosthesis

design [37ndash40] of magnitude and direction of loads [41ndash44]and of bone mechanical properties [45ndash47] as well as formodeling different clinical scenarios [48ndash54] Neverthelessmany effects related to the implant design and to the in-bonepositioning depth as well as their mutual influence on thestress-based implant performance have not yet been com-pletely understood and clarified especially for implants basedon platform-switching concept

In this study 11 threaded dental implants based onplatform-switching concept and different for dimensions andthread type were compared via a multiparametric three-dimensional (3D) finite-element approach Accurate andconvergent bone-implant models defined by consideringa maxillary premolar bone segment have been solved byemploying a linearly elastic displacement-based formulationand considering a static functional loading condition Stressdistributions were numerically evaluated at the peri-implantregions on both compact and cancellous bone furnishingquantitative risk measures of bone physiological failure Pro-posed numerical results highlighted the influence of implantshape in terms of implant length and diameter as well asin terms of thread features on possible overloading risksand onmechanisms of load transferThe influence of implantpositioning in bone was also investigated by consideringnumerical models based on both crestal and subcrestalimplant placements Finally in the case of a crestal position-ing and in order to contribute to the understanding of thebiomechanical relationship between mechanical stimuli andmarginal bone loss several numerical simulations were car-ried out for analyzing the effects of different cratering levelson stress patterns at the peri-implant bone

2 Material and Methods

Ten threaded dental implants different in diameter (119863)length (119871) thread shape and geometrical concept wereanalyzed and compared with each other and with an Ankylosimplant (Dentsply Friadent Mannheim Germany) charac-terized by 119863 = 35mm and 119871 = 110mm Figure 1 summa-rizes the main geometrical features of the implants analyzedin this study introducing also the corresponding notationSymbols T030 and T1030 refer to the implant thread T030denotes a saw-tooth thread with the side angled at 120∘ withrespect to the implant axis and with a free thickness of033mmat the internal diameter T1030 denotes a trapezoid-shaped thread with sides angled at 120∘ and 100∘ with respectto the implant axis and with a free thickness of 025mm atthe internal diameter Both threads are characterized by twostarts with a conical helix having the same anomaly and withan effective pitch of 12mm Moreover symbol ST indicatesthat both starts exhibit the same thread truncation resultingin a maximum thread depth of 038mm whereas symbol DTdenotes implants with a different thread truncation for eachstart resulting in maximum thread depths of 019mm and038mm respectively Implants except the Ankylos devicehave also a helical milling with the effective pitch equal to theimplant threaded length Depending on width and depth ofcut small and largemillings are identified by symbols SM and


(3)

(A)

Lead-inbevel

empty35 11

(1) D36-L55-T030-ST-SM

(2) D36-L55-T1030-ST-SM

(3) D43-L55-T1030-ST-SM

(4) D43-L9-T1030-DT-SM

(5) D43-L9-T1030-DT-LM

(6) D43-L9-T1030-ST-LM

(7) D36-L9-T030-DT-SM

(8) D36-L9-T1030-DT-SM

(9) D36-L9-T1030-DT-LM

(10) D36-L9-T1030-ST-LM

(A) D35-L11 Ankylos

empty36 empty3655

empty36 55

55empty43

empty43 9

empty43 9

empty43 9

9

empty36 9

empty36 9

empty36 9

Figure 1Threaded dental implants analyzed in this studyNotation and examples of implant-abutment coupled systems that allow a platform-switching configuration

LM respectively Implants denoted by 1 to 10 in Figure 1 werecharacterized by an internal lead-in bevel extending from theouter most diameter of the implant platform into a flattenedarea or ledge Moreover implants analyzed in this study havevertical cutting grooves for self-tapping insertion and havebeen coupled with abutments characterized by connectiondiameters narrower than the implant collars thereby allowinga platform-switching configuration (see Figure 1)

Models of implants and abutments were built up byusing a parametric CAD software (SolidWorks 9 DessaultSystemes ConcordMass) and in order to perform consistentcomparisons they were integrated within the model of a pre-molar bone segment obtained by the three-dimensional (3D)model of an edentulous maxilla (Figure 2) The latter wasreconstructed starting frommultislice computed tomography(MSCT) scans and by using a modeling commercial software(Mimics Materialise HQ Leuven Belgium) Moving fromthe different hues of gray displayed in the planar CT scanscorresponding to different radiolucency levels of substanceswith different density values the software allowed us todistinguish between mineralized and soft tissues by filteringpixels with a suitable Hounsfield units (HU) [55] In detaildisregarding gingival soft tissues the solid model of the

maxillary jaw was obtained by a segmentation procedure ofvoxels identified by HU gt 150 (Figure 2(a)) and based ona home-made smoothed linear interpolation algorithm Cor-tical and trabecular regions were distinguished considering150 lt HU le 750 for the cancellous bone and HU gt 750for the cortical bone With the aim of improving the modelquality ad hoc local geometry adjustments were performedensuring that the cortical bone regions were characterized bya mean thickness of about 2mm Starting from the completemaxillary jaw model the finite-element computations werecarried out on a submodel of the second premolar regiondefined by considering two coronal sections at the distance of40mmalong themesiodistal direction (119910 in Figure 2(b)) andpositioning implants at the mid-span of the bone segment

A subcrestal positioning was firstly investigated by con-sidering implant models positioned with the crestal platformat 1mm depth with respect to the outer bone surface Asa notation rule in the foregoing this configuration will bedenoted as P1 Moreover in order to analyze the positioninginfluence for implants similar in diameter and length numer-ical models relevant to the implants D36-L9-T1030-DT-SMand Ankylos (indicated as 8 and A resp in Figure 1) wereanalyzed by considering a crestal positioning (ie with the


(a)

xy

z

(b)

(c)

x

z

7 mm

250 N

100 N

(d)

Figure 2 (a)Three-dimensional solidmodel of the edentulousmaxilla considered in this study and obtained by a segmentation process basedon multislice computed tomography (MSCT) (b) Submodel of the second premolar maxillary region defined by considering two coronalsections at the distance of 40mm along the mesiodistal direction (119910 axis) and positioning implants at the mid-span of the bone segment (c)Examples of mesh details (d) Loading condition

1 mm

P0

P1

05 mm

Ankylos D36-L55-T10-30-ST-SM

Cortical bone Cancellous bone

02 mm

P05

Figure 3 Modeling of crestal bone geometries and different configurations of implant in-bone positioning analyzed in this study In the caseof the configuration P0 a crestal bone loss of about 10 in thickness is depicted

implant platform at the level of the outer bone surface anddenoted as P0) an intermediate subcrestal positioning at05mm depth (denoted as P05) With the aim of reproducingas realistically as possible the physiological structure of thecompact bone arising around a functioning implant after ahealing period different crestal geometries were modeled

In particular in agreement with well-established clinical evi-dence [25ndash27] and modeling approaches [40 47 53] and assketched in Figure 3 a crestal bone apposition at the implantplatform of about 025mm in mean thickness was mod-eled for subcrestal placements (ie for models denoted asP1 and P05) whereas a marginal bone loss of 10 in cortical


thickness was modeled for the crestal positioning (P0) Forimplants 8 and A crestally placed (P0) the influence ofdifferent levels of marginal bone loss (0ndash50 in corticalthickness) was also analyzed

All the involvedmaterials weremodeled as linearly elasticwith an isotropic constitutive symmetry and all materialvolumesweremodeled as homogeneousThereby bone livingtissue was described by considering a dry-material modelwherein viscous and fluid-solid interaction effects wereneglected Implants and abutments were assumed to be con-stituted by a titanium alloy Ti6Al4V whose Youngrsquos modulusand Poissonrsquos ratio were 1140GPa and 034 respectively [56]Bone elastic properties were assumed to approximate type IIbone quality [57] and in agreement with data available in theliterature [40 47 58] they were set as follows

(i) Poissonrsquos ratio of the bone tissue (both cortical andtrabecular) equal to 030

(ii) Youngrsquos modulus of the cortical bone equal to137 GPa

(iii) Youngrsquos modulus of the cancellous bone equal to05GPa corresponding to a mean bone density ofabout 05 gsdotcmminus3 [59]

Finite-element simulations were carried out consideringa static load applied at the top of the abutments withoutany eccentricity with respect to the implant axis and angledwith respect to the occlusal plane of about 68∘ The lateralforce component along the buccolingual direction (119909 inFigure 2) was assumed to be equal to 100N and the verticalintrusive one (along 119911 in Figure 2) was 250N In order toallow consistent comparisons abutments were adjusted insuch a way that the application points of the load were 7mmfrom the bone insertion surface in all numerical models (seeFigure 2(d))

Complete osseous integration between implant and bonetissue was assumed enforcing the continuity of the dis-placement field at the bone-implant interface Furthermoredisplacement continuity is imposed between each componentof a given prosthetic device As regards boundary conditionsfor numerical models describing the coupled bone-implantsystem all displacement degrees of freedom were preventedfor any boundary node lying on the coronal sections delim-iting the bone submodel In agreement with the theory ofelasticity [60] since the distance between submodel bound-ary sections and the implant location was much greater thanthe implantrsquos characteristic dimensions these boundary con-ditions did not significantly affect stress-based comparativeresults at the peri-implant regions

Discrete finite-element meshes were generated by em-ploying elements based on a pure displacement formulationand were analyzed with a commercial solver code (Ansys130 Ansys Inc Canonsburg PA) Computational modelswere obtained by considering 10-node tetrahedral elements[61] with quadratic shape functions and three degrees of free-dom per node In order to ensure suitable accuracy ofthe numerical finite-element solutions at the peri-implantregions mesh-size for the bone-implant models was setup as a result of a convergence analysis based on the

coupled estimate within the multiregion computationaldomain of the displacement error norm and of the energyerror norm [61] In detail following the numerical procedureproposed by Zienkiewicz and Zhu [62] implemented in theAnsys environment and recently applied for prosthetic den-tal applications [47] the proposed numerical results wereobtained by solving discrete models based on ℎ

0119863 = 01 and

ℎ119894119863 = 001 ℎ

0and ℎ

119894being mean mesh-size away from the

bone-implant interface and close to the peri-implant regionsrespectivelyThis choice was proved to ensure a good numer-ical accuracy resulting for all models analyzed in this studyin a value of the energy error norm lower than 5 and in avalue of the displacement error norm lower than 05

Jaw submodel treated by a single-implant prosthesiswas numerically compared by analyzing stress distributionsarising at the peri-implant regionsThe VonMises equivalentstress (120590VM) often used in well-established numerical dentalstudies (eg [35ndash54 63 64]) was used as a global stressindicator for characterizing load transfer mechanisms of agiven implant Nevertheless the Von Mises stress measurealways positive in sign does not allow a distinction betweentensile and compressive local stresses Since experimental evi-dence [24 58 65] confirms that bone physiological failure andoverload-induced resorption process are differently activatedin traction and compression more effective and direct riskindications were obtained by analyzing stress measures basedon principal stresses (120590

119894 with 119894 = 1 2 3) [44 47 53 63 64]

In detail in a given material point 119875 of the computationaldomain that models the peri-implant bone the followingstress measures were computed

120590119862 (119875) = min 120590

1 (119875) 1205902 (119875) 1205903 (119875) 0

120590119879 (119875) = max 120590

1 (119875) 1205902 (119875) 1205903 (119875) 0

(1)

120590119862and 120590

119879having the meaning of maximum compressive

and maximum tensile stress in 119875 respectively Therefore inorder to combine effects induced on bone by compressive andtensile local states which are simultaneously present the bonesafety in 119875 against overloading-related failureresorptionprocess activation was postulated to occur if the followinginequality was satisfied

119877 =

10038161003816100381610038161205901198621003816100381610038161003816

1205901198620

+120590119879

1205901198790

le 1 (2)

where symbol |119886| denotes the absolute value of the scalarquantity 119886 and where 120590

1198790 1205901198620

are the admissible stress levelsin pure traction and compression respectively Accordinglythe dimensionless positive quantity 119877 can be thought of asa quantitative risk indicator such that the condition 119877 gt 1identifies a local critical state of bone with respect tooverloading effects By assuming that overloads occur whenultimate bone strength is reached in this study it was assumedthat 120590

1198790= 180MPa and 120590

1198620= 115MPa for cortical bone and

1205901198790= 1205901198620= 5MPa for trabecular bone [58 65]

In order to perform significant numerical comparisonsthe previously introduced stress measures and the risk index119877were computed for each implant within a control volumeΩdefined by considering a bone layer surrounding the implant


D 120575

Ωa

t

Ωt

i

Ωt

c

Ωt

Ωc

Figure 4 Control regions employed for computing the local stressmeasures and the overloading risk index 119877 at the bone-implantinterface

with a mean thickness 120575 With reference to the sketch inFigure 4 the region Ω has been conveniently considered assubdivided in its complementary parts Ω

119888and Ω

119905(such that

Ω = Ω119888cup Ω119905) representing cortical and trabecular control

regions respectively In turnΩ119905has been further subdivided

by 2 planes orthogonal to the implant axis into 3 comple-mentary control subregions having equal length along theimplant axis These three trabecular regions will be denotedasΩ119888119905(crestal region)Ω119894

119905(intermediate region) andΩ119886

119905(apex

region) Results discussed in the foregoing were obtained byassuming 120575119863 = 025 and they refer to average and peakvalues of 120590VM 120590119862 120590119879 and 119877 over Ω

119888 Ω119888119905 Ω119894119905 Ω119886119905 These

results were computed via a postprocessing phase carried outby means of a MatLab (The MathWorks Inc Natick MA)home-made procedure taking as input by the solver codesome primary geometrical and topological data (nodes andelements lying in Ω) as well as stress solutions at the finite-element Gauss points withinΩ

3 Results

31 Subcrestal Positioning P1 For implants introduced inFigure 1 and considering the subcrestal positioning P1 (seeFigure 3) Figures 5 and 6 showVonMises stress distributionsrelevant to the loading coronal plane 119910 = 0 computed via thepresent 3D finite-element approach at the peri-implant cor-tical and trabecular bone regions Moreover Figure 7 showsaverage and peak values over the control volumes Ω

119888and

Ω119905(see Figure 4) of 120590VM and of the principal stress measures

defined by (1) Finally Figure 8 highlights mean and peakvalues of the overloading risk index 119877 computed at bothtrabecular and cortical peri-implant bone regions

By assuming complete osseous integration the higheststress concentrationswere computed at the cortical bone nearthe implant neck There stress patterns were significantlyaffected by implant diameter (119863) and bone-implant interfacelength (119871) In detail by increasing 119863 andor by increasing119871 mean and peak stress values decreased in Ω

119888and Ω

119905 and

stress distributions tended to be more homogenous Com-pressive mean and peak values at the cortical peri-implantregion always prevailed with respect to the correspondingtensile states This occurrence was not generally respected atthe trabecular interface wherein tensile stresses were higherat the crestal region (Ω119888

119905) and smaller at the implant apex

(Ω119886119905) than the compressive stresses Nevertheless the highest

trabecular stress peaks were associated with the compressivestates arising inΩ119886

119905(see Figure 7(b))

Referring to the notation introduced in Figure 1 implantsdenoted by D43-L9 (ie labeled as 4 5 and 6) exhibited thebest stress performances resulting in the smallest values ofthe stress measures as well as in the smallest values of theoverloading risk index 119877 On the contrary implants denotedby D36-L55 (labeled as 1 and 2) numerically experiencedthe worst loading transmission mechanisms Moreover thestress-based performance of the commercial implantAnkylosD35-L11 was estimated as fully comparable with that ofthe threaded implants D36-L9 (labeled as 7 8 9 and 10)although the greater Ankylosrsquo length induced more favorablestress distributions at the trabecular bone especially referringto the compressive states arising at the implant apex (seeFigure 7(b))

Proposed results clearly show that the parameter thatmainly affects the implant stress-based performances is thediameter119863 irrespective of the length 119871 In fact by comparingstress results relevant to implant 2with those of implant 3 thatis by increasing119863 of about 20 (passing from119863 = 36mmto119863 = 43mm) when 119871 = 55mm compressive (resp tensile)peak values reduced of about 27 in both Ω

119888and Ω

119905(resp

20 in Ω119888and 30 in Ω

119905) On the contrary by comparing

stress results relevant to implant 2 with those of implant 9that is by increasing 119871 of about 60 (passing from 119871 =55mm to 119871 = 9mm) when 119863 = 36mm compressive peaksreduced only by about 16 (resp 26) at the cortical (resptrabecular) bone whereas tensile peaks were almost compa-rable These considerations are qualitatively applicable alsowhen the overloading risk index119877 is addressed (see Figure 8)leading to similar conclusions

Within the limitations of this study overloading riskswere greater in cancellous region than those in cortical andproposed numerical results highlighted that under the sim-ulated loading condition the safety inequality 119877 lt 1 waseverywhere satisfied in bone for all the analyzed implants

Moreover the proposed numerical results suggest thatthread shape and thread details can induce significant effectson local stress patterns in bone around implants In particu-lar the use of the same thread truncation (ST) for both threadstarts induced a more uniform local stress distributions thanthe case characterized by a different thread truncation (DT)since all the threads had practically the same engaged depthAs a result mean and peak values of120590

119879reduced at the cortical

bone passing from DT to ST as it is shown in Figure 7(b) bycomparing results relevant to implants 5 and 6 (peaks reducedof about 20 andmean values of about 13) and to implants 9and 10 (peaks reduced of about 23 andmean values of about18)

The influence of the thread shape may be clearlyhighlighted by analyzing the stress-based performances of


(1) D36-L55-T030-ST-SM (2) D36-L55-T1030-ST-SM (3) D43-L55-T1030-ST-SM

(4) D43-L9-T1030-DT-SM (5) D43-L9-T1030-DT-LM (6) D43-L9-T1030-ST-LM

(7) D36-L9-T030-DT-SM (8) D36-L9-T1030-DT-SM (9) D36-L9-T1030-DT-LM

(10) D36-L9-T1030-ST-LM (A) D35-L11 Ankylos

(MPa)

z

x

0 10 15 20 25 30 50 60 70 Above

Figure 5 Von Mises stress contours (blue 0 red 70MPa) at the coronal section 119910 = 0 for implants defined in Figure 1 and in the case of thesubcrestal positioning P1 (see Figure 3) Cortical peri-implant bone interface





(MPa)

x

z

0 05 1 15 2 25 3 35 45 Above

Figure 6 VonMises stress contours (blue 0 red 45MPa) at the coronal section 119910 = 0 for implants defined in Figure 1 and in the case of thesubcrestal positioning P1 (see Figure 3) Trabecular peri-implant bone interface

implants 1 and 2 and of implants 7 and 8 In particulartrapezoid-shaped thread (labelled as T1030 in Figure 1)inducedmore favorable compressive and tensile states at bothcortical and trabecular regions than the saw-tooth thread(T030) leading to the reduction of the cortical peak valuesof about 24 for 120590

119862when the implants D36-L55 were

addressed and of about 35 for 120590119879in the case of the implants

D36-L9 Such an effect is also observable by analyzing therisk index 119877 (see Figure 8) In particular the thread shapeT1030 induced a significant reduction in 119877 (at both corticaland trabecular regions) especially for short implants

Finally indications on the influence of the helical-millingwidth and depth may be drawn by considering numericalresults relevant to implants 4 and 5 and to implants 8 and 9


(MPa

)

1 2 3 4 5 6 7 8 9 10 AImplant type

120590VM

0

10

20

30

40

50

60

70

0

1

2

3

4

5

(MPa

)

1 2 3 4 5 6 7 8 9 10 AImplant type

120590VM

Ωc

t

Ωi

t

Ωa

t

(a)

minus50

minus40

minus30

minus20

minus10

0

10

20

(MPa

)

1 2 3 4 5 6 7 8 9 10 AImplant type

1 2 3 4 5 6 7 8 9 10 AImplant type

120590T

120590C

120590T

120590C

minus4

minus3

minus2

minus1

0

1

2

3(M

Pa)

Ωc

t

Ωi

t

Ωa

t

(b)

Figure 7 Von Mises ((a) 120590VM) and principal ((b) 120590119879tensile and 120590

119862compressive) stress measures at cortical (left side) and trabecular (right

side) bone-implant interface for implants defined in Figure 1 and in the case of the subcrestal positioning P1 (see Figure 3) Average (bars)and peak (lines) values

Although almost comparable global stress patterns and localstress measures were experienced passing from SM (smallmilling) to LM (large milling) the analysis of the index 119877reveals that large milling shape can induce a reduction of therisk of overloading states at the cancellous bone especially forsmall values of 119871

32 Influence of In-Bone Positioning Depth In order to ana-lyze the influence of the implant in-bone positioning depthon loading transmission mechanisms reference has beenmade to the comparative numerical analyses carried out

for the implant D36-L9-T1030-DT-SM and for the implantAnkylos D35-L11 (ie for implants 8 and A in Figure 1)Addressing the positioning configurations introduced inFigure 3 Figure 9 shows Von Mises stress distributions rel-evant to the loading coronal plane 119910 = 0 computed atcortical and trabecular peri-implant bone regions andFigure 10 shows mean and peak values of 120590VM 120590119879 and 120590119862computed over the control volumesΩ

119888andΩ

119905(see Figure 4)

Finally Figure 11 summarizes mean and peak values of theoverloading risk index 119877 computed at both trabecular andcortical bone interfaces It is worth pointing out that the


00

01

02

03

04

05

06

07

R

1 2 3 4 5 6 7 8 9 10 AImplant type

Cortical boneTrabecular bone

Figure 8 Overloading risk index 119877 computed at cortical and trabecular peri-implant bone for implants defined in Figure 1 and in the caseof the subcrestal positioning P1 (see Figure 3) Average (bars) and peak (lines) values

(8) D36-L9-T1030-DT-SM

(A) D35-L11 Ankylos(MPa)

z

x

P0 P05 P1

0 10 15 20 25 30 50 60 70 Above

(a)

(8) D36-L9-T1030-DT-SM

(A) D35-L11 Ankylos

(MPa)x

z

P0 P05 P1

0 05 1 15 2 25 3 35 45 Above

(b)

Figure 9 Von Mises stress contours (blue 0 red 70MPa) at the coronal section 119910 = 0 for implants 8 and A (see Figure 1) and for differentimplant in-bone positioning levels (see Figure 3) Cortical (a) and trabecular (b) peri-implant bone interface


(MPa

)

P0 P05 P1

Implant 8Implant A

0

10

20

30

40

50

60

70120590VM

00

05

10

15

20

25

30

35

(MPa

)

P0 P05 P1 P0 P05 P1

120590VM Implant 8 Implant A

Ωc

t

Ωi

t

Ωa

t

(a)

Implant 8 Implant 8Implant A Implant A

P0 P05 P1 P0 P05 P1 P0 P05 P1 P0 P05 P1

(MPa

)

120590T

120590T

120590C

120590C

minus40

minus30

minus20

minus10

0

10

20

minus2

minus1

0

1

2

3(M

Pa)

Ωc

t

Ωi

t

Ωa

t

(b)

Figure 10 VonMises ((a) 120590VM) and principal ((b) 120590119879 tensile and 120590119862 compressive) stress measures at cortical (left side) and trabecular (rightside) bone-implant interface for implants 8 and A (see Figure 1) and for different implant in-bone positioning levels (see Figure 3) Average(bars) and peak (lines) values

results referred to the crestal positioning P0 were computedbymodeling a crestal bone loss of about 10 in cortical thick-ness (see Figure 3)

Proposed numerical results confirmed that the implantAnkylos inducedmore favorable loading transmissionmech-anisms than implant 8 also considering different values ofin-bone positioning depth Moreover the analysis of VonMises stress distributions as well as of the values of principal-stress-based measures suggests that the crestal positioning(P0) induced significant stress concentrations at the corticalbone around the implant neck In this case stress peakswere estimated as comparable with those obtained for thesubcrestal positioning P1 When the intermediate subcrestal

positioning P05 was analyzed the lowest compressive peaksatΩ119888were experienced for both implants although tractions

slightly greater than the other positioning configurationsoccurred In trabecular bone stress patterns were computedas almost comparable in the three cases under investigationNevertheless the positioning case P0 induced stress distribu-tions in trabecular regions that were slightly better than P05and P1

This evidence is fully confirmed by analyzing the resultsobtained for the risk index 119877 In particular referring to itspeak values overloading risk at the cortical bone for P05 waslower than that for P0 and P1 of about 14 and 19 forimplant 8 respectively and of about 6 and 3 for implantA


00

01

02

03

04

R

P0 P05 P1 P0 P05 P1

Implant 8 Implant A


Figure 11 Overloading risk index 119877 computed at cortical andtrabecular peri-implant bone for implants 8 and A (see Figure 1)and for different implant in-bone positioning levels (see Figure 3)Average (bars) and peak (lines) values

On the other hand values of 119877 for P0 were lower at thetrabecular bone than those for P05 and P1 of about 10 and18 for implant 8 respectively and of about 10 and 15 forimplant A

33 Influence of Marginal Bone Loss in Crestal PositioningFor implants 8 and A (see Figure 1) crestally positionedin agreement with the configuration P0 (see Figure 3) theinfluence of the amount in crestal bone losswas also analyzedIn particular numerical simulations were carried out consid-ering three different levels of marginal bone loss from theideal case consisting in the absence of cratering effects (boneloss equal to 0 in thickness of the cortical bone layer) upto the case of 50 bone loss For the sake of compactness inFigure 12 only peak and mean values of the Von Mises stressmeasure computed over Ω

119888and Ω

119905are shown together with

results computed for the overloading risk index 119877Numerical analyses showed that modeling an increase

in cratering depth induced an increase in stress levels atboth cortical and trabecular peri-implant regions and therebyinduced an increase in the risk of overloading In particularfor both implants the Von Mises stress peaks relevant to acrestal bone loss of 50 in thickness were greater of about120 in cortical bone and 105 in trabecular than those inthe ideal case of 0 bone loss

4 Discussion

The 11 dental implants that were analyzed by finite-elementsimulations exhibited different stress-based biomechanicalbehaviours dependent on implant shape and thread as wellas on positioning depth and bone geometry around theimplant neck Simulation results considered functioningimplants based on platform-switching concept and were

obtained by modeling the crestal bone geometry after ahealing and loading period

Numerical results obtained by considering a subcrestalin-bone positioning 1mmdepth of implants have highlightedthe influence of implant length and diameter on load transfermechanisms In agreement with numerical findings obtainedby other authors [37ndash41] an increase in implant diame-ter induced a significant reduction of stress peaks mainlyat cortical bone whereas the variation in implant length pro-duced a certain influence only on stress patterns at the cancel-lous bone-implant interface Accordingly the present numer-ical results suggest that in order to control overloading riskthe implant diameter can be considered as a more effectivedesign parameter than the implant length Similar findingswere proposed in [40 47] andwere relevant also to traditionalimplants crestally positioned Overloading risk quantita-tively estimated by combining compressive and tensile effectsvia a principal-stress-based strength criterion for bone wascomputed as significant at the cortical region around theimplant neck (mainly as a result of dominant compressivestates induced by the lateral load component) andor atcrestal (dominant tensile states) or apical (dominant com-pressive states) trabecular regions (induced by the verticalintrusive load component)

Stress analyses of implants with similar length anddiameter allowed us to investigate the influence of somethread features In particular the proposed numerical resultssuggest that thread shape and thread details can inducesignificant effects on the peri-implant stress patternsThreadsanalyzed in this study were characterized by two starts andnumerical results have shown that the use of the same threadtruncation for both starts induced more uniform local stressdistributions than the cases characterized by a differentthread truncation As regards the thread shape trapezoid-shaped thread produced compressive and tensile states atboth cortical and trabecular regions more favorable thanthose of the saw-tooth thread leading to reductions in stressvalues that were significantly affected by implant length anddiameter Moreover numerical evidence has highlighted thatthe presence of a wide helical-milling along the implant bodydoes not significantly affect the loading transmission mecha-nisms but it can contribute to reduce risks of overloading atthe trabecular apical bone especially when short implants areconsidered

Numerical simulations carried out on coupled bone-implant models defined by considering different levels of theimplant in-bone positioning depth have shown that a crestalplacement combined with a reduced marginal bone lossinduced great stress values at the crestal cortical regions con-firming the biomechanical relationship between the stress-based mechanical stimuli and the possible activation of boneresorption process at the implant collar [21] In agreementwith clinical evidence and with other numerical studies[4 18 19 25ndash34 40 47 53] present results confirm alsothat a subcrestal positioning of implants based on platform-switching concept may contribute to the preservation ofthe crestal bone as well as can induce more effective andhomogeneous stress distributions at the peri-implant regionsIn particular proposed simulation results have shown that


0

20

40

60

80

100

120

140

(MPa

)

0 25 50Crestal bone loss ()

Implant 8Implant A

120590VM

(a)

0

1

2

3

4

5

6

(MPa

)0 25 50 0 25 50

Crestal bone loss ()

Implant 8 Implant A

120590VM

Ωc

t

Ωi

t

Ωa

t

(b)

Implant 8 Implant A

0 25 50 0 25 50Crestal bone loss ()

00

02

04

06

08

10

R

CorticalTrabecular

(c)

Figure 12 Von Mises stress measure at cortical (a) and trabecular (b) bone-implant interface for implants 8 and A (see Figure 1) and with acrestal positioning characterized by different levels of crestal bone loss (c) Overloading risk index 119877 Average (bars) and peak (lines) values

in the case of subcrestal placements stress distributions weremainly affected by two counteracting effects On one handwhen the implantrsquos in-bone positioning depth increases thenthe vertical thickness of the cortical bone engaged in loadtransfer mechanisms reduces tending to generate stress con-centrations But on the other hand the horizontal bone appo-sition induced by the platform-switching configuration in asubcrestal positioning highly contributes to an effectiveredistribution of the stress field As a result of a balance con-dition between previous effects the best stress-based perfor-mance among cases herein analyzed has been experiencedconsidering an in-bone positioning depth of about 25 incortical thickness

In the case of crestal positioning the proposed numericalresults have shown that if the crestal bone morphologyaffected by possible marginal bone loss is not properly mod-eled then a significant underestimation of stress values andan inaccurate evaluation of loading transfer mechanisms aregenerally obtained Moreover the present finite-elementanalyses have confirmed that a progressivemarginal bone losscan lead to a progressive increase in stress intensity at theperi-implant interface that in turn can contribute to afurther overload-induced bone loss jeopardizing clinicaleffectiveness and durability of the prosthetic treatmentTheseresults are qualitatively in agreement with numerical evi-dence obtained in [19 40 41 47] although due to simplifiedandor different models used in those studies quantitativecomparisons cannot be made

It is worth remarking that contrary to a number ofrecent numerical approaches [33 38 39 41 46] the presentstudy accounted for the influence of posthealing crestal bonemorphology in functioning implants and was based on adetailed three-dimensional geometricalmodeling of the bone

segment wherein the implant is inserted Accordingly theresults herein proposed can be retained as complementarywith respect to several previous simplified studies furnishingmore refined and accurate indications for choosing andordesigning threaded dental implants as well as giving clearinsights towards the understanding of main factors affectingthe loading transmission mechanisms

Although in the current study a number of aspects influ-encing the biomechanical interaction between dental implantand bone have been accounted for some limitations canbe found in modeling assumptions herein employed Inparticular the ideal and unrealistic condition of 100osseousintegration was assumed stress analyses were performed bysimulating static loads and disregarding any muscle-jawinteraction bone wasmodeled as a dry isotropic linear elasticmaterial whose mechanical properties were assumed to betime independent the space dependence of bone density andmechanical response has been simply described by distin-guishing trabecular and cortical homogeneous regions Allthese assumptions do not completely describe possible clini-cal scenarios because of possible osseointegration defects atthe peri-implant regions different patient-dependent load-ing distributions much more complex and time-dependentforces and significant muscular effects anisotropic inhomo-geneous nonlinear and inelastic response of living tissuesbone remodeling and spatially graded tissue properties Nev-ertheless in agreement with other numerical studies [35ndash54]present assumptions can be accepted in a computationalsense in order to deduce significant and clinically usefulindications for the comparative stress-based assessment ofthreaded dental implants

In order to enhance the present finite-element approachfuture studies will be devoted to the modeling of bone


as a nonlinear anisotropic viscous and inhomogeneousregenerative tissue that responds to stress by resorption orregeneration under time-dependent muscular and externalloads accounting also for a more refined correlation betweenbone density and its mechanical response

5 Concluding Remarks

Within the limitations of this study numerical simulationsshowed that implant design (in terms of implant diameterlength thread shape) in-bone positioning depth and crestalbonemorphology highly affect themechanisms of load trans-mission Aiming at theminimization of the overloading risksthe implant diameter can be retained as a more effectivedesign parameter than the implant length In particular asignificant reduction of stress peaks mainly at the corticalbone occurred when implant diameter increased Never-theless implant length exhibited a certain influence onthe bone-implant mechanical interaction at the cancellousinterface resulting in more effective and homogeneous stressdistributions in trabecular bone when the implant lengthincreased Stress-based performances of dental implants werealso found to be significantly affected by thread featuresIn detail trapezoid-shaped thread induced compressive andtensile states at both cortical and trabecular regions morefavorable than the saw-tooth thread Moreover the use of thesame thread truncation for different thread starts induceda more uniform local stress distributions than the case of adifferent thread truncation In the case of short implants thepresence of a wide helical-milling along the implant bodyproduced a reduction in the overloading risk at the trabecularapical boneOverloading riskswere computed as high aroundthe implant neck (for compressive states) in cortical bone andat the crestal (for tensile states) or apical (for compressivestates) trabecular bone Risk of overloading reduced whensmall levels of crestal bone loss were considered as inducedby suitable platform-switching strategies

References

[1] T D Taylor U Belser and R Mericske-Stern ldquoProsthodonticconsiderationsrdquo Clinical oral Implants Research vol 11 pp 101ndash107 2000

[2] S E Eckert and P C Wollan ldquoRetrospective review of 1170endosseous implants placed in partially edentulous jawsrdquo Jour-nal of Prosthetic Dentistry vol 79 no 4 pp 415ndash421 1998

[3] R JWeyant ldquoShort-term clinical success of root-form titaniumimplant systemsrdquo Journal of Evidence-BasedDental Practice vol3 pp 127ndash130 2003

[4] A M Roos-Jansaker C Lindahl H Renvert and S RenvertldquoNine- to fourteen-year follow-up of implant treatment PartI implant loss and associations to various factorsrdquo Journal ofClinical Periodontology vol 33 no 4 pp 283ndash289 2006

[5] J B Brunski ldquoBiomechanics of dental implantsrdquo in Implants inDentistry M Block J N Kent and L R Guerra Eds pp 63ndash71WB Saunders Philadelphia Pa USA 1997

[6] J B Brunski D A Puleo and A Nanci ldquoBiomaterials andbiomechanics of oral and maxillofacial implants current status

and future developmentsrdquo International Journal of Oral andMaxillofacial Implants vol 15 no 1 pp 15ndash46 2000

[7] J E Lemons ldquoBiomaterials biomechanics tissue healingand immediate-function dental implantsrdquo The Journal of OralImplantology vol 30 no 5 pp 318ndash324 2004

[8] F Marco F Milena G Gianluca and O Vittoria ldquoPeri-implantosteogenesis in health and osteoporosisrdquoMicron vol 36 no 7-8 pp 630ndash644 2005

[9] M Cehreli S Sahin and K Akca ldquoRole of mechanical environ-ment and implant design on bone tissue differentiation currentknowledge and future contextsrdquo Journal of Dentistry vol 32 no2 pp 123ndash132 2004

[10] C D C Lopes and B K Junior ldquoHistological findings of boneremodeling around smooth dental titanium implants insertedin rabbitrsquos tibiasrdquo Annals of Anatomy vol 184 no 4 pp 359ndash362 2002

[11] B Helgason E Perilli E Schileo F Taddei S Brynjolfssonand M Viceconti ldquoMathematical relationships between bonedensity and mechanical properties a literature reviewrdquo ClinicalBiomechanics vol 23 no 2 pp 135ndash146 2008

[12] K G Strid ldquoRadiographic resultsrdquo in Tissue-Integrated Prosthe-ses Osseointegration in Clinical Dentistry P I Branemark GA Zarb and T Albrektsson Eds pp 187ndash198 QuintessenceChicago Ill USA 1985

[13] L Sennerby L E Ericson P Thomsen U Lekholm and PAstrand ldquoStructure of the bone-titanium interface in retrievedclinical oral implantsrdquo Clinical Oral Implants Research vol 2no 3 pp 103ndash111 1991

[14] YUjiie R Todescan and J EDavies ldquoPeri-implant crestal boneloss a putative mechanismrdquo International Journal of Dentistryvol 2012 Article ID 742439 14 pages 2012

[15] F W Neukam T F Flemmig C Bain et al ldquoLocal andsystemic conditions potentially compromising osseointegrationConsensus report of Working Group 3rdquo Clinical Oral ImplantsResearch vol 17 no 2 pp 160ndash162 2006

[16] S Sahin M C Cehreli and E Yalcin ldquoThe influence of fun-ctional forces on the biomechanics of implant-supportedprosthesesmdasha reviewrdquo Journal of Dentistry vol 30 no 7-8 pp271ndash282 2002

[17] D P Callan A OrsquoMahony and C M Cobb ldquoLoss of crestalbone around dental implants a Retrospective Studyrdquo ImplantDentistry vol 7 no 4 pp 258ndash266 1998

[18] J S Hermann D L Cochran P V Nummikoski and D BuserldquoCrestal bone changes around titanium implants A radio-graphic evaluation of unloaded nonsubmerged and submergedimplants in the caninemandiblerdquo Journal of Periodontology vol68 no 11 pp 1117ndash1130 1997

[19] K Akca and M C Cehreli ldquoBiomechanical consequences ofprogressive marginal bone loss around oral implants a finiteelement stress analysisrdquoMedical and Biological Engineering andComputing vol 44 no 7 pp 527ndash535 2006

[20] J T Irving ldquoFactors concerning bone loss associated withperiodontal diseaserdquo Journal of Dental Research vol 49 no 2pp 262ndash267 1970

[21] D R Carter M C H Van Der Meulen and G S BeaupreldquoMechanical factors in bone growth and developmentrdquo Bonevol 18 no 1 pp 5Sndash10S 1996

[22] A Kozlovsky H Tal B-Z Laufer et al ldquoImpact of implantoverloading on the peri-implant bone in inflamed and non-inflamedperi-implantmucosardquoClinical Oral Implants Researchvol 18 no 5 pp 601ndash610 2007


[23] S C Cowin Bone Mechanics Handbook CRC Press BocaRaton Fla USA 2001

[24] R B Martin D B Burr and N A Sharkey Skeletal TissueMechanics Springer New York NY USA 1998

[25] B Assenza A Scarano G Petrone et al ldquoCrestal bone remod-eling in loaded and unloaded implants and the microgap ahistologic studyrdquo Implant Dentistry vol 12 no 3 pp 235ndash2412003

[26] M P Hanggi D C Hanggi J D Schoolfield J Meyer D LCochran and J S Hermann ldquoCrestal bone changes around tita-nium implants Part I a retrospective radiographic evaluation inhumans comparing two non-submerged implant designs withdifferent machined collar lengthsrdquo Journal of Periodontologyvol 76 no 5 pp 791ndash802 2005

[27] Y-K Shin C-H Han S-J Heo S Kim and H-J ChunldquoRadiographic evaluation of marginal bone level aroundimplants with different neck designs after 1 yearrdquo InternationalJournal ofOral andMaxillofacial Implants vol 21 no 5 pp 789ndash794 2006

[28] J S Hermann J D Schoolfied R K Schenk D Buser andD LCochran ldquoInfluence of the size of the microgap on crestal bonechanges around titanium implants A histometric evaluationof unloaded non-submerged implants in the canine mandiblerdquoJournal of Periodontology vol 72 no 10 pp 1372ndash1383 2001

[29] F Hermann H Lerner and A Palti ldquoFactors influencingthe preservation of the periimplant marginal bonerdquo ImplantDentistry vol 16 no 2 pp 165ndash175 2007

[30] L Lopez-Marı J L Calvo-Guirado B Martın-CastelloteG Gomez-Moreno and M Lopez-Marı ldquoImplant platformswitching concept an updated reviewrdquoMedicinaOral PatologiaOral y Cirugia Bucal vol 14 no 9 pp e450ndashe454 2009

[31] D M Gardner ldquoPlatform switching as a means to achievingimplant estheticsrdquo The New York State Dental Journal vol 71no 3 pp 34ndash37 2005

[32] R J Lazzara and S S Porter ldquoPlatform switching a new conceptin implant dentistry for controlling postrestorative crestal bonelevelsrdquo International Journal of Periodontics and RestorativeDentistry vol 26 no 1 pp 9ndash17 2006

[33] Y Maeda J Miura I Taki and M Sogo ldquoBiomechanicalanalysis on platform switching is there any biomechanicalrationalerdquo Clinical Oral Implants Research vol 18 no 5 pp581ndash584 2007

[34] M Degidi A Piattelli J A Shibli R Strocchi and G IezzildquoBone formation around a dental implant with a platformswitching and another with a TissueCare Connection A his-tologic and histomorphometric evaluation in manrdquo Titaniumvol 1 pp 10ndash17 2009

[35] J-P A Geng K B C Tan and G-R Liu ldquoApplication of finiteelement analysis in implant dentistry a review of the literaturerdquoJournal of Prosthetic Dentistry vol 85 no 6 pp 585ndash598 2001

[36] R C Van Staden H Guan and Y C Loo ldquoApplication of thefinite element method in dental implant researchrdquo ComputerMethods in Biomechanics and Biomedical Engineering vol 9 no4 pp 257ndash270 2006

[37] H-J Chun S-Y Cheong J-H Han et al ldquoEvaluation ofdesign parameters of osseointegrated dental implants usingfinite element analysisrdquo Journal of Oral Rehabilitation vol 29no 6 pp 565ndash574 2002

[38] L Himmlova T Dostalova A Kacovsky and S KonvickovaldquoInfluence of implant length and diameter on stress distribu-tion a finite element analysisrdquo Journal of Prosthetic Dentistryvol 91 pp 20ndash25 2004

[39] C S Petrie and J L Williams ldquoComparative evaluation ofimplant designs influence of diameter length and taper onstrains in the alveolar crestmdasha three-dimensional finite-elementanalysisrdquoClinical Oral Implants Research vol 16 no 4 pp 486ndash494 2005

[40] L Baggi I Cappelloni M Di Girolamo F Maceri and GVairo ldquoThe influence of implant diameter and length on stressdistribution of osseointegrated implants related to crestal bonegeometry a three-dimensional finite element analysisrdquo Journalof Prosthetic Dentistry vol 100 no 6 pp 422ndash431 2008

[41] D Bozkaya SMuftu andAMuftu ldquoEvaluation of load transfercharacteristics of five different implants in compact bone atdifferent load levels by finite elements analysisrdquo Journal ofProsthetic Dentistry vol 92 no 6 pp 523ndash530 2004

[42] H-J Chun H-S Shin C-H Han and S-H Lee ldquoInfluenceof implant abutment type on stress distribution in bone undervarious loading conditions using finite element analysisrdquo Inter-national Journal of Oral and Maxillofacial Implants vol 21 no2 pp 195ndash202 2006

[43] I Alkan A Sertgoz and B Ekici ldquoInfluence of occlusal forceson stress distribution in preloaded dental implant screwsrdquoJournal of Prosthetic Dentistry vol 91 no 4 pp 319ndash325 2004

[44] G Sannino G Marra L Feo G Vairo and A Barlattani ldquo3Dfinite element non linear analysis on the stress state at the bone-implant interface in dental osteointegrated implantsrdquo Oral ampImplantology vol 3 no 3 pp 26ndash37 2010

[45] C-L Lin Y-C Kuo and T-S Lin ldquoEffects of dental implantlength and bone quality on biomechanical responses in bonearound implants a 3-D non-linear finite element analysisrdquoBiomedical Engineering vol 17 no 1 pp 44ndash49 2005

[46] T Kitagawa Y Tanimoto K Nemoto and M Aida ldquoInfluenceof cortical bone quality on stress distribution in bone arounddental implantrdquoDentalMaterials Journal vol 24 no 2 pp 219ndash224 2005

[47] L Baggi I Cappelloni F Maceri and G Vairo ldquoStress-basedperformance evaluation of osseointegrated dental implants byfinite-element simulationrdquo Simulation Modelling Practice andTheory vol 16 no 8 pp 971ndash987 2008

[48] F ChenK Terada KHanada and I Saito ldquoAnchorage effects ofa palatal osseointegrated implant with different fixation a finiteelement studyrdquo Angle Orthodontist vol 75 no 4 pp 593ndash6012005

[49] H-J Chun D-N Park C-H Han S-J Heo M-S Heo andJ-Y Koak ldquoStress distributions in maxillary bone surroundingoverdenture implants with different overdenture attachmentsrdquoJournal of Oral Rehabilitation vol 32 no 3 pp 193ndash205 2005

[50] ANNatali P G Pavan andA L Ruggero ldquoEvaluation of stressinduced in peri-implant bone tissue by misfit in multi-implantprosthesisrdquo Dental Materials vol 22 no 4 pp 388ndash395 2006

[51] M Bevilacqua T Tealdo M Menini et al ldquoThe influence ofcantilever length and implant inclination on stress distributionin maxillary implant-supported fixed denturesrdquo Journal ofProsthetic Dentistry vol 105 no 1 pp 5ndash13 2011

[52] C M Bellini D Romeo F Galbusera et al ldquoA finite elementanalysis of tilted versus nontilted implant configurations in theedentulousMaxillardquo International Journal of Prosthodontics vol22 no 2 pp 155ndash157 2009

[53] L Baggi S Pastore M Di Girolamo and G Vairo ldquoImplant-bone load transfer mechanisms in complete-arch prosthesessupported by four implants a three-dimensional finite elementapproachrdquo Journal of Prosthetic Dentistry vol 109 pp 9ndash212013


[54] G Sannino and A Barlattani ldquoMechanical evaluation of animplant-abutment self-locking taper connection finite elementanalysis and experimental testsrdquo International Journal of Oral ampMaxillofacial Implants vol 28 no 1 pp e17ndashe26 2013

[55] J Y Rho M C Hobatho and R B Ashman ldquoRelations ofmechanical properties to density and CT numbers in humanbonerdquo Medical Engineering and Physics vol 17 no 5 pp 347ndash355 1995

[56] J E Lemon and F Dietsh-Misch ldquoBiomaterials for dentalimplantsrdquo in Contemporary Implant Dentistry C E Misch Edpp 271ndash302 Mosby St Louis Mo USA 2nd edition 1999

[57] U Lekholm andG A Zarb ldquoPatient selection and preparationrdquoinTissue-Integrated Prostheses Osseointegration in Clinical Den-tistry P I Branemark G A Zarb and T Albrektsson Eds pp199ndash209 Quintessence Chicago Ill USA 1985

[58] A N Natali R T Hart P G Pavan and I Knets ldquoMechanics ofbone tissuerdquo in Dental Biomechanics A N Natali Ed pp 1ndash19Taylor amp Francis London UK 2003

[59] J Y Rho R B Ashman and H Turner ldquoYoungrsquos modulus oftrabecular and cortical bone material ultrasonic and microten-sile measurementsrdquo Journal of Biomechanics vol 26 no 2 pp111ndash119 1993

[60] C Truesdell and R A Toupin ldquoThe classical field theoriesrdquo inHandbuch Der Physik S Flugge Ed vol 3 Springer BerlinGermany 1960

[61] O C Zienkiewicz and R L TaylorThe Finite Element MethodMcGraw-Hill New York NY USA 4th edition 1998

[62] O C Zienkiewicz and J Z Zhu ldquoSimple error estimatorand adaptive procedure for practical engineering analysisrdquoInternational Journal for Numerical Methods in Engineering vol24 no 2 pp 337ndash357 1987

[63] F Maceri M Martignoni and G Vairo ldquoMechanical behaviourof endodontic restorations with multiple prefabricated posts afinite-element approachrdquo Journal of Biomechanics vol 40 no11 pp 2386ndash2398 2007

[64] F Maceri M Martignoni and G Vairo ldquoOptimal mechanicaldesign of anatomical post-systems for endodontic restorationrdquoComputer Methods in Biomechanics and Biomedical Engineer-ing vol 12 no 1 pp 59ndash71 2009

[65] X E Guo ldquoMechanical properties of cortical and cancellousbone tissuerdquo in BoneMechanics Handbook S C Cowin Ed pp101ndash1023 CRC Press Boca Raton Fla USA 2nd edition 2001


Research ArticleEffect of Pilates Training on Alpha Rhythm

Zhijie Bian1 Hongmin Sun2 Chengbiao Lu1 Li Yao3 Shengyong Chen4 and Xiaoli Li3

1 Institute of Electrical Engineering Yanshan University Qinhuangdao 066004 China2 College of Physical Education Yanshan University Qinhuangdao 066004 China3National Lab of Cognitive Neuroscience and Learning Beijing Normal University Xin Jie Kou Wai Avenue Haidian DistrictBeijing 100875 China

4College of Computer Science and Technology Zhejiang University of Technology Hangzhou 310023 China

Correspondence should be addressed to Xiaoli Li xiaolibnueducn

Received 13 April 2013 Accepted 26 May 2013


Copyright copy 2013 Zhijie Bian et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this study the effect of Pilates training on the brain function was investigated through five case studies Alpha rhythm changesduring the Pilates training over the different regions and the whole brain were mainly analyzed including power spectral densityand global synchronization index (GSI) It was found that the neural network of the brain was more active and the synchronizationstrength reduced in the frontal and temporal regions due to the Pilates training These results supported that the Pilates training isvery beneficial for improving brain function or intelligence These findings maybe give us some line evidence to suggest that thePilates training is very helpful for the intervention of brain degenerative diseases and cogitative dysfunction rehabilitation

1 Introduction

Pilates was created in the 1920s by physical trainer JosephH Pilates and has been developed based on the Easternand Western health preservation methods such as Yoga andTaichi This exercise is suitable for all the people and maybe one of the most attractive fitness trainings [1 2] Pilatesexercise was found to be able to correct body posture relaxthe waist and neck solve the problem of shoulder and reducefat of arm and abdomen [3ndash5] Pilates can improve the bloodcirculation and cardiopulmonary function as the exercise isdominated by the rhythmic breath particularly the lateralthoracic breathing that can effectively promote the exchangeof oxygen The Pilates has been proven to impact personalautonomy [6] pain control [1] improvedmuscle strength [7]flexibility [8] and motor skills [9] Physical activity can beconsidered as an approach to improve organic conditions andprevent physical degeneration [10] Further studies suggestthat Pilates can release the stress of mind increase brainrsquosoxygen supply and enhance brain function [11 12] andstudies in aged samples also suggest that Pilates is beneficialto mental state including sleep quality emotion and self-confidence [2]

However the direct evidence of Pilates on brain activitysuch as electroencephalographic (EEG) is lacking In thisstudy we recorded resting-state EEG signals before and afterPilates exercise We concentrated on the analysis of alpharhythm (8ndash13Hz) changes of the EEG which is associatedwith the intelligence The aim is to demonstrate whether ornot Pilates can impact the brain functions or intelligence

2 Methods

21 Subjects After providing informed consent five healthypostgraduate girls (mean age 24 plusmn 1 years) voluntarilyparticipated in this study They were free to withdraw fromthe experiments at any time All subjects included in thisexperiment were right-handed nonathletes and had neverbeen suffering from neurological and psychiatric disordersThe study was approved by the local ethics committee andall participants gave written informed consent for this study

22 Pilates Training The five girls were trained with Pilatesfour sessions a week (Monday Tuesday Thursday and Fri-day) in awell-ventilated room at least 90minutes per sessionFor the first three weeks they were taught Pilates movements


step by step and they reviewed the former movements ineach training session and were corrected by the coach afterlearning the new ones After they were taught a total of 24movements they practiced for 4ndash6 times in each session andthey were instructed to perform the sequences as accuratelyand smoothly coupled with breathingThe training lasted for10 weeks And the resting-state EEG rhythms were recordedwith eyes closed before Pilates training and after each twoweeks training

23 Data Acquisition EEG recordings were performed at sixdifferent time points The first recording was performed justprior to the onset of training week (week 0) After each twoweeks training there was one recording such as week 2week 4 week 6 week 8 and week 10 During recordings thesubjects were asked to close their eyes and sit in a comfortablearmchair who were relaxed and awake in a dim room for 5minutes during each recording

The EEG data acquisition was performedwith NeuroscanEEGERP recording system amplifiers (SynAmps2) with 64AgAgCl surface electrodes which were fixed in a cap at thestandard positions according to the extended international10ndash20 system and with 32 bit SCAN45 acquisition systemthat could also be used to continuously view the EEG record-ings A reference electrode was placed between Cz and CPzand ground electrode was placed between FPz and Fz Hori-zontal and vertical electrooculograms (EOG) were recordedaswellTheEEGwas recordedwith unipolarmontages exceptfor the EOG with bipolar montages The impedances of allelectrodes were lt10 kΩ During the recording the data wasband-pass filtered in the frequency range 005ndash200Hz andsampled at 2 KHz Digital conversion of the measured analogsignals was accomplished with a 24 bit digitizer

24 Data Analysis In this study the alpha rhythm (8ndash13Hz)in the EEG recordings was concentrated on In order to detectthe alpha rhythmrsquos changes over different regions the brainwas divided into five regions frontal left temporal centralright temporal and posterior (see Figure 1) Power spectraldensity and global synchronization index (GSI) at the alphafrequency band were computed in all regions

241 Preprocessing for EEG The raw EEG data was analyzedoffline using EEGLAB (httpsccnucsdedueeglab [13]) Itwas rereferenced to M1 (left mastoid process) and M2 (rightmastoid process) the two EOG channels were extracted theband-pass filter (8ndash13Hz) was initially used to include thefrequency band of interest and then the data was resampledto 250Hz for further analysis

242 Spectral Analysis After preprocessing we chose EEGdata of 4 minutes for analysis Power spectral density (PSD)was estimated using pwelch method which has a better noiseperformance compared with other power spectra estimationmethods The PSD was calculated using 10s epochs for eachsignal Each epoch was divided into overlapping segmentsusing periodic 10-s hamming window with 50 overlapAnd then the peak power and peak power frequency were

FPzFP2FP1

Fz

Cz

Pz

OzO1 O2

T7 T8

F7 F8

P7 P8

F3 F4

C3 C4

P3 P4

AF3 AF4

F5 F1 F2 F6

FCzFT7 FT8

FC5 FC3 FC1 FC2 FC4 FC6

CPzTP7 TP8

CP1CP3 CP2 CP4 CP6CP5

POz PO8PO7

P5 P2 P6

PO4 PO6PO3PO5

C2 C6C1C5

CB1 CB2

P1

1

2 3 4

5

Figure 1 Extended 10ndash20 electrodes system and area electrodesrsquopartition The dotted lines divided the whole into 5 regions thenumbers 1 2 3 4 and 5 separately denote the frontal left temporalcentral right temporal and posterior regions respectively

calculated for the alpha band in each epochOutliers rejectionwas performedusing generalized extreme studentized deviate(GESD) [14] for all epochs in each channel The remainedepochs were averaged

The PSD for each channel in all frequency bands wasobtained In order to estimate the changes of peak powerand corresponding frequency during the Pilates training overdifferent regions and the whole brain the PSD was averagedover each region and the whole brain

243 GSI Synchronization is known as a key feature to eval-uate the information process in the brain For long EEG dataglobal synchronization index (GSI) can reveal the true syn-chronization features of multivariable EEG sequences betterthan other methods [15]

To eliminate the effect of amplitude the EEG signals pre-processed need to be normalized by

119885 = 119911119894 (119899) (119894 = 1 119872 119899 = 1 119879)

119909119894 (119899) =

(119911119894 (119899) minus ⟨119885

119894⟩)

120590119894

119883 = 119909119894 (119899)

(1)

where 119885 is considered as the multivariate EEG data 119872 is thenumber of channels 119899 is the number of data points in timewindow 119879 119909

119894(119899) is the normalized signal and 119883 is a vector of

119909119894(119899) and ⟨119885

119894⟩ and 120590

119894are the mean and standard deviation of

119911119894(119899) respectively


Table 1 Comparisons of global changes before training (BT) and after training (AT) for each case

PersonsChanges

Alpha peak power Alpha peak frequency GSIBT (120583V2Hz) AT (120583V2Hz) BT (Hz) AT (Hz) BT AT

First 20926 21347 plusmn 3279 1005 1002 plusmn 006 053 043 plusmn 003

Second 653 967 plusmn 127 923 976 plusmn 009 037 031 plusmn 003

Third 355 391 plusmn 052 1189 1148 plusmn 025 032 028 plusmn 002

Forth 4506 6595 plusmn 1097 1023 961 plusmn 008 035 032 plusmn 005

Fifth 4428 5734 plusmn 925 1006 1006 plusmn 006 034 029 plusmn 002

Average 6174 7007 plusmn 1096 1029 1018 plusmn 011 038 033 plusmn 003

To calculate the GSI of multivariate EEG data a phasecorrelation matrix C was constructed The phase of the eachEEG series is estimated using continuous wavelet transformThe phase difference of two EEG traces is defined by

Δ120593119908

119909119894119909119896(119904 120591) = 120593

119908

119909119894(119904 120591) minus 120593

119908

119909119896(119904 120591) (119896 = 1 119872) (2)

Then the phase synchronization is calculated by

120574119894119896

=100381610038161003816100381610038161003816⟨119890119895Δ120593119908

119909119894119909119896(119904120591)

⟩119879

100381610038161003816100381610038161003816isin [0 1] (3)

where ⟨sdot⟩119879indicates the average of the time window 119879

120574119894119896indicates the phase synchronization of signals 119909

119894(119899) and

119909119896(119899) For all EEG series a phase correlation matrix can be

written as C = 120574119894119896

Then the eigenvalue decomposition of C is defined as

follows

Ck119894

= 120582119894k119894 (4)

where eigenvalues 1205821

le 1205822

le sdot sdot sdot le 120582119872are in increasing order

and k119894 119894 = 1 119872 are the corresponding eigenvectors

In order to reduce the ldquobiasrdquo caused by the algorithmand length of data amplitude adjusted Fourier transformed(AAFT) surrogate method [16] was used in this study Basedon the surrogate series 119883surr the normalized phase surrogatecorrelation matrix R was calculated and the 120582

119904

1le 120582119904

2le

sdot sdot sdot le 120582119904

119872were the eigenvalues of surrogate correlation

matrix R The distribution of the surrogate eigenvalues canreflect the random synchronization of the multivariate timeseries To reduce the effects of the random components inthe total synchronization the eigenvalues were divided by theaveraged surrogate eigenvalues The GSI was calculated by

120582119892

119894=

120582119894120582119904119894

sum119872

119894=1120582119894120582119904119894

(119894 = 1 119872)

GSI = 1 +sum119872

119894=1120582119892

119894log (120582

119892

119894)

log (119872)

(5)

where 120582119904119894is the averaged eigenvalues of the surrogate series

Calculating the GSI used 10 s epochs with 50 overlap forthe alpha rhythm over the five regions and the whole brainOutlierrsquos rejection [14] was also used and then the remainedepochs were averaged Average of GSI over different regionsand the whole brain was obtained as well

244 Calculation of the Relative Variable Ratio In order toestimate the changes during the Pilates training the relativevariable ratio may be calculated by

119903(119896)

119895119894=

119910(119896)

119895119894minus 119910(119896)

1198951

119910(119896)

1198951

(119894 = 1 119873 119873 = 6 119895 = 1 119870 119870 = 5 119896 = 1 2 3)

(6)

where 119873 is the number of tests 119870 is the number of subjectsand 119903(119896)

119895119894is the relative variable ratio to the first test 119910

(119896)

119895119894is the

feature value of EEG recordings When 119896 = 1 119903(119896)

119895119894presents

the changes of the peak power when 119896 = 2 119903(119896)

119895119894presents the

changes of the peak frequency when 119896 = 3 119903(119896)


changes of GSI All changes were over the Pilates trainingIf the variables increased over the Pilates training 119903(119896)

119895119894will

be greater than zero if they decreased 119903(119896)

119895119894will be less than

zero if there are no changes 119903(119896)

119895119894will be approximate to zero

For the limited numbers of only five subjects boxplot is usedto describe the changes over the Pilates training duration

3 Results

31 Spectral Analysis The results of alpha peak power andalpha peak frequency in each region and over the whole brainwere shown in Figure 2 The comparisons of global changesbefore training (BT) and after training (AT) for each casewereshown in Table 1

The alpha peak powers were different among the fivecases The power that is in the first case was the largestA relative lower peak power was observed in the secondand the third cases There may be individual difference butthe trend of changes was the same Table 1 presented thatthe alpha peak power increased in all cases and the averagevalue increased as well (6174 to 7007 plusmn 1096) (Table 1) Thechanges of alpha peak frequencies varied among differentindividuals decreased in three cases increased in one caseand unchanged in one case and the average value was slightlydecreased (1029 to 1018 plusmn 011) (Table 1)

The ratios of alpha peak power and alpha peak frequencycould eliminate the effect of individual factor (see Figure 2)The ratios were obtained to investigate the two indicatorsrsquochanges during Pilates training Figure 2(a) showed thatalpha peak power was increased in various regions and


Fron

tal r

atio

Righ

t tem

pora

l rat

io

Left

tem

pora

l rat

io

Cen

tral

ratio

Occ

ipita

l rat

io

Glo

bal r

atio

0

1

2

3

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6N test N test

minus1

0

1

2

3

minus1

0

1

2

3

minus1

0

1

2

3

minus1

0

1

2

3

minus1

0

1

2

3

minus1

N test

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6N test N testN test

(a) Alpha Peak Power

minus02

minus01

0

01

minus02

minus01

0

01

minus02

minus01

0

01

minus02

minus01

01

minus02

minus01

01

minus02

minus01

0 0 0

01

Fron

tal r

atio

Righ

t tem

pora

l rat

io

Left

tem

pora

l rat

io

Cen

tral

ratio

Occ

ipita

l rat

io

Glo

bal r

atio



(b) Alpha Peak Frequency

Figure 2 Relative changes of alpha peak power (a) and peak frequency (b) during the Pilates training Alpha peak power increased in thefive regions and the whole brain as (a) shows As (b) shows most of the median of alpha peak frequency decreased but was not significantOne box represented one test in (a) and (b)


minus05

0

05

minus05

0

05

minus05

0

05

minus05

0

05

minus05

0

05

minus05

0

05

Fron

tal r

atio

Righ

t tem

pora

l rat

io

Left

tem

pora

l rat

io

Cen

tral

ratio

Occ

ipita

l rat

io

Glo

bal r

atio



Figure 3 Relative changes of GSI for alpha rhythm during the Pilates training The GSI in the frontal and temporal regions was decreasedbut it almost increased in the central region and the changes in the occipital region were not obviousTheGSI over the whole brain decreasedobviously One box represented one test

the whole brain The median of ratios was greater than zeroThe ratios of alpha peak power versus alpha peak frequencywere increased by about 30 to 90 (especially in the secondtest which was two weeks after Pilates training) 10 to 3010 to 60 and 20 to 40 for the frontal temporalcentral occipital and the whole brain respectivelyThe alphapeak frequency decreased in small degree during Pilatestraining and the changeswere not statistically significant (seeFigure 2(b))

32 GSI TheGSI changes of the whole brain before and afterpilates training in individuals and the average value of the fivesubjects were listed in Table 1 The GSI values were decreasedduring the Pilates training significantly

The time-dependent changes of GSI during the Pilatestraining in different regions and over the whole brain werealso studied Figure 3 plotted the relative variable ratios ofGSI For the frontal region the GSI has decreased by about 0ndash10 8ndash10 and 5 after two four and six weeks trainingrespectively but increased in some subjects after eight weekstraining For the left temporal region the GSI decreasedat least by 5ndash25 after two weeks training For the righttemporal region the GSI decreased at least by 5ndash40 afterfour weeks training but there was inconsistent variationafter the two weeks training For the central region the GSIincreased in varying degrees after two weeks training Forthe occipital region there were no consistent changes duringPilates training For the whole area of the brain the GSI

decreased slightly after two weeks training but decreased atleast by 5 after four weeks training

4 Discussions

In this study we used the resting-state EEG recording toinvestigate the effects of the Pilates training on the brain EEGThe results showed that the Pilates training could increasethe power of the brain alpha rhythm and reduce the synchro-nization strength of alpha rhythm in the frontal and temporalregions These findings may support that the Pilates trainingmaybe beneficial for improving brain function because thealpha rhythm and its synchronization are associated withthe human brain higher function such as intelligence Theseresults suggest that Pilates training may be helpful for theintervention of brain degenerative diseases and cogitativedysfunction rehabilitation Future studywill demonstrate thishypothesis

Human EEG activity reflects the synchronization of cor-tical pyramidal neurons Alpha rhythm in the spontaneousEEG signals is an important predictor of the efficacy ofcortical information processing during cognitive and sen-sorimotor demand [17] Alpha rhythm is often consideredas one of the indicators of the brain function and has asignificant correlation with performance on memory tasks[18] and the alpha power is considered as an importantparameter to represent neural activities and processingmechanisms [19] Although the exact mechanisms of alpha


rhythm generation and its functional significance are notunderstood completely so far there is increasing evidencethat synchronized oscillatory activity in the cerebral cortexis essential for spatiotemporal coordination and integrationof activity of anatomically distributed but functionally relatedneural elements [20] Alpha power was positively correlatedwith intelligence variables while some lower frequency bandsnegatively correlated with them [21] The higher the absoluteamplitude or power of the EEG the stronger the backgroundneural synchronization then the better the cognitive per-formance [22] and the higher the IQ [23] Lower alphapower is associated with many diseases such as obsessive-compulsive disorder [24] Downrsquos syndrome [25] Alzheimerrsquo[26] and restless legs syndrome [27] Patients with thesediseases showed intelligence memory loss and alpha rhythmabnormalities [26] There is also a correlation between alphapower and intelligence [21] Cortical neural synchronizationat the basis of eye-closed resting-state EEG rhythms wasenhanced in elite karate athletes [28] In this study the alphapeak power was increased during the Pilates training whichsuggests the increased neural network activity and perhapsthe intelligence during the Pilates training

Previous study found that right postcentral gyrus andbilateral supramarginal gyrus were sensitive to themotor skilltraining [29] and the functional connectivity in the rightpostcentral gyrus and right supramarginal gyrus strength-ened from week 0 to week 2 and decreased from week 2 toweek 4 The findings in these case studies are very similarto the above results and the functional connectivity changesbased on the resting-state EEG recordings are associated withmotor skill learning Another similar study also demonstratesthat the frontoparietal network connectivity increased oneweek after two brief motor training sessions in a dynamicbalancing task [30] and there is an association betweenstructural greymatter alterations and functional connectivitychanges in prefrontal and supplementary motor areas TheGSI is a synchronization method of reflecting the multichan-nel synchronization strength As shown in Figure 3 the GSIvalues of the alpha rhythm decreased in varying degrees overthe frontal and temporal regions increased over the centralregion and decreased over the whole brain for all cases aftertwo weeks training The frontal and temporal regions areassociated with cognition (ie attention and planning) andthe central region is motor related Because the Pilates canimprove the balance control and muscle strength [7] theGSI of alpha rhythm in the frontal and temporal regionsdecreased when the subjects were in the resting state inwhich the subjects were in a very relaxed condition withoutattention and planning procession The reduction of thesynchronization strength in those regions can support whatis mentioned above This study demonstrates that the Pilatestraining may improve the function of control

Acknowledgments

This research was funded in part by the National ScienceFund forDistinguished Young Scholars (61025019) and by theNational Natural Science Foundation of China (81271422)

References

[1] K Caldwell M Harrison M Adams and N T Triplett ldquoEffectof Pilates and taiji quan training on self-efficacy sleep qualitymood and physical performance of college studentsrdquo Journal ofBodywork and Movement Therapies vol 13 no 2 pp 155ndash1632009

[2] V Gladwell S Head M Haggar and R Beneke ldquoDoes aprogram of pilates improve chronic non-specific low backpainrdquo Journal of Sport Rehabilitation vol 15 no 4 pp 338ndash3502006

[3] N H Turner ldquoSimple Pilates techniques for back and abdomenmusclesrdquo Exercise Pilates amp Yoga 2009 httpwwwheliumcom

[4] K S Keays S R Harris J M Lucyshyn and D L MacIntyreldquoEffects of pilates exercises on shoulder range of motion painmood and upper-extremity function in women living withbreast cancer a pilot studyrdquo Physical Therapy vol 88 no 4 pp494ndash510 2008

[5] D Curnow D Cobbin J Wyndham and S T B Choy ldquoAlteredmotor control posture and the Pilates method of exerciseprescriptionrdquo Journal of Bodywork and Movement Therapiesvol 13 no 1 pp 104ndash111 2009

[6] E G Johnson A Larsen H Ozawa C A Wilson and KL Kennedy ldquoThe effects of Pilates-based exercise on dynamicbalance in healthy adultsrdquo Journal of Bodywork and MovementTherapies vol 11 no 3 pp 238ndash242 2007

[7] J M Schroeder J A Crussemeyer and S J Newton ldquoFlexibiltyand heart rate response to an acute Pilates reformer sessionrdquoMedicine and Science in Sports and Exercise vol 34 no 5 articleS258 2002

[8] N A Segal J Hein and J R Basford ldquoThe effects of pilatestraining on flexibility and body composition an observationalstudyrdquo Archives of Physical Medicine and Rehabilitation vol 85no 12 pp 1977ndash1981 2004

[9] C Lange V B Unnithan E Larkam and P M Latta ldquoMax-imizing the benefits of Pilates-inspired exercise for learningfunctional motor skillsrdquo Journal of Bodywork and MovementTherapies vol 4 no 2 pp 99ndash108 2000

[10] B J May ldquoMobility training for the older adultrdquo Topics inGeriatric Rehabilitation vol 19 no 3 pp 191ndash198 2003

[11] W McNeill ldquoDecision making in Pilatesrdquo Journal of Bodyworkand Movement Therapies vol 15 no 1 pp 103ndash107 2011

[12] W McNeill ldquoNeurodynamics for Pilates teachersrdquo Journal ofBodywork and Movement Therapies vol 16 no 3 pp 353ndash3582012

[13] A Delorme and S Makeig ldquoEEGLAB an open source toolboxfor analysis of single-trial EEG dynamics including indepen-dent component analysisrdquo Journal of NeuroscienceMethods vol134 no 1 pp 9ndash21 2004

[14] J E Seem ldquoUsing intelligent data analysis to detect abnormalenergy consumption in buildingsrdquo Energy and Buildings vol 39no 1 pp 52ndash58 2007

[15] D Cui X Liu Y Wan and X Li ldquoEstimation of genuine andrandom synchronization in multivariate neural seriesrdquo NeuralNetworks vol 23 no 6 pp 698ndash704 2010

[16] K T Dolan and M L Spano ldquoSurrogate for nonlinear timeseries analysisrdquo Physical Review E vol 64 no 4 part 2 ArticleID 046128 6 pages 2001

[17] V K Lim J P Hamm W D Byblow and I J Kirk ldquoDecreaseddesychronisation during self-paced movements in frequency


bands involving sensorimotor integration and motor function-ing in Parkinsonrsquos diseaserdquo Brain Research Bulletin vol 71 no1ndash3 pp 245ndash251 2006

[18] E A Golubeva Individual Characteristics of Human MemoryA Psychophysiological Study Pedagogika Moscow Russia 1980

[19] T Liu J Shi D Zhao and J Yang ldquoThe relationship betweenEEG band power cognitive processing and intelligence inschool-age childrenrdquo Psychology Science Quarterly vol 50 no2 pp 259ndash268 2008

[20] A Anokhin and F Vogel ldquoEEG 120572 rhythm frequency andintelligence in normal adultsrdquo Intelligence vol 23 no 1 pp 1ndash141996

[21] R G SchmidW S Tirsch andH Scherb ldquoCorrelation betweenspectral EEG parameters and intelligence test variables inschool-age childrenrdquo Clinical Neurophysiology vol 113 no 10pp 1647ndash1656 2002

[22] WKlimesch ldquoEEG120572 and theta oscillations reflect cognitive andmemory performance a review and analysisrdquo Brain ResearchReviews vol 29 no 2-3 pp 169ndash195 1999

[23] R W Thatcher D North and C Biver ldquoEEG and intelligencerelations between EEG coherence EEG phase delay and powerrdquoClinical Neurophysiology vol 116 no 9 pp 2129ndash2141 2005

[24] Y W Shin T H Ha S Y Kim and J S Kwon ldquoAssociationbetween EEG 120572 power and visuospatial function in obsessive-compulsive disorderrdquo Psychiatry and Clinical Neurosciences vol58 no 1 pp 16ndash20 2004

[25] ODevinsky S Sato R A Conwit andM B Schapiro ldquoRelationof EEG 120572 background to cognitive function brain atrophyand cerebral metabolism in Downrsquos syndrome Age-specificchangesrdquo Archives of Neurology vol 47 no 1 pp 58ndash62 1990

[26] D Arnaldi G Rodriguez and A Picco ldquoBrain functional net-work in Alzheimerrsquos disease diagnostic markers for diagnosisand monitoringrdquo International Journal of Alzheimerrsquos Diseasevol 2011 Article ID 481903 10 pages 2011

[27] S Akpinar ldquoThe primary restless legs syndrome pathogene-sis depends on the dysfunction of EEG 120572 activityrdquo MedicalHypotheses vol 60 no 2 pp 190ndash198 2003

[28] C Babiloni N Marzano M Iacoboni et al ldquoResting statecortical rhythms in athletes a high-resolution EEG studyrdquoBrainResearch Bulletin vol 81 no 1 pp 149ndash156 2010

[29] L Ma S Narayana D A Robin P T Fox and J XiongldquoChanges occur in resting state network ofmotor system during4 weeks of motor skill learningrdquo NeuroImage vol 58 no 1 pp226ndash233 2011

[30] M Taubert G Lohmann D S Margulies A Villringer andP Ragert ldquoLong-term effects of motor training on resting-statenetworks and underlying brain structurerdquo NeuroImage vol 57no 4 pp 1492ndash1498 2011


Research ArticleFast Discriminative Stochastic Neighbor Embedding Analysis

Jianwei Zheng Hong Qiu Xinli Xu Wanliang Wang and Qiongfang Huang

School of Computer Science and Technology Zhejiang University of Technology Hangzhou 310023 China

Correspondence should be addressed to Jianwei Zheng zjwzjuteducn

Received 9 February 2013 Accepted 22 March 2013


Copyright copy 2013 Jianwei Zheng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Feature is important for many applications in biomedical signal analysis and living system analysis A fast discriminative stochasticneighbor embedding analysis (FDSNE) method for feature extraction is proposed in this paper by improving the existing DSNEmethodThe proposed algorithm adopts an alternative probability distributionmodel constructed based on itsK-nearest neighborsfrom the interclass and intraclass samples Furthermore FDSNE is extended to nonlinear scenarios using the kernel trick andthen kernel-based methods that is KFDSNE1 and KFDSNE2 FDSNE KFDSNE1 and KFDSNE2 are evaluated in three aspectsvisualization recognition and elapsed time Experimental results on several datasets show that compared with DSNE and MSNPthe proposed algorithm not only significantly enhances the computational efficiency but also obtains higher classification accuracy

1 Introduction

In recent years dimensional reduction which can reduce thecurse of dimensionality [1] and remove irrelevant attributes inhigh-dimensional space plays an increasingly important rolein many areas It promotes the classification visualizationand compression of the high dimensional data In machinelearning dimension reduction is used to reduce the dimen-sion by mapping the samples from the high-dimensionalspace to the low-dimensional spaceThere aremany purposesof studying it firstly to reduce the amount of storage sec-ondly to remove the influence of noise thirdly to understanddata distribution easily and last but not least to achieve goodresults in classification or clustering

Currently many dimensional reduction methods havebeen proposed and they can be classified variously from dif-ferent perspectives Based on the nature of the input datathey are broadly categorized into two classes linear subspacemethods which try to find a linear subspace as feature spaceso as to preserve certain kind of characteristics of observeddata and nonlinear approaches such as kernel-based tech-niques and geometry-based techniques from the class labelsrsquoperspective they are divided into supervised learning andunsupervised learning furthermore the purpose of the for-mer is tomaximize the recognition rate between classes whilethe latter is for making the minimum of information loss Inaddition judging whether samples utilize local information

or global information we divide them into local method andglobal method

We briefly introduce several existing dimensional reduc-tion techniques In the main linear techniques principalcomponent analysis (PCA) [2] aims at maximizing the vari-ance of the samples in the low-dimensional representationwith a linear mapping matrix It is global and unsupervisedDifferent from PCA linear discriminant analysis (LDA) [3]learns a linear projection with the assistance of class labelsIt computes the linear transformation by maximizing theamount of interclass variance relative to the amount of intra-class variance Based on LDAmarginal fisher analysis (MFA)[4] local fisher discriminant analysis (LFDA) [5] and max-min distance analysis (MMDA) [6] are proposed All of thethree are linear supervised dimensional reduction methodsMFA utilizes the intrinsic graph to characterize the intraclasscompactness and uses meanwhile the penalty graph to char-acterize interclass separability LFDA introduces the localityto the LFD algorithm and is particularly useful for samplesconsisting of intraclass separate clusters MMDA considersmaximizing the minimum pairwise samples of interclass

To deal with nonlinear structural data which can often befound in biomedical applications [7ndash10] a number of nonlin-ear approaches have been developed for dimensional reduc-tion Among these kernel-based techniques and geometry-based techniques are two hot issues Kernel-based techniques


attempt to obtain the linear structure of nonlinearly dis-tributed data bymapping the original inputs to a high-dimen-sional feature space For instance kernel principal compo-nent analysis (kernel PCA) [11] is the extension of PCA usingkernel tricks Geometry-based techniques in general areknown as manifold learning techniques such as isometricmapping (ISOMAP) [12] locally linear embedding (LLE)[13] Laplacian eigenmap (LE) [14] Hessian LLE (HLLE) [15]and local tangent space alignment (LTSA) [16] ISOMAPis used for manifold learning by computing the pairwisegeodesic distances for input samples and extending multi-dimensional scaling LLE exploits the linear reconstructionsto discover nonlinear structure in high-dimensional spaceLE first constructs an undirected weighted graph and thenrecovers the structure of manifold by graph manipulationHLLE is based on sparse matrix techniques As for LTSAit begins by computing the tangent space at every point andthen optimizes to find an embedding that aligns the tangentspaces

Recently stochastic neighbor embedding (SNE) [17] andextensions thereof have become popular for feature extrac-tionThe basic principle of SNE is to convert pairwise Euclid-ean distances into probabilities of selecting neighbors tomodel pairwise similarities As extension of SNE 119905-SNE [18]uses Studentrsquos 119905-distribution tomodel pairwise dissimilaritiesin low-dimensional space and it alleviates the optimizationproblems and the crowding problem of SNE by the methodsbelow (1) it uses a symmetrized version of the SNE cost func-tion with simpler gradients that was briefly introduced byCook et al [19] and (2) it employs a heavy-tailed distributionin the low-dimensional space Subsequently Yang et al [20]systematically analyze the characteristics of the heavy-taileddistribution and the solutions to crowding problem Morerecently Wu et al [21] explored how to measure similarityon manifold more accurately and proposed a projectionapproach called manifold-oriented stochastic neighbor pro-jection (MSNP) for feature extraction based on SNE and 119905-SNE MSNP employs Cauchy distribution rather than stan-dard Studentrsquos 119905-distribution used in 119905-SNE In addition forthe purpose of learning the similarity on manifold with highaccuracy MSNP uses geodesic distance for characterizingdata similarityThoughMSNP has many advantages in termsof feature extraction there is still a drawback in itMSNP is anunsupervised method and lacks the idea of class label so it isnot suitable for pattern identification To overcome the disad-vantage of MSNP we have done some preliminary work andpresented amethod called discriminative stochastic neighborembedding analysis (DSNE) [22] DSNE effectively resolvesthe problems above but since it selects all the training sam-ples as their reference points it has high computational costand is thus computationally infeasible for the large-scale clas-sification tasks with high-dimensional features [23 24] Onthe basis of our previous research we present amethod calledfast discriminative stochastic neighbor embedding analysis(FDSNE) to overcome the disadvantages of DSNE in thispaper

The rest of this paper is organized as follows in Section 2we introduce in detail the proposed FDSNE and brieflycompare it with MSNP and DSNE in Section 3 Section 4

gives the nonlinear extension of FDSNE Furthermore exper-iments on various databases are presented in Section 5 Final-ly Section 6 concludes this paper and several issues for futureworks are described

2 Fast Discriminative Stochastic NeighborEmbedding Analysis

Consider a labeled data samples matrix as

X = x11 x1

1198731 x21 x2

1198732 x119862

1 x119862

119873119862 (1)

where x119888119894isin 119877119889 is a 119889-dimensional sample and means the 119894th

sample in the 119888th class 119862 is the number of sample classes119873119888

is the number of samples in the 119888th class and119873 = 1198731+1198732+

sdot sdot sdot + 119873119862

In fact the basic principle of FDSNE is the same as 119905-SNE which is to convert pairwise Euclidean distances intoprobabilities of selecting neighbors to model pairwise sim-ilarities [18] Since the DSNE selects all the training samplesas its reference points it has high computational cost andis thus computationally infeasible for the large-scale classi-fication tasks with high-dimensional features So accordingto the KNN classification rule we propose an alternativeprobability distribution function which makes the label oftarget sample determined by its first 119870-nearest neighbors inFDSNE In this paper NH

119897(x119894) andNM

119897(x119894) are definedThey

respectively denote the 119897th-nearest neighbor of x119894from the

same class and the different classes in the transformed spaceMathematically the joint probability 119901

119894119895is given by

119901119894119895=

exp (minus119889211989411989521205822)

sum119905isin119867119898

exp (minus119889211989811990521205822)

forall119895 isin 119867119894

exp (minus119889211989411989521205822)

sum119905isin119872119898

exp (minus119889211989811990521205822)

forall119895 isin 119872119894

0 otherwise

(2)

In formula (2) 119889119894119895= x119894minus x119895 = radic(x

119894minus x119895)119879(x119894minus x119895) is the

Euclidian distance between two samples x119894and x119895 the param-

eter 120582 is the variance parameter of Gaussian which deter-mines the value of 119901

119894119895 119867119894= 119895 | 1 le 119895 le 119873 1 le 119894 le 119873

x119895= NH

119896(x119894) and 1 le 119896 le 119870

1 119867119898= 119905 | 1 le 119905 le 119873 1 le

119898 le 119873 x119905= NH

119896(x119898) and 1 le 119896 le 119870

1 119872119894= 119895 | 1 le

119895 le 119873 1 le 119894 le 119873 x119895= NH

119896(x119894) and 1 le 119896 le 119870

2 and

119872119898= 119905 | 1 le 119905 le 119873 1 le 119898 le 119873 x

119905= NH

119896(x119898) and

1 le 119896 le 1198702 and then the denominator in formula (2) means

all of the reference points under selection from the same classor the different classes In particular the joint probability 119901

119894119895

not only keeps symmetrical characteristics of the probabilitydistribution matrix but also makes the probability value ofinterclass data to be 1 and the same for intraclass data

For low-dimensional representations FDSNE uses coun-terparts y

119894and y119895of the high-dimensional datapoints x

119894and


x119895 It is possible to compute a similar joint probability via the

following expression

119902119894119895=

(1 + 1198892

119894119895(A))minus1

sum119905isin119867119898

(1 + 1198892119898119905(A))minus1

forall119895 isin 119867119894

(1 + 1198892

119894119895(A))minus1

sum119905isin119872119898

(1 + 1198892119898119905(A))minus1

forall119895 isin 119872119894

0 otherwise

(3)

In what follows we introduce the transformation by a lin-ear projection y

119894= Ax119894(A isin R119903times119889) so that 119889

119894119895(A) = y

119894minus

y119895 = Ax

119894minusAx119895 = radic(x

119894minus x119895)119879A119879A(x

119894minus x119895)Then by simple

algebra formulation formula (3) has the following equivalentexpression

119902119894119895

=

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119905isin119867119898

(1 + (x119898minus x119905)119879A119879A (x

119898minus x119905))minus1

forall119895 isin 119867119894

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119905isin119872119898

(1 + (x119898minus x119905)119879A119879A (x


forall119895 isin 119872119894

0 otherwise(4)

Note that all data have the intrinsic geometry distributionand there is no exception for intraclass samples and interclasssamples Then the same distribution is required to hold infeature space Since the Kullback-Leiber divergence [25] iswildly used to quantify the proximity of two probabilitydistributions we choose it to build our penalty function hereBased on the above definition the function can be formulatedas

min119862 (A) = sum

forall119895isin119867119894

119901119894119895log

119901119894119895

119902119894119895

+ sum

forall119895isin119872119894

119901119894119895log

119901119894119895

119902119894119895

(5)

In this work we use the conjugate gradient method tominimize119862(A) In order tomake the derivation less clutteredwe first define four auxiliary variables 119908

119894119895 119906119894119895 119906119867

119894119895 and 119906119872

119894119895

as

119908119894119895= [1 + (x

119894minus x119895)119879

A119879A (x119894minus x119895)]

minus1

119906119894119895= (119901119894119895minus 119902119894119895)119908119894119895

119906119867

119894119895=

119906119894119895

forall119895 isin 119867119894

0 otherwise

119906119872

119894119895=

119906119894119895

forall119895 isin 119872119894

0 otherwise

(6)

Then differentiating119862(A)with respect to the transforma-tion matrix A gives the following gradient which we adoptfor learning

119889119862 (A)119889 (A)

= sum

forall119895isin119867119894

119901119894119895

119902119894119895

(119902119894119895)1015840

+ sum

forall119895isin119872119894

119901119894119895

119902119894119895

(119902119894119895)1015840

= 2A[

[

sum

forall119895isin119867119894

119901119894119895

(x119894minus x119895) (x119894minus x119895)119879

1 + (x119894minus x119895)119879

A119879A (x119894minus x119895)

]

]

minus 2A[

[

sum

forall119895isin119867119894

119901119894119895( sum

119905isin119867119898

(1 + (x119898minus x119905)119879A119879A (x


times (x119898minus x119905) (x119898minus x119905)119879)

times( sum

119905isin119867119898

(1 + (x119898minus x119905)119879A119879A (x


)

minus1

]

]

+ 2A[

[

sum

forall119895isin119872119894

119901119894119895

(x119894minus x119895) (x119894minus x119895)119879

1 + (x119894minus x119895)119879

A119879A (x119894minus x119895)

]

]

minus 2A[

[

sum

forall119895isin119872119894

119901119894119895( sum

119905isin119872119898

(1 + (x119898minus x119905)119879A119879A (x



times( sum

119905isin119872119898

(1 + (x119898minus x119905)119879A119879A (x


)

minus1

]

]

= 2A[

[

sum

forall119895isin119867119894

119901119894119895119908119894119895(x119894minus x119895) (x119894minus x119895)119879

minus sum

119905isin119867119898

119902119898119905119908119898119905(x119898minus x119905) (x119898minus x119905)119879]

+ 2A[

[

sum

forall119895isin119872119894

119901119894119895119908119894119895(x119894minus x119895) (x119894minus x119895)119879

minus sum

119905isin119872119898

119902119898119905119908119898119905(x119898minus x119905) (x119898minus x119905)119879]

= 2A[

[

sum

forall119895isin119867119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879

+ sum

forall119895isin119872119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879]

]

(7)


Let U119867 be the 119873 order matrix with element 119906119867119894119895 and let

U119872 be the 119873 order matrix with element 119906119872119894119895 Note that U119867

andU119872 are symmetricmatrices thereforeD119867 can be definedas a diagonal matrix that each entry is column (or row) sumof U119867 and the same for D119872 that is D119867

119894119894= sum119895U119867119894119895and D119872

119894119894=

sum119895U119872119894119895 With this definition the gradient expression (7) can

be reduced to

119889119862 (A)119889 (A)

= 2A

sum

forall119895isin119867119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879

+ sum

forall119895isin119872119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879

= 2A

( sum

forall119895isin119867119894

119906119894119895x119894x119879119894+ sum

forall119895isin119867119894

119906119894119895x119895x119879119895

minus sum

forall119895isin119867119894

119906119894119895x119894x119879119895minus sum

forall119895isin119867119894

119906119894119895x119895x119879119894)

+ ( sum

forall119895isin119872119894

119906119894119895x119894x119879119894+ sum

forall119895isin119872119894

119906119894119895x119895x119879119895

minus sum

forall119895isin119872119894

119906119894119895x119894x119879119895minus sum

forall119895isin119872119894

119906119894119895x119895x119879119894)

= 4A (XD119867X119879 minus XU119867X119879)

+ (XD119872X119879 minus XU119872X119879)

= 4A X (D119867 minus U119867 +D119872 minus U119872)X119879

(8)

Once the gradient is calculated our optimal problem (5)can be solved by an iterative procedure based on the conjugategradientmethodThedescription of FDSNE algorithm can begiven by the following

Step 1 Collect the sample matrix X with class labels andset 119870-nearest neighborhood parameter 119870

1 1198702 the variance

parameter 120582 and the maximum iteration times119872119905

Step 2 Compute the pairwise Euclidian distance for X andcompute the joint probability 119901

119894119895by utilizing formula (2) and

class labels

Step 3 (set 119905 = 1 119872119905) We search for the solution in loopfirstly compute the joint probability 119902

119894119895by utilizing formula

(4) then compute gradient 119889119862(A)119889(A) by utilizing formula(8) finally update A119905 based on A119905minus1 by conjugate gradientoperation

Step 4 Judge whether 119862119905 minus 119862119905minus1 lt 120576 (in this paper we take120576 = 1119890 minus 7) converges to a stable solution or 119905 reaches the

maximum value 119872119905 If these prerequisites are met Step 5 isperformed otherwise we repeat Step 3

Step 5 Output A = A119905

Hereafter we call the proposed method as fast discrimi-native stochastic neighbor embedding analysis (FDSNE)

3 Comparison with MSNP and DSNE

MSNP is derived from SNE and 119905-SNE and it is a linearmethod and has nice properties such as sensitivity to non-linear manifold structure and convenience for feature extrac-tion Since the structure of MSNP is closer to that of FDSNEwe briefly compare FDSNE with MSNP and DSNE in thissection

FDSNE MSNP and DSNE use different probability dis-tributions to determine the reference points The differencecan be explained in the following aspects

Firstly MSNP learns the similarity relationship of thehigh-dimensional samples by estimating neighborhood dis-tribution based on geodesic distance metric and the samedistribution is required in feature space Then the linear pro-jection matrix A is used to discover the underlying structureof data manifold which is nonlinear Finally the Kullback-Leibler divergence objective function is used to keep pair-wise similarities in feature space So the probability distribu-tion function of MSNP and its gradient used for learning arerespectively given by

119901119894119895=

exp (minus119863geo1198941198952)

sum119896 = 119894

exp (minus119863geo1198941198962)

119902119894119895=

[1205742+ (x119894minus x119895)119879

A119879A (x119894minus x119895)]

minus1

sum119896 = 119897

[1205742 + (x119896minus x119897)119879A119879A(x

119896minus x119897)]minus1

min119862 (A) = sum119894119895

119901119894119895log

119901119894119895

119902119894119895

(9)

where 119863geo119894119895

is the geodesic distance for x119894and x119895and 120574 is the

freedom degree parameter of Cauchy distributionDSNE selects the joint probability to model the pair-

wise similarities of input samples with class labels It alsointroduces the linear projection matrix A as MSNP The costfunction is constructed to minimize the intraclass Kullback-Leibler divergence as well as to maximize the interclass KLdivergences Its probability distribution function and gra-dient are respectively given as by

119901119894119895=

exp (minus10038171003817100381710038171003817x119894 minus x119895

10038171003817100381710038171003817

2

21205822)

sum119888119896=119888119897


1003817100381710038171003817221205822)

if 119888119894= 119888119895


10038171003817100381710038171003817

2

21205822)

sum119888119896 =119888119898


1003817100381710038171003817221205822)

else


119902119894119895=

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119888119896=119888119897

(1 + (x119896minus x119897)119879A119879A (x


if 119888119894= 119888119895

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119888119896 =119888119898

(1 + (x119896minus x119898)119879A119879A (x


else

min119862 (A) = sum

119888119894=119888119895

119901119894119895log

119901119894119895

119902119894119895

+ sum

119888119894 =119888119896

119901119894119896log

119901119894119896

119902119894119896

(10)

Note that on the basis of the DSNE FDSNEmakes full use ofclass label which not only keeps symmetrical characteristicsof the probability distribution matrix but also makes theprobability value of interclass data and intraclass data to be1 and it can effectively overcome large interclass confusiondegree in the projected subspace

Secondly it is obvious that the selection of reference pointin MSNP or DSNE is related to all training samples whileFDSNEonly uses the first119870-nearest neighbors of each samplefrom all classes In other words we propose an alternativeprobability distribution function to determine whether x

119894

would pick x119895as its reference point or not Actually the

computation of gradient during the optimization processmainly determines the computational cost of MSNP andDSNE So their computational complexity can be written as119874(2119903119873119889+119873

2119889) in each iteration Similarly the computational

complexity of FDSNE is 119874(2119903119873119889 + 119870119873119889) in each iterationwhere 119870 = 119870

1+ 1198702 It is obvious that 119870 ≪ 119873 Therefore

FDSNE is faster thanMSNP andDSNE during each iteration

4 Kernel FDSNE

As a bridge from linear to nonlinear kernel method emergedin the early beginning of the 20th century and its applica-tions in pattern recognition can be traced back to 1964 Inrecent years kernel method has attracted wide attention andnumerous researchers have proposed various theories andapproaches based on it

The principle of kernel method is a mapping of the datafrom the input space119877119889 to a high-dimensional space119865 whichwe will refer to as the feature space by nonlinear functionData processing is then performed in the feature space andthis can be expressed solely in terms of inner product inthe feature space Hence the nonlinear mapping need notbe explicitly constructed but can be specified by definingthe form of the inner product in terms of a Mercer kernelfunction 120581

Obviously FDSNE is a linear feature dimensionality re-duction algorithm So the remainder of this section is devotedto extend FDSNE to a nonlinear scenario using techniques ofkernel methods Let

120581 (x119894 x119895) = ⟨120593 (x

119894) 120593 (x

119895)⟩ (11)

which allows us to compute the value of the inner product in119865 without having to carry out the map

It should be noted that we use 120593119894to denote 120593(x

119894) for

brevity in the following Next we express the transformationA with

A = [

119873

sum

119894=1

119887(1)

119894120593119894

119873

sum

119894=1

119887(119903)

119894120593119894]

119879

(12)

We define B = [119887(1) 119887

(119903)]119879

and Φ = [1205931 120593

119873]119879

and then A = BΦ Based on above definition the Euclidiandistance between x

119894and x119895in the 119865 space is

119889119865

119894119895(A) = 10038171003817100381710038171003817A (120593

119894minus 120593119895)10038171003817100381710038171003817=10038171003817100381710038171003817BΦ (120593

119894minus 120593119895)10038171003817100381710038171003817

=10038171003817100381710038171003817B (119870119894minus 119870119895)10038171003817100381710038171003817= radic(119870

119894minus 119870119895)119879

B119879B (119870119894minus 119870119895)

(13)

where 119870119894= [120581(x

1 x119894) 120581(x

119873 x119894)]119879 is a column vector It

is clear that the distance in the kernel embedding space isrelated to the kernel function and the matrix B

In this section we propose two methods to construct theobjective function The first strategy makes B parameterizethe objective function Firstly we replace 119889

119894119895(A) with 119889119865

119894119895(A)

in formula (3) so that 1199011119894119895 1199021119894119895which are defined to be applied

in the high dimensional space 119865 can be written as

1199011

119894119895

=

exp (minus (119870119894119894+ 119870119895119895minus 2119870119894119895) 21205822)

sum119905isin119867119898

exp (minus (119870119898119898

+119870119905119905minus2119870119898119905) 21205822)

forall119895 isin 119867119894

exp (minus (119870119894119894+ 119870119895119895minus 2119870119894119895) 21205822)

sum119905isin119872119898

exp (minus (119870119898119898

+119870119905119905minus2119870119898119905) 21205822)

forall119895 isin 119872119894

0 otherwise

1199021

119894119895

=

(1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895))

minus1

sum119905isin119867119898

(1+(119870119898minus119870119905)119879B119879B (119870

119898minus119870119905))minus1

forall119895 isin 119867119894

(1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895))

minus1

sum119905isin119872119898

(1+(119870119898minus119870119905)119879B119879B (119870

119898minus119870119905))minus1

forall119895 isin 119872119894

0 otherwise(14)

Then we denote 119862(B) by modifying 119862(A) via substituting Awith B into the regularization term of formula (5) Finally


Figure 1 Sample images from COIL-20 dataset

Figure 2 Samples of the cropped images from USPS dataset

by the same argument as formula (7) we give the followinggradient

119889119862 (B)119889 (B)

= sum

forall119895isin119872119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

+ sum

forall119895isin119867119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

= 2B[[

sum

forall119895isin119867119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879

+ sum

forall119895isin119872119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879]

]

(15)

In order to make formula (15) easy to be comprehended1199081

119894119895 1199061119894119895 1199061119867119894119895 and 1199061119872

119894119895are given by

1199081

119894119895= [1 + (119870

119894minus 119870119895)119879

B119879B (119870119894minus 119870119895)]

minus1

1199061

119894119895= (119901119894119895minus 119902119894119895)1199081

119894119895

1199061119867

119894119895=

1199061

119894119895forall119895 isin 119867

119894

0 otherwise

1199061119872

119894119895=

1199061

119894119895forall119895 isin 119872

119894

0 otherwise

(16)

Meanwhile the gradient expression (15) can be reduced to

119889119862 (B)119889 (B)

= 2B

sum

forall119895isin119867119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879

+ sum

forall119895isin119872119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879

Figure 3 Sample face images from ORL dataset

= 4B (KD1119867K119879 minus KU1119867K119879)

+ (KD1119872K119879 minus KU1119872K119879)

= 4B K (D1119867 minus U1119867 +D1119872 minus U1119872)K119879 (17)

where U1119867 is the119873 order matrix with element 1199061119867119894119895 and U119872

is the 119873 order matrix with element 1199061119872119894119895

Note that U1119867 andU1119872 are symmetric matrices therefore D1119867 can be definedas a diagonal matrix that each entry is column (or row) sumof U1119867 and the same for D1119872 that is D1119867

119894119894= sum119895U1119867119894119895

andD1119872119894119894

= sum119895U1119872119894119895

For convenience we name this kernel method as FKD-

SNE1Another strategy is that we let 119862119865(A) be the objective

function in the embedding space 119865 So its gradient can bewritten as

119889119862119865(A)

119889 (A)

= sum

forall119895isin119872119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

+ sum

forall119895isin119867119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

= 2[[

[

sum

forall119895isin119867119894

1199011

119894119895

B (119870119894minus 119870119895) (120593119894minus 120593119895)119879

(1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895))

]]

]

minus 2[

[

sum

forall119895isin119867119894

1199011

119894119895( sum

119905isin119867119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus2

timesB (119870119898minus 119870119905) (120593119898minus 120593119905)119879)

times( sum

119905isin119867119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus1

)

minus1

]

]

+ 2[

[

sum

forall119895isin119872119894

1199011

119894119895

B (119870119894minus 119870119895) (120593119894minus 120593119895)119879

1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895)

]

]

minus 2[

[

sum

forall119895isin119872119894

1199011

119894119895( sum

119905isin119872119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus2



(a) FKDSNE2 (b) FKDSNE1 (c) FDSNE

(d) MSNP (e) SNE (f) 119905-SNE

Figure 4 Visualization of 100 images from COIL-20 images dataset

times( sum

119905isin119872119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus1

)

minus1

]

]

= 2[

[

sum

forall119895isin119867119894

1199011

1198941198951199081

119894119895B119876(119870119894minus119870119895)119894119895

minus sum

119905isin119867119898

1199021

1198981199051199081

119898119905B119876(119870119898minus119870119905)119898119905

]

]

Φ

+ 2[

[

sum

forall119895isin119872119894

1199011

1198941198951199081

119894119895B119876(119870119894minus119870119895)119894119895

minus sum

119905isin119872119898

1199021

1198981199051199081

119898119905B119876(119870119898minus119870119905)119898119905

]

]

Φ

= 2[

[

sum

forall119895isin119867119894

1199061

119894119895B119876(119870119894minus119870119895)119894119895

+ sum

forall119895isin119872119894

1199061

119894119895B119876(119870119894minus119870119895)119894119895

]

]

Φ

(18)

in this form119876(119870119894minus119870119895)119894119895

can be regard as the119873times119873matrix withvector 119870

119894minus 119870119895in the 119894th column and vector 119870

119895minus 119870119894in the

119895th column and the other columns are all zerosThismethod is termed as FKDSNE2Note thatΦ is a con-

stant matrix Furthermore the observations of formula (18)make us know that updating thematrixA in the optimizationonly means updating the matrix B Additionally Φ does notneed to be computed explicitly Therefore we do not need toexplicitly perform the nonlinear map 120593(x) to minimize theobjective function 119862119865(A) The computational complexity of

FKDSNE1 and FKDSNE2 is respectively119874(21199031198732+119903119873119870) and119874(2119903119870119873 + 119903119873

2) in each iteration Hence it is obvious that

FKDSNE2 is faster than FKDSNE1 during each iteration

5 Experiments

In this section we evaluate the performance of our FDSNEFKDSNE1 and FKDSNE2 methods for feature extractionThree sets of experiments are carried out onColumbiaObjectImage Library (COIL-20) (httpwww1cscolumbiaeduCAVEsoftwaresoftlibcoil-20php) US Postal Service (USPS)(httpwwwcsnyuedusimroweisdatahtml) and ORL (httpwwwcam-orlcouk) face datasets to demonstrate theirgood behavior on visualization accuracy and elapsed timeIn the first set of experiments we focus on the visualization ofthe proposed methods which are compared with that of therelevant algorithms including SNE [17] 119905-SNE [18] andMSNP [21] In the second set of experiments we apply ourmethods to recognition task to verify their feature extractioncapability and compare them with MSNP and DSNE [22]Moreover the elapsed time of FDSNE FKDSNE1 FKDSNE2and DSNE is compared in the third set of experiments Inparticular the Gaussian RBF kernel 120581(x x1015840) = exp(minusxminusx1015840221205902) is chosen as the kernel function of FKDSNE1 andFKDSNE2 where 120590 is set as the variance of the trainingsample set of X




Figure 5 Visualization of 140 images from USPS handwritten digits dataset

51 COIL-20 USPS and ORL Datasets The datasets used inour experiments are summarized as follows

COIL-20 is a dataset of gray-scale images of 20 objectsThe images of each object were taken 5 degrees apart as theobject is rotated on a turntable and each object has 72 imagesThe size of each image is 40times40 pixels Figure 1 shows sampleimages from COIL-20 images dataset

USPS handwritten digit dataset includes 10 digit charac-ters and 1100 samples in total The original data format is of16 times 16 pixels Figure 2 shows samples of the cropped imagesfrom USPS handwritten digits dataset

ORL consists of gray images of faces from 40 distinctsubjects with 10 pictures for each subject For every subjectthe images were taken with varied lighting condition and dif-ferent facial expressions The original size of each imageis 112 times 92 pixels with 256 gray levels per pixel Figure 3illustrates a sample subject of ORL dataset

52 Visualization Using FDSNE FKDSNE1 and FKDSNE2We apply FDSNE FKDSNE1 and FKDSNE2 to visualizationtask to evaluate their capability of classification performanceThe experiments are carried out respectively on COIL-20USPS and ORL datasets For the sake of computational effi-ciency as well as noise filtering we first adjust the size of each

image to 32times32pixels onORL and thenwe select five samplesfromeach class onCOIL-20 fourteen samples fromeach classon USPS and five samples from each class on ORL

The experimental procedure is to extract a 20-dime-nsional feature for each image by FDSNE FKDSNE1 andFKDSNE2 respectively Then to evaluate the quality of fea-tures through visual presentation of the first two-dimensionalfeature

FDSNE FKDSNE1 and FKDSNE2 are compared withthree well known visualization methods for detecting classi-fication performance (1) SNE (2) 119905-SNE and (3) MSPNTheparameters are set as follows the 119870-nearest neighborhoodparameter of FDSNE FKDSNE1 and FKDSNE2 methods is1198701= ℎ minus 1 (let ℎ denote the number of training samples in

each class) 1198702= 40 for SNE and 119905-SNE the perplexity

parameter is perp = 20 and the iteration number is 119872119905 =

1000 for MSNP the degree freedom of Cauchy distributionis 120574 = 4 and the iteration number is 1000 as well

Figures 4 5 and 6 show the visual presentation resultsof FDSNE FKDSNE1 FKDSNE2 SNE 119905-SNE and MSNPrespectively on COIL-20 USPS and ORL datasets The vis-ual presentation is represented as a scatterplot in which a dif-ferent color determines different class information The fig-ures reveal that the three nearest-neighbor-based methods




Figure 6 Visualization of 200 face images from ORL faces dataset

10 20 30 40 50 6007

075

08

085

Dimensionality

Reco

gniti

on ra

te (

)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(a) ℎ = 5

10 20 30 40 50 60075

08

085

09

095

Dimensionality

Reco

gniti

on ra

te (

)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(b) ℎ = 10

Figure 7 Recognition rate () versus subspace dimension on COIL-20


FKDSNE2FKDSNE1FDSNE

DSNEMSNP

10 20 30 40 50 60065

07

075

08

085

Dimensionality

Reco

gniti

on ra

te (

)

(a) ℎ = 14

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

Reco

gniti

on ra

te (

)

10 20 30 40 50 6007

075

08

085

09

Dimensionality

(b) ℎ = 25

Figure 8 Recognition rate () versus subspace dimension on USPS

10 20 30 40 50 6006

065

07

075

08

085

Dimensionality

Reco

gniti

on ra

te (

)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(a) ℎ = 3

Reco

gniti

on ra

te (

)

10 20 30 40 50 6006

065

07

075

08

085

09

Dimensionality

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(b) ℎ = 5

Figure 9 Recognition rate () versus subspace dimension on ORL

that is FDSNE FKDSNE1 and FKDSNE2 give considerablybetter classification result than SNE 119905-SNE andMSNP on alldatasets for the separation between classes is quite obviousIn particular SNE and 119905-SNE not only get less separation forthe interclass data but also produce larger intraclass scatterFor MSNP it has smaller intraclass scatter but there existsan overlapping phenomenon among classes With regard toFDSNE FKDSNE1 and FKDSNE2 we can find from the fig-ures that FKDSNE1 shows the best classification performanceamong all the algorithms on ORL face dataset while noton the other two datasets COIL-20 and USPS thereinto theclassification performance of FKDSNE1 is inferior to FDSNE

on COIL-20 while on USPS it is inferior to FKDSNE2 Inaddition the clustering qualities and separation degree ofFKDSNE1 and FKDSNE2 are obviously better than that ofFDSNE

53 Recognition Using FDSNE FKDSNE1 and FKDSNE2 Inthis subsection we apply FDSNE FKDSNE1 and FKDSNE2to recognition task to verify their feature extraction capabilityNonlinear dimensional reduction algorithms such as SNEand 119905-SNE lack explicit projection matrix for the out-of-sample data which means they are not suitable for recogni-tion So we compare the proposed methods with DSNE and


10 20 30 40 50 60

10

20

30

40

50

Dimensionality

Elap

sed

time (

s)

FKDSNE2FKDSNE1

FDSNEDSNE

(a) ℎ = 5

10 20 30 40 50 60Dimensionality

Elap

sed

time (

s)

20

40

60

80

FKDSNE2FKDSNE1

FDSNEDSNE

(b) ℎ = 10

Figure 10 Elapsed time (seconds) versus subspace dimension on COIL-20

10 20 30 40 50 60

6

8

10

12

14

16

18

Dimensionality

Elap

sed

time (

s)

FKDSNE2FKDSNE1

FDSNEDSNE

(a) ℎ = 14

Elap

sed

time (

s)

10 20 30 40 50 60

25

30

35

40

DimensionalityFKDSNE2FKDSNE1

FDSNEDSNE

(b) ℎ = 25

Figure 11 Elapsed time (seconds) versus subspace dimension on USPS

MSNP both of them are linear methods and were provedto be better than existing feature extraction algorithms suchas SNE 119905-SNE LLTSA LPP and so on in [21 22] Theprocedure of recognition is described as follows firstly dividedataset into training sample set Xtrain and testing sample setXtest randomly secondly the training process for the optimalmatrixA or B is taken for FDSNE FKDSNE1 and FKDSNE2thirdly feature extraction is accomplished for all samplesusing A or B finally a testing image is identified by a near-est neighbor classifier The parameters are set as follows the119870-nearest neighborhood parameter119870

11198702in FDSNE FKD-

SNE1 and FKDSNE2 is 1198701= ℎ minus 1 119870

2= 40 for DSNE

the perplexity parameter is 120582 = 01 and the iteration numberis 119872119905 = 1000 for MSNP the freedom degree 120574 of Cauchydistribution in MSNP is determined by cross validation andthe iteration number is 1000 as well

Figure 7 demonstrates the effectiveness of different sub-space dimensions for COIL-20 ((a) ℎ = 5 (b) ℎ = 10)Figure 8 is the result of the experiment in USPS ((a) ℎ =

14 (b) ℎ = 25) and Figure 9 shows the recognition rateversus subspace dimension on ORL ((a) ℎ = 3 (b) ℎ = 5)The maximal recognition rate of each method and the corre-sponding dimension are given in Table 1 where the numberin bold stands for the highest recognition rate From Table 1


Elap

sed

time (

s)

10 20 30 40 50 60

5

10

15

20

25

30

35

40

Dimensionality

FKDSNE2FKDSNE1

FDSNEDSNE

(a) ℎ = 3

10 20 30 40 50 60

10

20

30

40

50

60

Dimensionality

FKDSNE2FKDSNE1

FDSNEDSNE

Elap

sed

time (

s)

(b) ℎ = 5

Figure 12 Elapsed time (seconds) versus subspace dimension on ORL

Table 1 The maximal recognition rates () versus the subspace dimension

COIL-20 h = 5 COIL-20 h = 10 USPS h = 14 USPS h = 25 ORL h = 3 ORL h = 5MSNP 08149 (32) 09063 (50) 07958 (38) 08395 (58) 07989 (59) 08690 (58)DSNE 08325 (36) 09130 (54) 08093 (50) 08522 (42) 08357 (42) 09150 (39)FDSNE 08396 (52) 09277 (54) 08150 (58) 08489 (59) 08279 (58) 09160 (39)FKDSNE1 08651 (22) 09575 (20) 08409 (26) 08848 (26) 08550 (26) 09405 (24)FKDSNE2 08689 (28) 09491 (22) 08585 (22) 09021 (28) 08470 (24) 09193 (20)

0 200 400 600 800 1000

Iteration number

Obj

ectiv

e fun

ctio

n va

lue (

log)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

minus7

minus6

minus4

minus5

Figure 13 Objective function value (log) versus iterative number onORL dataset

we can find that FKDSNE1 and FKDSNE2 outperformMSNP DSNE and FDSNE on COIL-20 USPS and ORL Ascan be seen FKDSNE1 and FKDSNE2 enhance the maximal

recognition rate for at least 2 compared with other threemethods Besides FKDSNE1 and FKDSNE2 achieve consid-erable recognition accuracy when feature dimension is 20 onthe three datasets It indicates that FKDSNE1 and FKDSNE2grasp the key character of face images relative to identificationwith a few features Though the maximal recognition rateof DSNE and FDSNE is closer to that of FKDSNE1 andFKDSNE2 on ORL dataset the corresponding dimension ofFKDSNE1 and FKDSNE2 is 20 while that of DSNE andFDSNE exceeds 30 From the essence of dimensional reduc-tion this result demonstrates that FDSNE and DSNE areinferior to FKDSNE1 and FKDSNE2

54 Analysis of Elapsed Time In this subsection we furthercompare the computational efficiency of DSNE FKDSNEFKDSNE1 and FKDSNE2The algorithmMSPN is not com-pared since its recognition rate is obviously worse than otheralgorithms The parameters of the experiment are the sameto Section 53 Figures 10 11 and 12 respectively show theelapsed time of four algorithms under different subspacedimensions on the three datasets It can be observed fromthe figures that FKDSNE2 has the lowest computational costamong the four algorithms while DSNE is much inferior toother nearest-neighbor-based algorithms on all datasets Par-ticularly on the COIL-20 dataset the elapsed time of FKD-SNE2 is more than 2 times faster than DSNE As for DSNE


and FDSNE the former is obviously slower than the latterBesides for the two kernel methods FKDSNE2 is notablyfaster than FKDSNE1 which confirms our discussion inSection 4

Furthermore kernel-based algorithms FKDSNE1 andFKDSNE2 can effectively indicate the linear structure onhigh-dimensional spaceTheir objective function can achievebetter values on desirable dimensions For instance Figure 13illustrates the objective function value ofMSNPDSNE FKD-SNE FKDSNE1 and FKDSNE2 versus iterative number onORL dataset It can be found that FKDSNE2 and FKDSNE1is close to the convergence value 1119890 minus 7 while FDSNE andDSNE only achieve 1119890 minus 6 and MSNP achieves 1119890 minus 54 whenthe iterative number is 400 It means that FKDSNE1 andFKDSNE2 can get the more precise objective function valuewith less iterative number compared with DSNE and FDSNEthat is to say that FKDSNE1 and FKDSNE2 can achieve thesame value by using forty percent of the elapsed time ofDSNEand FDSNE

6 Conclusion

On the basis of DSNE we present a method calledfast discriminative stochastic neighbor embedding analysis(FDSNE) which chooses the reference points in 119870-nearestneighbors of the target sample from the same class and thedifferent classes instead of the total training samples and thushas much lower computational complexity than that ofDSNE Furthermore since FDSNE is a linear feature dimen-sionality reduction algorithm we extend FDSNE to a nonlin-ear scenario using techniques of kernel trick and present twokernel-based methods FKDSNE1 and FKDSNE2 Experi-mental results onCOIL-20 USPS andORLdatasets show thesuperior performance of the proposed methods Our futurework might include further empirical studies on the learningspeed and robustness of FDSNE by using more extensiveespecially large-scale experiments It also remains importantto investigate acceleration techniques in both initializationand long-run stages of the learning

Acknowledgment

This project was partially supported by Zhejiang ProvincialNatural Science Foundation of China (nos LQ12F03011 andLQ12F03005)

References

[1] E Cherchi and C A Guevara ldquoA Monte Carlo experiment toanalyze the curse of dimensionality in estimating random coef-ficients models with a full variance-covariance matrixrdquo Trans-portation Research B vol 46 no 2 pp 321ndash332 2012

[2] M Turk and A Pentland ldquoEigenfaces for recognitionrdquo Journalof Cognitive Neuroscience vol 3 no 1 pp 71ndash86 1991

[3] S YanD Xu B ZhangH-J ZhangQ Yang and S Lin ldquoGraphembedding and extensions a general framework for dimen-sionality reductionrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 29 no 1 pp 40ndash51 2007

[4] P N Belhumeur J P Hespanha and D J Kriegman ldquoEigen-faces versus fisherfaces recognition using class specific linearprojectionrdquo IEEE Transactions on Pattern Analysis andMachineIntelligence vol 19 no 7 pp 711ndash720 1997

[5] M Sugiyama ldquoDimensionality reduction ofmultimodal labeleddata by local fisher discriminant analysisrdquo Journal of MachineLearning Research vol 8 pp 1027ndash1061 2007

[6] W Bian and D Tao ldquoMax-min distance analysis by using se-quential SDP relaxation for dimension reductionrdquo IEEE Trans-actions on Pattern Analysis andMachine Intelligence vol 33 no5 pp 1037ndash1050 2011

[7] Z Teng JHe et al ldquoCriticalmechanical conditions aroundneo-vessels in carotid atherosclerotic plaque may promote intra-plaque hemorrhagerdquoAtherosclerosis vol 223 no 2 pp 321ndash3262012

[8] Z Teng A J Degnan U Sadat et al ldquoCharacterization of heal-ing following atherosclerotic carotid plaque rupture in acutelysymptomatic patients an exploratory study using in vivo cardi-ovascular magnetic resonancerdquo Journal of Cardiovascular Mag-netic Resonance vol 13 article 64 2011

[9] C E Hann I Singh-Levett B L Deam J B Mander and J GChase ldquoReal-time system identification of a nonlinear four-sto-ry steel frame structure-application to structural health moni-toringrdquo IEEE Sensors Journal vol 9 no 11 pp 1339ndash1346 2009

[10] A Segui J P Lebaron and R Leverge ldquoBiomedical engineeringapproach of pharmacokinetic problems computer-aided designin pharmacokinetics and bioprocessingrdquo IEE ProceedingsD vol133 no 5 pp 217ndash225 1986

[11] FWu Y Zhong andQ YWu ldquoOnline classification frameworkfor data stream based on incremental kernel principal compo-nent analysisrdquo Acta Automatica Sinica vol 36 no 4 pp 534ndash542 2010

[12] J B Tenenbaum V de Silva and J C Langford ldquoA global geo-metric framework for nonlinear dimensionality reductionrdquo Sci-ence vol 290 no 5500 pp 2319ndash2323 2000

[13] S T Roweis and L K Saul ldquoNonlinear dimensionality reduc-tion by locally linear embeddingrdquo Science vol 290 no 5500pp 2323ndash2326 2000

[14] M Belkin and P Niyogi ldquoLaplacian eigenmaps for dimension-ality reduction and data representationrdquo Neural Computationvol 15 no 6 pp 1373ndash1396 2003

[15] H Li H Jiang R Barrio X Liao L Cheng and F Su ldquoIncre-mentalmanifold learning by spectral embeddingmethodsrdquoPat-tern Recognition Letters vol 32 no 10 pp 1447ndash1455 2011

[16] P Zhang H Qiao and B Zhang ldquoAn improved local tangentspace alignment method for manifold learningrdquo Pattern Recog-nition Letters vol 32 no 2 pp 181ndash189 2011

[17] GHinton and S Roweis ldquoStochastic neighbor embeddingrdquoAd-vances inNeural Information Processing Systems vol 15 pp 833ndash840 2002

[18] L van der Maaten and G Hinton ldquoVisualizing data using t-SNErdquo Journal of Machine Learning Research vol 9 pp 2579ndash2605 2008

[19] J A Cook I Sutskever AMnih andG E Hinton ldquoVisualizingsimilarity data with amixture ofmapsrdquo in Proceedings of the 11thInternational Conference on Artificial Intelligence and Statisticsvol 2 pp 67ndash74 2007

[20] Z R Yang I King Z L Xu and E Oja ldquoHeavy-tailed sym-metric stochastic neighbor embeddingrdquo Advances in Neural In-formation Processing Systems vol 22 pp 2169ndash2177 2009


[21] S Wu M Sun and J Yang ldquoStochastic neighbor projection onmanifold for feature extractionrdquoNeurocomputing vol 74 no 17pp 2780ndash2789 2011

[22] JWZhengHQiu Y B Jiang andWLWang ldquoDiscriminativestochastic neighbor embedding analysis methodrdquo Computer-Aided Design amp Computer Graphics vol 24 no 11 pp 1477ndash1484 2012

[23] C Cattani R Badea S Chen and M Crisan ldquoBiomedical sig-nal processing and modeling complexity of living systemsrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 298634 2 pages 2012

[24] X Zhang Y Zhang J Zhang et al ldquoUnsupervised clustering forlogo images using singular values region covariance matriceson Lie groupsrdquo Optical Engineering vol 51 no 4 Article ID047005 8 pages 2012

[25] P J Moreno P Ho and N Vasconcelos ldquoA Kullback-Leiblerdivergence based kernel for SVM classification in multimediaapplicationsrdquo Advances in Neural Information Processing Sys-tems vol 16 pp 1385ndash1393 2003


Research ArticleFractal Analysis of Elastographic Images forAutomatic Detection of Diffuse Diseases of SalivaryGlands Preliminary Results

Alexandru Florin Badea1 Monica Lupsor Platon2 Maria Crisan3 Carlo Cattani4

Iulia Badea5 Gaetano Pierro6 Gianpaolo Sannino7 and Grigore Baciut1

1 Department of Cranio-Maxillo-Facial Surgery University of Medicine and Pharmacy ldquoIuliu Hatieganurdquo Cardinal Hossu Street 37400 029 Cluj-Napoca Romania

2Department of Clinical Imaging University of Medicine and Pharmacy ldquoIuliu Hatieganurdquo Croitorilor Street 19-21400 162 Cluj-Napoca Romania

3 Department of Histology Pasteur 5-6 University of Medicine and Pharmacy ldquoIuliu Hatieganurdquo 400 349 Cluj-Napoca Romania4Department of Mathematics University of Salerno Via Ponte Don Melillo 84084 Fisciano Italy5 Department of Dental Prevention University of Medicine Pharmacy ldquoIuliu Hatieganurdquo Victor Babes Street400 012 Cluj-Napoca Romania

6Department of System Biology Phd School University of Salerno Via Ponte Don Melillo 84084 Fisciano Italy7 Department of Oral Health University of Rome Tor Vergata Viale Oxford 00100 Rome Italy

Correspondence should be addressed to Maria Crisan mcrisan7yahoocom

Received 10 March 2013 Accepted 12 April 2013


Copyright copy 2013 Alexandru Florin Badea et alThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

The geometry of some medical images of tissues obtained by elastography and ultrasonography is characterized in terms ofcomplexity parameters such as the fractal dimension (FD) It is well known that in any image there are very subtle details that are noteasily detectable by the human eye However in many cases like medical imaging diagnosis these details are very important sincethey might contain some hidden information about the possible existence of certain pathological lesions like tissue degenerationinflammation or tumors Therefore an automatic method of analysis could be an expedient tool for physicians to give a faultlessdiagnosisThe fractal analysis is of great importance in relation to a quantitative evaluation of ldquoreal-timerdquo elastography a procedureconsidered to be operator dependent in the current clinical practice Mathematical analysis reveals significant discrepancies amongnormal and pathological image patterns The main objective of our work is to demonstrate the clinical utility of this procedure onan ultrasound image corresponding to a submandibular diffuse pathology

1 Introduction

In some recent papers [1ndash4] the fractal nature of nucleotidedistribution in DNA has been investigated in order to classifyand compare DNA sequences and to single out some partic-ularities in the nucleotide distribution sometimes in order tobe used asmarkers for the existence of certain pathologies [5ndash9] Almost all these papers are motivated by the hypothesisthat changes in the fractal dimension might be taken asmarkers for the existence of pathologies since it is universallyaccepted nowadays that bioactivity and the biological systems

are based on some fractal nature organization [3 4 10ndash13]From amathematical point of view this could be explained bythe fact that the larger the number of interacting individualsthe more complex the corresponding system of interactionsis These hidden rules that lead to this complex fractaltopology could be some simple recursive rules typical of anyfractal-like structure which usually requires a large numberof recursions in order to fill the space

In recent years many papers [3ndash6 9 14 15] haveinvestigated the multi-fractality of biological signals such asDNA and the possible influence of the fractal geometry on


the functionality of DNA from a biological-chemical point ofview Almost all these papers concerning the multifractalityof biological signals are based on the hypothesis that thefunctionality and the evolution of tissuescellsDNA arerelated to and measured by the evolving fractal geometry(complexity) so that malfunctions and pathologies canbe linked with the degeneracy of the geometry during itsevolution time [5ndash7 16ndash18]

Fromamathematical point of view a fractal is a geometricobjectmainly characterized by the noninteger dimension andself-similarity so that a typical pattern repeats itself cyclicallyat different scales A more complex definition of a fractal isbased on the four properties self-similarity fine structureirregularities and noninteger dimension [19] The fractaldimension is a parameter which measures the relationshipbetween the geometric un-smoothness of the object and itsunderlying metric space Since it is a noninteger value it isusually taken as a measure of the unsmoothness thus beingimproperly related to the level of complexity or disorderFractality has been observed and measured in several fieldsof specialization in biology similar to those in pathology andcancer models [20 21] However only recently have beenmade some attempts to investigate the structural importanceof the ldquofractal naturerdquo of the DNA It has been observedin some recent papers that the higher FD corresponds tothe higher information complexity and thus to the evolutiontowards a pathological state [3 4]

In the following we will analyse the particularities ofthe fractal dimension focused on the pathological aspects ofsome tissuesmore specific those belonging to a submandibu-lar gland For the first time the FD is computed on imagesobtained by the new technology of elastographic imagingfocused on this salivary gland


21 Material A 55-year-old woman presented herself in theemergency room of the Maxilo-Facial Surgery Departmentfor acute pain and enlargement of the left submandibu-lar gland and was selected for ultrasound evaluation Theultrasound examination was performed using the ACUSONS2000 (Siemens) ultrasound equipment where the ARFI(acoustic radiation force impulse) and real-time elastographytechnique were implemented The ACUSON S2000 is apowerful non-invasive ultrasound based device which givesvery accurate B mode and Doppler images of tissues It hasbeen profitably used for the analysis of abdominal breastcardiac obstetrical and gynaecological imaging and also forsmall parts such as thyroid and vascular imaging

The patient was placed laying down and facing upwhile the transducer was placed in contact with skin onthe area of the right and then the left submandibular glandsuccessively The shear wave velocity within the right andthe left submandibular gland parenchyma was determinedfor each submandibular gland (in meterssecond) colourelastographic images were also acquired A colour map wasused where stiff tissues were coded in blue and soft tissues inredThese images were studied afterwards for fractal analysis

Figure 1 Gray scale ultrasonography of the submandibular gland(right side) The gland is enlarged (total volume around 12 cmc)with well-defined delineation inhomogeneous structure hypoe-choic area in the center (belongs to the hilum of the gland) andhyperechoic areas under the capsule (belong to the parenchyma)

Figure 1 represents a 2D ultrasound evaluation in a ldquogreyscalerdquo mode and Figure 2 represents a combination between2D ultrasonography and ldquocolour flowmaprdquo (CFM or ldquoduplexsonographyrdquo) From the first viewing we can easily detectby its enlargement the gland swelling (Figure 1) and thehyper vascular pattern (Figure 2) both of these pieces ofinformation being highly suggestive for the inflammationdiagnosis The combined clinical and ultrasound evaluationis conclusive for an acute inflammation of the submandibulargland Figures 3 and 5 (obtained on the right salivary swollengland) and Figures 4 and 6 (obtained on the left side normalgland) represent elastography in quantitative mode (Figures3 and 4) color mode (Figures 5 and 6) (ARFI tissue imagingmapping color)

22 Methods Concerning the fractal analysis in this sectionwe will summarize some definitions already given in [3]

23 Parameters for the Analysis of Complexity and FractalGeometry As a measure of the complexity and fractal geom-etry we will consider only the fractal dimension and regres-sion analysis (Shannon information entropy lacunarity andsuccolarity will be considered in a forthcoming paper)

Let 119901119909(119899) be the probability to find the value 119909 at the

position 119899 the fractal dimension is given by [3 4 22]

119863 =1

119873

119873

sum

119899=2

log 119901119909 (119899)

log 119899 (1)

In order to compute the FD we will make use of the glidingbox method on a converted black and white image Let 119878

119873

be a given black and white image (BW) with 1 and 0 incorrespondence with respectively black and white pixels wecan consider a gliding box of 119903-length so that

120583119903 (119896) =

119896+119903minus1

sum

119904=119896

Vlowastsh (2)


Figure 2 Colour coded Doppler ultrasonography (same case asFigure 1) In the central part of the gland there are vessels (blue andred according to the direction of the blood flow in relation to thetransducer) The amplitude and extension of the colour signal aresuggestive of hyperaemia (in this case it was an acute inflammationof the submandibular salivary gland)

Figure 3 Elastogram of the submandibular gland (on the rightside inflamed gland) using the ARFI procedureThemeasurementsare made in an area of glandular parenchyma in a predefinedrectangular area vessel free The ultrasound speed is 255msec

is the frequency of ldquo1rdquo within the box The correspondingprobability is

119901119903 (119896) =1

119903

119896+119903minus1

sum

119904=119896

Vlowastsh (3)

Then the boxmoves to the next position 119896+1 so that we obtainthe probability distribution

119901119903 (119896)119896=1119873 (4)

so that we can compute the frequency of ldquo1rdquo within the boxThe FD is computed on such gliding boxes through (1)

3 Results

31 Fractal Dimension for 2D Ultrasound and ElastographicImages Concerning the fractal dimension of the elasto-graphic images as given by (1) we can see (Table 1) that thehighest FD is shown by Figure 7 and lowest by the Figure 8

The images were analyzed in 8-bit using the Image Jsoftware (tools box counting)

Figure 4 Elastogram of the submandibular gland (left side normalgland) by means of ARFI procedure The sample rectangle ispositioned subscapular in a similar position as it was on the rightside glandThe ultrasound speed in the measured area is 136msec

Figure 5 Qualitative (black and white coded black is rigid white issoft) elastogram (ARFI procedure) of the submandibular inflamedgland (right side) The pathological area inside the gland is welldefined This area presents a high rigidity index in relation to theamplitude of the pathological process

The figures are referred to a patient with an acuteinflammation of the submandibular gland

Figure 1 shows a 2D ultrasound evaluation in grey scaleFigure 2 shows a 2D colour flow map evaluation (duplexsonography) Figures 3 and 4 were obtained by using themethod elastography ARFI-Siemens and they display quan-titative information The values of fractal dimension (FD) ofFigures 3 and 4 are similar and it is not possible to distinguishbetween pathological (Figure 3) and normal (Figure 4) statesThe Figures 5 and 6 are obtained through elastography ARFIwith qualitative information From the fractal analysis bythe box counting method we have noticed that the value ofFd is lower (1650) in Figure 5 (pathological condition) thanFigure 6 (normal state) Figures 7 (pathological state) and 8(normal state) were obtained through real time elastography

From the computations we can note that the highervalue of Fd belongs to the pathological state (1907) thussuggesting that the Fd increases during the evolution ofthe pathology (increasing degeneracy) Therefore from Fdanalysis is possible to distinguish between pathological stateand normal state of tissues by real time elastography becauseit is the better method to discriminate Fd values in a clearsharp way


Figure 6 Qualitative (black and white coded black is rigid white issoft) elastogram (ARFI procedure) of the normal gland (consideredto be the ldquowitnessrdquo on the left side) The dispersion of the vectors ofspeed is obvious There is no obvious compact hard parenchyma asin the right pathological gland (Figure 5)

Table 1 Fractal values

Type of image Fractal value2D evaluation ultrasound grey scale 1777Duplex sonography 1754ARFI (quantitative)mdashPs 1771ARFI (quantitative)mdashNs 1796ARFI (qualitative)mdashPs 1650ARFI (qualitative)mdashNs 1701Real-time elastographymdashPs 1907Real-time elastographymdashNs 1543Ps pathological state Ns normal situation

4 Discussion

Elastography is an ultrasonographic technique which appre-ciates tissue stiffness either by evaluating a colour map [2324] or by quantifying the shear wave velocity generated bythe transmission of an acoustic pressure into the parenchyma(ARFI technique) [25ndash27] In the first situation the visualiza-tion of the tissue stiffness implies a ldquoreal-timerdquo representationof the colour mode elastographic images overlapped on theconventional gray-scale images each value (from 1 to 255)being attached to a color The system uses a color map (red-green-blue) in which stiff tissues are coded in dark blueintermediate ones in shades of green softer tissues in yellowand the softest in red but the color scale may be reversed inrelation to how the equipment is calibratedDepending on thecolor and with the help of a special software several elasticityscores that correlate with the degree of tissue stiffness can becalculated [23] Numerous clinical applications using theseprocedures were introduced into routine practice many ofthem being focused on the detection of tumoral tissue inbreast thyroid and prostate

In the last years a new elastographic method basedon the ARFI technique (acoustic radiation force impulseimaging) is available on modern ultrasound equipmentThe ARFI technique consists in a mechanical stimulationof the tissue on which it is applied by the transmission of

Figure 7 Real-time elastography (qualitative colour coded elastog-raphy blue is rigid red is soft) obtained by the compression of theright submandibular gland The blue colour is in direct relation tothe rigid parenchyma which is considered to be pathological

Figure 8 Real-time elastography (qualitative colour coded elastog-raphy blue is rigid red is soft) obtained by the compression of theleft submandibular gland (normal) This is a normal pattern for thegland suggestive of parts of different elasticity

a short time acoustic wave (lt1ms) in a region of interestdetermined by the examiner perpendicular on the directionof the pressure waves and leading to a micronic scaleldquodislocationrdquo of the tissues Therefore in contrast with theusual ultrasonographic examination where the sound waveshave an axial orientation the shear waves do not interactdirectly with the transducer Furthermore the shear wavesare attenuated 10000 faster than the conventional ultrasoundwaves and therefore need a higher sensitivity in order tobe measured [25ndash29] Detection waves which are simulta-neously generated have a much lower intensity than thepressure acoustic wave (1 1000) The moment when thedetection waves interact with the shear waves representsthe time passed from the moment the shear waves weregenerated until they crossed the region of interest Theshear waves are registered in different locations at variousmoments and thus the shear wave velocity is automaticallycalculated the stiffer the organ the higher the velocity of theshear waves Therefore the shear wave velocity is actuallyconsidered to be an intrinsic feature of the tissue [25ndash29]In current clinical practice the same transducer is usedboth to generate the pressure acoustic wave and to registerthe tissue dislocation Since the technique is implemented


in the ultrasound equipment through software changes Bmode ultrasound examination color Doppler interrogationand ARFI images are all possible on the same machine [30]

Currently elastography is widely studied in relation todifferent clinical applications breast thyroid liver colon andprostate [29 31ndash36]The application in salivary gland pathol-ogy has been singularly considered at least in our literaturedatabase Some reports present the utility of elastography ina better delineation of tumors of these glands Applications ondiffuse disease are few although the importance of this kindof pathology is important Inflammations of salivary glandsoccur in many conditions and the incidence is significantThere is a need for accurate diagnosis staging and prognosisThe occurrence of complications is also very important Elas-tography represents a ldquovirtualrdquo way of palpation reproductiveand with possibility of quantification

Although there are several improvements the mainlimitation of elastography is the dependency of the procedureto the operatorrsquos experience This characteristic makes elas-tography vulnerable with a quite high amount of variationsof elastographic results and interpretation A more accurateanalysis of the elastographic picture based on very preciseevaluation as fractal analysis is an obvious step forward Inour preliminary study the difference between normal andpathologic submandibular tissue using the fractal analysiswas demonstrated Because of the very new technologiesaccessible in practice as elastography is and because of themathematical instruments available as fractal analysis of thepictures we are encouraged to believe that the ultrasoundprocedure might become operator independent and moreconfident for subtle diagnosis However a higher number ofpictures coming from different patients with diffuse diseasesin different stages of evolution are needed

5 Conclusion

In this work the multi-fractality of 2D and elastographicimages of diffuse pathological states in submandibular glandshas been investigated The corresponding FD has beencomputed and has shown that images with the highest FDcorrespond to the existence of pathology The extensionof this study with incrementing the number of ultrasoundimages and patients is needed to demonstrate the practicalutility of this procedure


The authors declare that there is no conflict of interestsconcerning the validity of this research with respect to somepossible financial gain

References

[1] V Anh G Zhi-Min and L Shun-Chao ldquoFractals in DNAsequence analysisrdquo Chinese Physics vol 11 no 12 pp 1313ndash13182002

[2] S V Buldyrev N V Dokholyan A L Goldberger et al ldquoAnal-ysis of DNA sequences using methods of statistical physicsrdquoPhysica A vol 249 no 1ndash4 pp 430ndash438 1998

[3] C Cattani ldquoFractals and hidden symmetries in DNArdquo Mathe-matical Problems in Engineering vol 2010 Article ID 507056 31pages 2010

[4] G Pierro ldquoSequence complexity of Chromosome 3 inCaenorhabditis elegansrdquo Advances in Bioinformatics vol 2012Article ID 287486 12 pages 2012

[5] V Bedin R L Adam B C S de Sa G Landman and K MetzeldquoFractal dimension of chromatin is an independent prognosticfactor for survival in melanomardquo BMC Cancer vol 10 article260 2010

[6] D P Ferro M A Falconi R L Adam et al ldquoFractalcharacteristics of May-Grunwald-Giemsa stained chromatinare independent prognostic factors for survival in multiplemyelomardquo PLoS ONE vol 6 no 6 Article ID e20706 2011

[7] K Metze R L Adam and R C Ferreira ldquoRobust variables intexture analysisrdquo Pathology vol 42 no 6 pp 609ndash610 2010

[8] K Metze ldquoFractal characteristics of May Grunwald Giemsastained chromatin are independent prognostic factors for sur-vival inmultiple myelomardquo PLoS One vol 6 no 6 pp 1ndash8 2011

[9] P Dey and T Banik ldquoFractal dimension of chromatin tex-ture of squamous intraepithelial lesions of cervixrdquo DiagnosticCytopathology vol 40 no 2 pp 152ndash154 2012

[10] R F Voss ldquoEvolution of long-range fractal correlations and 1fnoise in DNA base sequencesrdquo Physical Review Letters vol 68no 25 pp 3805ndash3808 1992

[11] R F Voss ldquoLong-range fractal correlations in DNA introns andexonsrdquo Fractals vol 2 no 1 pp 1ndash6 1992

[12] C A Chatzidimitriou-Dreismann and D Larhammar ldquoLong-range correlations in DNArdquo Nature vol 361 no 6409 pp 212ndash213 1993

[13] A Fukushima M Kinouchi S Kanaya Y Kudo and TIkemura ldquoStatistical analysis of genomic information long-range correlation in DNA sequencesrdquo Genome Informatics vol11 pp 315ndash3316 2000

[14] M Li ldquoFractal time series-a tutorial reviewrdquo MathematicalProblems in Engineering vol 2010 Article ID 157264 26 pages2010

[15] M Li and W Zhao ldquoQuantitatively investigating locally weakstationarity of modified multifractional Gaussian noiserdquo Phys-ica A vol 391 no 24 pp 6268ndash6278 2012

[16] F DrsquoAnselmi M Valerio A Cucina et al ldquoMetabolism andcell shape in cancer a fractal analysisrdquo International Journal ofBiochemistry and Cell Biology vol 43 no 7 pp 1052ndash1058 2011

[17] I Pantic L Harhaji-Trajkovic A Pantovic N T Milosevic andV Trajkovic ldquoChanges in fractal dimension and lacunarity asearly markers of UV-induced apoptosisrdquo Journal of TheoreticalBiology vol 303 no 21 pp 87ndash92 2012

[18] C Vasilescu D E Giza P Petrisor R Dobrescu I Popescu andV Herlea ldquoMorphometrical differences between resectable andnon-resectable pancreatic cancer a fractal analysisrdquoHepatogas-troentology vol 59 no 113 pp 284ndash288 2012

[19] B MandelbrotThe Fractal Geometry of Nature W H FreemanNew York NY USA 1982

[20] JW Baish andRK Jain ldquoFractals and cancerrdquoCancer Researchvol 60 no 14 pp 3683ndash3688 2000

[21] S S Cross ldquoFractals in pathologyrdquo Journal of Pathology vol 182no 1 pp 1ndash18 1997

[22] A R Backes and O M Bruno ldquoSegmentacao de texturas poranalise de complexidaderdquo Journal of Computer Science vol 5no 1 pp 87ndash95 2006


[23] M Friedrich-Rust M F Ong E Herrmann et al ldquoReal-timeelastography for noninvasive assessment of liver fibrosis inchronic viral hepatitisrdquo American Journal of Roentgenology vol188 no 3 pp 758ndash764 2007

[24] A Saftoui D I Gheonea and T Ciurea ldquoHue histogram analy-sis of real-time elastography images for noninvasive assessmentof liver fibrosisrdquoAmerican Journal of Roentgenology vol 189 no4 pp W232ndashW233 2007

[25] D Dumont R H Behler T C Nichols E P Merricksand C M Gallippi ldquoARFI imaging for noninvasive materialcharacterization of atherosclerosisrdquoUltrasound inMedicine andBiology vol 32 no 11 pp 1703ndash1711 2006

[26] L ZhaiM L Palmeri R R Bouchard RWNightingale andKR Nightingale ldquoAn integrated indenter-ARFI imaging systemfor tissue stiffness quantificationrdquo Ultrasonic Imaging vol 30no 2 pp 95ndash111 2008

[27] R H Behler T C Nichols H Zhu E P Merricks and C MGallippi ldquoARFI imaging for noninvasive material characteriza-tion of atherosclerosis part II toward in vivo characterizationrdquoUltrasound in Medicine and Biology vol 35 no 2 pp 278ndash2952009

[28] K Nightingale M S Soo R Nightingale and G TraheyldquoAcoustic radiation force impulse imaging in vivo demonstra-tion of clinical feasibilityrdquo Ultrasound in Medicine and Biologyvol 28 no 2 pp 227ndash235 2002

[29] M Lupsor R Badea H Stefanescu et al ldquoPerformance ofa new elastographic method (ARFI technology) comparedto unidimensional transient elastography in the noninvasiveassessment of chronic hepatitis C Preliminary resultsrdquo Journalof Gastrointestinal and Liver Diseases vol 18 no 3 pp 303ndash3102009

[30] B J Fahey K R Nightingale R C Nelson M L Palmeri andG E Trahey ldquoAcoustic radiation force impulse imaging of theabdomen demonstration of feasibility and utilityrdquo Ultrasoundin Medicine and Biology vol 31 no 9 pp 1185ndash1198 2005

[31] R S Goertz K Amann R Heide T Bernatik M F Neurathand D Strobel ldquoAn abdominal and thyroid status with acous-tic radiation force impulse elastometrymdasha feasibility studyacoustic radiation force impulse elastometry of human organsrdquoEuropean Journal of Radiology vol 80 no 3 pp e226ndashe2302011

[32] S R Rafaelsen C Vagn-Hansen T Soslashrensen J Lindebjerg JPloslashen and A Jakobsen ldquoUltrasound elastography in patientswith rectal cancer treated with chemoradiationrdquo EuropeanJournal of Radiology 2013

[33] G Taverna P Magnoni G Giusti et al ldquoImpact of real-time elastography versus systematic prostate biopsy method oncancer detection rate in men with a serum prostate-specificantigen between 25 and 10 ngmLrdquo ISRN Oncology vol 2013Article ID 584672 5 pages 2013

[34] L Rizzo G Nunnari M Berretta and B Cacopardo ldquoAcousticradial force impulse as an effective tool for a prompt and reli-able diagnosis of hepatocellular carcinomamdashpreliminary datardquoEuropean Review for Medical and Pharmacological Sciences vol16 no 11 pp 1596ndash1598 2012

[35] Y F Zhang H X Xu Y He et al ldquoVirtual touch tissue quan-tification of acoustic radiation force impulse a new ultrasoundelastic imaging in the diagnosis of thyroid nodulesrdquo PLoS Onevol 7 no 11 Article ID e49094 2012

[36] M Dighe S Luo C Cuevas and Y Kim ldquoEfficacy of thyroidultrasound elastography in differential diagnosis of small thy-roid nodulesrdquo European Journal of Radiology 2013


Research ArticleNonlinear Radon Transform Using Zernike Moment forShape Analysis

Ziping Ma12 Baosheng Kang1 Ke Lv3 and Mingzhu Zhao4

1 School of Information and Technology Northwest University Xirsquoan 710120 China2 School of Information and Computing Sciences North University for Nationalities Yinchuan 750021 China3 College of Computing amp Communication Engineering Graduate University of Chinese Academy of SciencesBeijing 100049 China


Correspondence should be addressed to Ziping Ma zipingmagmailcom

Received 18 January 2013 Accepted 22 March 2013


Copyright copy 2013 Ziping Ma et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We extend the linear Radon transform to a nonlinear space and propose a method by applying the nonlinear Radon transform toZernike moments to extract shape descriptors These descriptors are obtained by computing Zernike moment on the radial andangular coordinates of the pattern imagersquos nonlinear Radon matrix Theoretical and experimental results validate the effectivenessand the robustness of the methodThe experimental results show the performance of the proposed method in the case of nonlinearspace equals or outperforms that in the case of linear Radon

1 Introduction

Shape analysis methods have been broadly applied tobiomedical signal processing object recognition imageretrieval target tracking and so forth [1] Moments methods[2 3] can be referred to shape descriptors because of theirgood characterization in describing different shapes Themost important properties of shape descriptors achievedby different moments are invariance including translationrotation scaling and stretching stability to noise and com-pleteness [4]

In the past twenty years many attentions have been paidto the completeness property of the invariant descriptor setin pattern recognition and other similar application fieldsThese kinds of methods can be obtained by the followingprocesses Firstly Fourier transform or Radon transformis employed to map the image into other space Secondlythe different ideas can be conceived to construct invariantdescriptors based on the information in new space Simet al [5] gave a new method for texture image retrievalThey converted the images in Fourier domain and calculatedmodified Zernikemoments to extract the texture descriptors

It is tested that the descriptor has higher accuracy comparingto Gabor Radon and wavelet based methods and requireslow computational effort However it is not invariant toscale Wang et al [6] and Xiao et al [7] introduced theRadon transform to Fourier-Mellin transform to achieveRST (rotation scaling and translation) invariance and RSinvariance combined blur respectively In virtue of Xiaorsquosidea Zhu et al [8] constructed RST invariants using Radontransforms and complex moments in digital watermarkingSimilarly the Zernikemoments can be connectedwithRadontransform Rouze et al [9] described a method to design anapproach by calculating the Zernike moments of an imagefrom its Radon transform using a polynomial transformin the position coordinate and a Fourier transform in theangular coordinate However the proposed descriptors areonly invariant to rotation Meanwhile in order to improvethe precision of image retrieval and noise robustness Hoangand Tabbone [10] proposed a new method similar to Xiaorsquosdescriptor to obtain RST invariance based on the RadonFourier and Mellin transform

Then Radon transform is widely applied in many meth-odsmainly because of its better properties in projection space


[11ndash15] In the projective space a rotation of the originalimage results in a translation in the angle variable and ascaling of the original image leads to a scaling in the spatialvariable together with an amplitude scaling [16 17] Based onthese properties a rotation and scaling invariant function iseasy to construct and highly robust to noise

Enlightened by the peersrsquo research works we extendRadon transform to nonlinear Radon transform and proposea new set of complete invariant descriptors by applyingZernike moments to the radial coordinate of the patternrsquosnonlinear Radon space of an image [18ndash22]

The remainder of this paper is organized as follows InSection 2 we briefly review the definition of nonlinear Radontransform and Zernike moments and propose a newmethodbased on Zernike moment and nonlinear Radon transformIn Section 3 the comparative experiments of the proposedapproach with Hu moment invariance Chongrsquos method isconducted in terms of image retrieval efficiency differentnoise robustness Section 4 concludes this paper

2 Nonlinear Radon Transform andZernike Moments

21 Nonlinear Radon Transform Thenonlinear Radon trans-form of an image function 119891(119909 119910) is defined as [10]

119875 (119903 120579) = 119877 (119903 120579) 119891 (119909 119910)

= ∬

infin

minusinfin

119891 (119909 119910) 120575 (1199031199021 minus 119879 (120595 (119909 119910) 120579)) 119889119909 119889119910

(1)

where 120595(119909 119910) isin 1198712(119863) 119902

1is a real instance 120579 denotes

the angle vector formed by the function 120595(119909 119910) and119879(120595(119909 119910) 120579) is a rotation function by 120595(119909 119910) with an angelof 120579 and defined by

119879 (120595 (119909 119910) 120579) minus 1199031199021 = 0 (2)

The nonlinear Radon transform indicates curve integralof the image function 119891(119909 119910) along different curves Theparameter 119902

1can control the shape of curve Different curves

can be obtained by the values of parameter 1199021and function

120595(119909 119910)Especially when 120595(119909 119910) = 119909 and 119902

1= 1 119879(120595(119909 119910) 120579) =

119909 cos 120579 +119910 sin 120579 This reveals that the linear Radon transformis the special case of nonlinear Radon transform The resultsof different curvesrsquo Radon transform are shown in Table 1

The nonlinear Radon transform has some properties thatare beneficial for pattern recognition as outlined below

(1) Periodicity the nonlinear Radon transformof119891(119909 119910)is periodic in the variable 120579 with period 2120587 when120595(119909 119910) is an arbitrarily parametric inference

119875 (119903 120579) = 119875 (119903 120579 plusmn 2119896120587) (3)

(2) Resistance if 1198911(119909 119910) and 119891

2(119909 119910) are two images

with little difference when 120595(119909 119910) is arbitrarily para-metric inference the corresponding nonlinear Radontransform of 119891

1(119909 119910) and 119891

2(119909 119910) are as followes

10038161003816100381610038161198751 (119903 120579) minus 1198752 (119903 120579)1003816100381610038161003816

le ∬119863

100381610038161003816100381610038161003816100381610038161198911 (119903 120579)minus1198912 (119903 120579)

1003816100381610038161003816 120575 (1199031199021minus119879 (120595 (119909 119910) 120579))

1003816100381610038161003816 119889119909 119889119910

(4)

(3) Translation a translation of 119891(119909 119910) by a vector 997888119906 =

(1199090 1199100) results in a shift in the variable 119903 of 119875(119903 120579) by

a distance 119889 = 1199090cos 120579 + 119910

0sin 120579 and equals to the

length of the projection of 997888119906 onto the line 119909 cos 120579 +119910 sin 120579 = 119903

119875 (119903 120579) = 119875 (119903 minus 1199090 cos 120579 minus 1199100 sin 120579 120579) (5)

(4) Rotation a rotation of119891(119909 119910) by an angle 1205790implies a

shift in the variable 120579 of 119875(119903 120579) by a distance 1205790when

120595(119909 119910) is arbitrarily parametric inference

119875 (119903 120579) 997888rarr 119875 (119903 120579 + 1205790) (6)

(5) Scaling a scaling of 119891(119909 119910) by a factor of 119886 resultsin a scaling in the variable 119903 and 1119886 of amplitude of119875(119903 120579) respectively when 120595(119909 119910) represents ellipseor hyperbola curve

119891 (119886119909 119886119910) 997888rarr1

1198862119875 (119886119903 120579) (7)

22 Zernike Moment The radial Zernike moments of order(119901 119902) of an image function 119891(119903 120579) is defined as

119885119901119902=(119901 + 1)

120587int

2120587

0

int

1

0

119877119901119902 (119903) 119890

minus119902120579119891 (119903 120579) 119903119889119903 119889120579 (8)

where the radial Zernikemoment of order (119901 119902) is defined bythe following equation

119877119901119902 (119903) =

119901

sum

119896=119902

119901minus119896=even

119861119901|119902|119896

119903119896 (9)

With

119861119901|119902|119896

=

(minus1)((119901minus119896)2)

((119901+119896) 2)

((119901minus119896) 2) ((119902+119896) 2) ((119896minus119902) 2) 119901minus119896 = even

0 119901minus119896 = odd(10)

23 NRZM Descriptor Based on Nonlinear Radon Transformand Zernike Moment The Zernike moment is carried outto be computed after the projective matrix of nonlinearRadon transform ismapped to the polar coordinate (NRZM)


Table 1 The diagrams of results using different curvesrsquo Radon transform

Line Radontransform

Parabola Radontransform

Ellipse Radontransform

Hyperbola Radontransform

The computational process of our proposed method NRZMis illuminated in Figure 1

Supposed 119891(119909 119910) is the image 119891(119909 119910) rotated by rota-tional angle 120573 and scaled by scaling factor 120582 and Radontransform of 119891(119909 119910) is given by

(119903 120579) = 120582119875(119903

120582 120579 + 120573) (11)

The Zernike moments of (119903 120579) is

119885119901119902=119901 + 1

120587int

2120587

0

int

1

0

(119903 120579) 119877119901119902 (120582119903) 119890(minus119902120579)

119903119889119903 119889120579

=119901 + 1

120587int

2120587

0

int

1

0

120582119875(119903

120582 120579 + 120573)119877

119901119902 (120582119903) 119890(minus119902120579)

119903119889119903 119889120579

(12)

The radial Zernike polynomials 119877119901119902(120582119903) can be expressed as

a series of 119877119901119902(119903) as follows

119877119901119902 (120582119903) =

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

120582119894119861119901119902119894119863119901119894119896 (13)

Image

Ellipse-Radontransform

Parabola-Radontransform

Zernikemoment NRZM

Hyperbola-Radontransform

Figure 1 The computation process of NRZM

The derivation process of (13) is given in the AppendixAccording to (12) we have

119885119901119902=119901 + 1

120587

times int

2120587

0

int

1

0

120582119875(119903

120582 120579+120573)

times

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

120582119894119861119901119902119894119863119901119894119896119890(minus119902120579)

119903119889119903 119889120579

(14)


Let 120591 = 119903120582 120593 = 120579 + 120573 (14) can be rewritten as

119885119901119902=119901 + 1

120587

times int

2120587

0

int

1

0

120582119875 (120591 120593)

119901

sum

119896=119902

119877119901119896 (119903)

times

119896

sum

119894=119902

(120582119894119861119901119902119894119863119901119894119896) 119890(minus119902(120593minus120573))

1205822120591119889120591 119889120593

=119901 + 1

120587119890119902120573

times int

2120587

0

int

1

0

119875 (120591 120593)

times

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

(120582119894+3119861119901119902119894119863119901119894119896) 119890minus119902120593

120591119889120591 119889120593

=119901 + 1

120587119890119902120573

times

119901

sum

119896=119902

119896

sum

119894=119902

(120582119894+3119861119901119902119894119863119901119894119896)

times int

2120587

0

int

1

0

119875 (120591 120593) 119877119901119896 (119903) 119890

minus119902120593120591119889120591 119889120593

= 119890119902120573

119901

sum

119896=119902

119896

sum

119894=119902

(120582119894+3119861119901119902119894119863119901119894119896)119885119901119896

(15)

Equation (15) shows that the radial Zernike moments ofbeing rotated image can be expressed as a linear combinationof the radial Zernike moments of original image Based onthis relationship we can construct a set of rotation invariant119868119901119902

which is described as follows

119868119901119902= exp (119895119902119886119903119892 (119885

11))

119901

sum

119896=119902

(

119896

sum

119894=119902

11988500

minus((119894+3)3)119861119901119902119894119863119901119894119896)119885119901119896

(16)

Then 119868119901119902

is invariant to rotation and translation

3 Experimental Results and Discussions

This section is intended to test the performance of a completefamily of similarity invariants introduced in the previoussection for images retrieval by comparison Chongrsquos methodpresented in [12] Hu moment presented in [13] In theexperiments the feature descriptors are calculated by

119877119885119872 = [119868119891 (1 0) 119868119891 (1 1) 119868119891 (119872119872)] (17)

Three subsections are included in this section In thefirst subsection we test the retrieval efficiency of proposeddescriptors in shape 216 dataset This dataset is composed of

Table 2 The most suitable values of parameters

The kind of curves 1199020

1199021

Ellipse 19090 1Hyperbola 350100 2Parabola 2000 2

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

Chongrsquos method

Figure 2 The precision-recall curve of shape 216

18 shape categories with 12 samples per category and eachof every category cannot be obtained by RST transformingfrom any other shape from the same category In the secondsubsection we test robustness of proposed descriptors indifferent noisy dataset In the third subsection we verify therotation invariance of the proposed method

31 Experiment 1 The kind of curves is changing with thecontrolled parameters varying So the retrieval efficiency isdifferent with the controlled parameters Many experimentsare conducted to find the best parametersrsquo values of everycurve in nonlinear Radon transform and finally the mostsuitable values of parameters are listed in Table 2 In thesubsequent experiments we analyze the retrieval efficiencyof linear Radon transform ellipse Radon transform hyper-bola Radon transform and parabola Radon transform withZernike moment respectively which is referred to as NZEPZ HPZ and PRZ respectively

In order to obtain the best retrieval efficiency of everycurve Radon the comparative precisions-recall curves inShapes 216 are shown in Figure 2 It can be seen that theprecision-recall curve of PRZ moves downward more slowlythan those of others which indicates that the retrievalefficient of PRZ is slightly higher than that of RZ while HRZis weaker than PRZ and RZ

The comparative number of relevant image upon everycategory is a better insight into the performance of proposedmethod as shown in Figure 3 It is easy to see that almost the


Bird

Bone

Bric

k

Cam

el

Car

Ch

ildre

nCl

assic

El

epha

ntFa

ce

Fo

rk

Gla

ss

Ham

mer

H

eart

Ke

y

M

isk

Ra

y

Tu

rtle

0

2

4

6

8

10

12

The kind of category

PRZ

Foun

tain

The n

umbe

r of r

etrie

ved

rele

vant

imag

e

Figure 3 The retrieved number of every category in shape 216

number of relevant image in every category is higher than6 especially in bird children elephant face glass hammerheart and misk

32 Experiment 2 The robustness of the proposed descrip-tors is demonstrated using eight datasets added additive ldquosaltamp pepperrdquo and ldquoGaussianrdquo noise respectively The first sevendatasets are generated from original shape 216 database andeach image is corrupted by ldquosalt amp pepperrdquo noise with SNRvarying from 16 to 4 dB with 2 dB decrements The last one isgenerated from shape 216 added ldquoGaussianrdquo noise with noisedensity = 001 02

The retrieval experiments are conducted again in thedatasets mentioned above and the precision-recall curvesof comparative descriptors are depicted in Figure 4 FromFigures 4(a)ndash4(g) it can be observed that efficiency of thePRZ and RZ are similar It also can be seen that the PRZ andRZ descriptors have better performances than other compar-ative methods in ldquosalt and pepperrdquo noisy datasets from SNR= 16 to 8 while Hu moment and Chongrsquos descriptors havesimilarly the worse performance However when SNR = 6and SNR = 4 the situation has changed The deteriorationappears in the PRZ and RZ because their precision-recallcurvesmoves downwardmore rapidly than those of HPZ andEPZ while they move downward more slowly than those ofChongrsquos method and CMI This demonstrates that PRZ andRZ descriptor are sensitive than other nonlinear methodsrsquodescriptors when the value of SNR is low of 8 though it has thestronger robustness than Chongrsquos method and Hu momentIn short the impact of noise on RZ ERZ HRZ and PRZcurves sometimes were little similar or sometimes differ fromone to another It is also observed that

(1) as the values of SNR decrease the curves of all thedescriptors generally move downwards

(2) Hu moment and Chongrsquos descriptors are very sensi-tive to noise and their performance has not changedmuch under different levels of noise

(3) Hu moment method has more resistance to ldquosalt amppepperrdquo noise than Chongrsquos descriptors

(4) among the RZ ERZ PRZ and HRZ the resistanceof PRZ is the strongest to ldquosalt amp pepperrdquo noise andthat of RZ is close to PRZ when the values of SNR arehigher than 6

(5) PRZ is always slightly more robust to ldquosalt amp pepperrdquonoise than RZ except for SNR = 6 and SNR = 4

(6) EPZ and HPZ descriptors are more robust to ldquosalt amppepperrdquo noise than PRZ and RZ when values of SNRare higher than 6

However the retrieval results shown in Figure 4(h) areessentially different from those in Figures 4(a)ndash4(g) It isclear that ERZ and HRZ are more robust to ldquoGaussianrdquo noisethan other methods because their precision-recall curvesare absolutely on the top of others in the ldquoGaussianrdquo noisydatasetThis indicates that ldquoGaussianrdquo noise can result in poorperformance in the case of linear transform In these casesthe nonlinear Radon transform should be a top priority to beemployed in the proposed method

33 Experiment 3 The last test dataset is color objectivedataset generated by choosing 7 sample images from Coland View subset Each of the datasets is transformed bybeing rotated by 72 arbitrary angles (10ndash360) with 5 degreeincrement As a result the last dataset consists of 504 imagesand the retrieval results are shown in Figure 5 From thefigure it can be concluded that the proposed descriptors areinvariant to rotation and the retrieval performance of PRZ ismore efficient

4 Conclusion

In this paper we proposed amethod to derive a set of rotationinvariants using Radon transform and Zernike moments andextend linear Radon transform to nonlinear Radon trans-form

Comparing to linear Radon transform the proposedmethod can perform better or similar However the numeri-cal experiments show that different curve Radon transforms


09

08

07

06

05

04

03

02

01

0090807060504030201 1

(a) SNR = 16

09

08

07

06

05

04

03

02

01

0090807060504030201 1

(b) SNR = 14

09

08

07

06

05

04

03

02

01

0090807060504030201 1

(c) SNR=12

09

08

07

06

05

04

03

02

01

0090807060504030201 1

(d) SNR=10

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0090807060504030201 1

Chongrsquos method

(e) SNR = 8

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0090807060504030201 1

Chongrsquos method

(f) SNR = 6

Figure 4 Continued


PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0090807060504030201 1

Chongrsquos method

(g) SNR =4

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0

1

0 090807060504030201

Chongrsquos method

(h) Gaussian noisy dataset of shape 216

Figure 4 The precision upon recall curves of different descriptors on seven noisy datasets added ldquosalt amp pepperrdquo and one ldquoGaussianrdquo noisydataset

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

010 08060402 1

1

Chongrsquos method

Figure 5 The precision-recall curves of different descriptors onrotated dataset

and Zernike moment perform different In the noiselessdataset the retrieval efficiency of PRZ is higher than com-parative methods In the ldquosalt amp pepperrdquo noise and the PRZconsistently performs better except SNR = 6 and SNR =4 While when SNR = 6 SNR = 4 the EPZ and HPZ aremost robust than RZ And in ldquoGaussianrdquo noise dataset theproposed method in the cases of nonlinear Radon transformis more robust to ldquoGaussianrdquo noise than that in the caseof linear Radon transform Moreover the nonlinear Radontransform can be exploited to other application fields for

engineer application and recognition for the sake of the goodcharacteristic especially their robustness

Appendix

Proof of (13)From (12) the radial Zernike polynomials can be expressedas a series of decreasing power of as follows

(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)

=(

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)(

119903119902

119903119902+1

119903119901

)

(A1)

Since all the diagonal element 119861119901119894119894

are not zero the matrix 119861is nonsingular thus

(

119903119902

119903119902+1

119903119901

) = (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

minus1

times(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)


= (

119863119901119902119902

119863119901119902119902+1

sdot sdot sdot 119863119901119902119901

119863119901119902+1119902+1

sdot sdot sdot 119863119901119902+1119901

d

119863119901119901119901

)

times(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)

(

119877119901119902 (120582119903)

119877119901119902+1 (120582119903)

119877119901119901 (120582119903)

) = (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

times(

(120582119903)119902

(120582119903)119902+1

(120582119903)119901

)

= (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

times(

120582119902

120582119902+1

d120582119901

)(

119903119902

119903119902+1

119903119901

)

= (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

times(

120582119902

120582119902+1

d120582119901

)

times(

119863119901119902119902

119863119901119902119902+1

sdot sdot sdot 119863119901119902119901

119863119901119902+1119902+1

sdot sdot sdot 119863119901119902+1119901

d

119863119901119901119901

)

times(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)

=

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

119903119894sdot 119861119901119902119894sdot 119863119901119894119896

(A2)

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China underGrant no 61261043 and 61102008College Scientific research project of Ningxia province (noNGY2012147) The authors would like to thank the anony-mous referees for their valuable comments and suggestions

References

[1] Z Teng J He A J Degnan et al ldquoCritical mechanical condi-tions around neovessels in carotid atherosclerotic plaque maypromote intraplaque hemorrhagerdquo Atherosclerosis vol 223 no2 pp 321ndash326 2012

[2] S Y Chen J Zhang Q Guan and S Liu ldquoDetection andamendment of shape distortions based on moment invariantsfor active shape modelsrdquo IET Image Processing vol 5 no 3 pp273ndash285 2011

[3] J Wood ldquoInvariant pattern recognition a reviewrdquo Pattern Rec-ognition vol 29 no 1 pp 1ndash17 1996

[4] F Ghorbel S Derrode RMezhoud T Bannour and S DhahbildquoImage reconstruction from a complete set of similarity invari-ants extracted from complex momentsrdquo Pattern RecognitionLetters vol 27 no 12 pp 1361ndash1369 2006

[5] D G Sim H K Kim and R H Park ldquoInvariant textureretrieval using modified Zernike momentsrdquo Image and VisionComputing vol 22 no 4 pp 331ndash342 2004

[6] X Wang F X Guo B Xiao and J F Ma ldquoRotation invariantanalysis and orientation estimation method for texture classi-fication based on Radon transform and correlation analysisrdquoJournal of Visual Communication and Image Representation vol21 no 1 pp 29ndash32 2010

[7] B Xiao J Ma and J T Cui ldquoCombined blur translation scaleand rotation invariant image recognition byRadon and pseudo-Fourier-Mellin transformsrdquo Pattern Recognition vol 45 no 1pp 314ndash321 2012

[8] H Q Zhu M Liu and Y Li ldquoThe RST invariant digital imagewatermarking using Radon transforms and complexmomentsrdquoDigital Signal Processing vol 20 no 6 pp 1612ndash1628 2010

[9] N C Rouze V C Soon and G D Hutchins ldquoOn the connec-tion between the Zernike moments and Radon transform of animagerdquo Pattern Recognition Letters vol 27 no 6 pp 636ndash6422006

[10] T V Hoang and S Tabbone ldquoInvariant pattern recognitionusing the RFM descriptorrdquo Pattern Recognition vol 45 no 1pp 271ndash284 2012

[11] S R DeansThe Radon Transform and Some of Its ApplicationsWiley New York NY USA 1983

[12] H P Hiriyannaiah and K R Ramakrishnan ldquoMoments estima-tion in Radon spacerdquo Pattern Recognition Letters vol 15 no 3pp 227ndash234 1994

[13] R R Galigekere D W Holdsworth M N S Swamy and AFenster ldquoMoment patterns in the Radon spacerdquo Optical Engi-neering vol 39 no 4 pp 1088ndash1097 2000

[14] F Peyrin and R Goutte ldquoImage invariant via the Radon trans-formrdquo in Proceedings of the IEEE International Conference onImage Processing and its Applications pp 458ndash461 1992

[15] J Flusser and T Suk ldquoDegraded image analysis an invariantapproachrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 20 no 6 pp 590ndash603 1998


[16] C W Chong P Raveendran and R Mukundan ldquoTranslationand scale invariants of LegendremomentsrdquoPattern Recognitionvol 37 no 1 pp 119ndash129 2004

[17] X Zhang Y Zhang J Zhang X Li S Chen and D ChenldquoUnsupervised clustering for logo images using singular valuesregion covariance matrices on Lie groupsrdquo Optical Engineeringvol 51 no 4 8 pages 2012

[18] M K Hu ldquoVisual pattern recognition by moments invariantsrdquoIRE Transactions on Information Theory vol 8 no 2 pp 179ndash187 1962

[19] T B Sebastian P N Klein and B B Kimia ldquoRecognition ofshapes by editing their shock graphsrdquo IEEE Transactions onPatternAnalysis andMachine Intelligence vol 26 no 5 pp 550ndash571 2004

[20] httpstaffscienceuvanlsimaloi [21] H Zhu M Liu H Ji and Y Li ldquoCombined invariants to

blur and rotation using Zernike moment descriptorsrdquo PatternAnalysis and Applications vol 13 no 3 pp 309ndash319 2010

[22] httpmuseumvictoriacomaubioinformaticsbutterimagesbthumblivhtm


Research ArticleA Novel Automatic Detection System for ECGArrhythmias Using Maximum Margin Clusteringwith Immune Evolutionary Algorithm

Bohui Zhu12 Yongsheng Ding12 and Kuangrong Hao12

1 College of Information Sciences and Technology Donghua University Shanghai 201620 China2 Engineering Research Center of Digitized Textile amp Fashion Technology Ministry of Education Donghua UniversityShanghai 201620 China

Correspondence should be addressed to Yongsheng Ding ysdingdhueducn

Received 19 January 2013 Revised 1 April 2013 Accepted 2 April 2013


Copyright copy 2013 Bohui Zhu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents a novel maximum margin clustering method with immune evolution (IEMMC) for automatic diagnosis ofelectrocardiogram (ECG) arrhythmias This diagnostic system consists of signal processing feature extraction and the IEMMCalgorithm for clustering of ECG arrhythmias First raw ECG signal is processed by an adaptive ECG filter based on wavelettransforms and waveform of the ECG signal is detected then features are extracted from ECG signal to cluster different types ofarrhythmias by the IEMMC algorithmThree types of performance evaluation indicators are used to assess the effect of the IEMMCmethod for ECG arrhythmias such as sensitivity specificity and accuracy Compared with K-means and iterSVR algorithms theIEMMCalgorithm reflects better performance not only in clustering result but also in terms of global search ability and convergenceability which proves its effectiveness for the detection of ECG arrhythmias

1 Introduction

Electrocardiogram (ECG) iswidely used in cardiology since itconsists of effective simple noninvasive low-cost proceduresfor the diagnosis of cardiovascular diseases (CVDs) Sincethe state of cardiac heart is generally reflected in the shapeof ECG waveform and heart rate ECG is considered tobe a representative signal of cardiac physiology useful indiagnosing cardiac disorders and detecting any arrhythmia[1 2]

ECG arrhythmia can be defined as any of a group ofconditions in which the electrical activity of the heart isirregular and can cause heartbeat to be slow or fast It cantake place in a healthy heart and be of minimal consequencebut they may also indicate a serious problem that leadsto stroke or sudden cardiac death As ECG signal beingnonstationary signal the arrhythmia may occur at randomin the time-scale which means the arrhythmia symptomsmay not show up all the time but would manifest at certainirregular intervals during the day Therefore for effective

diagnostics the variability of ECG signal may have to beobserved over several hours For this reason together withthe fact that the volume of the ECG data is enormous thestudy is tedious and time consuming Thus automatic andcomputer-based detection and classification of arrhythmia iscritical in clinical cardiology especially for the treatment ofpatients in the intensive care unit [1]

In the recent years several methods have been developedin the literatures for detection and classification of ECGarrhythmias Artificial neural network (ANN) classificationmethod is one of the main methods for ECG arrhyth-mia recognition By integration of many data reductionand feature extraction techniques such as principal com-ponent analysis (PCA) independent component analysisfuzzy logic and wavelet transform (WT) improved ANNtechniques have been shown to be able to recognize andclassify ECG arrhythmia accurately [3ndash7] However manyANN algorithms suffer from slow convergence to local andglobal minima and from random settings of initial values ofweights [7] Since support vector machine (SVM) classifiers


do not trap in local minima points and need less traininginput various methods of SVM have been adopted for ECGsignals classification and proved to be effective [8ndash11]

Although many ECG arrhythmia classification methodsshow good performance in the laboratory there are only fewtechniques gaining popularity in practical applications Oneof the main reasons is that most methods are supervisedmethods which require multiple samples manually labeledwith the correct type of ECG signals in context Fromthese samples a supervised system can learn to predict thecorrect sense of the similar ECG signal in a new contextHowever these data sets are labor intensive time consumingand expensive to produce thus few data could be labeledand may be only for several ambiguous types Thereforeusing this technique to detect all kinds of arrhythmias isnot optimal in the diagnosis of cardiovascular arrhythmiaMoreover same state of cardiac heart presents different ECGwaveforms for different individual characteristics becauseof the differences in their body such as heart volume andcoronary artery Even for the same individual the waveformswould present different shapes when the sample is involvedin different activity states such as walking running andsleeping In order to address this problem some methodscontaining unsupervised techniques are developed to analyzethe ECG arrhythmia [4ndash6 12ndash16] which do not need anylabeled training sample and can find out unknown ECGarrhythmia In these methods the key point is the design ofan ideal clustering method as the accuracy of cluster analysissignificantly affects the overall performance

In this paper we propose a novel immune evolutionmaximum margin clustering method (IEMMC) for ECGarrhythmias detection Specifically we decompose the ECGarrhythmias diagnosis procedure into three steps includingsignal processing feature extraction and clustering First weapply a wavelet transform based adaptive filter to removethe noise and detect ECG waveform Then features areextracted to represent ECG signal Finally we employ max-imum margin clustering (MMC) method to recognize ECGarrhythmias Considering huge amount of ECG data andexpensive computation of traditional MMC algorithm [17]we propose the IEMMC algorithm as the improvement of theexisting MMC and make it more suitable for the detectionof ECG abnormalities Our key contribution is to utilizeimmune evolutionary algorithm to perform optimizationdirectly on the nonconvex optimization problem formulatedby original MMC problem and find the optimal solutionwhich has maximum margin Our IEMMC method avoidsthe requirement of solving a nonconvex integer problem andsemidefinite programming (SDP) relaxations in the tradi-tional MMC algorithm which is computationally expensiveand time consuming Due to the outstanding global searchability and robustness of immune evolutionary algorithmperformance of the IEMMC algorithm could maintain at ahigh level even with a poor quality of random initializationand the astringency of the IEMMC method is also superiorto the existing approaches

The rest of this paper is organized as follows Section 2describes our proposed ECG arrhythmias detection systemincluding signal preprocessing feature extraction and the

ECGsignal

Signalprocessing

Featureextraction

IEMMCalgorithm

Resultcompare

Figure 1 The automatic detection system for ECG arrhythmias

ClearECGAdaptive

Filter

ECG signal withouthigh-frequency

noise 1198641

RawECGsignal

Low-frequencynoise in ECG signal

1198642

Referenceinput

Wavelettransform

Figure 2 The adaptive ECG filter based on wavelet transforms

IEMMC method for ECG arrhythmias Then the clusterperformance is examined through simulation experimentsin Section 3 Finally the concluding remarks are given inSection 4

2 A Novel Automatic DetectionSystem for ECG Arrhythmias

The automatic detection system for ECG arrhythmias con-sists of three stages and is constructed as shown in Figure 1The first stage is the preprocessing which includes filteringbaseline correction and waveform detection The secondstage is the feature extraction which aims to find the bestcoefficients set to describe the ECG signal The last stage isdesigned to cluster ECGperiods using the IEMMCalgorithmaccording to the previously extracted features in order toconstruct the arrhythmia classes

21 Preprocessing

211 ECG Signal Filtering ECG signals can be contami-nated with several types of noise such as motion artifact(MA) electromyogram noise (EMG) and baseline wander-ing (BW) which can affect the feature extraction algorithmSo the ECG samples should be preprocessed before featureextraction and clustering Due to the frequency spectrumoverlapping between ECG signal and noise like motionartifact and baseline wandering which is less than 7Hz tradi-tional wavelet decomposition and wavelet threshold methodwould make ECG waveform distorted such as the distortionof 119875 wave or 119879 wave signal For this situation we applya wavelet transform based adaptive filter which combinesthe advantages of wavelet transform and adaptive filteringtechniques to preprocess the ECG signal The constructionof our ECG signal filter is demonstrated in Figure 2

As Figure 2 shows the procedures of the ECG signal filtercan be summarized as the following four steps

(1) According to the sampling frequency of ECG signalthe least wavelet decomposition level 119894 could be


Table 1 Nine features of ECG signal

119877119877119899(s) 119877119877

1015840

119899(s) 119876119877119878

119899(s) 119875119877

119899(s) 119876119879

119899(s) 119878119879

119899(s) 119877

119899(mv) 119875

119899(mv) 119879

119899(mv)

08477 08692 00742 01663 02930 02188 18149 00570 0681709023 08931 00742 01445 02891 02148 16339 00142 0592608594 08916 00781 01406 02852 02070 23085 00579 0612508281 08034 00742 01663 02931 02109 21007 00469 06247

determined by separating ECG signal from high-frequency noise Then the ECG signal with noisecould be wavelet decomposed into 119894 scales

(2) After wavelet decomposition and removal of precisecomponents containing high-frequency noise signalwe set the approximate components119864

1which contain

ECG signal without high-frequency noise as theprimary input signal of the adaptive filter

(3) In linewith spectrum relations between variouswave-form and low-frequency noise such as baseline driftand motion artifact the least wavelet decompositionlevel 119895 which can separate ECG signal from low-frequency noise would be determined By waveletdecomposition of119864

1into 119895 scales the left approximate

components 1198642containing baseline drift motion

artifact and other low-frequency interference wouldbe taken as the reference input signal of the adaptivefilter

(4) Least mean squares (LMS) adaptive filtering is usedto preprocess the primary input signal and get clearECG signals

212 Waveform Detection The waveform detection of theECG signal is the very basis of feature extraction Thereare actually three separate algorithms each of which isdesignated to detect certain waveform of ECG signal

(1) 119877 119863119890119905119890119888119905119894119900119899 The detection of 119876119877119878 complex takes a vitalrole in ECG waveform detection In order to achieve QRScomplex detection119877wavemust be located at first Accordingto the fact that 119877 wave boasts the largest slope differenceof ECG amplitude array is generated to make 119877 peaks morenoticeable Then a practically lower limit is employed toremove unrelated noisy peaks from the signal In orderto avoid interference of big 119879 wave the relative refractoryperiod which lasts 200ms after 119877 peak is detected shouldbe skipped Meanwhile every 119877119877 interval should be judgedin case of escaped inspection of 119877 peak

(2) 119876119878 Detection After finishing the positioning of 119877 wave119876 and 119878 peaks can be identified in accordance with themorphological characteristics 119876 and 119878 peaks occur aroundthe 119877 peak within 01 second The turning point connectingbaseline and falling edge is just the 119876 peak Similarly S peakcould be found in the right side

(3) 119875 and 119879 Wave Detection In the light of waveformcharacteristics of the normal ECG signal it is found that 119875wave 119876119877119878 wave and 119879 wave appear alternately Besides the

gap between the peak of 119875 wave and 119876119877119878 is no more than016 seconds This suggests that the maximum voltage pointwithin 016 seconds before the 119876 peak shall be 119875 peak whilethe maximum voltage point between 119878 peak and the next 119875peak shall be the 119879 peak

22 Feature Extraction Feature extraction is a process todetermine the best coefficients which could describe the ECGwaveform accurately In order to extract the best features thatrepresent the structure of the ECG signals nine times domaincoefficients belonging to two succeeding ECG periods areconsidered as shown in Table 1 The first row in the table isthe name of the features while the rest show the value of eachfeature All features are listed as follows

(a) normalized 119877119877 interval between the acquired 119877 waveand the preceding 119877 wave (119877119877

119899)

(b) normalized RR interval between the acquired 119877 waveand the following 119877 wave (1198771198771015840

119899)

(c) normalizedQRS interval of the acquired beat (119876119877119878119899)

(d) normalized PR interval of the acquired beat (119875119877119899)

(e) normalized QT interval belonging to the acquiredbeat (119876119879

119899)

(f) normalized ST interval of the acquired beat (119878119879119899)

(g) normalized 119877 amplitude of the acquired beat (119877119899)

(h) normalized 119875 amplitude of the acquired beat (119875119899)

(i) normalized 119879 amplitude of the acquired beat (119879119899)

119876119877119878 interval is calculated as the time interval between119876 wave and 119878 wave 119875119877 interval is calculated as the timeinterval between the 119875 peak and the 119877 peak 119878119879 interval iscalculated as the time interval between 119878 wave and 119879 peak119876119879 interval is measured as the time interval between 119879 waveand the onset time of the 119876 wave From the medical pointof view the detection of arrhythmia depends on two or moreECG signal periodsTheprevious period of anECG signal hasmany indicators of current arrhythmia So in our approachtwo 119876119877119878 periodsrsquo parameters 119877119877

119899and 119877119877

1015840

119899are considered to

be the features of ECG signal 119877 amplitude is measured as thedistance between the peak of the 119877 wave and the baseline 119875amplitude and 119879 amplitude are measured in the same way

23 Clustering Method for ECG Arrhythmia

231 Maximum Margin Clustering The MMC extends thetheory of SVM to the unsupervised scenario which aims tofind a way to label the samples by running SVM implicitlywith the maximummargin over all possible labels [18]


Mathematically given a point set 120594 = 1199091 119909

119899 and

their labels 119910 = 1199101 119910

119899 isin minus1 +1

119899 SVM seeks ahyperplane 119891(119909) = 119908

119879120601(119909) + 119887 by solving the following

optimization problem

min119908119887120585119894

1

21199082+ 119862

119899

sum

119894=1

120585119894

st 119910119894(119908119879120601 (119909) + 119887) ge 1 minus 120585

119894

120585119894ge 0 119894 = 1 119899

(1)

where 120601(sdot) is a nonlinear function that maps the data samplesin a high dimensional feature space and makes the nonsep-arable problem in the original data space to be separable inthe feature space The 120585

119894values are called slack variables and

119862 gt 0 is a manually chosen constantDifferent from SVM where the class labels are given and

the only variables are the hyperplane parameters (119908 119887)MMCaims at finding not only the optimal hyperplane (119908

lowast 119887lowast)

but also the optimal labeling vector 119910 [17] Originally thistask was formulated in terms of the following optimizationproblem [18]

min119910isinminus1+1

119899min119908119887120585119894

1

21199082+ 119862

119899

sum

119894=1

120585119894

st 119910119894(119908119879120601 (119909) + 119887) ge 1 minus 120585

119894

120585119894ge 0 119894 = 1 119899 119862 ge 0

(2)

However the previous optimization problem has a triv-ially ldquooptimalrdquo solution which is to assign all data to the sameclass and obtain an unbounded margin Moreover anotherunwanted solution is to separate a single outlier or a verysmall group of samples from the rest of the data To alleviatethese trivial solutions Xu et al [18] imposed a class balanceconstraint on 119910

minusℓ le 119890119879119910 le ℓ (3)

where ℓ ge 0 is a constant to control the class imbalance whichcould bound the difference in class size and avoid assigningall patterns to the same class and 119890 is an all-one vector

TheMMCmethod often outperforms common clusteringmethods with respect to the accuracy [17 18] It can beexpected that the detection of ECG arrhythmia by usingthe MMC algorithm will achieve a high level of accuracyHowever applying the approach requires solving a noncon-vex integer problem which is computationally expensiveand only small data sets can be handled by the MMCmethod so far At present various optimization techniqueshave been applied to handle this problem Xu et al [18]proposed to make several relaxations to the original MMCproblem and reformulate it as a SDP problem which canthen be solved by standard SDP solvers such as SDPT3and SeDuMi Valizadegan and Jin [19] further proposedthe generalized MMC algorithm which reduces the scaleof the original SDP problem significantly To make MMC

method more practical Zhang et al [17] put forward amethod which iteratively applied an SVM to improve aninitial candidate obtained by a 119870-means preprocessing stepRecently Zhao et al [20] proposed a cutting plane MMCmethod based on constructing a sequence of intermedi-ate tasks and each of the intermediate tasks was solvedusing constrained concave-convex procedure Although therecently proposed approaches have improved the efficiencyof the MMC method the application of these methods hasnot always been guaranteed For example as an iterativeapproach the performance of iterSVR algorithm [17] whichbegins with assigning a set of initial labels is crucial for thequality of initialization Random initialization will usuallyresult in poor clustering

232 Maximum Margin Clustering with Immune EvolutionThe concept of SVMs can be considered to be a special caseof regularization problems in the following form

inf119891isin119867

1

119899

119899

sum

119894=1

119871 (119910119894 119891 (119909119894)) + 120582

100381710038171003817100381711989110038171003817100381710038172

119867 (4)

where 120582 gt 0 is a fixed real number 119871 119884 times R rarr [0infin) isa loss function measuring the performance of the predictionfunction 119891 on the training set and 119891

2

119867is the squared norm

in a reproducing kernel Hilbert space 119867 sube R119909 = 119891

Χ rarr R induced by a kernel function In the SVM approach(1) the hinge loss 119871

ℎ(119910 119891) = max0 1 minus 119910119891(119909) with 119910 isin

minus1 +1 is used Instead of using the hinge loss our approachpenalizes overconfident predictions by using the square loss119871119904(119910 119891) = (119910 minus 119891(119909))

2 leading to

min119908119887120578

1

21199082+119862

2

119899

sum

119894=1

1205782

st 119910i ((119908119879120601 (119909119894)) + 119887) = 1 minus 120578 119894 = 1 119899

(5)

So in our MMC algorithm we aim at finding a solutionfor

minyisinminus1+1119899119908119887

119869 (119910 119908 119887) =1

21199082+119862

2

119899

sum

119894=1

1205782

st 119910i ((119908119879120601 (119909119894)) + 119887) = 1 minus 120578

119894 = 1 119899 minus119897 le

119899

sum

119894=1

119910119894le 119897

(6)

In order to solve problem (6) the original non-convexproblem is considered to be a special case of optimizationproblem and immune evolutionary algorithm is proposedto find optimal solution Recent studies have shown that theimmune evolutionary algorithm possesses several attractiveimmune properties that allow evolutionary algorithms toavoid premature convergence and improve local search capa-bility [21ndash25] By utilizing powerful global search capabilityand fast convergence of the immune evolutionary algorithm


IEMMC could avoid SDP relaxations and find optimalsolution of the MMCmethod efficiently

The Process of IEMMC Algorithm The framework of ourIEMMC algorithm is given by Algorithm 1

Algorithm 1 (Maximum Margin Clustering with ImmuneEvolution)

Step 1 Generate a set of candidate solutions 119875 = 1199101

119910119898+119903

sube minus1 +1119899 composed of the subset of memory cells

119875119898

added to the remaining 119875119903(119875 = 119875

119898+ 119875119903) 119875 should

fulfill the balance constraint (3) and 119910119894minus 119910119895 gt 119905119904 119905119904is the

suppression threshold

Step 2 Compute the affinity values 119865(119910) for each 119910119895isin 119875

Step 3 Determine the 119873119888best individuals 119875

119888of the popula-

tion 119875119903 based on an affinity measure Perform clone selection

on the population 119875119888to generate a temporary population of

clones 119875lowast119888

Step 4 Determine the 119873119898

best individuals 119875119898

of theremaining population 119875

119903minus 119875119888 based on an affinity measure

Apply mutation to the antibodies population 119875119898 where the

hypermutation is proportional to affinity of the antibody Amaturated antibody population 119875

lowast

119898is generated

Step 5 Re-select the improved individuals from 119875lowast

119888and 119875

lowast

119898to

compose the memory set and the population 119875119903

Step 6 Perform receptor editing replace some low affinityantibodies of the population 119875

119903by randomly created new

antibodies maintaining its diversity

Step 7 If termination conditions are not satisfied go to Step 2

Step 8 Return the best individual 119910119894

The starting point is generating a set of candidatesolutions 119875 = 119910

1 119910

119898+119903 sube minus1 +1

119899 composed ofthe subset of memory cells 119875

119898added to the remaining

119875119903(119875 = 119875

119898+ 119875119903) Each of these individuals constitutes a

possible solution for optimization problem (6) Throughoutour IEMMC algorithm we ensure that only valid individualsare created that is individuals 119910 should fulfill the balanceconstraint (3) In Step 2 the affinity value 119865(119910) is computedfor each of the initial individuals where

119865 (119910) = exp (minusmin 119869 (119910 119908 119887)) (7)

Depending on the affinity values the copies of the antibodiesare generated and clone selection is performed on superiorindividuals In Step 4 mutation process is applied to theantibodies If the affinity value of the new antibody isbetter than that of original value new antibody is storedin the place of the original one otherwise old antibodyis kept in population After the mutation process receptorediting is applied to the antibody population In the receptorediting process a percentage of antibodies in the antibodypopulation are replaced by randomly created new antibodies

When the best individual satisfies termination condition 119910119894

would be returned

Fitness Computation For fixed solution 119910 the problemformulated in the function (6) could be solved by the standardSVM learning algorithm So we can compute (119908 119887) from theKarush-Kuhn-Tucker (KKT) conditions as usual tomaximizemargin between clusters But this solution (119908 119887 119910) is not theoptimal clustering solutions for problem (6) Therefore wecontinue to find a better bias 119887 and cluster label 119910 by fixing 119908and minimizing problem (6) which is reduced to

min119910119887

119899

sum

119894=1

(119908 sdot 120601 (119909119894) + 119887 minus 119910

119894)2

st 119910119894isin plusmn1

119894 = 1 119899 minusℓ le 119890119879119910 le ℓ

(8)

Then problem (8) can be solved without the use of anyoptimization solver by the following proposition At firstwe sort 119908119879120601(119909

119894) and use the set of midpoints between any

two consecutive w119879120601(119909119894) values as the candidates of 119887 From

these candidates of 119887 the first (119899 minus 119897)2 and the last (119899 minus 119897)2

of the candidates should be removed for not satisfying theclass balance constraint (3) For each remaining candidatewe determine 119910 = sign(119908119879120593(119909) + 119887) and compute thecorresponding objective value in (8) Finally we choose 119887 andcorresponding 119910 that has the optimal objective Since both119908

and 119887 have been determined fitness value 119865(119910) for the newindividual119910 can be obtained by119865(119910) = exp(minusmin 119869(119910 119908 119887))

3 Experiment and Results

31 Experimental Data Experimental data of ECG arrhyth-mias used in this study are taken from MIT-BIH ECGArrhythmias Database [26] All ECG data are classifiedinto five classes according to standard of The Associationfor the Advancement of Medical Instrumentation (AAMI)[27] since this database urges all users to follow the AAMIrecommendations In this standard abnormal ECG couldbe divided into following four types Type S contains atrialpremature (AP) nodal premature (NP) and supraventricularpremature (SP) Type V contains premature ventricular con-traction (PVC) and ventricular ectopic (VE) Type F containsfusion of ventricular and normal beat Type Q contains pacedbeat fusion of paced and normal beat and unclassified beatThe other kinds of heartbeats are considered as N typeincluding normal beat atrial escape (AE) nodal escape (NE)right bundle branch block (R) and left bundle branch block(L)

Totally 1682 ECG periods are selected from seven recordsof MITBIH database to test the correctness of the IEMMCalgorithm The distribution of records is shown in Table 2Thefirst row corresponds to the labels according to theAAMIstandard And the first column is the name of the recordswhereas the others contain the number of heartbeats of eachtype


Table 2 The number of sample records according to arrhythmiatype

MIT code N S V F Q Total106 104 0 83 0 0 187200 125 0 112 0 0 237208 95 0 0 86 0 181209 102 106 0 0 0 208213 106 0 0 113 0 219217 205 0 0 0 211 416222 122 112 0 0 234Total 859 218 195 199 211 1682

Table 3 The ECG arrhythmias clustering results using the IEMMCalgorithm

Clustering resultArrhythmia type N S F V QN 803 15 12 13 16S 27 191 0 0 0V 35 0 164 0 0F 17 0 0 178 0Q 28 0 0 0 183

32 Experimental Results In this section we demonstratethe superiority of the proposed IEMMC procedure for ECGarrhythmias detection and the following three types ofperformance evaluation indicators are used to assess theeffect of ECG arrhythmias clustering method

sensitivity =TP

(TP + FN)

specificity =TN

(FP + TN)

accuracy =(TP + TN)

(TP + FN + FP + TN)

(9)

where true positive (TP) means the number of true arrhyth-mia that has been successfully detected false positive (FP)is the number of true arrhythmia that has been missed truenegative (TN)means the number of corresponding nontargetarrhythmia that has been correctly detected false negative(FN) is the count of nontarget arrhythmia that has beendetected wrongly

The simulation results are listed in Table 3 and theperformance analysis of the clustering result is in Table 4 Asshown in Tables 3 and 4 by using the IEMMC algorithm thecorrectness of ECG arrhythmias is at a high level

From the result we can find that type N is the mostregular and numerous heartbeats and easy to be separatedfrom the other types so its result is better than other typesHowever the performance of type F is lower than that in theprevious case Given that morphology of type F is often verysimilar to that of other types it is very difficult to characterizetype F

In order to verify and measure the IEMMC algorithmrsquossuperiority three methods are developed in parallel to

Table 4 The performance analysis result of the ECG arrhythmiasclustering method

Arrhythmia type Sensitivity () Specificity () Accuracy ()N 979 927 954S 830 980 958F 824 975 956V 828 987 966Q 839 979 960Total 903 974 959

compare with our algorithm including standard 119870-meansalgorithm iterSVR which is the first approach capable ofdealing with large data sets [17] and SVM which has beenproved to be a successful supervised learning method forECG recognition and classification [8ndash11] The performanceof all clustering methods is shown in Figure 3 Two initializa-tion schemes are developed for both iterSVR and IEMMC inthe experiment (1) random (2) standard119870-means clustering(KM) In the first scheme initial candidate solutions ofIEMMC and iterSVR are generated randomly In the secondscheme iterSVR is initialized by standard 119870-means cluster-ing Only one of IEMMC candidate solutions is initializedby standard 119870-means clustering and the rest solutions aregenerated at random The class balance parameter of bothIEMMC and iterSVR is always set as 119871 = 02 lowast 119899 Also20 of the ECG data are extracted randomly to be thetraining data of the SVM classification The radical basisfunction (RBF) kernel 119896(119909 1199091015840) = exp(minus119909 minus 119909

10158401205902) is used

for all the kernel methods in the experiment As for theregularization parameter 119862 we choose the best value froma set of candidates (1 10 100 500) for each data set Allalgorithms are respectively repeated three times because ofthe inherent randomness For eachmethod and each data setwe report the result with its best value chosen from a set ofcandidates

From Figure 3 the IEMMCrsquos performance is as similaras that of the SVM and better than those of all clusteringmethods Also we can find that the performance of iterSVRlargely depends on the superiority of initialization Withrandom initialization clustering result from iterSVR is evenworse than that of 119870-means algorithm Since the perfor-mance of 119870-means is also unsatisfactory even initializedby 119870-means iterSVR still cannot meet the expectation ofthe ECG arrhythmia diagnosis However inheriting the out-standing global optimization ability of immune evolutionaryalgorithm the IEMMC algorithm can find the best clusteringfor objective function in a very short evolution period evenin the case of random initialization Additionally IEMMCalgorithm not only excelled in performance but also inconvergence While iterSVR needs to iterate ten times to findsolution the IEMMC algorithm only needs to evolve fourgenerations Especially the IEMMC algorithm could obtainthe same optimal solution fromdifferent initializations in fewgenerations of evolutions due to the prominent convergenceand global search ability This excellent performance in the


100

90

80

70

60

50

40

30

200 1 2 3 4 5 6 7 8 9 10

Sens

itivi

ty (

)

The generations of evolutions

119870-meansIter SVR(119870-means initialization)Iter SVR(random initialization)

IEMMC(119870-means initialization)IEMMC(random initialization)SVM

(a) Sensitivity



Spec

ifici

ty (

)

100

95

90

85

80

75

70

65

600 1 2 3 4 5 6 7 8 9 10


(b) Specificity



Accu

racy

()

100

95

90

85

80

75

70

65

60

0 1 2 3 4 5 6 7 8 9 10The generations of evolutions

55

50

(c) Accuracy

Figure 3 The performance comparison of different clustering methods

experiment has proved that the IEMMC algorithm is veryeffective for the detection of ECG arrhythmia

4 Conclusions

In this paper a novel IEMMCalgorithm is proposed to clusterthe ECG signal and detect ECG arrhythmias which itera-tively updates the quality of candidates by means of immuneevolutionary without employing any training process The

experimental analysis reveals that our approach yields betterclustering performance than some competitive methods inmost cases

In the future we will use some other biological principlesbased evolutionary algorithm to solve the MMC problemlike ant colony optimization and particle swarm optimizersince they have been proved to have global optimizatonability Furthermore comparison with immune evolutionaryalgorithm will be done to find out a more efficient ECG dataclustering algorithm


Acknowledgments

This work was supported in part by the Key Project ofthe National Nature Science Foundation of China (no61134009) Specialized Research Fund for Shanghai LeadingTalents Project of the Shanghai Committee of Science andTechnology (nos 11XD1400100 and 11JC1400200) and theFundamental Research Funds for the Central Universities

References

[1] U R Acharya P S Bhat S S Iyengar A Rao and S DualdquoClassification of heart rate data using artificial neural networkand fuzzy equivalence relationrdquo Pattern Recognition vol 36 no1 pp 61ndash68 2003

[2] S Osowski and T H Linh ldquoECG beat recognition usingfuzzy hybrid neural networkrdquo IEEE Transactions on BiomedicalEngineering vol 48 no 11 pp 1265ndash1271 2001

[3] S N Yu and K T Chou ldquoIntegration of independent compo-nent analysis and neural networks for ECG beat classificationrdquoExpert Systems with Applications vol 34 no 4 pp 2841ndash28462008

[4] R Ceylan and Y Ozbay ldquoComparison of FCM PCA and WTtechniques for classification ECG arrhythmias using artificialneural networkrdquo Expert Systems with Applications vol 33 no2 pp 286ndash295 2007

[5] R Ceylan Y Ozbay and B Karlik ldquoA novel approach forclassification of ECG arrhythmias type-2 fuzzy clusteringneural networkrdquo Expert Systems with Applications vol 36 no3 pp 6721ndash6726 2009

[6] Y Ozbay R Ceylan and B Karlik ldquoA fuzzy clustering neuralnetwork architecture for classification of ECG arrhythmiasrdquoComputers in Biology and Medicine vol 36 no 4 pp 376ndash3882006

[7] A De Gaetanoa S Panunzia F Rinaldia A Risia and MSciandroneb ldquoA patient adaptable ECG beat classifier based onneural networksrdquo Applied Mathematics and Computation vol213 pp 243ndash249 2009

[8] B M Asl S K Setarehdan and M Mohebbi ldquoSupport vectormachine-based arrhythmia classification using reduced featuresof heart rate variability signalrdquoArtificial Intelligence inMedicinevol 44 no 1 pp 51ndash64 2008

[9] K Polat B Akdemir and S Gunes ldquoComputer aided diagnosisof ECGdata on the least square support vectormachinerdquoDigitalSignal Processing vol 18 no 1 pp 25ndash32 2008

[10] K Polat and S Gunes ldquoDetection of ECG Arrhythmia using adifferential expert system approach based on principal compo-nent analysis and least square support vector machinerdquo AppliedMathematics and Computation vol 186 no 1 pp 898ndash9062007

[11] M Moavenian and H Khorrami ldquoA qualitative comparison ofartificial neural Networks and support vector machines in ECGarrhythmias classificationrdquo Expert Systems with Applicationsvol 37 no 4 pp 3088ndash3093 2010

[12] M Korurek and A Nizam ldquoA new arrhythmia clustering tech-nique based on ant colony optimizationrdquo Journal of BiomedicalInformatics vol 41 no 6 pp 874ndash881 2008

[13] M Korurek and A Nizam ldquoClustering MIT-BIH arrhythmiaswith ant colony optimization using time domain and PCAcompressed wavelet coefficientsrdquo Digital Signal Processing vol20 no 4 pp 1050ndash1060 2010

[14] G Zheng and T Yu ldquoStudy of hybrid strategy for ambulatoryECG waveform clusteringrdquo Journal of Software vol 6 no 7 pp1257ndash1264 2011

[15] F Sufi I Khalil andANMahmood ldquoA clustering based systemfor instant detection of cardiac abnormalities from compressedECGrdquo Expert Systems with Applications vol 38 no 5 pp 4705ndash4713 2011

[16] B Dogan andM Korurek ldquoA new ECG beat clustering methodbased on kernelized fuzzy c-means and hybrid ant colonyoptimization for continuous domainsrdquo Applied Soft Computingvol 12 pp 3442ndash3451 2012

[17] K Zhang I W Tsang and J T Kwok ldquoMaximummargin clus-tering made practicalrdquo IEEE Transactions on Neural Networksvol 20 no 4 pp 583ndash596 2009

[18] L Xu J Neufeld B Larson and D Schuurmans ldquoMaximummargin clusteringrdquo Advances in Neural Information ProcessingSystems vol 17 pp 1537ndash1544 2005

[19] H Valizadegan and R Jin ldquoGeneralized maximum marginclustering and unsupervised kernel learningrdquo Advances inNeural Information Processing Systems vol 19 pp 1417ndash14242007

[20] FWang B Zhao andC Zhang ldquoLinear timemaximummarginclusteringrdquo IEEE Transactions on Neural Networks vol 21 no2 pp 319ndash332 2010

[21] Y-S Ding Z-H Hu andW-B Zhang ldquoMulti-criteria decisionmaking approach based on immune co-evolutionary algorithmwith application to garment matching problemrdquo Expert Systemswith Applications vol 38 no 8 pp 10377ndash10383 2011

[22] Y-S Ding X-J Lu K-R Hao L-F Li and Y F Hu ldquoTargetcoverage optimisation of wireless sensor networks using amulti-objective immune co-evolutionary algorithmrdquo Interna-tional Journal of Systems Science vol 42 no 9 pp 1531ndash15412011

[23] L-J Cheng Y-S Ding K-R Hao and Y-F Hu ldquoAn ensem-ble kernel classifier with immune clonal selection algorithmfor automatic discriminant of primary open-angle glaucomardquoNeurocomputing vol 83 pp 1ndash11 2012

[24] J T Tsai W H Ho T K Liu and J H Chou ldquoImprovedimmune algorithm for global numerical optimization and job-shop scheduling problemsrdquo Applied Mathematics and Compu-tation vol 194 no 2 pp 406ndash424 2007

[25] J Gao and J Wang ldquoA hybrid quantum-inspired immune algo-rithm for multiobjective optimizationrdquo Applied Mathematicsand Computation vol 217 no 9 pp 4754ndash4770 2011

[26] ldquoMIT-BIH arrhythmia databaserdquo httpphysionetorgphys-iobankdatabasemitdb

[27] Testing and Reporting Performance Results of Cardiac Rhythmand ST Segment Measurement Algorithms Association for theAdvancement of Medical Instrumentation 1998


Research ArticleStructural Complexity of DNA Sequence

Cheng-Yuan Liou Shen-Han Tseng Wei-Chen Cheng and Huai-Ying Tsai

Department of Computer Science and Information Engineering National Taiwan University Taipei 10617 Taiwan

Correspondence should be addressed to Cheng-Yuan Liou cylioucsientuedutw



Copyright copy 2013 Cheng-Yuan Liou et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

In modern bioinformatics finding an efficient way to allocate sequence fragments with biological functions is an important issueThis paper presents a structural approach based on context-free grammars extracted from original DNA or protein sequencesThis approach is radically different from all those statistical methods Furthermore this approach is compared with a topologicalentropy-based method for consistency and difference of the complexity results

1 Introduction

DNA sequence analysis becomes important part in modernmolecular biology DNA sequence is composed of fournucleotide basesmdashadenine (abbreviated A) cytosine (C)guanine (G) and thymine (T) in any order With fourdifferent nucleotides 2 nucleotides could only code formaximum of 42 amino acids but 3 nucleotides could codefor a maximum 4

3 amino acids George Gamow was the firstperson to postulate that every three bases can translate to asingle amino acid called a codon Marshall Nirenberg andHeinrich J Matthaei were the first to elucidate the natureof a genetic code A short DNA sequence can contain lessgenetic information while lots of bases may contain muchmore genetic information and any two nucleotides switchplace may change the meaning of genetic messages

Sequence arrangement can produce many differentresults but only few codons exist in living bodies Somesequences do not contain any information which is knownas junk DNA Finding an efficient way to analyze a sequencefragment corresponding to genetic functions is also a chal-lenging problem

In recent papersmethods broadly fall into two categoriessequence complexity [1 2] and structural pattern analysis [3ndash8] Koslicki [1] presented a method for computing sequencecomplexities He redefined topological entropy function sothat the complexity value will not converge toward zero formuch longer sequences With separate sequence into several

segments it can determine the segments where are exons orintrons and meaningful or meaningless Hao et al [7] givena graphical representation of DNA sequence according tothis paper we can find some rare occurred subsequencesR Zhang and C T Zhang [4] used four-nucleotide-relatedfunction drawing 3D curves graph to analyze the number offour-nucleotide occurrence probabilities Liou et al [9] hadgiven a new idea in modeling complexity for music rhythmsthis paper translated textmessages into computable values socomputers can score for music rhythms

In this paper we propose a new method for calculatingsequences different from other traditional methods It holdsnot only statistical values but also structural informationWereplace four nucleotides with tree structure presented in [9]and use mathematical tools to calculate complexity values ofthe sequences So we can compare two sequences with valuesand determine dissimilarity between these two sequencesIn biomedical section we can use this technique to find theeffective drugs for new virus with priority

2 DNA Sequence Representedwith Tree Structure

Our method uses Lindenmayer system [10ndash12] propertyamong calculated complexities from tree structure [9] it isa different way of computing complexities of sequences Atfirst we introduce DNA tree and convert DNA sequence to


A C T G

Figure 1 Nucleotide bases corresponding trees

A A T T C C G G A C T G C A G T

Figure 2 DNA sequence represented with tree structure

tree structure A DNA tree is a binary tree of which eachsubtree is also aDNA tree Every tree node is either a terminalnode or a nodewith two childrens (branches or descendants)

Lindenmayer system is a powerful rewriting system usedto model the growth processes of plant development We willintroduce it in Section 22 in detail Lindenmayer system usessome initial and rewriting rules to construct beautiful graphsSince it can construct a tree from rewriting rules it also canextract rewriting rules from a tree In this section we will usetools to generate the rules from tree

We use 4 fixed tree representations for nucleotide bases AT C and G (see Figure 1) When we apply this method toamino acid sequence we can construct more tree representa-tion for amino acids respectively

Whenwe transfer a sequence toDNA tree we will replaceevery word to tree elements step by step and two consecutivetrees can combine to a bigger tree Following the previoussteps a DNA sequence will be transfer to a DNA tree (seeFigure 2)

21 Bracketed Strings for a DNA Sequence For computingcomplexity of our DNA tree we need some rules for con-verting tree to another structure We use a stack similarlystructure to represent the hierarchy of DNA tree calledbracketed string DNA tree can transfer to a unique bracketedstring by the following symbols and it can transfer back tothe original tree

(i) 119865 the current location of tree nodes it can be replacedby any word or be omitted

(ii) + the following string will express the right subtree(iii) minus the following string will express the left subtree(iv) [ this symbol is pairing with ] ldquo[sdot sdot sdot]rdquo denotes a

subtree where ldquosdot sdot sdotrdquo indicates all the bracketed stringsof its subtree

(v) ] see [ description

Following the previous symbols Figure 3 shows thatnucleotide base A and T represented tree can transfer to[119865[minus119865][+119865]] and [119865[minus119865][+119865[minus119865][+119865]]] respectively

[ 119865[minus ]

[ 119865[minus ]

[ 119865[minus ]

[119865][119865]

[+119865]

[+119865]

[+119865]

[119865[minus119865][+119865[minus119865][+119865]]][119865[minus119865][+119865]]

Figure 3 Bracketed strings representation for two trees

And Figure 4 is the bracketed string of Figure 2 Wecan see that when the tree grows string seems to be moreredundant Since we focus here only on DNA trees we cansimplify the bracketed string representations First our treeshave only two subtrees Second the ldquo119865rdquo notation for the treeis trivial With these two characteristics we may omit the ldquo119865rdquonotation from the bracketed string and use only four symbols[ ] minus + to represent trees In our cases ldquo[sdot sdot sdot]rdquo denotesa subtree where ldquosdot sdot sdotrdquo indicates all the bracketed strings ofits subtrees ldquominusrdquo indicated the next ldquo[sdot sdot sdot]rdquo notation for a treeis a left subtree of current node and ldquo+rdquo is a right subtreevice versa Figure 5 is the simplified string of bracketed stringshown in Figure 4

22 DNA Sequence Represented with L-System When weobtain DNA tree and bracketed string representation weneed rewriting rules for analyzing tree structure There aresome types of rewriting mechanism such as Chomsky gram-mar andLindenmayer system (L-system for short)The largestdifference between two string rewriting mechanisms lies inthe technique used to apply productions Chomsky grammaris suitable for applying productions sequentially while L-system is for parallel In our structure applying L-system toour representations is better than Chomsky grammar

The L-system was introduced by the biologist Linden-mayer in 1968 [13] The central concept of the L-system isrewriting In general rewriting is a technique used to definecomplex objects by successively replacing parts of a simpleinitial object using a set of rewriting rules or productions Inthe next section we will present how we use L-system to ourDNA tree The L-system is defined as follows

Definition 1 L-system grammars are very similar to theChomsky grammar defined as a tuple [14]

119866 = (119881 120596 119875) (1)

where

(i) 119881 = 1199041 1199042 119904

119899 is an alphabet

(ii) 120596 (start axiom or initiator) is a string of symbolsfrom 119881 defining the initial state of the system

(iii) 119875 is defined by a production map 119875 119881 rarr 119881lowast with

119904 rarr 119875(119904) for each 119904 in 119881 The identity production119904 rarr 119904 is assumedThese symbols are called constantsor terminals

23 Rewriting Rules for DNA Sequences As discussed earlierwe want to generate the rules fromDNA trees In this section


A A T T C C G G A C T G C A G T[[minus119865[minus119865[minus119865[minus119865[minus119865][+119865]][+119865[minus119865][+119865]]][+119865[minus119865[minus119865][+119865[minus119865][+119865]]][+119865[minus119865][+119865[minus119865][+119865]]]]][+119865[minus119865[minus119865[minus119865[minus119865][+119865]]

[+119865]][+119865[minus119865[minus119865][+119865]][+119865]]][+119865[minus119865[minus119865[minus119865][+119865]][+119865[minus119865][+119865]]][+119865[minus119865[minus119865][+119865]][+119865[minus119865][+119865]]]]]][+119865[minus119865[minus119865[minus119865

[minus119865][+119865]][+119865[minus119865[minus119865][+119865]][+119865]]][+119865[minus119865[minus119865][+119865[minus119865][+119865]]][+119865[minus119865[minus119865][+119865]][+119865[minus119865][+119865]]]]][+119865[minus119865[minus119865[minus119865[minus119865]

[+119865]][+119865]][+119865[minus119865][+119865]]][+119865[minus119865[minus119865[minus119865][+119865]][+119865[minus119865][+119865]]][+119865[minus119865][+119865[minus119865][+119865]]]]]]]

Figure 4 Bracketed strings representation for Figure 2

[minus[minus[minus[minus[minus+]+[minus+]]+[minus[minus+[minus+]]+[minus+[minus+]]]]+[minus[minus[minus[minus+]+]+[minus[minus+]+]]+[minus[minus[minus+]+[minus+]]+[minus[minus+]+[minus+]]]]]

+[minus[minus[minus[minus+]+[minus[minus+]+]]+[minus[minus+[minus+]]+[minus[minus+]+[minus+]]]]+[minus[minus[minus[minus+]+]+[minus+]]+[minus[minus[minus+]+[minus+]]+[minus+[minus+]]]]]]

Figure 5 More simply bracketed strings representation for Figure 2

we will explain how we apply rewriting rules to those treesWe can apply distinct variables to each node Since thetechnique described previously always generates two subtreesfor each node for every nonterminal node they always can beexplained in the following format

119875 997888rarr 119871119877 (2)

where 119875 denotes the current node 119871 denotes its left subtreeand 119877 denotes its right subtree respectively We give anexample shown in Figure 6 left tree has three nodes and onlyroot is nonterminal node it can be rewritten as 119875 rarr 119871119877Right tree has five nodes root 119875 with left subtree 119871 and rightsubtree 119877 Left subtree is terminal but right is not 119877 has twoterminal subtrees 119877

119871and 119877

119877 so this tree can be rewritten as

119875 rarr 119871119877 and 119877 rarr 119877119871119877119877

24 Rewriting Rules for Bracketed Strings Similarly we canalso use rewriting rules to generate bracketed strings Inrewriting rules for DNA trees shown in Section 23 we write119875 rarr 119871119877 for a tree with left and right subtrees Note thatwe call 119871 and 119877 as the nonterminals In this section terminalnodes will be separated from trees and we use ldquonullrdquo torepresent a terminal Such tree will have a correspondingbracketed string as follows [[minus119865 sdot sdot sdot][+119865 sdot sdot sdot]] ldquo[minus119865 sdot sdot sdot]rdquo rep-resents the left subtree while ldquo[+119865 sdot sdot sdot]rdquo represents the rightsubtree Therefore we can replace the rewriting rules with

119875 997888rarr [minus119865119871] [+119865119877]

119865 997888rarr sdot sdot sdot


(3)

where ldquosdot sdot sdotrdquo is the rewriting rule for the bracketed string ofeach subtree For the sake of readability we replace the wordssuch as ldquo119877

119877119871rdquo and ldquo119877

119877119877rdquo In Figure 7 we show the rewriting

rules for the bracketed string of the tree in Figure 3

119875

119871 119871119877 119877

119875

119877119871 119877119877

119875 rarr 119871119877 119875 rarr 119871119877

119877 rarr 119877119871119877119877

Figure 6 Example of rewriting rules for trees

As we can see there are ldquonullsrdquo in the rules Those ldquonullsrdquodo not have significant effects to our algorithm so we simplyignore the nulls Now Figure 3 can apply new rewriting ruleswithout trivial nulls as Figure 8

When tree grows up the rewriting rules may generateidentical rules Assume that we have the following rules

119875 997888rarr [minus119865119879119871] [+119865119879

119877]

119879119871997888rarr [minus119865] [+119865]

119879119877997888rarr [minus119865] [+119865119879119877119877

]

119879119877119877

997888rarr [minus119865] [+119865119879119877119877119877]

119879119877119877119877

997888rarr [minus119865]

(4)

These rules can generate exactly one bracketed string andthus exactly one DNA tree All these rules form a rule setthat represents a unique DNA tree When we look at 119879

119877rarr

[minus119865][+119865119879119877119877] and 119879

119877119877rarr [minus119865][+119865119879

119877119877119877] they have the same

structure since they both have a right subtree and do not havea left subtree The only difference is that one of the subtreesis 119879119877119877

and that the other is 119879119877119877119877

We will define two terms to


119875119875

119879119871

119879119871119879119877

119879119877

119879119877119877

119879119877119871

119875 rarr [minus119865119879119871][+119865119879119877]119875 rarr [minus119865119879119871][+119865119879119877]

119879119877 rarr [minus119865119879119877119871][+119865119879119877119877

]

119879119877 rarr null

119879119871 rarr null119879119871 rarr null

119879119877119871rarr null

119879119877119877rarr null

Figure 7 Rewriting rules for the bracketed string of trees

119875

119879119871 119879119877

119875

119879119871 119879119877

119879119877119877119879119877119871

119875 rarr [minus119865119879119871][+119865119879119877] 119875 rarr [minus119865119879119871][+119865119879119877]

119879119877 rarr [minus119865119879119877119871][+119865119879119877119877

]

Figure 8 Rewriting rules for the bracketed string without nulls oftrees

express the similarity between two rewriting rules and theseterms can simplify complexity analysis

25 Homomorphism and Isomorphism of Rewriting Rules Atthe end of the previous section we discussed that 119879

119877rarr

[minus119865][+119865119879119877119877] and 119879

119877119877rarr [minus119865][+119865119879

119877119877119877] are almost the same

How can we summarize or organize an effective feature tothem Liou et al [9] gave two definitions to classify similarrewriting rules described before as follows

Definition 2 Homomorphism in rewriting rules We definethat rewriting rule119877

1and rewriting rule119877

2are homomorphic

to each other if and only if they have the same structure

In detail rewriting rule 1198771and rewriting rule 119877

2in DNA

trees both have subtrees in corresponding positions or bothnot Ignoring all nonterminals if rule119877

1and rule119877

2generate

the same bracketed string then they are homomorphic bydefinition

Definition 3 Isomorphism on level 119883 in rewriting rulesRewriting rule 119877

1and rewriting rule 119877

2are isomorphic on

depth119883 if they are homomorphic and their nonterminals arerelatively isomorphic on depth 119883 minus 1 Isomorphic on level 0indicates homomorphism

Applying to the bracketed string we ignore all nontermi-nals in (4) as follows

119875 997888rarr [minus119865119879119871] [+119865119879

119877] 997888rarr [minus119865] [+119865]

119879119871997888rarr [minus119865] [+119865] 997888rarr [minus119865] [+119865]

119879119877997888rarr [minus119865] [+119865119879119877119877

] 997888rarr [minus119865] [+119865]

119879119877119877


119879119877119877119877

997888rarr [minus119865] 997888rarr [minus119865]

(5)

We find that 119875 119879119871 119879119877 and 119879

119877119877are homomorphic to each

other they generate the same bracketed string [minus119865][+119865]But 119879

119877119877119877is not homomorphic to any of the other rules its

bracketed string is [minus119865]Let us recall DNA tree example in Figure 2 we will use

this figure as an example to clarify these definitions Now wemarked some nodes shown in Figure 9 there are tree rootedat A B C and D respectively tree A tree B tree C and treeD Tree A is isomorphic to tree C on depth 0 to 3 but they arenot isomorphic on depth 4 Tree B is isomorphic to tree C ondepth from 0 to 2 but they are not isomorphic on depth 3 Dis not isomorphic to any other trees nor is it homomorphicto any other trees

Afterwe define the similarity between rules by homomor-phism and isomorphism we can classify all the rules intodifferent subsets and every subset has the same similarityrelation Now we list all the rewriting rules of Figure 2 intoTable 1 but ignore terminal rules such as ldquorarr nullrdquo andtransfer rulersquos name to class name (or class number) Forexample we can give terminal rewriting rule a class ldquo119862

3rarr

nullrdquo and a rule link to two terminals we can give themldquo1198622rarr 11986231198623rdquo here119862

3is the terminal class After performing

classification we obtain not only a new rewriting rule setbut also a context-free grammar which can be converted toautomata

In Table 1 rules such as 119879119877119871119871119871

rarr [minus119865][+119865] and119879119877119877119877119871119871

rarr [minus119865][+119865] and 119879119877119871119877119871119877

rarr [minus119865][+119865] are isomor-phic on depth 1 and assigned to Class 4There are twenty suchrules before classification so we write ldquo(20)119862

4rarr [minus119865][+119865]rdquo

Similar rules such as 119875 rarr [minus119865119879119871][+119865119879

119877] 119879119877119871119871119871

rarr

[minus119865][+119865] and 119879119877119877119877119877

rarr [minus119865][+119865119879119877119877119877119877119877

] are isomorphic ondepth 0 and there are 47 such rules They are all assignedto Class 1 by following a similar classification procedure Theclassification of the all rules is listed in Table 2 Note that thissection also presents a new way to convert a context-sensitivegrammar to a context-free one

3 DNA Sequence Complexity

When we transfer the DNA sequence to the rewritingrules and classify all those rules we attempt to explore theredundancy in the tree that will be the base for buildingthe cognitive map [15] We compute the complexity of thetree which those classified rules represent We know that aclassified rewriting rule set is also a context-free grammarso there are some methods for computing complexity ofrewriting rule as follows

Definition 4 Topological entropy of a context-free grammarThe topological entropy 119870

0of (context-free grammar) CFG

can be evaluated by means of the following three procedures[16 17]


Table 1 Rewriting rules for the DNA tree in Figure 2

119875 rarr [minus119865119879119871] [+119865119879

119877]

119879119871rarr [minus119865119879

119871119871] [+119865119879

119871119877]

119879119871119871

rarr [minus119865119879119871119871119871

] [+119865119879119871119871119877

]

119879119871119871119871

rarr [minus119865119879119871119871119871119871

] [+119865119879119871119871119871119877

]

119879119871119871119871119871

rarr [minus119865] [+119865]

119879119871119871119871119877

rarr [minus119865] [+119865]

119879119871119871119877

rarr [minus119865119879119871119871119877119871

] [+119865119879119871119871119877119877

]

119879119871119871119877119871

rarr [minus119865] [+119865119879119871119871119877119871119877]

119879119871119871119877119871119877

rarr [minus119865] [+119865]

119879119871119871119877119877

rarr [minus119865] [+119865119879119871119871119877119877119877]

119879119871119871119877119877119877

rarr [minus119865] [+119865]

119879119871119877

rarr [minus119865119879119871119877119871

] [+119865119879119871119877119877

]

119879119871119877119871

rarr [minus119865119879119871119877119871119871

] [+119865119879119871119877119871119877

]

119879119871119877119871119871

rarr [minus119865119879119871119877119871119871119871

] [+119865]

119879119871119877119871119871119871

rarr [minus119865] [+119865]

119879119871119877119871119877

rarr [minus119865119879119871119877119871119877119871

] [+119865]

119879119871119877119871119877119871

rarr [minus119865] [+119865]

119879119871119877119877

rarr [minus119865119879119871119877119877119871

] [+119865119879119871119877119877119877

]

119879119871119877119877119871

rarr [minus119865119879119871119877119877119871119871

] [+119865119879119871119877119877119871119877

]

119879119871119877119877119871119871

rarr [minus119865] [+119865]

119879119871119877119877119871119877

rarr [minus119865] [+119865]

119879119871119877119877119877

rarr [minus119865119879119871119877119877119877119871

] [+119865119879119871119877119877119877119877

]

119879119871119877119877119877119871

rarr [minus119865] [+119865]

119879119871119877119877119877119877

rarr [minus119865] [+119865]

119879119877rarr [minus119865119879

119877119871] [+119865119879

119877119877]

119879119877119871

rarr [minus119865119879119877119871119871

] [+119865119879119877119871119877

]

Table 1 Continued

119879119877119871119871

rarr [minus119865119879119877119871119871119871

] [+119865119879119877119871119871119877

]

119879119877119871119871119871

rarr [minus119865] [+119865]

119879119877119871119871119877

rarr [minus119865119879119877119871119871119877119871

] [+119865]

119879119877119871119871119877119871

rarr [minus119865][+119865]

119879119877119871119877

rarr [minus119865119879119877119871119877119871

] [+119865119879119877119871119877119877

]

119879119877119871119877119871

rarr [minus119865] [+119865119879119877119871119877119871119877]

119879119877119871119877119871119877

rarr [minus119865][+119865]

119879119877119871119877119877

rarr [minus119865119879119877119871119877119877119871

] [+119865119879119877119871119877119877119877

]

119879119877119871119877119877119871

rarr [minus119865][+119865]

119879119877119871119877119877119877

rarr [minus119865] [+119865]

119879119877119877

rarr [minus119865119879119877119877119871

] [+119865119879119877119877119877

]

119879119877119877119871

rarr [minus119865119879119877119877119871119871

] [+119865119879119877119877119871119877

]

119879119877119877119871119871

rarr [minus119865119879119877119877119871119871119871

] [+119865]

119879119877119877119871119871119871

rarr [minus119865] [+119865]

119879119877119877119871119877

rarr [minus119865][+119865]

119879119877119877119877

rarr [minus119865119879119877119877119877119871

] [+119865119879119877119877119877119877

]

119879119877119877119877119871

rarr [minus119865119879119877119877119877119871119871

] [+119865119879119877119877119877119871119877

]

119879119877119877119877119871119871

rarr [minus119865][+119865]

119879119877119877119877119871119877

rarr [minus119865][+119865]

119879119877119877119877119877

rarr [minus119865] [+119865119879119877119877119877119877119877]

119879119877119877119877119877119877

rarr [minus119865][+119865]

(1) For each variable 119881119894with productions (in Greibach

form)

119881119894997888rarr 11990511989411198801198941 11990511989421198801198942 119905

119894119896119894119880119894119896119894 (6)

where 1199051198941 1199051198942 119905

119894119896119894 are terminals and 119880

1198941 1198801198942

119880119894119896119894 are nonterminals The formal algebraic

expression for each variable is

119881119894=

119896119894

sum

119895=1

119905119894119895119880119894119895 (7)

(2) By replacing every terminal 119905119894119895

with an auxiliaryvariable 119911 one obtains the generating function

119881119894 (119911) =

infin

sum

119899=1

119873119894 (119899) 119911

119899 (8)

where 119873119894(119899) is the number of words of length 119899

descending from 119881119894

(3) Let 119873(119899) be the largest one of 119873119894(119899) 119873(119899) =

max119873119894(119899) for all 119894 The previous series converges


Table 2 Classification based on the similarity of rewriting rules

Classification of rules Isomorphic Isomorphic Isomorphic IsomorphicDepth 0 Depth 1 Depth 2 Depth 3

Class 1(19) 119862

1rarr 11986211198621

(4) 1198621rarr 11986211198622

(4) 1198621rarr 11986221198621

(20) 1198621rarr 11986221198622

(8) 1198621rarr 11986211198621

(3) 1198621rarr 11986211198621

(1) 1198621rarr 11986211198621

(1) 1198621rarr 11986211198623

(1) 1198621rarr 11986241198622

(1) 1198621rarr 11986241198623

(1) 1198621rarr 11986221198622

(1) 1198621rarr 11986271198625

(1) 1198621rarr 11986251198622

(1) 1198621rarr 11986221198624

(1) 1198621rarr 11986281198628

(1) 1198621rarr 11986231198621

(1) 1198621rarr 11986231198621

(1) 1198621rarr 11986231198623

(1) 1198621rarr 11986281198626

(1) 1198621rarr 11986241198622

(5) 1198621rarr 11986241198624

Class 2 (48) 1198622rarr null (4) 119862

2rarr 11986241198625

(1) 1198622rarr 119862811986210

(1) 1198622rarr 11986281198626

Class 3 (4) 1198623rarr 11986251198624

(1) 1198623rarr 11986291198629

(1) 1198623rarr 11986291198627

Class 4 (20) 1198624rarr 11986251198625

(1) 1198624rarr 119862911986211

(1) 1198624rarr 1198621211986210

Class 5 (48) 1198625rarr null (1) 119862

5rarr 119862101198628

(1) 1198625rarr 1198621311986211

Class 6 (1) 1198626rarr 1198621011986210

(1) 1198626rarr 1198621311986213

Class 7 (1) 1198627rarr 119862111198629

(1) 1198627rarr 1198621311986215

Class 8 (5) 1198628rarr 1198621111986211

(1) 1198628rarr 1198621411986214

Class 9 (4) 1198629rarr 1198621111986212

(1) 1198629rarr 1198621411986216

Class 10 (4) 11986210

rarr 1198621211986211

(1) 11986210

rarr 1198621511986213

Class 11 (20) 11986211

rarr 1198621211986212

(1) 11986211

rarr 1198621511986215

Class 12 (48) 11986212

rarr null (1) 11986212

rarr 1198621611986214

Class 13 (5) 11986213

rarr 1198621611986216

Class 14 (4) 11986214

rarr 1198621611986217

Class 15 (4) 11986215

rarr 1198621711986216

Class 16 (20) 11986216

rarr 1198621711986217

Class 17 (48) 11986217

rarr null

when 119911 lt 119877 = 119890minus1198700 The topological entropy is given

by the radius of convergence 119877 as

1198700= minus ln119877 (9)

Our productions have some difference from the afore-mentioned definitions First our productions are written inChomsky-reduced form instead of Greibach form SecondDNA is finite sequence it generates finite tree but theprevious formulas are applied on infinite sequences Forconvenience in the DNA tree case we rewrite the definitionas follows [9]

Definition 5 Topological entropy of context free grammar forDNA tree

(1) Assume that there are 119899 classes of rules and that eachclass 119862

119894contains 119899

119894rules Let 119881

119894isin 1198621 1198622 119862

119899

119880119894119895isin 119877119894119895 119894 = 1 2 119899 119895 = 1 2 119899

119894 and 119886

119894119895119896isin

119909 119909 = 1 2 119899 where each 119880119894119895has the following

form

1198801198941997888rarr 119881

1198861198941111988111988611989412

1198801198942997888rarr 119881

1198861198942111988111988611989422

sdot sdot sdot 997888rarr sdot sdot sdot

119880119894119899119894

997888rarr 1198811198861198941198991198941

1198811198861198941198991198942

(10)

(2) The generating function of119881119894 119881119894(119911) has a new form as

follows

119881119894 (119911) =

sum119899119894

119901=11198991198941199011199111198811198861198941199011

(119911) 1198811198861198941199012(119911)

sum119899119894

119902=1119899119894119902

(11)

If 119881119894does not have any nonterminal variables we set

119881119894(119911) = 1

(3) After formulating the generating function 119881119894(119911) we

intend to find the largest value of 119911 119911max at which1198811(119911

max) converges Note that we use119881

1to denote the


rule for the root node of theDNA tree After obtainingthe largest value 119911max of 119881

1(119911) we set 119877 = 119911

maxthe radius of convergence of 119881

1(119911) We define the

complexity of the DNA tree as

1198700= minus ln119877 (12)

Now we can do some examples of computation pro-cedure for the complexity According to our definitionthe given values for the class parameters are listed inTable 3 There are five classes so we obtain the formulas for1198815(1199111015840) 1198814(1199111015840) 1198813(1199111015840) 1198812(1199111015840) and119881

1(1199111015840) successivelyThey are

1198815(1199111015840) = 1 (by definition)

1198814(1199111015840) =

sum1198994

119901=11198994119901119911101584011988111988641199011

(1199111015840)11988111988641199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=1199111015840times (20 times 119881

5(1199111015840) times 1198815(1199111015840))

20= 1199111015840

1198813(1199111015840) =

sum1198993

119901=11198993119901119911101584011988111988631199011

(1199111015840)11988111988631199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=1199111015840times (4 times 119881

5(1199111015840) times 1198814(1199111015840))

4= 11991110158402

1198812(1199111015840) =

sum1198992

119901=11198992119901119911101584011988111988621199011

(1199111015840)11988111988621199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=1199111015840times (4 times 119881

4(1199111015840) times 1198815(1199111015840))

4= 11991110158402

1198811(1199111015840) =

sum1198991

119901=11198991119901119911101584011988111988611199011

(1199111015840)11988111988611199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=81199111015840times 1198811(1199111015840)2

+ 2(1199111015840)3

times 1198811(1199111015840)

19

+

(2(1199111015840)5

+ 2(1199111015840)4

+ 5(1199111015840)3

)

19

(13)

Rearranging the previous equation for 1198811(1199111015840) we obtain

a quadratic for 1198811(1199111015840)

8

19(1199111015840) times 1198811(1199111015840) + (1 minus

2

19(1199111015840)3

) times 1198811(1199111015840)

+1

19(2(1199111015840)5

+ 2(1199111015840)4

+ 5(1199111015840)3

) = 0

(14)

Solving 1198811(1199111015840) we obtain the formula

1198811(1199111015840) = (

(1199111015840)2

4minus

19

81199111015840) plusmn

19

81199111015840radic1198612 minus 119860 (15)

Table 3 The values for the class parameters of Table 2

Classification of rules Isomorphic depth 111989911

119899111

119899112

(8) 1198621rarr 11986211198621

11989912

119899121

119899122

(1) 1198621rarr 11986211198623

11989913

119899131

119899132

(1) 1198621rarr 11986221198622

11989914

119899141

119899142

(119899 = 5) Class 1 (1198991= 8)

(1) 1198621rarr 11986221198624

11989915

119899151

119899152

(1) 1198621rarr 11986231198621

11989916

119899161

119899162

(4) 1198621rarr 11986231198623

11989917

119899171

119899172

(1) 1198621rarr 11986241198622

11989918

119899181

119899182

(5) 1198621rarr 11986241198624

Class 2 (1198992= 1)

11989921

119899211

119899212

(4) 1198622rarr 11986241198625

Class 3 (1198993= 1)

11989931

119899311

119899312

(4) 1198623rarr 11986251198624

Class 4 (1198994= 1)

11989941

119899411

119899412

(20) 1198624rarr 11986251198625

Class 5 (1198995= 1)

11989951

119899511

119899512

(48) 1198625rarr null

Table 4 Test data with topological entropy method and ourmethod

Type Name Koslicki method Our methodE colia Available AvailableEV71b Available Available

DNA H1N1c Available AvailableH5N1d Available AvailableSARSe Available AvailableAbrin Too short Available

Amino acid Ricin Too short AvailableBSEf Too short AvailableCJDg Too short Available

aEscherichia coli O157H7bEnterovirus 71cInfluenza A virus subtype H1N1dInfluenza A virus subtype H5N1eSevere acute respiratory syndromefBovine spongiform encephalopathygCreutzfeldt-Jakob disease

where

119860 =32

361(2(1199111015840)6

+ 2(1199111015840)5

+ 5(1199111015840)4

)

119861 = 1 minus2

19(1199111015840)3

(16)


B

D

A C

Figure 9 Example of homomorphism and isomorphism

04

06

08

1

1 101 201 301 401 501 601 701 801 901

234

Figure 10 Koslicki method (topological entropy method TE forshort) example

Finally the radius of convergence 119877 and complexity1198700

= minus ln119877 can be obtained from this formula Butcomputing the 119911max directly is difficult so we use iterationsand region tests to approximate the complexity details are asfollows

(1) Rewrite the generating function as

119881119898

119894(1199111015840) =

sum119899119894

119901=11198991198941199011199111015840119881119898minus1

1198861198941199011(1199111015840)119881119898minus1

1198861198941199012(1199111015840)

sum119899119894

119902=1119899119894119902

1198810

119894(1199111015840) = 1

(17)

(2) The value from 1198810

119894(1199111015840) to 119881

119898

119894(1199111015840) When 119881

119898minus1

119894(1199111015840) =

119881119898

119894(1199111015840) for all rules we say that 119881119898

119894(1199111015840) reach the

convergence but 1199111015840 is not the 119911max we want Here weset119898 = 1000 for each iteration

(3) Now we can test whether 119881119894(1199111015840) is convergent or

divergent at a number 1199111015840 We use binary search totest every real number between 0 and 1 in every testwhen 119881

119894(1199111015840) converges we set bigger 119911

1015840 next timebut when 119881

119894(1199111015840) diverges we set smaller 1199111015840 next time

Running more iterations will obtain more preciseradius

4 Results

In 2011 Koslicki [1] gave an efficient way to computethe topological entropy of DNA sequence He used fixed

0

02

04

06

08

1

12

1 11 21 31 41 51 61 71 81 91

0

02

04

06

08

1

12

1 51 101 151 201 251

TEIso 1

Iso 2Iso 3

Figure 11 Our method compared with TE using test sequences

002040608

11214

1 101 201

Bovine spongiform encephalopathy

Figure 12 An amino acid sequence example Bovine spongiformencephalopathy

length depending on subword size to compute topologi-cal entropy of sequence For example in Figure 10 (allDNA and amino acid data can be found in NCBI websitehttpwwwncbinlmnihgov) the sequence length is 1027characters and there are three subword sizes 2 3 and 4 withblue red and green lines respectively For larger subwordsize much larger fragment is required for complexity compu-tationThe required fragment size grows exponentially whilethe length of sequence is not dependent on the growth rate ofsubword size so it is not a good method for us overall

We present a new method called structural complexity inprevious sections and there are several benefits from usingour method instead of Koslicki method described as follows

(1) Our results are very different from those obtainedby the topological entropy method see the coloredlines in Figures 11sim14 These figures showed that ourmethod is much sensitive to certain arrangements ofthe elements in the sequence


0

02

04

06

08

1

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3

(a) Fragment size 16

0

02

04

06

08

1

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3

(b) Fragment size 32

0

02

04

06

08

1

12

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3

(c) Fragment size 64

0

02

04

06

08

1

12

14

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3

(d) Fragment size 128

Figure 13 Compare with different methods

(2) Two different characters that exchange position willchange value since Koslicki method just calculatesthe statistical values without structural informationResult was shown in Figure 11 bottom chart the testsequence repeats the same subword several timesFor blue line all complexity values from topologicalentropy are equal within the region of repeatedsubwords For red line complexity values dependon the structure of subword When the fragment ofsequence is different from each other ourmethodwillevaluate to different values

(3) Our method can also calculate amino acid sequencesThe Koslicki method depends on alphabet size andsubword size for example in the basic length 2

substring calculation since standard amino acid typeshave up to 20 it requires a minimum length of 202 +2minus1 to calculate but the amino acid strings are usuallyvery short Sometimes Koslicki method cannot com-pute the amino acid sequence efficiently Figure 12shows that complexity of amino acid sequence canalso be calculated by our method

We also did experiments with lots of data includingfixed fragment size and fixed method on test sequences (seeFigures 13 and 14) Here we redefine the Koslicki method

the fragment size is no longer dependent on subword sizeInstead fixed length fragment like our method is appliedThis change allows us to compare the data easier andnot restricted to the exponentially growing fragment sizeanymore In Figure 13 we found that for larger fragment thecomplexity curve will become smoothly because fragmentsfor each data point contain more information And we notethat there is a common local peak value of those figures thesimple sequence region is big enough that our fragment sizestill contains the same simple sequence

When we compare with the same method shown inFigure 14 we found the same situation more obviously Thusif we have many complexity values with different sizes wehave the opportunity to restore the portion of the DNA

41 Application to Virus Sequences Database and OtherSequences Now we can apply our technique to Chineseword sequences Togawa et al [18] gave a complexity ofChinese words but his study was based on the number ofstrokes which is different fromourmethod Here we use Big5encoding for our system Since the number of Chinese wordsis larger than 10000 we cannot directly usewords as alphabetso we need some conversion We read a Chinese word intofour hexadecimal letters so that we can replace the sequencewith tree representation and compute the complexity


0

02

04

06

08

1 101 201 301 401 501 601 701 801 901

1632

64128

(a) Koslicki method

0

02

04

06

08

1

12

14

1 101 201 301 401 501 601 701 801 901

1632

64128

(b) Our method isomorphism level 1

0

02

04

06

08

1

12

14

1 101 201 301 401 501 601 701 801 901

1632

64128

(c) Our method isomorphism level 2

0

02

04

06

08

1

12

1 101 201 301 401 501 601 701 801 901

1632

64128

(d) Our method isomorphism level 3

Figure 14 Compare with different fragment sizes

When it comes to biomedical section we can create viruscomparison database Once a new virus or prion has beenfound it will be easy to select corresponding drugs at thefirst time according to cross comparison with each otherby complexity in the database We focus on most importantviruses in recent years such as Escherichia coli O157H7 (Ecoli o157) Enterovirus 71 (EV71) Influenza A virus subtypeH1N1 (H1N1) Influenza A virus subtype H5N1 (H5N1) andsevere acute respiratory syndrome (SARS) In recent yearsthese viruses have a significant impact and threat on thehuman world We test these viruses and prions listed inTable 4 Here we can see that all prion regions cannot beanalyzed by Koslicki method but we can do it

Finally if any object can be written as a sequence andthere exists tree representation with alphabet of sequence wecan compute the complexity of the object

5 Summary

In this paper we give a method for computing complexityof DNA sequences The traditional method focused on thestatistical data or simply explored the structural complexitywithout value In our method we transform the DNAsequence to DNA tree with tree representations at first

Then we transform the tree to context-free grammarformat so that it can be classified Finally we use redefined

generating function and find the complexity values We givea not only statistical but also structural complexity for DNAsequences and this technique can be used inmany importantapplications

Acknowledgment

This work was supported by the National Science Councilunder project NSC 100-2221-E-002-234-MY3

References

[1] D Koslicki ldquoTopological entropy of DNA sequencesrdquo Bioinfor-matics vol 27 no 8 Article ID btr077 pp 1061ndash1067 2011

[2] C Cattani G Pierro and G Altieri ldquoEntropy and multi-fractality for the myeloma multiple tet 2 generdquo MathematicalProblems in Engineering vol 2012 Article ID 193761 14 pages2012

[3] S Manna and C Y Liou ldquoReverse engineering approach inmolecular evolution simulation and case study with enzymeproteinsrdquo in Proceedings of the International Conference onBioinformatics amp Computational Biology (BIOCOMP rsquo06) pp529ndash533 2006

[4] R Zhang and C T Zhang ldquoZ curves an intutive tool forvisualizing and analyzing the DNA sequencesrdquo Journal of


Biomolecular Structure andDynamics vol 11 no 4 pp 767ndash7821994

[5] P Tino ldquoSpatial representation of symbolic sequences throughiterative function systemsrdquo IEEE Transactions on Systems Manand Cybernetics A vol 29 no 4 pp 386ndash393 1999

[6] C K Peng S V Buldyrev A L Goldberger et al ldquoLong-rangecorrelations in nucleotide sequencesrdquoNature vol 356 no 6365pp 168ndash170 1992

[7] B L Hao H C Lee and S Y Zhang ldquoFractals related to longDNA sequences and complete genomesrdquo Chaos solitons andfractals vol 11 no 6 pp 825ndash836 2000


[9] C Y Liou T H Wu and C Y Lee ldquoModeling complexity inmusical rhythmrdquo Complexity vol 15 no 4 pp 19ndash30 2010

[10] P Prusinkiewicz ldquoScore generation with lsystemsrdquo in Proceed-ings of the International Computer Music Conference pp 455ndash457 1986

[11] P Prusinkiewicz and A Lindenmayer The Algorithmic Beautyof Plants Springer New York NY USA 1996

[12] P Worth and S Stepney ldquoGrowing music musical interpreta-tions of L-systemsrdquo in Applications of Evolutionary Computingvol 3449 of Lecture Notes in Computer Science pp 545ndash550Springer Berlin Germany 2005

[13] A Lindenmayer ldquoMathematicalmodels for cellular interactionsin development II Simple and branching filaments with two-sided inputsrdquo Journal of Theoretical Biology vol 18 no 3 pp300ndash315 1968

[14] ldquoWikipedia L-systemmdashWikipedia the free encyclopediardquo 2012[15] H Barlow ldquoUnsupervised learningrdquo Neural Computation vol

1 no 3 pp 295ndash311 1989[16] R Badii and A Politi Complexity Hierarchical Structures

and Scaling in Physics vol 6 Cambridge University PressCambridge UK 1999

[17] W Kuich ldquoOn the entropy of context-free languagesrdquo Informa-tion and Control vol 16 no 2 pp 173ndash200 1970

[18] T Togawa K Otsuka S Hiki and H Kitaoka ldquoComplexity ofchinese charactersrdquo Forma vol 15 pp 409ndash414 2001


Research ArticleImproving Spatial Adaptivity of Nonlocal Means in Low-DosedCT Imaging Using Pointwise Fractal Dimension

Xiuqing Zheng1 Zhiwu Liao2 Shaoxiang Hu3 Ming Li4 and Jiliu Zhou1

1 College of Computer Science Sichuan University No 29 Jiuyanqiao Wangjiang Road Chengdu 610064 Sichuan China2 School of Computer Science Sichuan Normal University No 1819 Section 2 of Chenglong RoadChengdu 610101 Sichuan China

3 School of Automation Engineering University of Electronic Science and Technology of China No 2006 Xiyuan AveWest Hi-Tech Zone Chengdu 611731 Sichuan China

4 School of Information Science and Technology East China Normal University No 500 Dong-Chuan RoadShanghai 200241 China

Correspondence should be addressed to Zhiwu Liao liaozhiwu163com



Copyright copy 2013 Xiuqing Zheng et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

NLMs is a state-of-art image denoising method however it sometimes oversmoothes anatomical features in low-dose CT (LDCT)imaging In this paper we propose a simple way to improve the spatial adaptivity (SA) of NLMs using pointwise fractal dimension(PWFD) Unlike existing fractal image dimensions that are computed on the whole images or blocks of images the new PWFDnamed pointwise box-counting dimension (PWBCD) is computed for each image pixel PWBCD uses a fixed size local windowcentered at the considered image pixel to fit the different local structures of imagesThen based on PWBCD a newmethod that usesPWBCD to improve SA of NLMs directly is proposedThat is PWBCD is combined with the weight of the difference between localcomparison windows for NLMs Smoothing results for test images and real sinograms show that PWBCD-NLMs with well-chosenparameters can preserve anatomical features better while suppressing the noises efficiently In addition PWBCD-NLMs also hasbetter performance both in visual quality and peak signal to noise ratio (PSNR) than NLMs in LDCT imaging

1 Introduction

Radiation exposure and associated risk of cancer for patientsfrom CT examination have been increasing concerns inrecent years Thus minimizing the radiation exposure topatients has been one of the major efforts in modern clinicalX-ray CT radiology [1ndash8] However the presentation ofserious noise and many artifacts degrades the quality of low-dose CT images dramatically and decreases the accuracyof diagnosis dose Although many strategies have beenproposed to reduce their noise and artifacts [9ndash14] filteringnoise from clinical scans is still a challenging task since thesescans contain artifacts and consist of many structures with

different shape size and contrast which should be preservedfor making correct diagnosis

Recently nonlocalmeans (NLMs) is proposed for improv-ing the performance of classical adaptive denoising methods[15ndash17] and shows good performance even in low-dose CT(LDCT) imaging [18ndash20]

There are two novel ideas for NLMs One is that thesimilar points should be found by comparing the differencebetween their local neighborhoods instead of by comparingtheir gray levels directly Since gray levels of LDCT will bepolluted seriously by noises and artifacts finding similarpoints by local neighborhoods instead of by gray levelsdirectly will help NLMs find correct similar pointsThe other


important idea for NLMs is that the similar points shouldbe searched in large windows to guarantee the reliability ofestimation

Following the previous discussion the NLMs denoisingshould be performed in two windows one is comparisonpatch and the other is searching window The sizes of thesetwo windows and the standard deviation 120590

119903of the Gaussian

kernel which is used for computing the distance betweentwo neighborhoods should be determined according tothe standard deviation of noises [15ndash17] and these threeparameters are identical in an image

Some researchers find that identical sizes of two windowsand identical Gaussian kernel 120590

119903in an image are not the

best choice for image denoising [21ndash25]The straightest moti-vation is that the parameters should be modified accordingto the different local structures of images For example theparameters near an edge should be different from parametersin a large smooth region

An important work to improve the performance of NLMsis quasi-local means (QLMs) proposed by us [21 22] Weargue that nonlocal searching windows are not necessary formost of image pixels In fact for points in smooth regionswhich are the majority of image pixels local searchingwindows are big enough while for points near singularitiesonly the minority of image pixels nonlocal search windowsare necessary Thus the method is named quasi-local whereitis local for most of image pixels and nonlocal only for pixelsnear singularities The searching windows for quasi-localmeans (QLMs) are variable for different local structuresand QLMs can get better singularity preservation in imagedenoising than classical NLMs

Other important works about improving spatial adaptiv-ity of NLMs are proposed very recently [23ndash25] The startingpoint for these works is that the image pixels are parted intodifferent groups using supervised learning or semisupervisedlearning and clustering However the learning and clusteringwill waste a lot of computation time and resource which willhamper them to be applied inmedical imagingThuswemustpropose a new method for improving the spatial adaptivitywith a simple way

In this paper we propose a simple and powerful methodto improve spatial adaptivity for NLMs in LDCT imagingusing pointwise fractal dimension (PWFD) where PWFDis computed pixel by pixel in a fixed-size window centeredat the considering pixel According to the new definition ofPWFD different local structures will be with different localfractal dimensions for example pixels near edge regions willbe with relatively big PWFDs while PWFDs of pixels insmooth regions will be zeros Thus PWFD can provide localstructure information for image denoising After definedPWFD which can fit different local structures of images wellwe design a new weight function by combining the newPWFD difference between two considering pixels with theweight of original NLMs measured by gray level differencebetween two comparison windows Thus using this newweight function the proposed method will not only preservethe gray level adaptivity of NLMs but also improve the SA ofNLMs

The arrangement of this paper is as follows In Section 2the backgrounds are introduced then the new proposedmethod is presented in Section 3 the experiment results areshown and discussed in Section 4 and the final part is theconclusions and acknowledgment

2 Backgrounds

In this section we will introduce related backgrounds of theproposed method

21 Noise Models Based on repeated phantom experimentslow-mA (or low-dose) CT calibrated projection data afterlogarithm transform were found to follow approximately aGaussian distribution with an analytical formula between thesample mean and sample variance that is the noise is asignal-dependent Gaussian distribution [11]

The photon noise is due to the limited number of photonscollected by the detector For a given attenuating path in theimaged subject 119873

0(119894 120572) and119873(119894 120572) denote the incident and

the penetrated photon numbers respectively Here 119894 denotesthe index of detector channel or bin and 120572 is the index ofprojection angle In the presence of noises the sinogramshould be considered as a randomprocess and the attenuatingpath is given by

119903119894= minus ln [ 119873 (119894 120572)

1198730 (119894 120572)

] (1)

where 1198730(119894 120572) is a constant and 119873(119894 120572) is Poisson distribu-

tion with mean119873Thus we have

119873(119894 120572) = 1198730 (119894 120572) exp (minus119903119894) (2)

Both its mean value and variance are119873Gaussian distributions of ployenergetic systems were

assumed based on limited theorem for high-flux levels andfollowed many repeated experiments in [11] We have

1205902

119894(120583119894) = 119891119894exp(

120583119894

120574) (3)

where 120583119894is the mean and 1205902

119894is the variance of the projection

data at detector channel or bin 119894 120574 is a scaling parameter and119891119894is a parameter adaptive to different detector binsThe most common conclusion for the relation between

Poisson distribution and Gaussian distribution is that thephoton count will obey Gaussian distribution for the casewith large incident intensity and Poisson distribution withfeeble intensity [11]

22 Nonlocal Means (NLMs) Given a discrete noisy image119910 the estimated value (

119894) for a pixel 119894 is computed as a

weighted nonlocal average

119894=

1

119862 (119894)sum

119895isin119861(119894 119903)

119910119895120596 (119894 119895) (4)


where 119861(119894 119903) indicates a neighborhood centered at 119894 and size(2119903 + 1) times (2119903 + 1) called searching window and 119862(119894) =

sum119895isin119861(119894 119903)

120596(119894 119895) The family of weights 120596(119894 119895) depend on thesimilarity between the pixels 119894 and 119895 and satisfy 0 le 120596(119894 119895) le 1and sum

119895isin119861(119894 119903)120596(119894 119895) = 1

The similarity between two pixels 119894 and 119895 1198892(119894 119895) dependson the similarity of the intensity gray level vectors 119861(119894 119891) and119861(119895 119891) where 119861(119896 119891) denotes a square window with fixedsize (2119891 + 1) times (2119891 + 1) and centered at a pixel 119896 namedcomparison patch

1198892(119894 119895) =

1

(2119891 + 1)2

sum

119896isin119861(0 119891)

(119910119894+119896minus 119910119895+119896)2

(5)

and the weights 120596(119894 119895) are computed as

120596 (119894 119895) = 119890minusmax(1198892minus21205902

119873 0)ℎ2

(6)

where 120590119873denotes the standard deviation of the noise and ℎ

is the filtering parameter set depending on the value 120590119873

23 Box-CountingDimension Box-counting dimension alsoknown as Minkowski dimension or Minkowski-Bouliganddimension is a way of determining the fractal dimensionof a set 119878 in a Euclidean space 119877119899 or more generally in ametric space (119883 119889) To calculate this dimension for a fractal119878 putting this fractal on an evenlyspaced grid and count howmany boxes are required to cover the set The box-countingdimension is calculated by seeing how this number changes aswemake the grid finer by applying a box-counting algorithm

Suppose that119873(120576) is the number of boxes of side length 120576required to cover the set Then the box-counting dimensionis defined as

dim (119878) = lim120576rarr0

log119873(120576)

log (1120576) (7)

Given an 119873 times 119873 image whose gray level is G then theimage is part into the 120576 times 120576 grids which are related to 120576 times 120576 times 120576cube grids If for the 119895th grid the greatest gray level is in the120580th box and the smallest is in the 120581th box then the boxnumberfor covering the grid is

119899120576= 120580 minus 120581 + 1 (8)

Therefore the box number for covering the whole image is

119873120576= sum

119895

119899120576(119895) (9)

Selecting different scale 120576 we can get related119873120576Thuswe have

a group of pairs (120576119873120576) The group can be fit with a line using

least-squares fitting the slope of the line is the box-countingdimension

3 The New Method

In this section wewill present our newproposed algorithm indetail The motivation for the proposed method is that SA of

NLMs should be improved in a simpler way The new PWFDis introduced firstly to adapt complex image local structuresand then the new weight functions based on PWFD arediscussed At the end of this section the procedures of theproposed method are shown

31 Pointwise Box-CountingDimension In image processingthe fractal dimension usually is used for characterizingroughness and self-similarity of images However most ofworks only focus on how to compute fractal dimensions forimages or blocks of images [26ndash30] Since fractal dimensioncan characterize roughness and self-similarity of images italso can be used for characterizing the local structures ofimages by generalizing it to PWFD which is computed pixelby pixel using a fixed-size window centered in the consideredpixel Thus each pixel in an image has a PWFD and it equalsthe fractal dimension of the fixed-size window centered in theconsidered pixel

Following the previous discussion the pointwise box-counting dimension (PWBCD) starts from replacing eachpixel 119894 to a fixed-size window 119903 times 119903 centered at 119894 It is obviousthat PWFD can be generalized to all definitions of fractaldimensions However in order tomake our explanationmoreclearly we only extend the new definition to PWBCD

According to the new PWFD PWBCD should be com-puted for each pixel in the image For each pixel 119894 thePWBCD is computed in a fixed-size 119903times 119903window centered at119894

The 119903 times 119903 window is parted into the 120576 times 120576 grids which arerelated to 120576 times 120576 times 120576 cube grids If for the 119895th grid the greatestgray level is in the 120580th box and the smallest is in the 120581th boxthen the box number for covering the grid is

119899120576 (119894) = 120580 minus 120581 + 1 (10)

Therefore the box number for covering the whole 119903 times 119903

window is

119873120576 (119894) = sum

119895

119899120576(119895) (11)

Selecting different scale 120576 we can get related 119873120576(119894) Thus we

have a group of pairs (120576 119873120576(119894)) The group can be fit with a

line using least-squares fitting the slope 119896(119894) of the line is thebox-counting dimension

Note that each pixel in an image has a PWBCD valueThus we can test the rationality for PWBCD by showingPWBCD values using an image In these PWBCD imageshigh PWBCD values are shown as white points while lowPWBCD values are shown as gray or black points If PWBCDimages are similar to the original images with big PWBCDvalues near singularities and small PWBCD values in smoothregions the rationality is testified

Figure 1 shows PWBCD images for three images an testimage composed by some blocks with different gray levelsa LDCT image and 512 times 512 barbara The white pointssignify the pixels with big fractal dimensions while blackpoints signify the pixels with small fractal dimensions Here119903 = 32 and 120576 = 2 4 8 16 32 Note that the white partscorrespond the texture parts of barbara and soft tissues of the


(a) (b) (c)

(d) (e) (f)

Figure 1 Images and their pointwise box-counting dimension images the first row shows images while the second row shows their pointwisebox-counting dimension images Here 119903 = 32 and 120576 = 2 4 8 16 32

second image in the first row Moreover the PWBCD imagesare very similar to the original imageswhich demonstrate thatthe PWBCDcan be used for characterizing the local structureof images

32 The New Weight Function After defining the PWBCDwe must find an efficient and powerful way to use thePWBCD in NLMs directly Just as discussed in the previoussubsection PWBCD can characterize the local structures forimages well Thus PWBCD should be used to weight thepoints in the searching patch That is (6) should be changedas

120596 (119894 119895) = 119890minusmax(1198892minus21205902

119873 0)ℎ2

1minus(119896(119894)minus119896(119895))

2ℎ2

2 (12)

where 119896(sdot) is FDBCD value for the considering pixel and iscomputed according to the method proposed in Section 31120590119873

denotes the standard deviation of the noise ℎ1 ℎ2are

the filtering parameters 1198892(119894 119895) is the similarity between twopixels 119894 and 119895 depending on the similarity of the intensitygray level vectors 119861(119894 119891) and 119861(119895 119891) where 119861(119896 119891) denotes asquarewindowwith fixed size (2119891+1) times (2119891+1) and centeredat a pixel 119896

1198892(119894 119895) =

1

(2119891 + 1)2

sum

119896isin119861(0 119891)

(119910119894+119896minus 119910119895+119896)2

(13)

Given a discrete noisy image 119910 the estimated value (119894)

for a pixel 119894 is computed as a weighted nonlocal average

119894=

1

119862 (119894)sum

119895isin119861(119894 119903)

119910119895120596 (119894 119895) (14)

where 119861(119894 119903) indicates a neighborhood centered at 119894 andsize (2119903 + 1) times (2119903 + 1) called searching window and119862(119894) = sum

119895isin119861(119894 119903)120596(119894 119895) Note that the family of weights

120596(119894 119895) depend on the similarity between the pixels 119894 and 119895and satisfy 0 le 120596(119894 119895) le 1 and sum

119895isin119861(119894 119903)120596(119894 119895) = 1

33 The Steps of the New Method The steps of PWBCD-NLMs are as follows

(1) Compute pointwise box-counting dimension for eachofthe pixelsFor each of the pixels given 119903 = 2

119899 119899 isin 119885 and

120576 = 2 4 119903 compute PWBCD according toSection 31 and get a matrix 119870 with the same size asthe image

(2) Compute weights determine parameters 120590119873 ℎ1 ℎ2

the size of comparison window 119888119903 and the size of thesearching patch 119904119903Compute the difference between two comparisonwindows 1198892 using (13)Compute the weights 120596(119894 119895) using (12)

(3) Estimate real gray levels estimate real levels (119894) using(14)

4 Experiments and Discussion

The main objective for smoothing LDCT images is to deletethe noise while preserving anatomy features for the images

In order to show the performance of PWBCD-NLMs a 2-dimensional 512 times 512 test phantom is shown in Figure 1(a)


(a) Noisy image with 119891119894 = 25 119879 =2119890 + 4

(b) Reconstructed image from (a)using NLMs

(c) Reconstructed image from (a)using PWBCD-NLMs

(d) Noisy image with 119891119894 = 40 119879 =2119890 + 4

(e) Reconstructed image from (d)using NLMs

(f) Reconstructed image from (d)using PWBCD-NLMs

Figure 2 Noisy test images and reconstructed images

The number of bins per view is 888 with 984 views evenlyspanned on a circular orbit of 360∘ The detector arrays areon an arc concentric to the X-ray source with a distance of949075mm The distance from the rotation center to the X-ray source is 541mmThe detector cell spacing is 10239mm

The LDCT projection data (sinogram) is simulated byadding Gaussian-dependent noise (GDN) whose analyticform between its mean and variance has been shown in (3)with 119891

119894= 25 35 40 and 119879 = 2119890 + 4 The projection data

is reconstructed by standard Filtered Back Projection (FBP)Since both the original projection data and sinogram havebeen provided the evaluation is based on peak signal to noiseration (PSNR) between the ideal reconstructed image andreconstructed image

The PWBCDs for images are computed according toSection 31 and the parameters are 119903 = 32 and 120576 =

2 4 8 16 32 The new proposed method is compared withNLMs and their common parameters includes the standarddeviation of noise 120590

119873= 15 the size of comparison window

is 7 times 7 (119888119903 = 7) while the size of searching patch is 21 times21 (119904119903 = 21) The other parameter for NLMswhick is theGaussian kernel for weights defined on (13) is ℎ = 12 andthe parameters for the new method are the sizes of Gaussiankernel for two weights defined on (12) ℎ

1= 15 for the

weights of difference between comparison window and ℎ2=

10 for the weights between two PWBCDs All parameters arechosen by hand with many experiments which has the bestperformance

Table 1 summarized PSNR between the ideal recon-structed image and filtered reconstructed image The

Table 1 PSNR for the test image

Noise PSNR of PSNR of PSNR ofparameters the noisy image NLMs PWBCD-NLMs119891119894= 25 119879 = 2119890 + 4 2329 3419 3495

119891119894= 35 119879 = 2119890 + 4 2188 3379 3459

119891119894= 4 119879 = 2119890 + 4 2130 3345 3416

PWBCD-NLMs has better performance in different noiselevels in the term of PSNR than NLMs

Figure 2 shows noisy test images and their reconstructedimages using NLMs and the proposed method Althoughthe reconstructed images are very similar to each other thereconstructed images using the newmethod also show betterperformance in edge preservation especially in weak andcurve edge preserving than the NLMs Since PWBCD-NLMsprovides a more flexible way for handling different localimage structures it hasmuch good performance in denoisingwhile preserving structures

One abdominal CT images of a 62-year-old woman werescanned from a 16 multidetector row CT unit (SomatomSensation 16 Siemens Medical Solutions) using 120 kVp and5mm slice thickness Other remaining scanning parametersare gantry rotation time 05 second detector configuration(number of detector rows section thickness) 16 times 15mmtable feed per gantry rotation 24mm pitch 1 1 and recon-struction method Filtered Back Projection (FBP) algorithmwith the soft-tissue convolution kernel ldquoB30f rdquo Different CTdoses were controlled by using two different fixed tube


(a) Original SDCT image with tube current timeproduct 150mAs

(b) Original LDCT image with tube current timeproduct 60mAs

(c) Reconstructed image from (b) using NLMs (d) Reconstructed image from (b) usingPWBCD-NLMs

Figure 3 (b) Real LDCT reconstructed image (a) related SDCT reconstructed images and (c)-(d) reconstructed images fromLDCT sinogramusing NLMs and the new method

currents 60mAs for LDCT and 150mAs (60mA or 300mAs)for SDCT resp) The CT dose index volumes (CTDIvol)for LDCT images and SDCT images are in positive linearcorrelation to the tube current and are calculated to beapproximately ranged between 1532mGy and 316mGy [18]

On sinogram space the PWBCDs for images are com-puted according to Section 31 and the parameters are 119903 =

32 and 120576 = 2 4 8 16 32 The new proposed methodis compared with NLMs and their common parametersincludes the standard deviation of noise 120590

119873= 15 the size

of comparison window is 7 times 7 (119888119903 = 7) while the size ofsearching patch is 21 times 21 (119904119903 = 21) The other parameterfor NLMswhich is the Gaussian kernel for weights definedon (13) is ℎ = 12 and the parameters for the new method arethe sizes of Gaussian kernel for two weights defined on (12)ℎ1= 15 for the weights of difference between comparison

window and ℎ2= 10 for the weights between two PWBCDs

Comparing the original SDCT images and LDCT imagesin Figure 3 we found that the LDCT images were severelydegraded by nonstationary noise and streak artifacts InFigure 3(d) for the proposed approach experiments obtain

more smooth images Both in Figures 3(c) and 3(d) wecan observe better noiseartifacts suppression and edgepreservation than the LDCT image Especially comparedto their corresponding original SDCT images the fine fea-tures representing the hepatic cyst were well restored byusing the proposed method We can observe that the noisegrains and artifacts were significantly reduced for the NLMsand PWBCD-NLMs processed LDCT images with suitableparameters both in Figures 3(c) and 3(d) The fine anatomi-calpathological features can be well preserved compared tothe original SDCT images (Figure 3(a)) under standard doseconditions

5 Conclusions

In this paper we propose a new PWBCD-NLMs methodfor LDCT imaging based on pointwise boxing-countingdimension and its new weight function Since PWBCD cancharacterize the local structures of image well and also can becombined with NLMs easily it provides a more flexible way


to balance the noise reduction and anatomical details preser-vation Smoothing results for phantoms and real sinogramsshow that PWBCD-NLMs with suitable parameters has goodperformance in visual quality and PSNR

Acknowledgments

This paper is supported by the National Natural ScienceFoundation of China (no 60873102) Major State BasicResearch Development Program (no 2010CB732501) andOpen Foundation of Visual Computing and Virtual RealityKey Laboratory Of Sichuan Province (no J2010N03) MingLi also acknowledges the supports by the NSFC under theProject Grant nos 61272402 61070214 and 60873264 and the973 plan under the Project Grant no 2011CB302800

References

[1] D J Brenner and E J Hall ldquoComputed tomography-an increas-ing source of radiation exposurerdquo New England Journal ofMedicine vol 357 no 22 pp 2277ndash2284 2007

[2] J Hansen and A G Jurik ldquoSurvival and radiation risk inpatients obtaining more than six CT examinations during oneyearrdquo Acta Oncologica vol 48 no 2 pp 302ndash307 2009

[3] H J Brisse J Brenot N Pierrat et al ldquoThe relevance ofimage quality indices for dose optimization in abdominalmulti-detector row CT in children experimental assessment withpediatric phantomsrdquo Physics in Medicine and Biology vol 54no 7 pp 1871ndash1892 2009

[4] L Yu ldquoRadiation dose reduction in computed tomographytechniques and future perspectiverdquo Imaging in Medicine vol 1no 1 pp 65ndash84 2009

[5] J Weidemann G Stamm M Galanski and M KeberleldquoComparison of the image quality of various fixed and dosemodulated protocols for soft tissue neck CT on aGE Lightspeedscannerrdquo European Journal of Radiology vol 69 no 3 pp 473ndash477 2009

[6] W Qi J Li and X Du ldquoMethod for automatic tube currentselection for obtaining a consistent image quality and doseoptimization in a cardiac multidetector CTrdquo Korean Journal ofRadiology vol 10 no 6 pp 568ndash574 2009

[7] A Kuettner B Gehann J Spolnik et al ldquoStrategies for dose-optimized imaging in pediatric cardiac dual source CTrdquo RoFovol 181 no 4 pp 339ndash348 2009

[8] P Kropil R S Lanzman C Walther et al ldquoDose reduction andimage quality in MDCT of the upper abdomen potential of anadaptive post-processing filterrdquo RoFo vol 182 no 3 pp 248ndash253 2009

[9] H B Lu X Li L Li et al ldquoAdaptive noise reduction towardlow-dose computed tomographyrdquo in Proceedings of the MedicalImaging 2003 Physics of Medical Imaging parts 1 and 2 vol5030 pp 759ndash766 February 2003

[10] J C Giraldo Z S Kelm L S Guimaraes et al ldquoCompar-ative study of two image space noise reduction methods forcomputed tomography bilateral filter and nonlocal meansrdquo inProceedings of the Annual International Conference of the IEEEEngineering in Medicine and Biology Society vol 1 pp 3529ndash3532 2009

[11] H B Lu I T Hsiao X Li and Z Liang ldquoNoise properties oflow-dose CT projections and noise treatment by scale transfor-mationsrdquo in Proceedings of the IEEE Nuclear Science SymposiumConference Record vol 1ndash4 pp 1662ndash1666 November 2002

[12] P J La Riviere ldquoPenalized-likelihood sinogram smoothing forlow-dose CTrdquo Medical Physics vol 32 no 6 pp 1676ndash16832005

[13] S Hu Z Liao and W Chen ldquoReducing noises and artifactssimultaneously of low-dosed X-ray computed tomographyusing bilateral filter weighted by Gaussian filtered sinogramrdquoMathematical Problems in Engineering vol 2012 Article ID138581 14 pages 2012

[14] S Hu Z Liao and W Chen ldquoSinogram restoration for low-dosed X-ray computed tomography using fractional-orderPerona-Malik diffusionrdquo Mathematical Problems in Engineer-ing vol 2012 Article ID 391050 13 pages 2012

[15] A Buades B Coll and J M Morel ldquoA review of imagedenoising algorithms with a new onerdquoMultiscale Modeling andSimulation vol 4 no 2 pp 490ndash530 2005

[16] A Buades B Coll and J M Morel ldquoA non-local algorithm forimage denoisingrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) vol 2 pp 60ndash65 June 2005

[17] A Buades B Coll and J MMorel ldquoNonlocal image andmoviedenoisingrdquo International Journal of Computer Vision vol 76 no2 pp 123ndash139 2008

[18] C Yang C Wufan Y Xindao et al ldquoImproving low-doseabdominal CT images by weighted intensity averaging overlarge-scale neighborhoodsrdquo European Journal of Radiology vol80 no 2 pp e42ndashe49 2011

[19] Y Chen Z Yang W Chen et al ldquoThoracic low-dose CT imageprocessing using an artifact suppressed largescale nonlocalmeansrdquo Physics in Medicine and Biology vol 57 no 9 pp 2667ndash2688 2012

[20] Y Chen D Gao C Nie et al ldquoBayesian statistical recon-struction for low-dose X-ray computed tomography usingan adaptive-weighting nonlocal priorrdquo Computerized MedicalImaging and Graphics vol 33 no 7 pp 495ndash500 2009

[21] Z Liao S Hu and W Chen ldquoDetermining neighborhoodsof image pixels automatically for adaptive image denoisingusing nonlinear time series analysisrdquoMathematical Problems inEngineering vol 2010 Article ID 914564 2010

[22] Z Liao S HuM Li andW Chen ldquoNoise estimation for single-slice sinogram of low-dose X-ray computed tomography usinghomogenous patchrdquoMathematical Problems in Engineering vol2012 Article ID 696212 16 pages 2012

[23] T Thaipanich B T Oh P-H Wu and C-J Kuo ldquoAdaptivenonlocal means algorithm for image denoisingrdquo in Proceedingsof the IEEE International Conference on Consumer Electronics(ICCE rsquo10) 2010

[24] T Thaipanich and C-C J Kuo ldquoAn adaptive nonlocal meansscheme formedical image denoisingrdquo in Proceedings of the SPIEMedical Imaging 2010 Image Processing vol 7623 March 2010

[25] R Yan L Shao S D Cvetkovic and J Klijn ldquoImprovednonlocal means based on pre-classification and invariant blockmatchingrdquo Journal of Display Technology vol 8 no 4 pp 212ndash218 2012

[26] A K Bisoi and J Mishra ldquoOn calculation of fractal dimensionof imagesrdquo Pattern Recognition Letters vol 22 no 6-7 pp 631ndash637 2001


[27] R Creutzberg and E Ivanov ldquoComputing fractal dimensionof image segmentsrdquo in Proceedings of the 3rd InternationalConference of Computer Analysis of Images and Patterns (CAIPrsquo89) 1989

[28] M Ghazel G H Freeman and E R Vrscay ldquoFractal imagedenoisingrdquo IEEE Transactions on Image Processing vol 12 no12 pp 1560ndash1578 2003

[29] M Ghazel G H Freeman and E R Vrscay ldquoFractal-waveletimage denoising revisitedrdquo IEEE Transactions on Image Process-ing vol 15 no 9 pp 2669ndash2675 2006

[30] B Pesquet-Popescu and J L Vehel ldquoStochastic fractal modelsfor image processingrdquo IEEE Signal Processing Magazine vol 19no 5 pp 48ndash62 2002


Research ArticleThree-Dimensional Identification of Microorganisms Usinga Digital Holographic Microscope

Ning Wu1 Xiang Wu2 and Tiancai Liang3

1 Shenzhen Key Lab of Wind Power and Smart Grid Harbin Institute of Technology Shenzhen Graduate SchoolShenzhen 518055 China

2 School of Mechanical and Electrical Engineering Harbin Institute of Technology 92 West Dazhi Street Nan Gang DistrictHarbin 150001 China

3 GRG Banking Equipment Co Ltd 9 Kelin Road Science Town Guangzhou 510663 China

Correspondence should be addressed to Xiang Wu xiangwuhiteducn



Copyright copy 2013 Ning Wu et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper reports a method for three-dimensional (3D) analysis of shift-invariant pattern recognition and applies to holographicimages digitally reconstructed from holographic microscopes It is shown that the sequential application of a 2D filter to the plane-by-plane reconstruction of an optical field is exactly equivalent to the application of amore general filter with a 3D impulse responseWe show that any 3D filters with arbitrary impulse response can be implemented in this wayThis type of processing is applied to thetwo-class problem of distinguishing different types of bacteria It is shown that the proposed technique can be easily implementedusing a modified microscope to develop a powerful and cost-effective system with great potential for biological screening

1 Introduction

In the past high-resolution imaging of three-dimensional(3D) objects or matter suspended in a volume of fluid hasmainly been accomplished using confocal microscopes [1]In recent years however attention has returned to wide-field optical microscopy using coherent illumination andholographic recording techniques that exploit advances indigital imaging and image processing to compute 3D imagesIn contrast with confocal imaging coherent microscopyprovides 3D information from a single recording that canbe processed to obtain imaging modes analogous to darkfield phase or interference contrast as required [2ndash7] Incomparison with incoherent microscopes a coherent instru-ment provides an image that can be focused at a later stageand can be considered as a microscope with an extendeddepth of field For screening purposes the increased depthof field is significant particularly at high magnifications andhigh numerical aperture For example a conventional highmagnification microscope has a depth of field of only afew microns whereas a comparable coherent instrument can

have a depth of field of a few millimetres or so This meansthat around 1000 times the volume of fluid can be screenedfrom the information contained in a single digital recording[8]

The potential of coherent microscopes for automatedbiological screening is clearly dependent on the developmentof robust image or pattern recognition algorithms [9] Inessence the application of pattern recognition techniques tocoherent images is similar to that applied to their incoherentcounterpart The task can be defined as that of highlightingobjects of interest (eg harmful bacteria) from other clutter(eg cell tissue and benign bacteria) This process should beaccomplished regardless of position and orientation of theobjects of interest within the image It can be accomplishedusing variations on correlation processing Linear correlationprocessing has been criticized in the past for its lack ofrotation invariance and its inability to generalize in themanner of neural network classifiers however a cascadeof correlators separated by nonlinear (decision) layers hasconsiderably enhanced performance [5 10] Furthermore wehave shown that this is the architecture a neural network


classifier assumes if it is trained to provide a shift-invariantoutput [11 12]

The application of linear correlation processing tothe complex images recorded by a digital phase shiftinginterferometer has recently been demonstrated by Javidiand Tajahuerce [13] Pattern recognition techniques imple-mented using a holographic microscope for the detection ofmicroscale objects has also been considered by Dubois et al[5 14] In these works the 3D sample field was reconstructedplane by plane and image classification was performed bythe application of a 2D correlation filter to each of thereconstructed planes It is noted however that although 2Dcorrelation can be applied independently to different imageplanes it does not take into account the true nature of 3Doptical fields nor that the information in any two planes ofthese fields is in fact highly correlated [15]

In this paper we considered from first principles 3Dshift-invariant pattern recognition applied to optical fieldsreconstructed from digital holographic recordings It willbe shown that the sequential application of a 2D filter toplane-by-plane reconstructions is exactly equivalent to theapplication of a 3D filter to the full 3D reconstruction ofthe optical field However a linear filter designed based onthe plane of focus will not necessarily work for planes outof focus and therefore a 3D nonlinear filtering scheme isintroduced into the optical propagation field The 3D non-linear filter is a system implemented with a general impulseresponse and followed by a nonlinear threshold We willprove with experiment that a 3D nonlinear filtering structurecan significantly improve the classification performance in3D pattern recognition In the experiment we will apply the3D nonlinear filter to 3D images of two types of bacteriarecorded from a holographic microscope and the enhancedclassification performance will be shown

2 Theory

Firstly we define the 3D cross-correlation of complex func-tions 119906(r) and ℎ(r) as

119877 (r) = int+infin

minusinfin

119906 (x) ℎ (x minus r) 119889x (1)

where r is a position vector and 119889x conventionally denotesthe scalar quantity (119889119909 119889119910 119889119911) Assume that119867(k) and 119880(k)are the Fourier transforms of ℎ(r) and 119906(r) respectivelyaccording to the convolution theorem 119877(r) can also bewritten


minusinfin

119880 (k)119867lowast (k) 1198901198952120587ksdotr119889k (2)

where the superscript lowast denotes complex conjugation Forpattern recognition purposes (1) and (2) are equivalent waysto describe the process of correlation filtering defined in spacedomain and frequency domain respectively

It is clear from (1) and (2) that in general 3D correlationfiltering requires 3D integration (in either the space orfrequency domains) However this is not the case whencorrelation filtering is applied to monochromatic optical

fields propagating forward typically the holographic recon-struction of optical fields by digital or optical means Inessence this is because 119880(k) is nonzero only within an areaof a 2D surface and consequently 119906(r) is highly correlated

According to scalar diffraction theory the complexamplitude 119906(r) representing a monochromatic optical fieldpropagation in a uniform dielectric must obey the Helmholtzequation [16] such that

nabla2119906 (r) + 412058721198962119906 (r) = 0 (3)

where 119896 is a constant Neglecting evanescent waves that occurclose to boundaries and other obstructions it is well knownthat the solutions to this equation are planewaves of the form

119906 (r) = 119860 exp (1198952120587k sdot r) (4)

where 119860 is a complex constant In these equations 119896 andk are the wave number and wave vector respectively andare defined here such that 119896 = |k| = 1120582 where 120582is wavelength In consequence any monochromatic opticalfield propagating a uniform dielectric is described completelyby the superposition of plane waves such that


minusinfin

119880 (k) exp (1198952120587k sdot r) 119889k (5)

where 119880(k) is the spectral density and 119880(k) is the Fouriertransform of 119906(r) such that

119880 (k) = int+infin

minusinfin

119906 (r) exp (minus1198952120587k sdot r) 119889k (6)

It is noted that because 119906(r) consists of plane wavesof single wavelength the values of 119880(k) only exist on aninfinitely thin spherical shell with a radius 119896 = |k| = 1120582 Inconsequence if a general 3D correlation filter with transferfunction 119867(k) is applied to a monochromatic optical field119880(k) then in frequency domain the product 119880(k)119867lowast(k) isalso nonzero only on the spherical shell and consequently willobey the Helmholtz equation If we expand (5) we have

119906 (119903119909 119903119910 119903119911)

=∭infin

119880(119896119909 119896119910 119896119911) exp (1198952120587 (119896

119909119903119909+ 119896119910119903119910+ 119896119911119903119911)) 120575

times (119896119911plusmn radic

1

1205822minus 1198962119909minus 1198962119910)119889119896119909119889119896119910119889119896119911

= ∬infin

119880(119896119909 119896119910 plusmnradic

1

1205822minus 1198962119909minus 1198962119910)

times exp(1198952120587(119896119909119903119909+ 119896119910119903119910

∓119903119911radic1

1205822minus 1198962119909minus 1198962119910))119889119896

119909119889119896119910

(7)

The square root in these equations represents light prop-agating through the 119909119910 plane in the positive and negative


119911-directions respectively Since most holographic recordingsrecord the flux in only one direction we will consider onlythe positive root According to (7) we can define 119880

119911(119896119909 119896119910)

as the 2D projection of the spectrum onto the plane 119896119911= 0

such that

119880119911(119896119909 119896119910) = 119880(119896

119909 119896119910 radic

1

1205822minus 1198962119909minus 1198962119910) (8)

If 119906119885(119903119909 119903119910) represents the optical field in the plane 119903

119911= 119885

we have

119906119885(119903119909 119903119910)

= ∬infin

119880119885(119896119909 119896119910) exp(1198952120587119885radic 1

1205822minus 1198962119909minus 1198962119910)

times exp (1198952120587 (119896119909119903119909+ 119896119910119903119910)) 119889119896119909119889119896119910

(9)

In addition taking the Fourier transform we have

119880119885(119896119909 119896119910)

= exp(minus1198952120587119885radic 1

1205822minus 1198962119909minus 1198962119910)

times∬infin

119906119885(119903119909 119903119910) exp (minus1198952120587 (119896

119909119903119909+ 119896119910119903119910)) 119889119903119909119889119903119910

(10)

Equation (10) allows the spectrum to be calculated from theknowledge of the optical field propagating through a singleplane Equation (9) allows the field in any parallel plane to becalculated

If we consider the application of a general 3D filter tothe reconstruction of a propagating monochromatic field weremember that the product 119880(k)119867lowast(k) only exists on thesurface of a sphere Consequently according to the derivationfrom (7) to (9) we have

119877119885(119903119909 119903119910) = int

+infin

minusinfin

119880119885(119896119909 119896119910)119867lowast

119911(119896119909 119896119910)

times exp(1198952120587119885radic 1

1205822minus 1198962119909minus 1198962119910)

times exp (1198952120587 (119903119909119896119909+ 119903119909119896119910)) 119889119896119909119889119896119910

(11)

where119877119885(119903119909 119903119910) is the 3D correlation output in the plane 119903

119911=

119885 and

119867119885(119896119909 119896119910) = 119867(119896

119909 119896119910 radic

1

1205822minus 1198962119909minus 1198962119910) (12)

Finally we note that in the space domain the correlation is

119877119885(119903119909 119903119910) = int

+infin

minusinfin

119906119885 (119906 V) ℎ119885 (119906 minus 119903119909 V minus 119903119910) 119889119906 119889V

(13)

Object beam

Sample

Microscope lens

CCD

Beam splitterReference beam

He-Ne laser Fibre optic probes

120572 (3∘)

Figure 1 Holographic microscope with a coherent laser source

Figure 2 Holographic image with a field of view of 72 times 72120583m(absolute value shown)

where

ℎ119885(119903119909 119903119910) = int

+infin

minusinfin

119867119885(119896119909 119896119910)

times exp (minus1198952120587 (119903119909119896119909+ 119903119909119896119910)) 119889119896119909119889119896119910

(14)

Equation (13) shows that a single plane (119903119911= 119885) of the

3D correlation of a propagating optical field 119906(r) with ageneral impulse response function ℎ(r) can be calculated asa 2D correlation of the field in that plane 119906

119885(119903119909 119903119910) with an

impulse function ℎ119885(119903119909 119903119910) that is defined by (14)

In the recent literature 2D correlation filtering has beenapplied to complex images reconstructed from a digital holo-graphic microscope [14] Practically a digital holographicmicroscope measures the complex amplitude in the planeof focus and the complex amplitude images in the parallelplanes are calculated based on optical propagation theory It isnoted that a linear filter that is designed to performwell in oneplane of focus will not necessarily perform well in anotherand therefore a nonlinear filtering process is required

When the 3D complex amplitude distribution of samplesis reconstructed from the digital holographic recordingcorrelation filters can be applied for pattern recognition


In the field of statistical pattern recognition it is common todescribe a digitized image of any dimension by the orderedvariables in a vector [17] and we adopt this notation hereIn this way the discrete form of a complex 3D image canbe written in vector notation by lexicographically scanningthe 3D image array Thus an 119899-dimensional vector x =

[1199091 1199092 119909

119899]119879 represents a 3D image with 119899 volume ele-

mentsWe define a correlation operator with a filter kernel(or impulse response) h = [ℎ

1 ℎ2 ℎ

119899]119879 is defined as

x =119899

sum

119894=1

ℎlowast

119894minus119899+1119909119894 (15)

where the superscript ldquolowastrdquo denotes the complex conjugate andthe subscript is taken to be modulo 119899 such that

ℎ119899+119886

= ℎ119886 (16)

A nonlinear threshold operator can be defined in the sameway to operate on the individual components of a vector suchthat

x = [11988611990931+ 1198871199092

1+ 1198881199091+ 119889 119886119909

3

2+ 1198871199092

2+ 1198881199092

+119889 1198861199093

119899+ 1198871199092

119899+ 119888119909119899+ 119889]119879

(17)

In general image data from a hologram is a complex-amplitude field however we consider only the intensitydistribution and define a modulus operator that operateson the the output such that

x = [10038161003816100381610038161199091100381610038161003816100381621003816100381610038161003816119909210038161003816100381610038162

100381610038161003816100381611990911989910038161003816100381610038162] (18)

In this way a 3D nonlinear filter can be expressed as

= 119894119894 (19)

where the subscript to each operator denotes the layer inwhich a given operator is applied

Without loss of generality we design the 3D nonlinearfilter to generate a delta function for the objects to berecognized and zero outputs for the patterns to be rejectedFor this purpose we define a matrix set S of 119898 referenceimages such that S = [s

1 s2 s

119898] and the corresponding

output matrix R is given by

R = S (20)

For the optimization of the 3D nonlinear filter a matrix119874 with all the desired outputs intensity images is defined Ingeneral the desired outputs for in-class images will be a zero-valued vector with the first element set to be unit magnitudeand for an out-of-class image the desired output is zero Inorder to train the filter with the desired performance theerror function below is requested to be minimized

119864 =

119899119898

sum

119894=1 119895=1

(119877119894119895minus 119874119894119895)2

+ 119899

119898

sum

119895=1

(1198771119895minus 1198741119895)2

(21)

40

35

30

25

20

15

10

5

0

119885po

sitio

ns (120583

)

8070

6050

4030

2010

0

119884 positions (120583) 0 10 20 30 40 50 60 70 80

119883 positions (120583)

7060

5040

3020

10

119884 positions 20 30 40 50 60 70

itions (120583)

Figure 3 3D image of the optical field reconstructed from Figure 2

where119877119894119895and119874

119894119895represent the ith pixel of the jth training and

output image respectivelyThe first term in this expression isthe variance of the actual output from the desired outputThesecond term represents the signal peaks (that for simplicityare defined to be the first term in the output vector) andis given extra weight to ensure that they have the desiredunit magnitude Because (21) is a nonlinear function witha large number of variables it is not possible to find ananalytical solution Hence an iterative method is used inthe minimization process In this case a simulated annealingalgorithm was implemented in the optimization because it ismore likely to reach a global minimum [18]

In the practical implementations of the 3Dnonlinear filterdescribed in this paper we require a filter to identify thepresence of fairly small objects in a relatively large field Inthese cases a relatively small filter kernel is used and thekernel is zero-padded to the same size as the input image Inthe test of this paper the training images are selected to be32 times 32 times 16 elements and we use 16 times 16 elements transferfunction (2D) The filter output the filter kernel and thedesired output images are all zero-padded to a resolution of32 times 32 times 16 elements In this way edge effects in patternrecognition for large images can be avoided

3 Experiment

The objective of the work described in this section was todemonstrate 3D rotationally invariance pattern recognitionbased on digital holographicmicroscopy for the classificationof two species of live bacteria E coli and Pantoea

The digital holographic microscope setup used for thisstudy is illustrated in Figure 1 In this arrangement a He-Nelaser (633 nm) is used as coherent light source and is dividedby a beam splitter and launched into a pair of optical fibresof equal length One fibre supplies the light that forms theobject beam for the holographic recording and is collimatedThe microscope is used in a transmission mode and has anobjective lens with 100x magnification and an oil immersionobjective with an equivalent numerical aperture of NA =125 The object plane is imaged onto a CCD array placed


(a) (b)

Figure 4 Typical bacteria (a) E coli and (b) Pantoea in different rotated orientations

approximately 200mm from the objective It is noted thatbecause the microscope is holographic the object of interestneed not be located in the object plane

The fibre that supplies the reference beam has an opentermination that is arranged to diverge from a point in therear focal plane of the microscope objective In this waythe interference of the light from the reference beam andthe light scattered is recorded at the CCD Phase curvatureintroduced by the imaging process [19] is precisely matchedby the reference curvature and straight interference fringesare observed in the image plane in the absence of anyscattering objects From the analysis in Section 2 we can seethat the interference pattern recorded by the CCD can bedemodulated to give the complex amplitude describing thepropagating field in the object plane For reasons of process-ing efficiency care was taken to adjust the magnification ofthe microscope to match the CCD resolution such that anoptimally sampled (Nyquist) reconstruction is produced

The holographic microscope is implemented with a flowcell that defines an experimental volume The nutrient fluidwith two species of living bacteria E coli and Pantoea issyringed into the flow cell through a pipe Figure 2 showsan image taken from the microscope corresponding tothe absolute value of the complex amplitude in the objectplane In this image the bacteria understood to be E coliare highlighted with circles some out-of-focus bacteria areinvisible on this plane Figure 3 shows a 3D image of the fieldin Figure 2 reconstructed using the method demonstrated inthe above section

In this study a 3D nonlinear filter was trained to highlightlive E coli bacteria floating in the flow cell while thePantoea bacteria will be ignored However the reference setpreparation is one of the most challenging problems forthe identification of the living cells because each of the livebacteria varies in size and shape and appears at randomorientation To recognise the bacteria regardless of theirshapes and orientations adequate representative distortionsof bacteria images must be provided for the 3D nonlinearfilter as reference images

The bacteria images registered as training set can beobtained by directly cropping the cell images from the 3Dreconstructed field or by simulating from the recordedimages For example a selected bacteria image can be rotatedto generate several orientation versions Figure 4(a) showseight absolute value images of a typical rod-shaped E colirotated in steps of 45 degrees Pantoea bacteria have asimilar rod shape but slightly different in size from Ecoli Figure 4(b) shows one of the selected Pantoea in eightdifferent rotated versions

To demonstrate the performance of the 3D nonlinearfilter we train the system to detect E coli bacteria with 42

40

35

30

25

20

15

10

5

0

119885po

sitio

ns (120583

)

8070

6050

4030

2010

0 0 10 20 30 40 50 60 70 80119884 positions (120583) 119883 positions (120583)

Figure 5 3D output for the 3D nonlinear filter trained to recognizeE coli (absolute amplitude value shown)

Figure 6 The projection of the output volume (absolute amplitudevalue shown)

images including 25 E coli and 17 Pantoea images and thefiler is tested with the complex amplitude image in Figure 2Figure 5 shows the 3D image of the 3D filter output Figure 6reports the projection of the output volume onto a planeIt can be seen that most of the E coli bacteria had beenhighlighted by correlation peaks and the Pantoea had beenignored However a small portion of the E coli cannot bedetected this is because the training set with limited numberof reference images does not represent all the distortions andorientations of the bacteria It is expected that classificationrate can be improved if more reference images are includedin the training set


4 Conclusion

This paper describes 3D pattern recognition with a 3D non-linear filter applied to monochromatic optical fields that canbe recorded and reconstructed by holographic microscopesThe 3D extension and formulation of the nonlinear filterconcept has been introduced We have shown with experi-mental data that the 3D nonlinear filtering system providesadditional capability as a means to perform 3D patternrecognition in a shift and rotationally invariant means Wedemonstrate this in practice by applying the 3D nonlinear fil-ter to a holographic recording of the light scattered from twokinds of living bacteria suspended in waterThe experimentaldata demonstrated that the 3D nonlinear filter has good shiftand rotationally invariant property in 3D space

Acknowledgment

Financial support from The Research Fund for the DoctoralProgram of Higher Education (No 20122302120072) to initi-ate this research is gratefully acknowledged

References

[1] M Minsky ldquoMemoir on inventing the confocal scanningmicroscoperdquo Scanning vol 10 no 4 pp 128ndash138 1988

[2] U Schnars and W P O Juptner ldquoDigital recording andnumerical reconstruction of hologramsrdquo Measurement Scienceand Technology vol 13 no 9 pp R85ndashR101 2002

[3] T Zhang and I Yamaguchi ldquoThree-dimensional microscopywith phase-shifting digital holographyrdquo Optics Letters vol 23no 15 pp 1221ndash1223 1998

[4] E Cuche P Marquet and C Depeursinge ldquoSimultaneousamplitude-contrast and quantitative phase-contrastmicroscopyby numerical reconstruction of Fresnel off-axis hologramsrdquoApplied Optics vol 38 no 34 pp 6994ndash7001 1999

[5] F Dubois L Joannes and J C Legros ldquoImproved three-dimensional imaging with a digital holography microscopewith a source of partial spatial coherencerdquo Applied Optics vol38 no 34 pp 7085ndash7094 1999

[6] S Y Chen Y F Li Q Guan and G Xiao ldquoReal-time three-dimensional surface measurement by color encoded light pro-jectionrdquo Applied Physics Letters vol 89 no 11 Article ID 1111083 pages 2006

[7] Z Teng A J Degnan U Sadat et al ldquoCharacterization ofhealing following atherosclerotic carotid plaque rupture inacutely symptomatic patients an exploratory study using invivo cardiovascular magnetic resonancerdquo Journal of Cardiovas-cular Magnetic Resonance vol 13 no 1 article 64 2011

[8] L Lin S Chen Y Shao and Z Gu ldquoPlane-based sampling forray casting algorithm in sequential medical imagesrdquo Computa-tional and Mathematical Methods in Medicine vol 2013 ArticleID 874517 5 pages 2013

[9] Q Guan and B Du ldquoBayes clustering and structural supportvector machines for segmentation of carotid artery plaques inmulti-contrast MRIrdquo Computational and Mathematical Meth-ods in Medicine vol 2012 Article ID 549102 6 pages 2012

[10] F Dubois ldquoNonlinear cascaded correlation processes toimprove the performances of automatic spatial-frequency-selective filters in pattern recognitionrdquo Applied Optics vol 35no 23 pp 4589ndash4597 1996

[11] S Reed and J Coupland ldquoStatistical performance of cascadedlinear shift-invariant processingrdquoApplied Optics vol 39 no 32pp 5949ndash5955 2000

[12] N Wu R D Alcock N A Halliwell and J M CouplandldquoRotationally invariant pattern recognition by use of linear andnonlinear cascaded filtersrdquo Applied Optics vol 44 no 20 pp4315ndash4322 2005

[13] B Javidi and E Tajahuerce ldquoThree-dimensional object recogni-tion by use of digital holographyrdquo Optics Letters vol 25 no 9pp 610ndash612 2000

[14] F Dubois C Minetti O Monnom C Yourassowsky J CLegros and P Kischel ldquoPattern recognition with a digital holo-graphicmicroscopeworking in partially coherent illuminationrdquoApplied Optics vol 41 no 20 pp 4108ndash4119 2002

[15] S Chen and M Zhao ldquoRecent advances in morphological cellimage analysisrdquo Computational and Mathematical Methods inMedicine vol 2012 Article ID 101536 10 pages 2012

[16] A Sommerfeld Partial Differential Equations in Physics Aca-demic Press New York NY USA 1949

[17] K Fukunaga Introduction to Statistical Pattern RecognitionAcademic Press New York NY USA 1972

[18] S Kirkpatrick C D Gelatt and M P Vecchi ldquoOptimization bysimulated annealingrdquo Science vol 220 no 4598 pp 671ndash6801983

[19] J W Goodman Introduction to Fourier Optics McGraw-HillNew York NY USA 1968


Research ArticleThresholded Two-Phase Test Sample Representation forOutlier Rejection in Biological Recognition

Xiang Wu1 and Ning Wu2

1 Harbin Institute of Technology 92 West Dazhi Street Nan Gang District Harbin 150001 China2 Shenzhen Key Lab of Wind Power and Smart Grid Harbin Institute of Technology Shenzhen Graduate SchoolShenzhen 518055 China

Correspondence should be addressed to Ning Wu aningwugmailcom

Received 22 January 2013 Accepted 9 February 2013


Copyright copy 2013 X Wu and N Wu This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The two-phase test sample representation (TPTSR) was proposed as a useful classifier for face recognition However the TPTSRmethod is not able to reject the impostor so it should be modified for real-world applications This paper introduces a thresholdedTPTSR (T-TPTSR) method for complex object recognition with outliers and two criteria for assessing the performance of outlierrejection and member classification are defined The performance of the T-TPTSR method is compared with the modified globalrepresentation PCA and LDA methods respectively The results show that the T-TPTSR method achieves the best performanceamong them according to the two criteria

1 Introduction

Object recognition has become a hot topic in the field ofcomputer vision and pattern recognition in recent yearsand many approaches have been proposed for face imageclassification with a given database One type of the methodsis to reduce the dimensionality of sample by extracting thefeature vector with linear transformation methods such asthe principal component analysis (PCA) [1ndash3] and the lineardiscriminant analysis (LDA) [4 5] In the PCA method thetraining samples and the testing samples are transformedfrom the original sample space into a space with the max-imum variance of all the samples while the LDA methodconverts the samples to a feature space where the distancesof the centers of different classes are maximized In these twotransformation methods both the training samples and thetesting samples have their corresponding representations inthe new feature space and the classification is carried outbased on the distance between the representations related tothe training set and the testing set

Another type of transformation-based method was pro-posed to focus on local information of the training samplesInstead of using the whole training set this type of method

only uses part of the samples since the performance ofthe classifier is usually limited within some local areas Byconcentrating on the local distribution of training data thedesign and testing of the classifier can be muchmore efficientthan the global methods [6] Typical examples of local LDAmethods include the method for multimodal data projection[7 8] and the approach to use the local dependenciesof samples for classification [9] It is also found that thelocal PCA is more efficient than the global PCA in featureextraction [10] or sample clustering [11]

In recent years the sparse representation theory has beenapplied to pattern recognition problems and has drawn a lotof attentions [12ndash21] The sparse representation method alsouses only part of the training data for classification by linearlyrepresenting a testing sample with the training set and partof the linear combination coefficients is set to zero Theclassification criterion of the sparse representation methodis based on the biggest contribution from the sample classesduring the linear representation

In a recent study a two-phase test sample representation(TPTSR) method was proposed for face recognition [22] Inthis method classification process is divided into two stepsthe first step selects119872-nearest neighbors of the testing sample


from the training set by using linear representation methodand the second step processes the selected119872 samples furtherby using them to linearly represent the testing sample Theclassification result is based on the linear contribution ofthe classes among the 119872-nearest neighbors in the secondphase of the TPTSR By selecting 119872-closest neighbors fromthe training set for further processing the TPTSR methodidentifies a local area thatmay contain the target class samplereducing the risk of misclassification because of a similarnontarget sample

Even the TPTSR method has been proven to be veryuseful in face classification however for face recognitionapplications with outliers the classification emphasis is dif-ferent and the performance measurement criterion is alsonew In face recognition problems with outliers like securityregistration systems only a small and particular group ofmembers is required to be classified and compared with alarge population of irrelevant people or intruders In theapplication of identifying wanted criminals at airports trainstation and other public places the classifier is also requiredto identify a minor number of target members from a largenumber of irrelevant passengers In previous studies theapproaches for pattern classificationwith outliers include twomain methods one is to train the classifier with only themember samples and the other is to take into account a smallnumber of outliers as a separate class in the training set [23]However neither of the methods can guarantee a low falsealarm rate while maintaining a reasonable recognition ratefor members

In this paper we further develop the TPTSR methodby applying a threshold in the classification process foroutlier rejection and member classification and it is referredto as thresholded TPTSR (T-TPTSR) method In the T-TPTSR the distance between the testing sample and theweighted contribution of the target class in the second-phase linear representation is measured and compared witha threshold by which an outlier will be identified In thisstudy we also propose two different criteria for assessingthe performance of classifier for outlier rejection as wellas member classification and based on these criteria wetest the thresholded global representation (T-GR) methodthresholded PCA (T-PCA) method and thresholded LDA(T-LDA) method respectively The test results show thatthe T-TPTSR achieves better performance in rejecting theoutliers while maintaining outstanding classification rate formembers

In Sections 2 and 3 of this paper we will introducethe theory of the T-TPTSR T-GR T-PCA and T-LDArespectively Section 4 presents our experimental results withdifferent face image databases and finally a conclusion willbe drawn in Section 5

2 Thresholded Two-Phase Test SampleRepresentation (T-TPTSR)

In this section the TTPTSR method will be introducedwith a threshold applied to the second-phase output in theclassification process

21 First Phase of the T-TPTSR with M-Nearest NeighborSelection The first phase of the T-TPTSR is to select 119872-nearest neighbors from all the training samples for furtherprocessing in the second phase narrowing the sample spacedown to a local area for the target class [22] The 119872-nearestneighbors are selected by calculating the weighted distancesof the testing sample from each of the training samplesFirstly let us assume that there are 119871 classes and 119899 trainingimages 119909

1 1199092 119909

119899 and if some of these images are from

the 119895th class (119895 = 1 2 119871) then 119895 is their class label It isalso assumed that a test image 119910 can be written in the form oflinear combination of all the training samples such as

119910 = 11988611199091+ 11988621199092+ sdot sdot sdot + 119886

119899119909119899 (1)

where 119886119894(119894 = 1 2 119899) is the coefficient for each training

image 119909119899 Equation (1) can also be written in the form of

vector operation such as

119910 = 119883119860 (2)

where 119860 = [1198861sdot sdot sdot 119886119899]119879 119883 = [119909

1sdot sdot sdot 119909119899]1198791199091sdot sdot sdot 119909119899 and 119910 are

all column vectors If119883 is a singular square matrix (2) can besolved by using 119860 = (119883

119879119883 + 120583119868)

minus1

119883119879119910 or it can be solved

by using 119860 = 119883minus1119910 where 120583 is a small positive constant and

119868 is the identity matrix In our experiment with the T-TPTSRmethod 120583 in the solution is set to be 001

By solving (2) we can represent the testing image usingthe linear combination of the training set as shown in (1)which means that the testing image is essentially an approxi-mation of the weighted summation of all the training imagesand the weighted image 119886

119894119909119894is a part of the approximation

In order to measure the distance between the training image119909119894and the testing image 119910 a distance metric is defined as

followed

119890119894=1003817100381710038171003817119910 minus 119886

119894119909119894

10038171003817100381710038172 (3)

where 119890119894is called the distance function and it gives the

difference between the testing sample 119910 and the trainingsample 119909

119894 It is clear that a smaller value of 119890

119894means that the

119894th training sample is closer to the testing sample and it ismore probable to be themember of the target classThese119872-nearest neighbors are chosen to be processed further in thesecond phase of the T-TPTSR where the final decision will bemade within a much smaller sample space We assume thatthe 119872-nearest neighbors selected are denoted as 119909

1sdot sdot sdot 119909119872

and the corresponding class labels are 119862 = 1198881sdot sdot sdot 119888119872 where

119888119894isin 1 2 119871 In the second phase of the T-TPTSR if a

sample 119909119901rsquos class label does not belong to 119862 then this class

will not be considered as a target class and only a class from119862 will be regarded as a potential target class

22 Second Phase of the T-TPTSR for Outlier Rejection Inthe second phase of the T-TPTSR method the 119872-nearestneighbors selected from the first phase are further calculatedto obtain a final decision for the recognition task Werepresent the testing sample with the linear combinationof the training samples again but only with the 119872-nearest


neighbors selected from the first phase If the 119872-nearestneighbors selected are denoted as 119909

1sdot sdot sdot 119909119872 and their linear

combination for the approximation of the testing image 119910 isassumed to be satisfied such as

119910 = 11988711199091+ sdot sdot sdot + 119887

119872119909119872 (4)

where 119887119894(119894 = 1 2 119872) are the coefficients In vector

operation form (4) can be written as

119910 = 119861 (5)

where 119861 = [1198871sdot sdot sdot 119887119872]119879 and = [119909

1sdot sdot sdot 119909119872] In the same

philosophy as above if is a nonsingular square matrix (5)can be solved by

119861 = ()minus1

119910 (6)

or otherwise 119861 can be solved by

119861 = (119879

+ 120574119868)minus1

119879

119910 (7)

where 120574 is a positive small value constant and it is usually setto 001 and 119868 is the identity matrix

When we obtain the coefficients 119887119894for each of the nearest

neighbors the contribution of each of the classes to the testingimage will be measured and the classification output willbe based on the distance between the contribution and thetesting image If the nearest neighbors 119909

119904sdot sdot sdot 119909119905are from the

119903th class (119903 isin 119862) and the linear contribution to approximatethe testing sample by this class is defined as

119892119903= 119887119904119909119904+ sdot sdot sdot + 119887

119905119909119905 (8)

The measurement of the distance between the testing sampleand the 119903th class samples in the 119872-nearest neighbors iscalculated by the deviation of 119892

119903from 119910 such as

119863119903=1003817100381710038171003817119910 minus 119892

119903

10038171003817100381710038172 119903 isin 119862 (9)

It is clear that a smaller value of 119863119903means a better approx-

imation of the training samples from the 119903th class for thetesting sample and thus the 119903th class will have a higherpossibility over other classes to be the target class Howeverif outliers are considered a threshold must be applied tothe classification output to differentiate the members of classfrom outliers such as

119863119896= min119863

119903lt 119879 (119896 119903 isin 119862 119879 isin [0 +infin)) (10)

where 119879 is the threshold If 119863119896ge 119879 the testing sample will

be regarded as an outlier and therefore will be rejected Onlywhen119863

119896lt 119879 the testing sample 119910 can be classified to the 119896th

class with the smallest deviation from 119910In the second phase of the T-TPTSR the solution in (6)

or (7) finds the coefficients for the linear combination ofthe 119872-nearest neighbors to approximate the testing sampleand the training class with the minimum deviation of theapproximation will be considered as the target class forthe testing sample However the value of the minimum

deviation must be less than the threshold 119879 If the minimumdistance between the testing sample and the member classrsquosapproximations is greater than the threshold 119879 the testingsample will be classified as an outlier and thus rejectedHowever if the value of the minimum deviation of thelinear combinations to an outlier is less than the threshold119879 this outlier will be classified into the member class withthe minimum deviation and a misclassification will occurLikewise if a testing image belongs to a member class buttheminimumdeviation from the linear combinations of eachof the classes is greater than the threshold 119879 this testingimage will be classified as an outlier and a false alarm isresulted Since the samples used in the T-TPTSR method areall normalized in advanced the value of 119863

119903in (9) will be

within a certain range such that 0 le 119863119903le 119904 where 119904 asymp 1

and therefore it is practical to determine a suitable thresholdfor the identification task before the testing

3 The T-GR T-PCA and T-LDA Methods forOutlier Rejection

As a performance comparison with the T-TPTSR method inthe following section we also introduce themodified versionsof the GR PCA and LDA methods respectively for outlierrejection and member classification in face recognition

31The T-GRMethod The thresholded global representation(T-GR) method is essentially the T-TPTSR method with allthe training samples that are selected as the119872-nearest neigh-bors (119872 is selected as the number of all the training samples)and it also finds the target class directly by calculating the bestrepresenting sample class for the testing image

In the T-GR method the testing sample is representedby the linear combination of all the training samples andthe classification is not just based on the minimum deviationof the linear contribution from each of the classes to thetesting sample but also based on the value of the minimumdeviation If the minimum deviation is greater than thethreshold applied the testing sample will be identified as anoutlier

32 The T-PCA Method The PCA method is based onlinearly projecting the image space onto a lower-dimensionalfeature space and the projection directions are obtained bymaximizing the total scatter across all the training classes [2425] Again we assume that there are 119871 classes and 119899 trainingimages 119909

1 1199092 119909

119899 each of which is119898-dimensional where

119899 lt 119898 If a linear transformation is introduced to map theoriginal 119898-dimensional image space into an 119897-dimensionalfeature space where 119897 lt 119898 the new feature vector 119906

119894isin 119877119897

can be written in the form of

119906119894= 119882119879119909119894 (119894 = 1 2 119899) (11)

where 119882119879 isin 119877119898times119897 is a matrix with orthonormal columns If

the total scatter matrix 119878119879 is defined as

119878119879=

119899

sum

119894=1

(119909119894minus 120583) (119909

119894minus 120583)119879 (12)


where 120583 isin 119877119898 is the mean of all the training samples we

can see that after applying the linear transformation119882119879 thescatter of all the transformed feature vectors 119906

1 1199062 119906

119899is

119882119879119878119879119882 which can be maximized by finding a projection

direction119882119898 such as

119882119898= arg max

119882

119882119879119878119879119882

= [1199081 1199082sdot sdot sdot 119908119897]

(13)

where 119908119894(119894 = 1 119897) is the set of 119898-dimensional eigenvec-

tors of 119878119879 corresponding to the 119897 biggest eigenvalues Duringthe recognition process both the testing sample 119910 and all thetraining samples are projected into the new feature space via119882119898before the distance between them is calculated such as

119863119894=10038171003817100381710038171003817119882119879

119898119910 minus119882

119879

119898119909119894

10038171003817100381710038171003817

2

=10038171003817100381710038171003817119882119879

119898(119910 minus 119909

119894)10038171003817100381710038171003817

2

(119894 = 1 2 119899)

(14)

In the thresholded PCA method the testing sample 119910 willbe classified to the class whose member has the minimumdistance119863

119894 but this distance must be less than the threshold

119879 such that

119863119896= min119863

119894lt 119879 (119896 119894 = 1 2 119899 119879 isin [0 +infin)) (15)

The testing sample 119910 whose corresponding minimum dis-tance 119863

119896is less than the threshold 119879 will be classified as an

outlier and therefore rejected otherwise 119910 will be classifiedinto the class with 119909

119896

33 The T-LDA Method The LDA is a class-specific linearmethod for dimensionality reduction and simple classifiers ina reduced feature space [26ndash29] The LDA method also findsa direction to project the training images and testing imagesinto a lower dimension space on the condition that the ratioof the between-class scatter and the within-class scatter ismaximized

Likewise if there are 119871 classes and 119899 training images1199091 1199092 119909

119899 each of which is119898-dimensional where 119899 lt 119898

and in the 119894th class there are119873119894samples (119894 = 1 2 119871) the

between-class scatter matrix can be written as

119878119887=

119871

sum

119894=1

119873119894(120583119894minus 120583) (120583

119894minus 120583)119879 (16)

and the within-class scatter matrix can be defined as

119878119908=

119871

sum

119894=1

119873119894

sum

119895=1

(119909119895minus 120583119894) (119909119895minus 120583119894)119879

(17)

where 120583119894is the mean image of the 119894th class and 120583 is

the mean of all the samples It is noted that 119878119908must be

nonsingular in order to obtain an optimal projection matrix119882119898with the orthonormal columns to maximize the ratio of

the determinant of the projected 119878119887and projected 119878

119908 such

that

119882119898= argmax

119882

1003816100381610038161003816100381611988211987911987811988711988210038161003816100381610038161003816

119882119879119878119908119882

= [11990811199082sdot sdot sdot 119908119897]

(18)

where119908119894(119894 = 1 119897) is the set of119898-dimensional generalized

eigenvectors of 119878119887and 119878

119908corresponding to the 119897 biggest

eigenvalues such as

119878119887119908119894= 120582119894119878119908119908119894 (119894 = 1 2 119897) (19)

where 120582119894(119894 = 1 119897) is the 119897 generalized eigenvalues Since

there are the maximum number of 119871minus 1 nonzero generalizedeigenvalues available the maximum 119897 can only be 119871 minus 1

The distance between the projection of the testing sample119910 and the training samples with119882

119898in the new feature space

is calculated as

119863119894=10038171003817100381710038171003817119882119879

119898119910 minus119882

119879

119898119909119894

10038171003817100381710038171003817

2

=10038171003817100381710038171003817119882119879

119898(119910 minus 119909

119894)10038171003817100381710038171003817

2

(119894 = 1 2 119899)

(20)

If the sample 119909119896rsquos projection into the feature space has a

minimum distance from the projection of the testing sample119910 the testing sample will be classified into the same class as119909119896 such that

119863119896= min119863

119894lt 119879 (119896 119894 = 1 2 119899 119879 isin [0 +infin))

(21)

where 119879 is a threshold to screen out the outliers For thethreshold LDA method all the target membersrsquo projectiondistance 119863

119894must be less than 119879 or otherwise they will be

classified as outliers and rejected

4 Experimental Results

In this experiment we test the performance of the T-TPTSRthe T-GR the T-PCA and the T-LDA methods for outlierrejection and member classification respectively One ofthe measurement criteria for comparing the performance ofthese methods is to find the minimum overall classificationerror rate During the classification task an optimal threshold119879 can be found for the above methods so that the overallclassification error rate is minimized The overall classifi-cation error rate is calculated based on three classificationerror rates such as the misclassifications among memberrsquosclasses (when the testing sample is a member and 119863

119896lt

119879 but misclassified as another class) the misclassificationsof a member to outlierrsquos group (when the testing sampleis a member but 119863

119896gt 119879 and thus misclassified) and

misclassifications for outliers (when the testing sample is anoutlier but 119863

119896lt 119879 and therefore accepted wrongly as a

member) If ERRoverall(119879) represents the overall classificationerror rate as a function of the threshold 119879 ERRmember(119879)denotes the classification error rate for errors that occurredamong members (misclassifications recorded for testing


samples from memberrsquos group versus the total number oftesting samples from memberrsquos group) and ERRoutlier(119879) isthe misclassification rate for outliers (classification errorsrecorded for testing samples from the outlierrsquos group versusthe total number of testing outliers) their relationship can bewritten as

ERRoverall (119879) = ERRmember (119879) + ERRoutlier (119879) (22)

It is noted that the value of ERRmember varies with thethreshold 119879 and when 119879 = 0 ERRmember takes the valueof 100 and it generally decreases when the value of 119879increases until it reaches a constant classification error rateThe classification error rate for outlier also changes its valueaccording to the threshold 119879 however ERRoutlier = 0when119879 = 0 and its value increases until reaching 100 Theminimum ERRoverall(119879) can be found between the range of119879 = 0 and 119879 = 119879

119898 where ERRmember(119879) becomes a constant

or ERRoverall(119879) reaches 100 such that

ERRopt = min ERRoverall (119879) 119879 isin [0 +infin) (23)

The value of ERRopt is an important criterion showing theperformance of a classifier for both of outlier rejection andmember recognition

Another measuring criterion for measuring the perfor-mance of the thresholded classifiers is the receiver operationcharacteristics (ROC) curve which is a graphical plot ofthe true positive rate (TPR) versus the threshold 119879 in theapplication of thresholded classification for outlier rejectionWe firstly define the true positive detection rate for theoutliers TPRoutlier(119879) and it can be written in the form ofthe classification error rate for the outliers such that

TPRoutlier (119879) = 100 minus ERRoutlier (119879) 119879 isin [0 +infin)

(24)

We also define the false alarm rate caused in the memberrsquogroup as a function of the threshold ERRFA(119879) which isthe number of errors recorded for misclassifying a memberto an outlier versus the number of testing samples from thememberrsquos group An optimal classifier for outlier rejectionand member classification needs to find a suitable threshold119879 so that the TPRoutlier(119879) can be maximized as well asthe ERRFA(119879) can be minimized Therefore the followingfunction119863

119874-119865(119879) is defined for this measurement such that

119863119874-119865 (119879) = TPRoutlier (119879) minus ERRFA (119879)

= 100 minus ERRoutlier (119879)

minus ERRFA (119879) 119879 isin [0 +infin)

(25)

It is obvious that119863119874-119865(119879) is required to be maximized so that

a classifier can be optimized for both outlier rejection andmember classification such that

119863opt = max119863119874-119865 (119879) 119879 isin [0 +infin) (26)

and the value of 119863opt is an important metric for comparingthe performance of classifier for outlier rejection analysis

Figure 1 Part of the face images from the Feret database for testing

The minimum overall classification error rates ERRoptand the maximum difference of the true positive outlierrecognition rate and the false-alarm rate 119863opt are essentiallythe same performance assessment metric for a classifierwith outlier rejection The difference is that the overallclassification error rate represents the efficiency of memberclassification while 119863

119874-119865 and 119863opt show the performanceof outlier rejection In the following experiment we testand compare the minimum overall classification error ratesERRopt and the maximum 119863opt of the T-TPTSR T-GR T-PCA and T-LDA methods respectively and based on thesetwo criteria we find the optimal classifier for outlier rejectionand member classification

In our experiment we test and compare the performanceof the above methods using the online face image databasesFeret [30 31] ORL [32] and AR [33] respectively Thesedatabases provide face images from different faces withdifferent facial expression and facial details under differentlighting conditions The Feret database provides 1400 faceimages from 200 individuals for the training and testing andthere are 7 face images from each of the classes In the ARdatabase there are totally 3120 face images from 120 peopleeach of which provides 26 different facial details For theORL database there are 400 face images from 40 differentindividuals each of which has 10 face images

In this experiment the training set and the testing setare selected randomly from each of the individuals For eachof the databases the people included are divided into twogroups and one is memberrsquos group and the other is outlierrsquosgroup For individuals chosen as the memberrsquos class thetraining samples are prepared by selecting some of theirimages from the database and the rest of the images aretaken as the testing set For the outliers that is supposed tobe outside the memberrsquos group there is no training set forthe classification and all the samples included in the outlierrsquosgroup are taken as the testing set

We firstly test the Feret database with the above outlierrejection methods The Feret database is divided into twogroups 100 members from the 200 individuals are randomlyselected into the memberrsquos group and the rest of the 100individuals are the outliers in the test For each of the 100


01 02 03 04 05 06 07 08 09 10

102030405060708090

100

Threshold value 119879

Clas

sifica

tion

erro

r rat

e (

)

(a) T-TPTSR

0 01 02 03 04 05 06 07 08 09 10

102030405060708090

100


Clas

sifica

tion

erro

r rat

e (

)

(b) T-GR

0 005 01 015 02 0250

102030405060708090

100

Clas

sifica

tion

erro

r rat

e (

)


ERRoverallERRoutlierERRmember

(c) T-PCA

005 01 015 02 025 030

102030405060708090

100

Clas

sifica

tion

erro

r rat

e (

)



(d) T-LDA

Figure 2 Classification error rates for outliers members and overall of (a) the T-TPTSR method (b) the T-GR method (c) the T-PCAmethod and (d) the T-LDA method respectively on the Feret database

member classes 4 images out of 7 are selected randomlyas the training set and the rest of the 3 images are for thetesting set For the 100 individuals in the outlierrsquos groupall 7 images from each of them are the testing set for theclassification task Therefore there are 400 training imagesand 1000 testing images in this test and among the testingimages there are 300 images from memberrsquos group and700 images from outlierrsquos group Figure 1 shows part of themember and outlierrsquos images from the Feret database for thetesting and all the images have been resized to a 40times40-pixelimage by using a downsampling algorithm [34] Since thenumber of classes in the Feret database ismuchmore than theORL and AR databases also the number of training images isless and the resolution of the images is lower the testing withthe Feret database would be more challenging and the resultis generally regarded as more convincing

In the test of the T-TPTSR method with the Feretdatabase the number of nearest neighbors 119872 selected for

the first-phase processing is 60 (according to the empiricaldata the optimal number 119872 is selected about 10sim15 ofthe number of training samples) In the test with the abovemethods the threshold value 119879 varies from 0 to a constantthat can result in 100 of ERRoutlier with the interval of 01or 05 where all outliers are accepted as members Figures2(a)sim2(d) show different classification error rates of the abovemethods as the function of the threshold 119879 respectively Itcan be seen that the ERRopt values of the T-TPTSR methodand the T-GR method are much lower than the T-PCA andT-LDA methods and the ERRmember curves of the T-TPTSRand T-GR decrease from 100 to a much lower constantthan those of the T-PCA and T-LDA when the threshold 119879

increasesThe second row of Table 1 lists all the ERRopt valuesshown in Figure 2 and we can see that the T-TPTSR methodachieves the lowest overall classification error rate Figure 3shows the ROC curves of the T-TPTSR T-GR T-PCA andT-LDA methods respectively and the third row of Table 1


0 01 02 03 04 05 06 070

102030405060708090

100

Det

ectio

n ra

te (

)


(a) T-TPTSR

01 02 03 04 05 06 07 080

102030405060708090

100

Det

ectio

n ra

te (

)


(b) T-GR

005 01 015 02 025 030

102030405060708090

100

Det

ectio

n ra

te (

)


TPRoutlier

ERRFA

119863119874-119865

(c) T-PCA

0 005 01 015 02 025 03 035 04

0

20

40

60

80

100

Det

ectio

n ra

te (

)


minus20

TPRoutlier

ERRFA

119863119874-119865

(d) T-LDA

Figure 3 ROC curves for (a) T-TPTSR method (b) T-GR method (c) T-PCA method and (d) T-LDA method respectively on the Feretdatabase

gives details of all the 119863opt values shown in Figure 3 It canbe seen that the T-TPTSR also has a higher value of 119863optthan other methods

For the testing with the AR database we randomlyselected 80 classes as themember and the rest of the 40 peopleare taken as outliers For each of the members 13 images areselected randomly from the 26 images as the training set andthe rest of the 13 images are included in the testing set Hencethere are 1040 training images and 2080 testing images in thistest and in the testing set there are 1040memberrsquos images and1040 outlierrsquos images Figure 4 shows part of the memberrsquosand outlierrsquos images from the AR database and the images fortraining and testing have been downsized to be a 40times50-pixelimage [34]

Whenwe test the T-TPTSRmethodwith theARdatabasethe number of nearest neighbors 119872 selected is 150 Table 2describes the ERRopt values and119863opt values of the T-TPTSRT-GR T-PCA andT-LDAmethods respectively when testedwith the AR database It is obvious from the ERRopt values

Table 1 Minimum overall classification error rate and maximumROC difference for T-TPSR T-GR T-PCA and T-LDA methodsrespectively on the Feret database

Methods T-TPTSR T-GR T-PCA(150) T-LDA(149)ERRopt () 204 232 300 300119863opt () 330 328 119 124T-PCA(150) indicate that the T-PCA used 150 transform axes for featureextraction and T-LDA(119) means that the T-LDA used 119 transform axesfor feature extraction Tables 2 and 3 show the method and number oftransform axes used in the same way

and 119863opt values that the T-TPTSR method outperforms theT-GR the T-PCA and the T-LDA methods in the outlierrejection and member classification applications

We also test the above methods with the ORL face imagedatabase There are totally 40 classes in the ORL databaseand we select 30 random classes to be the members and


Figure 4 Part of the face images from the AR database for testing

Table 2 Minimum overall classification error rate and maximumROC difference for T-TPSR T-GR T-PCA and T-LDA methodsrespectively on the AR database

Methods T-TPTSR T-GR T-PCA(1040) T-LDA(79)ERRopt () 272 302 330 500119863opt () 455 418 434 218

the other 10 individuals to be the outliers Among the 30members 5 images out of 10 for each of the members areselected randomly as the training samples and the rest of the5 images are the testing samples So in the test we have 150training images and 250 testing images and in the testingset there are 150 memberrsquos images and 100 outlierrsquos imagesFigure 5 shows some sample images from the ORL databaseand the images used are also resized to 46 times 56 [34]

The number of nearest neighbors selected for the T-TPTSR method for the ORL database is 40 Table 3 givesthe details of the ERRopt values and 119863opt values of thefour methods respectively It can be seen that the T-TPTSRmethod also shows better performance than all the T-GR T-PCA and T-LDA methods and it has been confirmed thatthe T-TPTSRmethod is the optimal solution among them foroutlier rejection and member classification

It is noted that in the test with theAR andORLdatabasesthe performance of the T-TPTSR the T-GR and the T-PCA are comparable This is because under redundant andreasonable resolution sample situation the performance ofthe T-PCA method is close to the T-TPTSR and T-GRmethods However when the T-PCA method is tested with asmall number of training samples and low-resolution imageslike the Feret database the advantages of the T-TPTSRmethod are very obvious

The criterion we use for judging whether a sample isan outlier or not is to measure the distance between thetesting sample and the selected target class If this distanceis greater than the threshold this sample will be classified asan outlier In T-TPTPR method the first-phase process findsa local distribution close to the testing sample in the widesample space by selecting119872-nearest samples In the second-phase processing of the T-TPTSR method the testing sample

Figure 5 Part of the face images from the ORL database for testing

Table 3 Minimum overall classification error rate and maximumROC difference for T-TPSR T-GR T-PCA and T-LDA methodsrespectively on the ORL database

T-TPTSR T-GR T-PCA(200) T-LDA(29)ERRopt () 212 240 228 600119863opt () 586 573 573 300

is classified based on the distance between the testing sampleand the closest class among the 119872-nearest neighbors If thetesting sample is an outlier the measure of distance will onlybe limited within the local distribution within the samplespace and therefore the measurement is not confused withother training samples that happen to be close to the outlier

By applying a suitable threshold a classifier can reject theoutliers and classify the members with the minimum overallclassification error rate and the maximum gap between theoutlier detection rate and false alarm rate formembersTheT-TPTSR method linearly representing the testing sample withthe training samples and the distance between the testingsample and the target class are measured by calculating thedifference between the testing sample and the weighted con-tribution of the class in the linear representation In our testabove the T-TPTSR method achieves the best performancein outlier rejection as well as member classification This isbecause in the T-TPTSR the two-phase linear representationof the testing sample results in a closer approximationand assessment by the training samples Thus the distancebetween the testing sample and the target class can beminimized and the distance between the testing sample andan outlier can be maximized leading to a better overallclassification rate and greater ratio of outlier recognition rateversus the false alarm rate

5 Conclusion

This paper introduces the modified versions of four usefulapproaches in face recognition the T-TPTSR method the T-GRmethod the T-PCAmethod and the T-LDAmethod for


the application of outlier rejection as well as member classifi-cationTheir performance is tested with three different onlineface image databases the Feret AR and ORL databasesrespectively The results show that the T-TPTSR methodachieves the lowest overall classification error rate as wellas the greatest difference between the outlier detection rateand false-alarm rate Even the T-PCA method may achievecomparable performance with the T-TPTSR method underideal sample conditions the test result of the T-PCA methodis generally poor under bad sample conditionsThe T-TPTSRmethod achieves the best performance in outlier rejectionas well as member classification because of the two-phaselinear representation of the testing sample with the trainingsamples

Acknowledgment

Financial supports fromThe Research Fund for the DoctoralProgram of Higher Education (no 20122302120072) to initi-ate this research project are gratefully acknowledged

References

[1] M Kirby and L Sirovich ldquoApplication of the Karhunen-Loeve procedure for the characterization of human facesrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol12 no 1 pp 103ndash108 1990

[2] Y XuD Zhang J Yang and J Y Yang ldquoAn approach for directlyextracting features from matrix data and its application in facerecognitionrdquo Neurocomputing vol 71 no 10ndash12 pp 1857ndash18652008

[3] J YangD ZhangA F Frangi and J Y Yang ldquoTwo-dimensionalPCA a new approach to appearance-based face representationand recognitionrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 26 no 1 pp 131ndash137 2004

[4] Y Xu and D Zhang ldquoRepresent and fuse bimodal biomet-ric images at the feature level complex-matrix-based fusionschemerdquo Optical Engineering vol 49 no 3 Article ID 0370022010

[5] S W Park and M Savvides ldquoA multifactor extension of lineardiscriminant analysis for face recognition under varying poseand illuminationrdquo EURASIP Journal on Advances in SignalProcessing vol 2010 Article ID 158395 11 pages 2010

[6] Z Fan Y Xu and D Zhang ldquoLocal linear discriminant analysisframework using sample neighborsrdquo IEEE Transactions onNeural Networks vol 22 no 7 pp 1119ndash1132 2011


[8] C Cattani R Badea S Chen and M Crisan ldquoBiomedicalsignal processing and modeling complexity of living systemsrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 298634 2 pages 2012

[9] V Vural G Fung B Krishnapuram J G Dy and B Rao ldquoUsinglocal dependencies within batches to improve large marginclassifiersrdquo Journal of Machine Learning Research vol 10 pp183ndash206 2009

[10] Z Y Liu K C Chiu and L Xu ldquoImproved system forobject detection and stargalaxy classification via local subspaceanalysisrdquo Neural Networks vol 16 no 3-4 pp 437ndash451 2003

[11] Y Yang D Xu F Nie S Yan and Y Zhuang ldquoImage clusteringusing local discriminant models and global integrationrdquo IEEETransactions on Image Processing vol 19 no 10 pp 2761ndash27732010

[12] Z Lai Z Jin J Yang and W K Wong ldquoSparse local discrim-inant projections for face feature extractionrdquo in Proceedings ofthe 20th International Conference on Pattern Recognition (ICPRrsquo10) pp 926ndash929 August 2010

[13] J Wright Y Ma J Mairal G Sapiro T S Huang and SYan ldquoSparse representation for computer vision and patternrecognitionrdquo Proceedings of the IEEE vol 98 no 6 pp 1031ndash1044 2010

[14] JWright A Y Yang A Ganesh S S Sastry and YMa ldquoRobustface recognition via sparse representationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 31 no 2 pp210ndash227 2009

[15] Y Shi D Dai C Liu and H Yan ldquoSparse discriminant analysisfor breast cancer biomarker identification and classificationrdquoProgress in Natural Science vol 19 no 11 pp 1635ndash1641 2009

[16] M Dikmen and T S Huang ldquoRobust estimation of foregroundin surveillance videos by sparse error estimationrdquo in Proceedingsof the 19th International Conference on Pattern Recognition(ICPR rsquo08) December 2008

[17] S Chen and Y Zheng ldquoModeling of biological intelligence forSCM system optimizationrdquo Computational and MathematicalMethods in Medicine vol 2012 Article ID 769702 10 pages2012

[18] Q Guan B Du Z Teng J Gillard and S Chen ldquoBayes cluster-ing and structural support vector machines for segmentationof carotid artery plaques in multicontrast MRIrdquo Computationaland Mathematical Methods in Medicine vol 2012 Article ID549102 6 pages 2012

[19] S Chen H Tong and C Cattani ldquoMarkov models for imagelabelingrdquo Mathematical Problems in Engineering vol 2012Article ID 814356 18 pages 2012

[20] S Chen and X Li ldquoFunctional magnetic resonance imag-ing for imaging neural activity in the human brain theannual progressrdquo Computational and Mathematical Methods inMedicine vol 2012 Article ID 613465 9 pages 2012

[21] Z Lai W Wong Z Jin J Yang and Y Xu ldquoSparse approxi-mation to the eigensubspace for discriminationrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 23 no12 pp 1948ndash1960 2012

[22] Y XuD Zhang J Yang and J Y Yang ldquoA two-phase test samplesparse representation method for use with face recognitionrdquoIEEE Transactions on Circuits and Systems for Video Technologyvol 21 no 9 pp 1255ndash1262 2011

[23] Y L Chen and Y F Zheng ldquoFace recognition for target detec-tion onPCA featureswith outlier informationrdquo inProceedings ofthe 50thMidwest SymposiumonCircuits and Systems (MWSCASrsquo07) pp 823ndash826 August 2007

[24] L Sirovitch and M Kirby ldquoLow-dimensional procedure for thecharacterization of human facesrdquo Journal of the Optical Societyof America A vol 4 no 3 pp 519ndash524 1987


[26] B Scholkopf and A Smola Learning with Kernels MIT PressCambridge Massm USA 2002

[27] K-R Muller S Mika G Ratsch K Tsuda and B ScholkopfldquoAn introduction to kernel-based learning algorithmsrdquo IEEETransactions onNeural Networks vol 12 no 2 pp 181ndash201 2001


[28] D Tao and X Tang ldquoKernel full-space biased discriminantanalysisrdquo in Proceedings of IEEE International Conference onMultimedia and Expo (ICME rsquo04) pp 1287ndash1290 June 2004

[29] S Yan D Xu Q Yang L Zhang X Tang and H J ZhangldquoMultilinear discriminant analysis for face recognitionrdquo IEEETransactions on Image Processing vol 16 no 1 pp 212ndash2202007

[30] P Jonathon Phillips H Moon S A Rizvi and P J RaussldquoTheFERET evaluationmethodology for face-recognition algo-rithmsrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 22 no 10 pp 1090ndash1104 2000

[31] P J Phillips ldquoThe Facial Recognition Technology (FERET)Databaserdquo httpwwwitlnistgoviadhumanidferetferetmasterhtml

[32] httpwwwclcamacukresearchdtgattarchivefacedatabasehtml

[33] httpcobwebecnpurdueedualeixaleixfaceDBhtml[34] Y Xu and Z Jin ldquoDown-sampling face images and low-

resolution face recognitionrdquo in Proceedings of the 3rd Inter-national Conference on Innovative Computing Information andControl (ICICIC rsquo08) pp 392ndash395 June 2008


Research ArticleComputational Approach to Seasonal Changes of Living Leaves

Ying Tang12 Dong-Yan Wu12 and Jing Fan12

1 School of Computer Science and Technology Zhejiang University of Science and Technology Hangzhou 310023 China2 Key Laboratory of Visual Media Intelligent Processing Technology of Zhejiang Province Hangzhou 310023 China

Correspondence should be addressed to Jing Fan fanjingzjuteducn

Received 10 December 2012 Accepted 17 January 2013


Copyright copy 2013 Ying Tang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper proposes a computational approach to seasonal changes of living leaves by combining the geometric deformations andtextural color changes The geometric model of a leaf is generated by triangulating the scanned image of a leaf using an optimizedmesh The triangular mesh of the leaf is deformed by the improved mass-spring model while the deformation is controlled bysetting different mass values for the vertices on the leaf model In order to adaptively control the deformation of different regions inthe leaf the mass values of vertices are set to be in proportion to the pixelsrsquo intensities of the corresponding user-specified grayscalemask map The geometric deformations as well as the textural color changes of a leaf are used to simulate the seasonal changingprocess of leaves based on Markov chain model with different environmental parameters including temperature humidness andtime Experimental results show that the method successfully simulates the seasonal changes of leaves

1 Introduction

The seasonal changes of trees vary the appearances of treesthrough seasons which include shapes and textures of theleaves flowers and fruits Among these the change of leavesconstitutes the most important part of the seasonal changesof trees In this paper we focus on how to compute the leafchanging during different seasons

As we observe the changes of leaves from spring towinter most leaves become withered and curled up due tothe influences of environmental factors [1] Besides the leavesusually turn from green to yellow during the aging processand finally fall off to the ground According to the aboveobservation the seasonal changes of leaves are simulatedin terms of their geometric deformations as well as theirtextural colors transitions There is a lot of research workdone in simulating 3D shape changes of leaves the occurringduring the withering process of leavesMost of thesemethodsgenerate the 3Ddeformation of leaves based on the changes ofveins [2ndash7] For veins-driven methods [3 4 6 7] each vertexin the 3D model of a leaf is deformed to the nearest vertex inthe interactively generated veins and deformations are con-trolled by dragging some vertices in the veinsThesemethodsinvolve much user interaction to extract the skeleton of

the leaf and the generated results are not realistic enoughThe method proposed by Chi et al [8] combines the veinswith a double-layered model of the leaf and simulates thedeformation processmore realistically However thismethodis computationally intensive and difficult to implement due tothe complex computation In this paper we propose a newimproved method using mass-spring model and grayscalemask map to simulate the deformation process of leaves withsimplified computations and realistic results

In order to simulate textural colors of leaves the Phonglighting model with a diffuse component derived from leafpigments is adopted to directly compute the reflections onthe surfaces of leaves [9] Other methods use the techniqueof texture mapping to produce the leavesrsquo appearances andthe textures can be changed to reflect the appearance changesof leaves [10] In our method we apply multiple textures torepresent appearance changing of leaves in different seasons

In order to efficiently simulate the seasonal changes ofleaves we combine the changes of geometric shape and tex-tural color of the above methods in our algorithm to producethe resultsTheMarkov chain model is used to show the statetransfer of leaves in the dynamic growing process of treesThe following sections are arranged as follows In Section 2the related work is introduced We describe the modeling of


three-dimensional leaves in Section 3 Section 4 focuses onthe implementation of geometrical changes of leaves basedon improved mass-spring model In Section 5 the Markovchain-based method is described to compute different statesof leaves combining the texture and geometry changes Weshow our experimental results in Section 6 and conclusion inSection 7

2 Related Work

The work related to the simulation of seasonal changesof leaves includes leaf modeling leaf deformation andleaf appearances rendering For leaf modeling there areL-system-based and image-based methods The L-system-based methods model leaves with self-similarity [11 12]As for image-based modeling methods [13 14] usually thefeature points on the edge of the leaf are extracted from thescanned leaf image and the geometric shape of the leaf isrepresented by the triangular meshes produced by Delaunayalgorithm [15] According to the botanical characteristicsof the leaf Dengler and Kang claim that leaf shapes havea close relationship with leaf veins [16] which is used togenerate the shapes of leaves Runions et al present thebiologically motivated method to construct leaf veins withuser interaction [17] Besides user interaction the leaf veinsare generated by fixing the start points and setting the controlpoints of veins according to the sum of a fixed value anda random parameter between zero and ten [18] Chi et al[8] introduce an improved method to construct the leaf veinskeleton which generates the main vein and the branch veinseparately and the leaf model is built by a double-layeredmass-spring model These methods produce the relativelycomplex leaf models which reflect the characteristics of leaf rsquosgeometric shapes In this paper we generate the optimizedtriangular mesh to represent the leaf model by two stepsIn the first step the key points on the edge of the leafare obtained through user interaction Then the optimizedleaf triangular mesh is generated by improved Delaunayalgorithm in the second step Instead of generating the leafveins explicitly in the modeling procedure we emphasizeleaf veins with a user-specified mask in the process of leafdeformation

The leaves gradually become withered and curled upduring the transitions of different seasons The deformationof geometric shapes of leaves is very important to simulate theseasonal changesThe 3D deformation algorithms are mainlyclassified into two categories which are free-form-baseddeformation methods [19] and physically based deformationmethods [20] Free-form-based deformation methods arewidely used in the field of computer animation and geometricmodeling [21] These kinds of methods embed the objectsinto a local coordinate space and transform the local space tomake the objects deformedThere are two commonphysicallybased deformation methods skeleton-based method andmass-spring-based method The deformation method basedon skeleton is relatively simple [7] andproducesmore realisticdeformation results of leaves However it requires muchhuman interaction Mass-spring model is more frequentlyused in fabric deformation [22] Tang and Yang [23] adopt

the mass-spring model to generate the deformation of leavesin which the mesh of the leaf is not optimized and thedeformation effects are relatively unnatural and difficult tocontrol Double mass-springmodel proposed by Chi et al [8]is capable of simulating the changes of leaves more realisti-cally However it is complex and difficult to be implemented

In order to simulate color changes of leaf surfaces invarious environmental conditions Phong lighting modelconsidering leaf rsquos pigments [9] and the technique of texturemapping [24] have been adopted The texture images ofleaves can be obtained by scanning real leaves [25] or texturesynthesis [26] Desbenoit et al [10] applies open Markovchain model to decide which texture images are mapped tocertain leaves to simulate the aging process of the leavesIn this paper we also adopt the Markov chain model tostatistically determine the distribution of leaves textureson the tree under the influence of environmental factorsincluding temperature and humidness

3 Modeling Three-Dimensional Leaves

In this paper we apply the image-based approach to modelthe geometric shapes of three-dimensional leaves [27 28]First the key points on the edge of the leaf are obtainedthrough user interaction and then the triangular mesh of theleaf is constructed by Delaunay triangulation through incre-mental insertion of points [29 30] Finally the optimizationprocedure is employed to compute the high qualitymeshwitheven-sized triangles

Instead of adopting the automatic edge detection meth-ods to extract the leaf contour we provide the interfaceto make the user interactively select the edge points ofthe leaf After the selection of edge points the smooth B-spline curve running through these points is automaticallygenerated to approximate the leaf edges [31] The B-splineedge which passes through the user-selected points is shownin Figure 1(a) from which we find that the curve representsthe real leaf edge well If more control points are selectedthe edge is more accurate The generated B-spline curveis sampled to get the key points which are to be used inDelaunay triangulation

The Delaunay triangulation method is usually used togenerate a triangulated irregular network (TIN) [32] TheDelaunay triangles are a set of connected but not overlappingtriangles and the circumscribed circle of the triangles doesnot contain any other point in the same regionUnfortunatelythe initially triangular mesh generated with key points onthe edge usually contains some long and narrow triangles asshown in Figure 1(b)The leaf mesh with such bad quality tri-angles would make the leaf deformation unnatural Insteadwe need to generate a high quality leaf mesh with even-sizedtriangles So we optimize the triangular mesh based on thesubdivision method in [33] An even-sized triangular meshis obtained by repeating the following two steps (1) relocatethe vertex position (2) modify the connection properties oftriangles

The high-resolution triangular mesh produces more nat-ural and smooth deformations However more trianglesin the mesh would lead to more time to compute the


(a) (b)

Figure 1 (a) The B-spline curve with key points selected by the user (b) the Delaunay triangulated mesh of the leaf

Figure 2 Triangular meshes of the maple leaf produced by adifferent number of iterations

deformation According to the triangulation algorithm thesubdivision level of triangular mesh is related to the numberof iterations Usually we set the number of iterations to be160 in our implementation which is enough to produce thesubdivided triangular mesh capable of natural deformationwithin acceptable time In Figure 2 we show the triangularmesh models of the maple leaf produced by a differentnumber of iterations

4 Deformations of Leaves Based onImproved Mass-Spring Model

Leaves become slowly curled up as the season changes Thisphenomenon is mainly caused by the different structuresof the upper and bottom surfaces of a leaf which havedifferent amounts of contraction during the dehydrationprocess To take into account the differences between theupper and bottom internal structures of a leaf we introducethe improved mass-spring model to make leaf deformationmore realistic

41 Numerical Calculation and Constraints Themass-springmodel is widely used in the simulation of the deformationof soft fabrics [34] This model consists of two importantparts a series of virtual particles and the corresponding lightsprings of natural length nonequal to zero The deformationof the object is determined by the displacements of particlesafter they are stressed The springs connecting the particlesconstrain the movement of particles The triangular meshmodel of a leaf can be used as the mass-spring model where

the mesh vertices are regarded as particles and the edges areas springs [8]

There are internal and external forces acting on thesprings and we denote the joined forces as 119865

119894119895(119905) The force

distribution is computed by Newtonrsquos laws of motion andexplicit Eulerrsquos method is adopted to find the numericalsolution of the model The equations to compute the accel-eration particle velocity and particle displacement are listedas follows

119886119894119895 (119905 + Δ119905) =

1

120583119894119895

119865119894119895 (119905)

V119894119895 (119905 + Δ119905) = V119894119895 (119905) + Δ119905 sdot 119886119894119895 (119905 + Δ119905)

119875119894119895 (119905 + Δ119905) = 119875119894119895 (119905) + Δ119905 sdot V119894119895 (119905 + Δ119905)

(1)

In the above equations the mass of a particle is denotedas 120583119894119895 the acceleration is denoted as 119886

119894119895 the velocity of a

particle is denoted as V119894119895 and the particlersquos displacement is

denoted as 119875119894119895 The time step is denoted as Δ119905 the value of

which is important in computing the desirable deformationThe time step needs to be small enough to ensure the stabilityof the numerical calculation Otherwise dramatic changes ofparticle positions would be incurred by large time step values

Actually the deformation curve of a leaf under forces isnot ideally linear If we directly compute the deformationwiththe above equations the problem of ldquoover elasticityrdquo wouldoccur that is the deformation of the springs would exceed100 To overcome this problem we adopt the method ofconstraining velocities to constrain the deformation of thesprings [35] The basic idea is as follows Particle 119906 and par-ticle V are the ends of spring 119904119881

120583(119905) and 119881V(119905) respectively

represent the velocity of particle 119906 and particle V at time 119905Assume that the relative velocity between the two particlesis 119881120583V(119905) and the relative position is 119875

120583V(119905) the new relativeposition after one time step 119875

119906V(119905 + Δ119905) is computed byconstraining the velocity of the particle If 119875

119906V(119905+Δ119905) satisfies(2) the velocity is updated [35] Otherwise it is not updated

119875119906V (119905 + Δ119905) =

1003816100381610038161003816119875119906V (119905) + 119881119906V (119905 + Δ119905) sdot Δ1199051003816100381610038161003816 le (1 + 120591119888) sdot 119871

(2)


(a) (b)

Figure 3 (a) The texture of a maple leaf (b) mask map of the maple model

In (2) 119871 presents the natural length of the spring withoutany forces exerted and 120591

119862is the threshold of deformation

This equation guarantees that when the value of 120591119888is set to be

01 the maximum deformation length of the spring does notexceed 10 percent of the natural length In other words thedifference between 119875

119906V(119905+Δ119905) and 119875119906V(119905) should be within 10percent of the natural length

42 Deformation The key of shape deformation is to com-pute the changes of the position of each particle If eachparticle has the same mass value the relative displacementsin directions 119909 119910 and 119911 only depend on the joint force ineach direction For a relatively high-resolution mesh modelwith nearly even-sized triangles the joint forces betweenmost particles and its adjacent particles would not differenough to make desirable deformations Thus the uniformmass of all particles is not in favor of generating the nonuni-form deformation results relative to different leaf regionsfor example the regions near edges usually undergo moredeformation than the center regions To enhance the changeof the relative displacement of each particle and generatethe adaptively deformed results for different leaf regions weadaptively allocate themass values to different particles in ourimproved deformation model

According to Newtonrsquos law of motion 119865 = 119898119886 for thesame force 119865 the smaller the objectrsquos mass119898 is the larger theacceleration 119886 is So we can control the deformation of leavesby setting different masses of the particlersquos We introducethe mask map to adaptively control the particles masses Themask map is generated according to the texture image of theleaf Suppose that we have a texture image of a leaf calledleaf1bmp which is obtained by scanning the real leaf Weselect out the leaf region from the texture and paint differentgrayscale colors to this region The intensities of the paintedpixels are in proportion to the particlersquos masses For exampleif we try to set a smallermass value for a particle we can paintthis pixel in black or an other color close to black A mapleleaf is shown in Figure 3(a) According to our observations ofnatural maple leaves the regions around the leaf corner andclose to petiole usually undergomore deformation than otherregions So we paint these regions in black or darker gray

values while other regions in brighter gray values as shown inFigure 3(b) Differentmask mapsmap different masses to thesame particles which results in different deformation resultsThe correspondingmask map needs to be generated based onthe natural deformation pattern of the specific leaf

According to the texture coordinates of the particles oftriangular mesh we find in the mask map the pixels whichcorrespond to particles in the leaf mesh model The grayvalues of pixels in the mask map are mapped to the value ofparticle masses119898 by the following

119898 = 05 gray = 0ln (gray + 1) gray = 0

(3)

In (3) the mass value is computed as logarithm of thegrayscale value which makes the change of the masses moregentle and smooth compared with the changes of grayscalevalues Such mass distribution is more amenable to yieldnatural deformation of leaves

The detailed steps to implement deformation process areshown as follows

(1) Generate themask map to determine the mass distri-bution of the leaf

(2) Initialize parameter values in our improved mass-spring model Set the initial velocity and accelerationof particles to be zero Initializemasses of the particlesaccording to themask map

(3) Establish constraints amongparticlesThe connectionbetween particles (ie the mesh topology) deter-mines what other particles directly exert forces on thecurrent particle for the computation of displacementsThe constraints are built by three steps as follows

Step 1 Find the adjacent triangle faces of cur-rent particle Adjacent faces are those triangleswhich include a current particle as one of theirverticesStep 2 Find the adjacent particles of a currentparticle The other two vertices in adjacenttriangles are the adjacent particles of a currentparticle


Figure 4 Several deformations using the mask map in Figure 3(b)

Step 3 Establish the constraints Set a flagvalue for each particle to describe whether thisparticle had been traversed and initialize theflag value as false If one particle is traversed setits flag value as true Set the constraints betweenthis particle and its adjacent particles if they arenot traversed Thus all particles are traversedonly once and the constraints are set withoutduplication When this particle is moved theparticles having constraints move with it too

(4) Exert the force and compute the change of positionof each particle by numerical calculation in one timestep

(5) Repeat the numerical calculation in each time stepto obtain the new velocities and accelerations andupdate particle positions accordingly to producedeformation effects at different time steps

For example the deformation results at different timesteps of the maple leaf under the mask map in Figure 3(b)are showed in Figure 4 (the first model is the original meshmodel)

The deformation results in Figure 4 show that the leafregions with darker gray values are deformed more thanthe regions with brighter gray values The masses of thoseregions with darker gray values are smaller so that they movemore distances under forces The regions with brighter grayvalues have largermasseswhichmake themmovemuchmoreslowly Different movements of particles distributed overthe leaf surfaces produce the adaptive deformation resultsover the leaf surface If we paint the veins white or brightgray values we can get the deformation result in whichthe veins are kept unmoved and two-side regions aroundveins become curly With this method we can control theleaversquos deformation flexibly For the same leaf model we cangenerate different deformation results by differentmaskmapsIn Figure 6 we show the different deformation results forthe same leaf model for a different mask map in Figure 5Therefore in order to achieve desirable deformations we canconstruct the corresponding mask map to make the leavesdeformed as expected

Figure 5 Another mask map of the maple leaf model

Figure 6 Different deformation results of the maple leaf for maskmap shown in Figure 5

119875119894119894(119890 119905)

119875 119894119895(119890 119905)

119875119894119896(119890 119905)State 119878119894

State 119878119895

State 119878119896

larr997892

Figure 7 Transition relationship for Markov chain model

5 Textural and Geometric Changes

To simulate the seasonal changes of leaves we need to takethe transitions of textural colors of leaves into account besidesgeometric deformations The whole seasonal changing pro-cess of leaves can be regarded as the sequences of a seriesof discrete states The leaves transform from one state tothe other with certain probabilities conditioned by environ-mental factors This transformation can be approximated byMarkov chain model [10]

Markov chain model has two properties (1)The state ofthe system at time 119905 + 1 is only related to the state at time119905 and has nothing to do with the states at a previous time(2) Transformation of the state from time 119905 to time 119905 + 1has nothing to do with the value of 119905 The leaf changingprocess can be regarded as the Markov chain Differenttexture images as well as the deformed geometric shapes are


Texture 1 Texture 2 Texture 3 Texture 4 Texture 5 Texture 6 Texture 7

Figure 8 Seven texture states of a maple model

organized to constitute different states in the Markov chainWe simulate various distributions of leaves on the tree by therandomness of the Markov chain model The environmentalfactors including temperature and humidness are used asthe conditions to determine the probability to transfer fromone state to another By setting different environmentalparameters we get the seasonal appearances of trees with thecorresponding distributions of leaves

The leaf rsquos state is denoted as 119878119909 where 0 le 119909 lt 119899 and 119899

represent the total number of possible states of leaves Assumethat we have three states 119878

119894 119878119895 and 119878

119896and the transition

relationship among these three states are shown in Figure 7It shows that for the state 119878

119894at time 119905 it may evolve to states 119878

119895

and 119878119896or remain in the original state at time 119905+1with certain

probabilitiesThe arc119875

119894119894(119890 119905) in Figure 7 represents the possibility that a

leaf at a given state 119878119894stays in the same state at the next time It

is defined as the probability of keeping self-stateThe functionof this probability is denoted as follows [10]

119875119894119894 (119890 119905) = 119890

minus120582119894(119890)119905 0 le 119894 le 119899 (4)

120582119894 (119890) =

ln 2120591119894 (119890) (5)

Function 120591119894(119890) is the bilinear interpolation of the temper-

ature and humidnessThe probability that the leaf transfers to other states is

denoted as 1 minus 119875119894119894(119890 119905) 119875

119894119895(119890 119905) is defined as the probability

of the leaf at state 119878119894transferring to another state 119878

119895 and it is

computed by (6) as follows

119875119894119895 (119890 119905) = (1 minus 119875119894119894 (119890 119905))119883119894119895 (119890) 0 le 119894 ≺ 119899 119894 =119895 (6)

Function 119883119894119895(119890) is the bilinear interpolation of four con-

stants between zero and oneThese four constants correspondto the transition possibilities in the four extreme cases wetand cold wet andwarm dry and cold and dry andwarmThevalues of these constants are interactively specified by users

The parameters of time temperature and humidnessare set by users Taking the maple leaves in Figure 8 forexample we use three specific combinations of textures andshapes for each season For instance three main states areused to represent leaves in summer which are texture 2 inFigure 8 combined with the first deformation in Figure 4texture 3 combined with the second deformation and texture4 combined with the third deformation

Several states which combine changes of textures andshapes in different seasons are showed in Figure 9 Giventhe combinations of states we calculate the transition prob-abilities of leaves according to the specific temperature and

Figure 9 The basic triangular mesh model of the maple leaf andseven states combining textures and geometric deformations

Begin

End

Specify all states of leavesincluding textures and deformed

shapes

Set the parameters of seasontime temperature humidityand some constants through

user interaction

Compute the transitionprobabilities

Compute the distribution ofstates of leaves by the transition

probabilities

Import geometric leaf models andperform texture mapping withcorresponding leaf textures

Figure 10 Seasonal changing process of leaves based on Markov-chain model

humidness set for certain seasons and get the correspondingleaversquos distributions in that season

To summarize the seasonal changing process of leavesunder certain environmental parameters is showed inFigure 10


Figure 11 Tree growing process based on L-system

Figure 12 Seasonal changes of a maple tree based onMarkov chainmodel

6 Results

To produce the results of seasonal changes of trees we growthe leaves on the trees and simulate their distributions fordifferent seasons In order to get the 3D model of the treewe adopt the L-system method to produce the trunks andbranches of the tree The trunks and branches of the treeare drawn with quadratic surface and the leaves grown onbranches are modeled as triangular meshes In Figure 11 wemodel the tree and its growth through the iteration of theL-system and the leaves grown on the tree are shown Tosimulate leaves seasonal changes we distribute various leaveson the tree under different environments based on Markovchain model Figure 12 shows some seasonal changes of the

maple tree and the enlarged picture at the lower right cornershow the change of the individual leaf more clearly

7 Conclusion

In this paper we propose a computational approach to sim-ulate the seasonal changes of living leaves by combining thechanges in geometric shapes and textural colors First the keypoints are selected on the leaf image by user interactionThenthe triangular mesh of the leaf is constructed and optimizedby improved Delaunay triangulation After the models ofleaves have been obtained the deformations of leaves arecomputed by improved mass-spring models The seasonalchanges of trees under different environmental parametersare computed based on Markov chain The improved mass-spring model is based on the user-specifiedmask map whichadaptively determines the masses of particles on the leafsurface

In the future we are interested in the following work

(1) Work on how to generate the mask map more natu-rally according to the characteristics of the deforma-tions of leaves

(2) Intend to simulate the dynamic procedure of theleaves falling onto ground out of gravity

(3) Develop a more precise model to compute the colorsof leaves which takes into account of the semitrans-parency of leaves

Acknowledgments

This work is supported by National Natural Science Founda-tion of China (61173097 61003265) Zhejiang Natural ScienceFoundation (Z1090459) Zhejiang Science and TechnologyPlanning Project (2010C33046) Zhejiang Key Science andTechnology Innovation Team (2009R50009) and Tsinghua-Tencent Joint Laboratory for Internet Innovation Technol-ogy

References


[2] QXuResearch on techniques ofmesh deformation [PhD thesis]Zhejiang University 2009

[3] P Prusinkiewicz L Mundermann R Karwowski and B LaneldquoThe use of positional information in the modeling of plantsrdquoin Proceedings of the Computer Graphics Annual Conference(SIGGRAPH 2001) pp 289ndash300 August 2001

[4] L Mundermann P MacMurchy J Pivovarov and P Prusink-iewicz ldquoModeling lobed leavesrdquo in Proceedings of the ComputerGraphics International (CGIrsquo03) pp 60ndash65 July 2003

[5] S Y Chen ldquoCardiac deformation mechanics from 4D imagesrdquoElectronics Letters vol 43 no 11 pp 609ndash611 2007

[6] S M Hong B Simpson and G V G Baranoski ldquoInteractivevenation-based leaf shape modelingrdquo Computer Animation andVirtual Worlds vol 16 no 3-4 pp 415ndash427 2005


[7] S L Lu C J Zhao and X Y Guo ldquoVenation skeleton-basedmodeling plant leaf wiltingrdquo International Journal of ComputerGames Technology vol 2009 Article ID 890917 8 pages 2009

[8] X Y Chi B Sheng Y Y Chen and E H Wu ldquoPhysicallybased simulation of weathering plant leavesrdquo Chinese Journal ofComputers vol 32 no 2 pp 221ndash230 2009

[9] M Braitmaier J Diepstraten and T Ertl ldquoReal-time renderingof seasonal influenced treesrdquo in Proceedings of the Theory andPractice of Computer Graphics pp 152ndash159 Bournemouth UKJune 2004

[10] B Desbenoit E Galin S Akkouche and J Grosjean ldquoModelingautumn sceneriesrdquo in Proceeding of the Eurographics pp 107ndash110 2006

[11] P Prusinkiewicz and A Lindennmyer Algorithmic Beauty ofPlants Springer Berlin Germany 1990

[12] S B Zhang and J Z Wang ldquoImprovement of plant structuremodeling based on L-systemrdquo Journal of Image and Graphicsvol 7 no 5 pp 457ndash460 2002

[13] L Quan P Tan G Zeng L Yuan J D Wang and S B KangldquoImage-based plant modelingrdquo ACM Transactions on Graphicsvol 25 no 3 pp 599ndash604 2006

[14] P Tan G Zeng J D Wang S B Kang and L Quan ldquoImage-based tree modelingrdquo in Proceedings of the ACM SIGGRAPH2007 New York NY USA August 2007

[15] L P Chew ldquoGuaranteed-quality triangular meshesrdquo TechRep TR-89-983 Department of Computer Science CornellUniversity 1989

[16] N Dengler and J Kang ldquoVascular patterning and leaf shaperdquoCurrent Opinion in Plant Biology vol 4 no 1 pp 50ndash56 2001

[17] A Runions M Fuhrer B Lane P Federl A G Rolland-Lagan and P Prusinkiewicz ldquoModeling and visualization of leafvenation patternsrdquo ACM Transactions on Graphics vol 24 no3 pp 702ndash711 2005

[18] Z J Ma and Y M Jiang ldquoChinar leaf simulationrdquo ComputerSimulation vol 26 no 2 2009

[19] TW Sederberg and S R Parry ldquoFree-formdeformation of solidgeometric modelsrdquo Computer Graphics vol 20 no 4 pp 151ndash160 1986

[20] L H de Figueiredo J de Miranda Gomes D Terzopoulosand L Velho ldquoPhysically-based methods for polygonization ofimplicit surfacesrdquo in Proceedings of the Graphics Interface rsquo92pp 250ndash257 May 1992

[21] G R Liu J H Lin X D Liu and F R Zhao ldquoFree-formdefinition based on three-dimensional spacerdquo Microelectronicsand Computer vol 25 no 7 2008

[22] X Provot ldquoDeformation constraints in a mass-spring modelto describe rigid cloth behaviorrdquo in Proceedings of the GraphicsInterface Conference rsquo95 pp 147ndash154 May 1995

[23] Y Tang and K F Yang ldquoResearch on visualization of deforma-tion of three-dimensional leavesrdquoComputer Simulation vol 28no 5 2011

[24] N Chiba K Ohshida K Muraoka and N Saito ldquoVisualsimulation of leaf arrangement and autumn coloursrdquo Journal ofVisualization and Computer Animation vol 7 no 2 pp 79ndash931996

[25] N ZhouWDong and XMei ldquoRealistic simulation of seasonalvariant maplesrdquo in Proceedings of the 2nd International Sympo-sium on Plant Growth Modeling and Applications (PMArsquo06) pp295ndash301 Beijing China November 2006

[26] X Y Chi B Sheng M Yang Y Y Chen and E H WuldquoSimulation of autumn leavesrdquo Journal of Software vol 20 no3 pp 702ndash712 2009

[27] S Y Chen Y HWang and C Cattani ldquoKey issues in modelingof complex 3D structures from video sequencesrdquoMathematicalProblems in Engineering vol 2012 Article ID 856523 17 pages2012

[28] J Zhang S Chen S Liu and Q Guan ldquoNormalized weightedshape context and its application in feature-based matchingrdquoOptical Engineering vol 47 no 9 Article ID 097201 2008

[29] B A Lewis and J S Robinson ldquoTriangulation of planar regionswith applicationsrdquoTheComputer Journal vol 21 no 4 pp 324ndash332 1978

[30] G Macedonio and M T Pareschi ldquoAn algorithm for the trian-gulation of arbitrarily distributed points applications to volumeestimate and terrain fittingrdquo Computers and Geosciences vol 17no 7 pp 859ndash874 1991

[31] S Y Chen and Q Guan ldquoParametric shape representation bya deformable NURBS model for cardiac functional measure-mentsrdquo IEEE Transactions on Biomedical Engineering vol 58no 3 pp 480ndash487 2011

[32] V J D Tsai ldquoDelaunay triangulations in TIN creation anoverview and a linear-time algorithmrdquo International Journal ofGeographical Information Systems vol 7 no 6 pp 501ndash5241993

[33] L Markosian J M Cohen T Crulli and J Hughes ldquoSkina constructive approach to modeling free-form shapesrdquo inProceedings of the SIGGRAPHConferencersquo99 pp 393ndash400 1999

[34] H Liu C Chen and B L Shi ldquoSimulation of 3D garment basedon improved spring-mass modelrdquo Journal of Software vol 14no 3 pp 619ndash627 2003

[35] X P Sun W W Zhao and X D Liu ldquoDynamic clothsimulation based on velocity constraintrdquo Computer Engineeringand Applications vol 44 no 31 pp 191ndash194 2008


Research ArticleReliable RANSAC Using a Novel Preprocessing Model

Xiaoyan Wang1 Hui Zhang2 and Sheng Liu1

1 School of Computer Science and Technology Zhejiang University of Technology Hangzhou 310023 China2 College of Information Engineering Zhejiang University of Technology Hangzhou 310023 China

Correspondence should be addressed to Xiaoyan Wang xw292camacuk

Received 8 December 2012 Revised 8 January 2013 Accepted 17 January 2013


Copyright copy 2013 Xiaoyan Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Geometric assumption and verification with RANSAC has become a crucial step for corresponding to local features due to its wideapplications in biomedical feature analysis and vision computing However conventional RANSAC is very time-consuming due toredundant sampling times especially dealing with the case of numerous matching pairs This paper presents a novel preprocessingmodel to explore a reduced set with reliable correspondences from initial matching dataset Both geometric model generation andverification are carried out on this reduced set which leads to considerable speedups Afterwards this paper proposes a reliableRANSAC framework using preprocessingmodel which was implemented and verified usingHarris and SIFT features respectivelyCompared with traditional RANSAC experimental results show that our method is more efficient

1 Introduction

Feature matching is a basic problem in computer visionCorresponding to local features has become the dominantparadigm for structure from motion [1 2] image retrieval[3] and medical image processing [4] It is a crucial issueto correspond to the features accurately and efficiently [5 6]Most applications are built upon a general pipeline consistingof steps for extracting features from images matching themto obtain correspondences and applying some forms ofgeometric verification to reject the outliers The geometricverification is extremely critical for the pipelinersquos success Ithas been proven that RANSAC [7] is the best method ofchoice for this pipeline [8] However there are two obviousshortcomings in RANSAC processing On one hand it istime-consuming On the other hand when the sampling timeis restricted artificially the selected matching pairs may notbe correct

Consequently numerous extensions for RANSAC havebeen proposed to speed up different RANSAC stages suchas SCRANSAC [8] optimal randomized RANSAC [9] andother improved methods [10ndash12] However even with these

extensions the geometric verification is still a major bot-tleneck in applications In addition most of the improvedmethods cost considerable implementation runtime and aredifficult to tune for optimal performance

This paper proposes a fast and simple RANSAC frame-work based on a preprocessing model It can result in areduced correspondence set with a higher inlier percentageon which RANSAC will converge faster to a correct solutionThis model can successfully acquire a subset 119864 with higherprobability being inliers from the initial corresponding set119875 Then a reliable fundamental matrix F or a homographymatrix H can be estimated from subset 119864 Owing to 119864 withhigher inliers ratio the estimated H or F is more reliableFinally the outliers in set 119875 can be rejected according to theestimatedH or F Comparing with other improved methodsthe proposed approach in this paper can achieve similarspeedup while being considerably simpler to implement

The rest of this paper is organized as follows In Section 2this paper discusses RANSAC for outlier rejection andintroduces preprocessingmodel including itsmotivation andalgorithm flowchart In Section 3 a novel RANSAC frame-work based on Preprocessing Model is proposed Section 4


presents the experimental results and data analysis The lastpart is a summarization of this paper

2 Outlier Rejection

RANSAC has become the most popular tool to solve the geo-metric estimation problems in datasets containing outlierswhich was first proposed by Fischler and Bolles in 1981 [7]It is a nondeterministic algorithm with a purpose that it canproduce a reasonable result only with a certain probability

21 RANSAC RANSAC operates in a hypothesized-and-verified framework The basic assumption of RANSACalgorithm is that the data consists of ldquoinliersrdquo that is thedata whose distribution can be explained by some set ofmodel parameters And ldquooutliersrdquo are the data which donot fit the model The outliers probably result from errorsof measurement unreasonable assumptions or incorrectcalculations RANSAC randomly samples a minimal subset 119904of size from the initial set in order to hypothesize a geometricmodel This model is then verified against the remainingcorrespondences and the number of inliers that is ofcorrespondences consistent with the model is determined asits score RANSAC achieves its goal by iteratively selecting arandom subset of the original data which are hypotheticalinliers This procedure is iterated until a certain terminationcriterion is met In confidence 119901 ensure that at least onesampling within 119873 times sampling the elements are allinliers The equation is

119873 =log (1 minus 119901)log (1 minus 120593119904)

(1)

where 119904 is the mean of the minimal size of sampling subsetto hypothesize the geometric model and 120593 represents theprobability of a point being an inlier

The iteration ensures a bounded runtime aswell as a guar-antee on the quality of the estimated result As mentionedabove there are some limits in RANSAC processing Time-consuming is the most urgent problem especially when theinitial inliers rate is low Hence this paper proposes a novelRANSAC framework with a preprocessing model to improveit

22 Preprocessing Model The main effort of this prepro-cessing model is to explore a reduced set with reliablecorrespondences from initial matching dataset and estimatethe geometric model This model can be divided into thefollowing two steps

221 Selecting Reliable Corresponding Pairs When verify-ing hypotheses in RANSAC the corresponding pairs arecategorized into inliers and outliers Since the number ofsamples taken by RANSAC depends on the inlier ratio it isdesirable to reduce the fraction of outliers in the matchingset Selecting a reduced set with higher inlier ratio is the firststep of this preprocessing model Our approach is motivatedby the observation that extracting and exploring a subset 119864

Number of matches

Bucket

Random

Variable

0 1

0

2 3

1

119871 minus 1

Figure 1 Monte Carlo sampling method

with higher probability being inliers is an efficacious idea toimprove the runtime of RANSAC The idea underlying thepreprocessing model is to use relaxation technique [13] toacquire a reduced set of more confident correspondencesIt leads to a significant speedup of the RANSAC procedurefor two reasons First RANSAC only needs to operate on asubstantially smaller set 119864 for verifying model hypothesesSecond the additional constraints enforced in relaxationmethod lead to an increased inlier ratio in reduced set 119864This directly affects the number 119873 of iterations Hencethe preprocessing model converges faster to a correct solu-tion

222 Fundamental Matrix 119865 Estimation Zhang et al [13]used LMedS technique to discard false matches and estimatefundamental matrix However when the inlier ratio is lessthan 50 the result estimated by LMedS method maybe unreliable RANSAC is one of the robust methods forfundamental matrix estimation which can obtain robustresult even when the outlier ratio is more than 50

RANSAC is a stochastic optimization method whoseefficiency can be improved byMonte Carlo sampling method[14]Thismethod is shown in Figure 1However the samplingresults may be very close to each other Such a situationshould be avoided because the estimation result may beinstable and useless The bucketing technique [14] is usedto achieve higher stability and efficiency which is shownin Figure 2 It works as follows The min and max of thecoordinates of the points are calculated in the first imageTheregion of the image is then divided into 119887 times 119887 buckets (shownin Figure 2) To each bucket is attached a set of feature pointsand indirectly a set of correspondences which fall into itThose buckets which have no matches attached are excludedIn order to estimate fundamental matrix 119865 a subsample of8 points should be generated It is selected in 8 mutuallydifferent buckets and then onematch in each selected bucketis randomly selected

Therefore the fundamental matrix 119865 can be estimatedaccurately and efficiently This is the second step of thepreprocessing model


0 1 2 3 4 5 6

1

2

3

4

5

6

7

7

0

Figure 2 Bucketing technique

(1) Computation of the reduced set E from initialmatching set P

If (119902lowast ge 119902) store this pair in dataset E(2) RANSAC application

do21 select the minimal sample s in set E22 compute solution(s) for Fwhile 119901 = 1 minus (1 minus 120593red119904)

119873

lt 1199010 compute and store

H(F)(3) Compute the hypothesisrsquos support on full set P with

matrixH or F

Algorithm 1 RANSAC with preprocessing model

3 RANSAC Framework with PreprocessingModel

An improved RANSAC algorithm with preprocessing modelis proposed in this section This model can be easily inte-grated into the RANSAC procedure The main idea is tosuppose knowing somematching pairs being inlierswith highprobability which are put into subset 119864 (119864 sub 119875) Thereforeif RANSAC operates in subset 119864 with the same confidenceit can calculate closer to the correct fundamental matrix F(or homography matrix H) with much less time of iterationThus the preprocessing model can achieve the speedups inthe whole RANSAC procedure The steps of our frameworkare described as in Algorihm 1

In Algorithm 1 119902lowast is the threshold of relaxation iterationIn this paper 119902 is set to 60 119901

0is the RANSAC threshold

parameter which is usually set to 95 Let 120593red denote theratio of inliers to all correspondences in set 119864 Then theprobability 119901 that in 119873 steps RANSAC ensures that at leastone sampling within times 119873 sampling the elements areall inliers follow as 119901 = 1 minus (1 minus 120593red

119904)119873 Once matrix

F is obtained in set 119864 we can additionally compute thehypothesisrsquos support on the whole set 119875 In our experiments

we however only perform this last step to report the inliernumbers

4 Experiment and Analysis

In the following this paper experimentally evaluatesthe improved RANSAC and compares it with a classicalapproach As we know Harris and SIFT features are mostcommonly used in correspondence [15 16] In order toevaluate an approach comprehensively choose both Harrisand SIFT feature in initial corresponding The environmentof the experiments is Matlab R2010 Computer configurationis 210G (CPU) and 400G (RAM)The experimental imagesin this paper are from open databases Visual GeometryGroup Peter Kovesirsquos home page and the internet

41 Experiment Based on Harris Feature In the experi-ments based on Harris feature this paper chooses match-by-correlation algorithm to obtain the initial matching set119875 Then the proposed RANSAC framework is operated onset 119875 The consequent of the Preprocessing Model directlydetermines the effect of the whole procedure The reliable set119864 can be acquired by adjusting the model parameters

Figure 3 is the comparison between our approach andthe traditional RANSAC Figure 3(a) shows the matchingresult calculated by our improved RANSAC The resultof traditional RANSAC method in the same experimentalcondition is shown in Figure 3(b) The numbers of iterationsin Figures 3(a) and 3(b) are 260 and 361 respectively 51140means extracting 51 inliers from 140 initial putative matchingset From the comparison it is obvious that the result ofour approach is better The most important is that theiteration times are reducedThus it can improve the runtimeof RANSAC successfully Compared with other improvedRANSAC algorithms our RANSAC framework can achievethe same result while it is simpler to implement and thesampling times are reduced

42 Experiment Based on SIFT Feature Currently SIFT is apopular and reliable algorithm to detect and describe localfeatures in images However the initial matching by SIFT stillexists in outliers In this section this paper uses the proposedapproach to reject the outliers for the initial correspondingbased on SIFT The object is a model of scalp which isusually used in biomedical modeling The results are shownin Figure 4 Figure 4(a) is the result of initial matching bySIFT and the number of pairs is 68 Figure 4(b) shows theresult of our proposed RANSAC the number of inliers is 50and iteration times are 14 Figure 4(c) illuminates the resultof classical RANSAC in the same experimental condition thenumber of inliers is 42 and iteration times are 31

From the comparison results in Figure 4 it can be foundthat our method is more effective for outlier rejectionMoreover the iteration times are reduced to almost 45 Itis the most important benefit of our approach

In conclusion this paper argues that our method can begenerally used in outlier rejection no matter which kind of


(a) 51140

(b) 47140

Figure 3 Comparison between our proposed RANSAC and tradi-tional RANSAC

feature is usedMoreover the preprocessingmodel is adaptivefor the condition of low-matching rate

43 Analysis As is shown above the proposed RANSACsucceeds in reducing the iteration times Our frameworkrsquossuccess owes to the preprocessing model which is effectivefor selecting the reliable corresponding pairs Figure 5 illus-trates the comparison of iteration times operating RANSACin subset 119864 and set 119875 It is obvious that there are hugedifferences especially when the initial matching rate is lowThe main reason of the differences is that the elements ofset 119864 are much more reliable and with less scale Throughexperimental statistics it can be found that in the case of120593 le 06 the proposed RANSAC needs much less iterationsthan direct RANSAC processing does While if the conditionof120593 is selected in 06 le 120593 le 09 the twomethods usually havethe same time complexity Therefore our model is beneficialto screen a reliable matching set 119864 from the initial set 119875with lower matching rate 120593 and can reduce the followup ofRANSAC iterations successfully

5 Conclusion

In this paper a novel framework was presented for improvingRANSACrsquos efficiency in geometric matching applicationsThe improvedRANSAC is based onPreprocessingModel thatlets RANSAC operate on a reduced set of more confidentcorrespondences with a higher inlier ratio Compared with

50100150200250300350

100 200 300 400 500 600 700 800

(a) Initial matching by SIFT

50100150200250300350

100 200 300 400 500 600 700 800

(b) Result of our RANSAC approach

50100150200250300350

100 200 300 400 500 600 700 800

(c) Result of classical RANSAC

Figure 4 Results of the proposed method and classical RANSACfor correspondences based on SIFT

0

200

400

600

800

1000

02 03 04 05 06 07 08 09120593

119879

RANSAC(P)RANSAC(E)

Figure 5 The number of iterations for RANSAC in set 119864 and set 119875at the condition of different initial matching rates 119879 represents theiteration time of RANSAC and 120593means the initial matching rate

classic screening model this model is simpler and efficientin implement especially in the case of low-initial matchingrate The experimental results show that our approach canreduce much more iteration times especially when the initialmatching rate is lower than 60 In addition the experimentswere operated on two current features Harris and SIFTTherefore it can be concluded that the proposed RANSACframework is applicable


In conclusion this paper makes the following contribu-tions (1) this paper proposed a RANSAC framework whichdoes not only rely on appearance but takes into account thequality of neighboring correspondences in the image space(2) preprocessingmodelwas introduced for selecting reducedset with higher inlier ratio which improves runtime

Acknowledgments

This work was supported by State Scholarship Fund fromChina Scholarship Council (no 2011833105) ResearchProject of Department of Education of Zhejiang Province(no Y201018160) Natural Science Foundation of ZhejiangProvince (nos Y1110649 and 61103140) and CommonwealProject of Science and Technology Department of ZhejiangProvince (nos 2012C33073 and 2010C33095) China

References

[1] N Snavely S M Seitz and R Szeliski ldquoModeling the worldfrom Internet photo collectionsrdquo International Journal of Com-puter Vision vol 80 no 2 pp 189ndash210 2008

[2] N Snavely S M Seitz and R Szeliski ldquoPhoto tourism explor-ing photo collections in 3DrdquoACMTransactions onGraphics vol25 pp 835ndash846 2006

[3] J PhilbinO ChumM Isard J Sivic andA Zisserman ldquoObjectretrieval with large vocabularies and fast spatial matchingrdquo inProceedings of IEEE Computer Society Conference on ComputerVision and Pattern Recognition (CVPR rsquo07) vol 1ndash8 pp 1545ndash1552 New York NY USA June 2007

[4] S Chen M Zhao G Wu C Yao and J Zhang ldquoRecentadvances in morphological cell image analysisrdquo Computationaland Mathematical Methods in Medicine vol 2012 Article ID101536 10 pages 2012

[5] S Chen Z Wang H Tong S Liu and B Zhang ldquoOptimalfeature matching for 3D reconstruction by combination ofglobal and local informationrdquo Intelligent Automation and SoftComputing vol 17 no 7 pp 957ndash968 2011

[6] S Y Chen andZ JWang ldquoAcceleration strategies in generalizedbelief propagationrdquo IEEETransactions on Industrial Informaticsvol 8 no 1 pp 41ndash48 2012

[7] M A Fischler and R C Bolles ldquoRandom sample consensus aparadigm for model fitting with applications to image analysisand automated cartographyrdquo in Readings in Computer VisionIssues Problems Principles and Paradigms A F Martin and FOscar Eds pp 726ndash740 Morgan Kaufmann New York NYUSA 1987

[8] T Sattler B Leibe and L Kobbelt ldquoSCRAMSAC improvingRANSACrsquos efficiency with a spatial consistency filterrdquo in Pro-ceedings of the 12th International Conference on Computer Vision(ICCV rsquo09) pp 2090ndash2097 October 2009

[9] O Chum and J Matas ldquoOptimal randomized RANSACrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol30 no 8 pp 1472ndash1482 2008

[10] F Mufti R Mahony and J Heinzmann ldquoRobust estima-tion of planar surfaces using spatio-temporal RANSAC forapplications in autonomous vehicle navigationrdquo Robotics andAutonomous Systems vol 60 pp 16ndash28 2012

[11] L Zhang Z Liu and J Jiao ldquoAn improved RANSAC algorithmusing within-class scatter matrix for fast image stitchingrdquo in

Image Processing Algorithms and Systems IX J T Astola andK O Egiazarian Eds vol 7870 of Proceedings of SPIE SanFrancisco Calif USA January 2011

[12] J Civera O G Grasa A J Davison and J M M Montiel ldquo1-point RANSAC for extended Kalman filtering application toreal-time structure from motion and visual odometryrdquo Journalof Field Robotics vol 27 no 5 pp 609ndash631 2010

[13] Z Zhang R Deriche O Faugeras and Q T Luong ldquoArobust technique formatching twouncalibrated images throughthe recovery of the unknown epipolar geometryrdquo ArtificialIntelligence vol 78 no 1-2 pp 87ndash119 1995

[14] Z Zhang ldquoDetermining the epipolar geometry and its uncer-tainty a reviewrdquo International Journal of Computer Vision vol27 no 2 pp 161ndash195 1998

[15] S Chen Y Wang and C Cattani ldquoKey issues in modeling ofcomplex 3D structures from video sequencesrdquo MathematicalProblems in Engineering vol 2012 Article ID 856523 17 pages2012



Research ArticlePlane-Based Sampling for Ray Casting Algorithm in SequentialMedical Images

Lili Lin1 Shengyong Chen1 Yan Shao2 and Zichun Gu2

1 School of Computer Science and Technology Zhejiang University of Technology Hangzhou 310023 China2Department of Plastic and Reconstructive Surgery Sir Run Run Shaw Hospital Medical College Zhejiang UniversityHangzhou 310016 China

Correspondence should be addressed to Shengyong Chen syieeeorg

Received 9 December 2012 Accepted 28 December 2012


Copyright copy 2013 Lili Lin et al is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

is paper proposes a plane-based sampling method to improve the traditional Ray Casting Algorithm (RCA) for the fastreconstruction of a three-dimensional biomedical model from sequential images In the novel method the optical properties ofall sampling points depend on the intersection points when a ray travels through an equidistant parallel plan cluster of the volumedataset e results show that the method improves the rendering speed at over three times compared with the conventionalalgorithm and the image quality is well guaranteed

1 Introduction

Modeling three-dimensional (3D) volume of biomedicaltissues from 2D sequential images is an important techniqueto highly improve the diagnostic accuracy [1] Volume ren-dering refers to the process that maps the 3D discrete digitaldata into image pixel values [2] It can be classied into twocategories one is direct volume rendering which generatesimages by compositing pixel values along rays cast into a3D image and the other one is indirect volume renderingwhich visualizes geometry element graphics extracted fromthe volume data [3] e importance of volume rendering isresampling and synthesizing image [4] Ray casting splattingand shear-warp are the three popular volume renderingalgorithms now [5]

Ray Casting Algorithm (RCA) is a direct volume ren-dering algorithm e traditional RCA is widely used for itcan precisely visualize various medical images with details ofboundary and internal information from sequential imageswhile real-time rendering with traditional RCA is still anobstacle due to its huge computation

In recent years numerous techniques have been proposedto accelerate the rendering speed In general there arethree primary aspects including hardware-based parallel

and soware-based acceleration algorithms Liu et al [6]proposed a method combined that Graphics Processing Unit(GPU) and octree encoding and accelerated RCA at a rate of85 times Wei and Feng [7] presented a GPU-based real-timeray castingmethod for algebraic B-spline surfaces via iterativeroot-nding algorithms hang et al [8] accelerated RCA onCompute Unied Device Architecture (CUDA) which canperformmore samplings within a ray segment using cubic B-spline

However both hardware-based and parallel techniquesare inseparable from the development of computer hardwareBy comparison soware-based algorithms can be quicklytransplanted among different machines What is more theycan show exibility of the procedure and reect the thoughtsof researchers Yang et al [9] sampled points based on allintersection points at which the ray transacts with the voxelAll intersections in a voxel depend on four vertexes on oneface However the condition whether two intersection pointswere on adjacent or opposite surface in a voxel was neglectedLing andQian [10] used a bounding volumemethod to avoidcasting the viewing rays that do not intersect with the volumeSince such situation can be judged quickly by comparingthe world coordinates of sampling point with the volumedataset it did not obviously speed up the rendering process


Recently Qian et al [11] replaced the sampling points withintersection points when rays travel through three groupsof parallel planes along three orthometric axes to reducethe rendering time However it cannot guarantee the imagedensity when the distance between adjacent parallel planesfar surpasses the sampling interval

is paper proposes an improved RCA to speed therendering process e main idea is when the ray travelsthrough one group of equidistant parallel planes of thevolume intersection points are obtaineden the propertiesof sampling points between adjacent intersection pointscan be calculated by the formula of denite proportionand separated points By this method a small number ofintersection points are considered meanwhile the methoddoes not sacrice the sampling density

2 Ray Casting Algorithm

21 Ray Casting Algorithm Overview e traditional RCAinvolves two steps (1) assign optical properties such as colorand opacity to all 3D discrete vertexes according to their grayvalue and (2) apply a sampling and composing process Foreach output image pixel in sequence do the following

(i) Cast the ray through the volume from back to front(ii) Sample the color 119888119888119894119894 and opacity 119886119886119894119894 at each regular

sampling point along the ray(iii) Set the color of the current output pixel according to

119888119888out =11989911989911989911989910055761005576119894119894=119894119888119888 (119894119894)

11989411989411989911989910055771005577119895119895=119894

119899 119899 119886119886 1007649100764911989511989510076651007665

= 119888119888119894 + 119888119888119899 10076491007649119899 119899 11988611988611989410076651007665 + 1198881198882 10076491007649119899 119899 11988611988611989910076651007665 10076491007649119899 119899 11988611988611989410076651007665 + ⋯

(1)

e rendering time is mainly comprised of four partsin the above-mentioned rendering process [11] ey areconverting gray value into optical property (about 30)computing position of sampling points (about 3) samplingoptical properties (about 39) and compositing propertiesinto output pixel color (about 6) e time proportion ofsampling is the highest Moreover the time ratio of four partsis not constant e greater the sampling data is the largerthe proportion of sampling time iserefore sampling has adirect impact on speed of RCA

22 Traditional Sampling Method Traditionally the opticalproperty of each sampling point depends on eight vertexesof its voxel by trilinear interpolation [12 13] In detail thereare four steps for the sampling one point First locate itsvoxel and convert the world coordinates of sampling pointinto voxelrsquos local coordinates e following three steps areprocesses of linear interpolations along three different axes inordere interpolation diagram of Ray Casting Algorithm isshown in Figure 1

For example to sample point 119878119878(119878119878119878 119878119878119878 119878119878) in white circle(Figure 1) rst obtain the voxel (119894119894119878 119895119895119878 119894119894) and local coordinates(119878119878119899119899119878 119878119878119899119899119878 119878119878119899119899) of 119878119878 which are expressed in (2) en the opticalproperty of four points (119865119865119899119878 1198651198652119878 1198651198653119878 1198651198654) on the plane through

Image plane

Output pixelVolume dataset

0

F 1 Interpolation for ray casting

119878119878 is deduced according to eight vertexes (119868119868119894 sim 1198681198688) along z-axis e next property of two points (1198651198655119878 1198651198656) forming theline segment through 119878119878 is computed along 119878119878-axis At last 119878119878 isobtained along 119878119878-axis by denite proportional division pointformula

In Figure 1 assume the pixel spacing along 119878119878- 119878119878- 119878119878- axesis Δ119878119878 Δ119878119878 and Δ119878119878 respectively with 119868119868119894(119878119878119894119894119878 119878119878119895119895119878 119878119878119894119894)

119894119894 = 10077161007716119878119878Δ119878119878

10077321007732 119878 119895119895 = 10077171007717119878119878Δ119878119878

10077331007733 119878 119894119894 = 10077161007716119878119878Δ119878119878

10077321007732 119878

119878119878119894119894 = 119894119894 119894 Δ119878119878119878 119878119878119895119895 = 119895119895 119894 Δ119878119878119878 119878119878119894119894 = 119894119894 119894 Δ119878119878119878

119878119878119899119899 =119878119878 119899 119878119878119894119894Δ119878119878

119878 119878119878119899119899 =119878119878 119899 119878119878119895119895Δ119878119878

119878 119878119878119899119899 =119878119878 119899 119878119878119894119894Δ119878119878

119878

(2)

where operator [sdot] represents taking the oor integrale property119865119865 of 119878119878 can be calculated by1198651198655 and1198651198656 which

are obtained by 119865119865119899119878 1198651198652119878 1198651198653 and 1198651198654 e relationship betweenthem is shown in

119865119865119899 = 119868119868119894 + 119878119878119899119899 119894 100764910076491198681198683 119899 11986811986811989410076651007665 119878 1198651198652 = 119868119868119899 + 119878119878119899119899 119894 100764910076491198681198682 119899 11986811986811989910076651007665 119878

1198651198653 = 1198681198685 + 119878119878119899119899 119894 100764910076491198681198686 119899 119868119868510076651007665 119878 1198651198654 = 1198681198684 + 119878119878119899119899 119894 100764910076491198681198687 119899 119868119868410076651007665 119878

1198651198655 = 119865119865119899 + 119878119878119899119899 119894 100764910076491198651198652 119899 11986511986511989910076651007665 119878 1198651198656 = 1198651198654 + 119878119878119899119899 119894 100764910076491198651198653 119899 119865119865410076651007665 119878

119865119865 = 1198651198655 + 119878119878119899119899 119894 100764910076491198651198656 119899 119865119865510076651007665 (3)

According to the above equations 17 additions and 16multiplications are executed for sampling each point such as 119878119878(see Figure 1) including 3 additions and 9 multiplications tolocate the voxel (119894119894119878 119895119895119878 119894119894) and get the local coordinates In Figure1 there are 6 sampling points in two voxels 102 additionsand 96multiplications performed To simplify the calculationof sampling process a new RCA based on plane clusterssampling is proposed

23 Proposed Plan-Based SamplingMethod e basic idea ofthe plan-based sampling method is to acquire all samplingpoints based on intersection points when ray travels througha group of parallel planes in the volume data eld


e sampling process specically consists of three stepsFirst intersections and the corresponding plane are obtainedbased on some necessary initial conditions en the opticalproperty of all the intersection points is obtained by linearinterpolation according to vertexes on plane clusters eoptical property of sampling points between intersectionpoints along the ray is computed by denite proportion andseparated point formula

Assuming that the direction vector of ray is 120577120577 120577 120577120577120577120577120577120577120577 120577120577120577and the extent of gridding volume data is 119864119864119864119864119864119864119864119864119864119864119864119864119864119864 withthe spacing Δ119864119864120577 Δ119864119864120577 Δ119864119864 along 119864119864-120577 119864119864-120577 119864119864- axes respectively thethree plane clusters are as follows

119883119883119894119894 120577 119894119894Δ119864119864 120577119894119894 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 119894120577 120577

119884119884119895119895 120577 119895119895Δ119864119864 10076491007649119895119895 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 11989410076651007665 120577

119885119885119896119896 120577 119896119896Δ119864119864 120577119896119896 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 119894120577

(4)

Parallel plane clusters along 119864119864 axis are selected Let theorigin point of ray be 119874119874120577119864119864119900119900120577 119864119864119900119900120577 119864119864119900119900120577 e ray intersects withplane 119884119884119895119895 at entry point 119864119864120577119864119864119894119894120577 119864119864119895119895120577 119864119864119896119896120577 and 119864119864 belongs to thevoxel 120577119894119894120577 119895119895120577 119896119896120577 e coordinates of 119864119864 and voxel 120577119894119894120577 119895119895120577 119896119896120577 arededuced next e derivation is shown as follows Since

119864119864119895119895 120577 119864119864119900119900 + 120577120577 119864 119898119898119895119895 120577 119895119895Δ119864119864 10076491007649119895119895 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 11989410076651007665 120577 (5)

where 119898119898119895119895 means the distance from119874119874 to 119864119864 along ray the valueof 119895119895 can be obtained from

119895119895 120577 10077171007717119864119864Δ119864119864

10077331007733 (6)

erefore

119898119898119895119895 120577119895119895Δ119864119864 119894 119864119864119900119900

120577120577120577 (7)

and 119864119864119894119894120577 119864119864119896119896 of 119864119864120577119864119864119894119894120577 119864119864119895119895120577 119864119864119896119896120577 can be expressed as follows

119864119864119894119894 120577 119864119864119900119900 + 120577120577 119864 119898119898119895119895 119864119864119896119896 120577 119864119864119900119900 + 120577120577 119864 119898119898119895119895 (8)

Considering that 119864119864 belongs to voxel 120577119894119894120577 119895119895120577 119896119896120577 then 119894119894 and 119896119896 areexpressed as follows

119894119894 120577 10077171007717119864119864119894119894Δ119864119864

10077331007733 120577

119896119896 120577 10077171007717119864119864119896119896Δ119864119864

10077331007733 (9)

erefore when 119895119895is given 119864119864120577119864119864119894119894120577 119864119864119895119895120577 119864119864119896119896120577 119894119894 and 119896119896 can beobtained through the above equations

From the mathematical derivation when original posi-tion direction vector and the extent of volume data are givenall the intersections and associated voxels can be quicklyobtained

In Figure 1 the property 119868119868119864119864 of entry point 119864119864 can becomputed by the property (119868119868119894120577 119868119868119894120577 1198681198683) of three vertexes onvoxel 120577119894119894120577 119895119895120577 119896119896120577 that is

119868119868119864119864 120577 119868119868119894 + 10076491007649119868119868119894 119894 11986811986811989410076651007665 10076651007665119864119864119894119894Δ119864119864

119894 11989411989410076681007668 + 100764910076491198681198683 119894 11986811986811989410076651007665 10076651007665119864119864119896119896Δ119864119864

119894 11989611989610076681007668 (10)

T 1 Comparison of two sampling methods

Objects and sizes Head512 119864 512 119864 295

Heart512 119864 512 119864 41

Spacing(mm 119864mm 119864mm)

0486 119864 0486 1198640700

0318 119864 0318 1198642000

Sampling distance (mm) 03 03Time by the traditional (s) 58274 7192Time by the proposed (s) 17158 2043Acceleration rate 3606 352

In the same way the property 119868119868119876119876 of exit point 119876119876 can beobtained At last the property 119868119868119878119878 is expressed as follows

119868119868119878119878 120577 119868119868119864119864 +119898119898 119894 119898119898119895119895

119898119898119895119895+119894 119894 11989811989811989511989510076501007650119868119868119876119876 119894 11986811986811986411986410076661007666 (11)

In addition when one component of the direction vector120577120577 is zero a plane cluster along another axis can be chosen Iftwo components are zero the plane clusters along the thirdaxis are taken into account

24 Comparison of Two Sampling Methods In the new RCAsampling process only intersection points on a plane clusteralong one axis need to be considered without convertingcoordinates While in the conventional sampling processthe world coordinates of each sampling point are convertedinto voxelrsquos local coordinates and computed by trilinearinterpolation [14 15]

As is shown in Figure 1 there are 6 sampling pointsbetween 119864119864 and 119876119876 15 additions and 19 multiplications areexecuted to sample 119864119864 and 119876119876 and 24 additions and 12multiplications are run to sample six points based on 119864119864and 119876119876 Totally 39 additions and 31 multiplications aretaken compared with 102 additions and 96 multiplicationswith trilinear interpolation Furthermore not all vertexes arereferred because some vertexes (such as 1198681198684120577 1198681198687120577 119868119868119894 in Figure 1)are not used as reference by the newmethodus in theorythe calculation amount is reduced to less than one third onthe whole

3 Experiments and Analysis

31Data Experiments are carried out onheadCT sequencesand heart CT sequences Both sequences are scanned bySiemens spiral CT e detail information is shown in Table1 Taking head for an example the extents are 5119894119894119864511989411989411986411989495and the pixel spacing is 0486mm 0486mm and 0700mmalong119864119864-119864119864- 119864119864- axis respectivelye sampling distance alongray is 03mm

32 Results e reconstructed results of two datasets areshown in Figures 2 and 3 e rendering time of the data isshown in Table 1 For example it takes 17158 seconds torender the head sequences with the new sampling methodwhile 58274 seconds using the traditional method

33 Analysis e new sampling method does not consultall 3D vertexes of the volume data For this reason it is


(a) Traditional method (b) Proposed method

F 2 Head images of ray casting


(c) the details of (a) (d) the details of (b)

F 3 Heart images with ray casting

a question whether the image quality can be guaranteed Itcan be seen in Figures 2 and 3 that images reconstructed byRCA based on plan cluster sampling method are almost thesame as those based on traditional trilinear interpolation inRCA ey can clearly show the details of the boundary andinternal information of the volume with the new samplingmethod erefore the image quality can be well ensured

By comparing the amount of computation (39102-3196) in the two samplingmethods the newmethod can reducethe amount of traditional one to about one third It can beseen that the total rendering time (Table 1) using newmethodis less than one third of that using conventional trilinearinterpolation It indicates that the time saved to inquire theproperty of the vertexes not for reference should not beunderestimated

Moreover it is shown that the acceleration rate of thehead images is higher than that of the heart images emain difference between them is that the spacing of head CTsequences is denser than the heart dataerefore the denserthe data is the more efficient the new method is

4 Conclusion

is paper presented a novel RCA based on a parallelplan cluster sampling method e proposed method can

efficiently speed up the sampling process at more than threetimes and still clearly display the boundary and internalinformation of the volume thus the image quality is wellguaranteed In addition the comparison of acceleration rateindicates that the new method is more effective for datasetwith denser spacinge newmethod can meet the real-timerequirements of interactive rendering

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (61105073 61173096 and 61103140)and the Science and Technology Department of ZhejiangProvince (R1110679 and 2010C33095)

References

[1] C Cattani R Badea S Y Chen and M Crisan ldquoBiomedicalsignal processing and modeling complexity of living systemsrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 298634 2 pages 2012

[2] Y Mishchenko ldquoAutomation of 3D reconstruction of neu-ral tissue from large volume of conventional serial sectiontransmission electron micrographsrdquo Journal of NeuroscienceMethods vol 176 no 2 pp 276ndash289 2009

[3] B Lee J Yun J Seo B Shim Y G Shin and B Kim ldquoFasthigh-quality volume ray casting with virtual samplingsrdquo IEEETransactions on Visualization and Computer Graphics vol 16no 6 pp 1525ndash1532 2010

[4] S Y Chen and X Li ldquoFunctional magnetic resonance imag-ing for imaging neural activity in the human brain theannual progressrdquo Computational and Mathematical Methods inMedicine vol 2012 Article ID 613465 9 pages 2012

[5] N Max ldquoOptical models for direct volume renderingrdquo IEEETransactions on Visualization and Computer Graphics vol 1 no2 pp 99ndash108 1995

[6] B Q Liu G J Clapworthy F Dong and E C Prakash ldquoOctreerasterization accelerating high-quality out-of-coreGPUvolumerenderingrdquo IEEE Transactions on Visualization and ComputerGraphics no 99 pp 1ndash14 2012

[7] F F Wei and J Q Feng ldquoReal-time ray casting of algebraicB-spline surfacesrdquo Computers amp Graphics vol 35 no 4 pp800ndash809 2011

[8] C G Zhang P Xi and C X Zhang ldquoCUDA-based volume ray-casting using cubic B-splinerdquo in Proceedings of the InternationalConference on Virtual Reality and Visualization (ICVRV rsquo11) pp84ndash88 November 2011

[9] A R Yang C X Lin and J Z Luo ldquoA ray-casting approachbased on rapid direct interpolationrdquoControl ampAutomation vol26 no 7 pp 8ndash10 2010

[10] L Tao and Z Y Qian ldquoAn improved fast ray casting volumerendering algorithm of medical imagerdquo in Proceedings of the4th International Conference on Biomedical Engineering andInformatics (BMEI rsquo11) pp 109ndash112 2011

[11] Y Qian X Zhang and J Lai ldquoImproved ray casting algo-rithmrdquo Computer Engineering and Design vol 32 no 11 pp3780ndash3783 2011

[12] J Meyer-Spradow T Ropinski J Mensmann and K HinrichsldquoVoreen a rapid-prototyping environment for ray-casting-based volume visualizationsrdquo IEEE Computer Graphics andApplications vol 29 no 6 pp 6ndash13 2009


[13] H R Ke and R C Chang ldquoRay-cast volume rendering acceler-ated by incremental trilinear interpolation and cell templatesrdquoe Visual Computer vol 11 no 6 pp 297ndash308 1995

[14] B Lee J Yun J Seo B Shim Y G Shin and B Kim ldquoFasthigh-quality volume ray casting with virtualsamplingsrdquo IEEETransactions on Visualization and Computer Graphics vol 16no 6 pp 1525ndash1532 2010

[15] A Knoll Y Hijazi R Westerteiger M Schott C Hansenand H Hagen ldquoolume ray casting with pea nding anddifferential samplingrdquo IEEE Transactions on Visualization andComputer Graphics vol 15 no 6 pp 1571ndash1578 2009

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2012 Article ID 125321 7 pagesdoi1011552012125321

Research Article

Self-Adaptive Image Reconstruction Inspired byInsect Compound Eye Mechanism

Jiahua Zhang1 Aiye Shi1 Xin Wang1 Linjie Bian2 Fengchen Huang1 and Lizhong Xu1

1 College of Computer and Information Engineering Hohai University Nanjing Jiangsu 211100 China2 College of Computer Science and Technology Zhejiang University of Technology Hangzhou Zhejiang 310023 China

Correspondence should be addressed to Lizhong Xu lzhxuhhueducn

Received 23 November 2012 Accepted 17 December 2012

Academic Editor Sheng-yong Chen

Copyright copy 2012 Jiahua Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Inspired by the mechanism of imaging and adaptation to luminosity in insect compound eyes (ICE) we propose an ICE-basedadaptive reconstruction method (ARM-ICE) which can adjust the sampling vision field of image according to the environmentlight intensity The target scene can be compressive sampled independently with multichannel through ARM-ICE MeanwhileARM-ICE can regulate the visual field of sampling to control imaging according to the environment light intensity Based on thecompressed sensing joint sparse model (JSM-1) we establish an information processing system of ARM-ICE The simulation of afour-channel ARM-ICE system shows that the new method improves the peak signal-to-noise ratio (PSNR) and resolution of thereconstructed target scene under two different cases of light intensity Furthermore there is no distinct block effect in the resultand the edge of the reconstructed image is smoother than that obtained by the other two reconstruction methods in this work

1 Introduction

The classical reconstruction methods include the near-est neighbor algorithm bilinear interpolation and bicu-bic interpolation algorithm [1 2] According to existingresearch the reconstruction accuracy of bilinear interpola-tion is higher than that of the nearest neighbor algorithmand the former can get better image reconstruction resultsHowever the reconstructed image by bilinear interpolationappears saw-tooth and blurring sometimes [3] Althoughthe reconstruction results of bicubic interpolation are betterthan the others they always lose efficiency and take muchmore time As a compromise bilinear interpolation isoften used for research These algorithms can improve thereconstruction quality of the original image to some extentHowever only the correlation between the local and globalpixels is considered in these algorithms Interpolation-basedreconstruction methods do improve the effect of imagereconstruction but they destroy the high-frequency detailedinformation of the original image [4 5]

Some studies have found that insects have a relativelybroad living environment for instance the mantis shrimp

can live between 50 m and 100 m depth underwater Insuch living environment the light condition changes dra-matically due to the combined effect of sunlight and watermedia To adapt to the changing environment this specieswhose ommatidia structure is fixed must regulate the lightacceptance angle adaptively [6 7] Through the joint actionof the lens and the rhabdome the mantis shrimp hasdifferent degrees of overlapping images in the whole regionof the ommatidia The ommatidia get the different opticalinformation depending on the different lighting conditionsUnder the light and the dim environment conditions themantis shrimp can regulate the length of rhabdome andlens through relaxing or contracting the myofilament Basedon the biological mechanism above the ommatidia visualfield can be narrowed or expanded to get a relatively stablenumber of incoming photons and a better spatial resolutionUltimately the imaging system can reach balance betweenthe visual field and the resolution [8] as shown in Figure 1According to Schiff rsquos [9] research the imaging angle andvisual field of the mantis shrimp ommatidia both changewhile the light intensity condition changes For instance theommatidia visual field is 5 under dim-adapted pattern but


Dim Light

(a)

(b)

Low sensitivityHigh spatial resolution

High sensitivityLow spatial resolution

Figure 1 Light-dim adaptive regulatory mechanism of ommatidia(a) Structure adaptation in ommatidia visual system (b) Adapta-tion in the view-field of ommatidia and compound eyes

the corresponding visual field will be only 2 under bright-adapted pattern and some other species also have similarcharacteristics [10ndash14]

Recently the compressed sensing theory provides a newapproach for computer vision [15ndash17] image acquisition[18 19] and reconstruction [20ndash22] This method can getthe reconstruction results as effectively as the traditionalimaging systems do or even higher quality (in resolutionSNR etc) with fewer sensors lower sampling rate less datavolume and lower power consumption [23ndash27] Accordingto the compressed sensing theory the compressive samplingcan be executed effectively if there is a corresponding sparserepresentation space Currently the compressed sensingtheory and application of the independent-channel signalhave been developed in-depth such as single-pixel cameraimaging [28]

By the combined insect compound eye imaging mecha-nism with compressed sensing joint sparse model (JSM-1)model [29ndash32] we use the spatial correlation of multiplesampled signals to get the compressive sampling and recon-struction Inspired by the light-dim self-adaptive regulatorymechanism of insect compound eyes (ICE) this paper pro-poses an ICE-based adaptive reconstruction method (ARM-ICE) The new method can execute multiple compressivesampling on the target scene According to the environmentlight intensity it can regulate the sampling visual fieldto control imaging The simulation results show that incontrast to the image-by-image reconstruction and bilinearinterpolation algorithm the new method can reconstructthe target scene image under two kinds of light intensityconditions with higher-peak signal-to-noise ratio (PSNR)The new method also improves the resolution and detailedinformation of reconstruction

In the first section we describe the imaging controlmechanism of insect compound eyes compressed sensingtheory and current research of bionic compound eyesimaging system Section 2 demonstrates the ARM-ICE imag-ing system pattern from three aspects visual field self-adaptive adjusting sampling and reconstruction Section 3completes the ARM-ICE system simulation under the dimand light conditions and then analyzes the imaging resultsand the comparison of relevant parameters In Section 4 weconclude with possible topics for future work

2 Compressed Sensing-Based Arm-IceImaging System Pattern

Figure 2 shows an ARM-ICE imaging system pattern Thepurple lines represent the light environment visual fieldwhile the blue lines represent the dim environment visualfield The target scene is imaged respectively by thecompound eye lens array The isolation layer is composedby multichannel opening shade blocks which can be con-trolled And each port of shade blocks is connected toa corresponding little lens of compound eye lenses Thisstructure sets a number of independent controllable light-sensitive cells Each port of isolation layer opens at differenttime The feedback signal controls them to regulate therelative position to make the light from target scene to then light-sensitive cells The corresponding area is sparselysampled in the digital micromirror device Measurementdata can be obtained in the imaging plane Ultimately theprocessor reconstructs the target scene according to the k-sparse property of data sensed on the wavelet basis Ψ and theuncorrelated measurement matrix Φ

21 Arm-ICE Visual Field Self-Adaptive Regulation Accord-ing to the biological research in the insect compound eyessystem under different light intensities the angle of imagingand the visual field change accordingly [33ndash37] Inspiredby this self-adaptive ability this paper mimics the insectcompound eye system on its imaging control mechanismbased on light intensity sensitivity to expand or narrow thescope of visual field and overlapping field by regulating theposition of the lenses

According to the results of biological research therelationship between light intensity imaging pore size andother factors can be described as (1) hereby to regulate thelenses position to achieve the overlap visual field [12]

ΔρT = 0530υmax

radicln cNp minus 1

2ln[Np + σ2

D

] (1)

where ΔρT indicates the visual field range υmax indicatesthe maximum detectable spatial frequency which can beregarded as a constant c is the mean contrast of the sceneNp indicates the number of the photons captured by an inputport and σ2

D shows the total variance for environmental lightintensity

From (1) the visual field can be calculated accordingto the υmax set while the light intensity changes Based on


light intensity

Self-adaptivelyregulate

visual fielddue to the

Lens 2

Lens 1

Target scene

DMDgenerates

themeasurement

matrix Φdynamically

min∥θ∥1

subject to

^λJ

^λJ asymp λJ

λJ = XN

^XN =

ARM-ICE sampling ARM-ICE reconstruction

Visual field in light environment

Visual field in dim environment

Lens N

XN

XN

ΦXN

YM =YM =ΦΨθ

=Ψθ

=Ψθlowast

Ψθlowast

Figure 2 ARM-ICE imaging system pattern

the biological principle above the visual field range can beregulated according to the environment light intensity

22 Compressive Sampling The digital micromirror device(DMD) senses the optical information from the lenses arrayand then makes sparse sampling The principle is innerproduct the optical signal from the lenses array perceptionX(m) and DMD measurement basis vector ϕ(m) and makethe result as the output voltage (v)m of the DMD device atthe moment m The output voltage v(m) of the photodiodecan be expressed as the inner product of the desired image xwith a measurement basis vector [26 28 29]

v(m) prop langX(m)ϕ(m)

rang+ ODC (2)

where the value of ϕ(m) is related to the position of DMDmicro-mirror when the micromirror turns +10 φi(m) = 1when the micromirror turns minus10 φi(m) = 0 ODC is thedirect current offset which can be measured by setting allmirrors to minus10

Based on the principle of measurement matrix of a singleDMD device we can use the DMD device array to get sparsesignals of image system The compound eye lenses and theisolation layer constitute n light-sensitive independent cellseach of which is controlled by the isolation layer to open atdifferent time The array jointly senses the target scene dataXi

Xi = XiC + XiS (3)

where XiC expresses the common information of the percep-tion data and XiS expresses the specific information of eachlens Vector XN = (X1X2 XN )T indicates the perceptiondata from n light-sensitive units The perception data can be

regarded as k-sparse on wavelets basis Ψ due to the spatialcorrelation

XN = Ψθ (4)

where θ = (λ0 γ0 γ1 γJminus1)T is the sparse vector coeffi-cient consisting of the high-frequency subset γ0 γ1 γJminus1

(γk is subset at scale J minus k) and the low-frequency subset λ0

of wavelet transform After light-sensitive lenses obtain XN k-sparse signal XN is used to generate M measurement dataof the image plane from the M times N measurement matrix Φon the DMD device

YM = (Y1Y2 YM)T = ΦXN (5)

where matrix Φ is a 0-1 matrix which consists of the outputvoltage v(m) of the DMD device in (2) at the moment mEquation (5) can also be described as follows

⎡⎢⎢⎢⎢⎣Y1

Y2

YM

⎤⎥⎥⎥⎥⎦ =

⎡⎢⎢⎢⎢⎣Φ1 0

Φ2

0 ΦM

⎤⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎣X1

X2

XN

⎤⎥⎥⎥⎥⎦ (6)

23 Joint Reconstrucion According to the multichannelcaptured data which are k-sparse on wavelet basis andthe inconsistency of the measurement matrix Φ with thewavelet basis Ψ the processor runs the decoding algorithmto reconstruct the target scene

minθ0 subject to YM = ΦΨθ (7)

The optimized sparse solution θlowast can be gotten bysolving the issue of optimizing l0 norm The reconstructionof captured data from each lens can be indicated as follows


(a) (b)

(c) (d)

Figure 3 ARM-ICE imaging results and comparison under strong light (a) target scene whose brightness value is 1448527 Nits (b) ARM-ICE reconstructed image whose PSNR is 419113 dB (c) result of bilinear interpolation reconstruction whose PSNR is 349112 dB (d)result of image-by-image reconstruction whose PSNR is 278246 dB

XN = (X1 X2 XN )T = Ψθlowast An important issue during

the reconstruction process is how to calculate the waveletbasis Ψ Assume the set of captured data XN is alreadyknown and λJ = XN Each light-sensitive sensor capturesthe target scene from different views so its obtained datacan be divided into two parts the common part λJ P and theparticular part λJ D T indicates the lifting wavelet transformafter J timesrsquo recursion

for k = J to 1

⎧⎪⎪⎨⎪⎪⎩λkminus1 = λkP + U

(γkminus1

)

γkminus1 = λkD minus P(λkP

)

T(λk) = (λkminus1 γkminus1)

(8)

where λkminus1 is the low-frequency coefficient set γkminus1 is thehigh-frequency coefficient set P is the linear predictionoperator and U is the linear update operator Using thespatial correlation of captured data λk D can be calculatedby λkP γkminus1 contains fewer information relatively

For λk after k timesrsquo recursive lifting wavelet transform

Tk(λk) = λ0 γ0 γ1 γkminus1 (9)

After resetting the wavelet coefficients which are underthreshold value in γi the sparsely structured γi can be usedto reconstruct the original signal λk exactly Assuming thatTminusk(bull) is a lifting wavelet inverse transform as the linearprediction operator and the linear update operator are bothlinear operations thereforeTk(bull) and Tminusk(bull) are both lineartransforms Tminusk(bull) can be expressed as follows

TminusK(λ0 γ0 γ1 γkminus1

) = λk

λK = Ψθlowast asymp λk(10)

where θlowast = (λ0 γ0 γ1 γkminus1)T Since λJ = XN the initialdata XN = Ψθlowast can be reconstructed exactly


(a) (b)

(c) (d)

Figure 4 ARM-ICE imaging results and comparison under low light (a) target scene whose brightness value is 1033661 Nits (b) ARM-ICEreconstructed image whose PSNR is 444705 dB (c) result of bilinear interpolation reconstruction whose PSNR is 365021 dB (d) result ofimage-by-image reconstruction whose PSNR is 295852 dB

3 Four-Channel Arm-ICE ImagingSystem Pattern Simulation

According to the ARM-ICE visual field self-adaptive adjust-ment mechanism under different surrounding light inten-sities described in Section 21 in this section we simulatea four-channel ARM-ICE imaging system When the sur-rounding light intensity turns strong the lenses array regu-lates their relative positions according to (1) automaticallyThe simulation results are shown in Figure 3 Figure 3(a)is the target scene under strong illumination environmentwhose brightness value is 1448527 Nits Figure 3(b) is thejoint reconstruction image from photoelectric coupler arrayand its reconstructed PSNR is 419113 dB Figure 3(c) is areconstructed image by linear interpolation method and itsPSNR is 278246 dB under the same sampling rate as ARM-ICE Figure 3(d) is an image-by-image reconstruction andits PSNR is 278246 dB under the same sampling rate asARM-ICE

When the surroundings are dim the compound eyelenses array contracts to the central area sacrificing the visualfield to improve the reconstruction resolution of target sceneThe simulation results are shown in Figure 4 Figure 4(a) isthe target scene under the dim conditions whose brightnessvalue is 1033661 Nits Put the brightness values into (1) andcalculate the lensesrsquo positions at the moment Figure 4(b) isthe joint reconstruction image from photoelectric couplerarray and its reconstructed PSNR is 444705 dB Figure 4(c)is the reconstructed image by linear interpolation methodPSNR is 365021 dB at the same sampling rate Figure 4(d) isthe reconstruction result of image-by-image whose PSNR is295852 dB

From the reconstruction effect the result of linearinterpolation method is superior to the result reconstructedby image-by-image However there is still obvious blockeffect and lack of smoothness at the edge direction Cor-respondingly the image reconstructed by ARM-ICE has asignificant improvement in resolution From Figures 3 and 4


02 03 04 05 06 07 0820

25

30

35

40

45

50

55

60

Sampling rate

PSN

R

ARM-ICE reconstruction under low lightARM-ICE reconstruction under strong lightBI reconstruction under low light condition

Image-by-image reconstruction under strong lightImage-by-image reconstruction under low lightBI reconstruction under strong light condition

Figure 5 The comparison of PSNR-Sampling rates under low lightand strong light conditions

we can see that there is no distinct block effect in the resultand the edges of the reconstructed image are smoothercompared to the results of the other two reconstructionmethods studied in this work

Figure 5 is the comparison of PSNR-Sampling ratesunder low light and strong light conditions (1448527 Nits)The three black lines in the figure show the comparisonresults under the strong light condition in which the blackdotted line shows the result of ARM-ICE the black diamondline shows the result of bilinear interpolation and the blackfive-pointed star-shaped line shows the result of image-by-image reconstruction It can be concluded from the figurethat the PSNR of ARM-ICE is higher than bilinear inter-polation and image-by-image reconstruction under differentsampling rates under the strong light condition

The three red lines in the figure show the comparisonobtained under the low light condition (1033661 Nits) inwhich the red dotted line shows the result of ARM-ICEreconstruction the red diamond line shows the result ofbilinear interpolation and the red five-pointed star-shapedline shows the result of image-by-image reconstruction Itcan be seen from the figure that when the target sceneis under low light condition the PSNR of ARM-ICE atdifferent sampling rates is higher than bilinear interpolationand image-by-image reconstruction

4 Conclusion

Inspired by the imaging mechanism and the adaptive regula-tory regulation mechanism of the insect compound eyes thispaper proposes a reconstruction method which regulatesthe scale of the sampling area adaptively according to thesurrounding light intensity condition The imaging system

pattern of the new method can complete the multichannelindependent sampling in the target scene almost at the sametime Meanwhile the scale of the sampling area and theoptical signal redundancy can be regulated adaptively toachieve the imaging control Compared with the traditionalmethods the resolution of the reconstructed image byARM-ICE method has been significantly improved Thereconstructed image with the proposed method has threefeatures higher resolution no distinct block effect andsmooth edge

Simulation results indicate that the new method makesthe PSNR of the reconstructed image higher under two kindsof light conditions However the reconstruction qualityunder low light conditions is improved by the proposedalgorithm at the cost of the scale of the visual field Thereforethe key issue in the future work would be how to reconstructhigh-resolution large scenes in low light conditions

Acknowledgments

This paper was supported by the National Natural ScienceFoundation of China (No 61263029 and No 61271386)The authors thank Wang Hui a graduate student of HohaiUniversity for helping in research work

References

[1] R C Kenneth and R E Woods Digital Image ProcessingPublishing House of Electronics Industry Beijing China2002

[2] F G B D Natale G S Desoli and D D Giusto ldquoAdaptiveleast-squares bilinear interpolation (ALSBI) a new approachto image-data compressionrdquo Electronics Letters vol 29 no 18pp 1638ndash1640 1993

[3] L Chen and C M Gao ldquoFast discrete bilinear interpolationalgorithmrdquo Computer Engineering and Design vol 28 p 152007

[4] S Y Chen and Z J Wang ldquoAcceleration strategies in gen-eralized belief propagationrdquo IEEE Transactions on IndustrialInformatics vol 8 p 1 2012

[5] N M Kwok X P Jia D Wang et al ldquoVisual impactenhancement via image histogram smoothing and continuousintensity relocationrdquo Computers amp Electrical Engineering vol37 p 5 2011

[6] L Z Xu M Li A Y Shi et al ldquoFeature detector model formulti-spectral remote sensing image inspired by insect visualsystemrdquo Acta Electronica Sinica vol 39 p 11 2011

[7] F C Huang M Li A Y Shi et al ldquoInsect visual systeminspired small target detection for multi-spectral remotelysensed imagesrdquo Journal on Communications vol 32 p 9 2011

[8] H Schiff ldquoA discussion of light scattering in the Squillarhabdomrdquo Kybernetik vol 14 no 3 pp 127ndash134 1974

[9] B Dore H Schiff and M Boido ldquoPhotomechanical adapta-tion in the eyes of Squilla mantis (Crustacea Stomatopoda)rdquoItalian Journal of Zoology vol 72 no 3 pp 189ndash199 2005

[10] B Greiner ldquoAdaptations for nocturnal vision in insect apposi-tion eyesrdquo International Review of Cytology vol 250 pp 1ndash462006

[11] A Horridge ldquoThe spatial resolutions of the appositioncompound eye and its neuro-sensory feature detectors obser-vation versus theoryrdquo Journal of Insect Physiology vol 51 no3 pp 243ndash266 2005


[12] H Ikeno ldquoA reconstruction method of projection image onworker honeybeesrsquo compound eyerdquo Neurocomputing vol 52ndash54 pp 561ndash566 2003

[13] J Gal T Miyazaki and V B Meyer-Rochow ldquoComputa-tional determination of refractive index distribution in thecrystalline cones of the compound eye of Antarctic krill(Euphausia superba)rdquo Journal of Theoretical Biology vol 244no 2 pp 318ndash325 2007

[14] S Y Chen H Tong Z Wang S Liu M Li and BZhang ldquoImproved generalized belief propagation for visionprocessingrdquo Mathematical Problems in Engineering vol 2011Article ID 416963 12 pages 2011

[15] V Cevher P Indyk L Carin and R Baraniuk ldquoSparse signalrecovery and acquisition with graphical modelsrdquo IEEE SignalProcessing Magazine vol 27 no 6 pp 92ndash103 2010

[16] M F Duarte and R G Baraniuk ldquoSpectral compressivesensingrdquo IEEE Transactions on Signal Processing vol 6 2011

[17] L Z Xu X F Ding X Wang G F Lv and F C HuangldquoTrust region based sequential quasi-Monte Carlo filterrdquo ActaElectronica Sinica vol 39 no 3 pp 24ndash30 2011

[18] J Treichler and M A Davenport ldquoDynamic range andcompressive sensing acquisition receiversrdquo in Proceedings ofthe Defense Applications of Signal Processing (DASP rsquo11) 2011

[19] S Y Chen and Y F Li ldquoDetermination of stripe edge blurringfor depth sensingrdquo IEEE Sensors Journal vol 11 no 2 pp389ndash390 2011

[20] S Y Chen Y F Li and J Zhang ldquoVision processing forrealtime 3-D data acquisition based on coded structuredlightrdquo IEEE Transactions on Image Processing vol 17 no 2pp 167ndash176 2008

[21] C Hegde and R G Baraniuk ldquoSampling and recovery of pulsestreamsrdquo IEEE Transactions on Signal Processing vol 59 no 4pp 1505ndash1517 2011

[22] A Y Shi L Z Xu and F Xu ldquoMultispectral and panchromaticimage fusion based on improved bilateral filterrdquo Journal ofApplied Remote Sensing vol 5 Article ID 053542 2011

[23] E J Candes J Romberg and T Tao ldquoRobust uncertaintyprinciples exact signal reconstruction from highly incompletefrequency informationrdquo IEEE Transactions on InformationTheory vol 52 no 2 pp 489ndash509 2006

[24] E J Candes J K Romberg and T Tao ldquoStable signalrecovery from incomplete and inaccurate measurementsrdquoCommunications on Pure and Applied Mathematics vol 59 no8 pp 1207ndash1223 2006

[25] E J Candes and T Tao ldquoNear-optimal signal recovery fromrandom projections universal encoding strategiesrdquo IEEETransactions on Information Theory vol 52 no 12 pp 5406ndash5425 2006

[26] D L Donoho ldquoCompressed sensingrdquo IEEE Transactions onInformation Theory vol 52 no 4 pp 1289ndash1306 2006

[27] L Z Xu X F Li and S X Yang ldquoWireless network andcommunication signal processingrdquo Intelligent Automation ampSoft Computing vol 17 pp 1019ndash1021 2011

[28] D Takhar J N Laska M B Wakin et al ldquoA new compressiveimaging camera architecture using optical-domain compres-sionrdquo in Computational Imaging IV vol 6065 of Proceedings ofSPIE January 2006

[29] D Baron B Wakin and S Sarvotham ldquoDistributed Com-pressed Sensingrdquo Rice University 2006

[30] D Baron and M F Duarte ldquoAn information-theoreticapproach to distributed compressed sensingrdquo in Proceedingsof the Allerton Conference on Communication Control andComputing vol 43 Allerton Ill USA 2005

[31] D Baron M F Duarte S Sarvotham M B Wakin andR G Baraniuk ldquoDistributed compressed sensing of jointlysparse signalsrdquo in Proceedings of the 39th Asilomar Conferenceon Signals Systems and Computers pp 1537ndash1541 November2005

[32] M B Wakin S Sarvotham and M F Duarte ldquoRecoveryof jointly sparse signals from few random projectionsrdquo inProceedings of the Workshop on Neural Information ProccessingSystems 2005

[33] S Chen Y Zheng C Cattani and W Wang ldquoModelingof biological intelligence for SCM system optimizationrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 769702 10 pages 2012

[34] C Cattani S Y Chen and G Aldashev ldquoInformation andmodeling in complexityrdquo Mathematical Problems in Engineer-ing vol 2012 Article ID 868413 3 pages 2012

[35] S Y Chen and X L Li ldquoFunctional magnetic resonanceimaging for imaging neural activity in the human brain theannual progressrdquo Computational and Mathematical Methodsin Medicine vol 2012 Article ID 613465 9 pages 2012

[36] C Cattani ldquoOn the existence of wavelet symmetries inArchaea DNArdquo Computational and Mathematical Methods inMedicine vol 2012 Article ID 673934 21 pages 2012

[37] X H Wang M Li and S Chen ldquoLong memory from Sauer-brey equation a case in coated quartz crystal microbalancein terms of ammoniardquo Mathematical Problems in Engineeringvol 2011 Article ID 758245 9 pages 2011


Research Article

Bayes Clustering and Structural Support Vector Machines forSegmentation of Carotid Artery Plaques in Multicontrast MRI

Qiu Guan1 Bin Du1 Zhongzhao Teng2 Jonathan Gillard2 and Shengyong Chen1

1 College of Computer Science Zhejiang University of Technology Hangzhou 310023 China2 Department of Radiology University of Cambridge Hills Road Cambridge CB2 0SP UK


Received 6 October 2012 Accepted 19 November 2012


Copyright copy 2012 Qiu Guan et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Accurate segmentation of carotid artery plaque in MR images is not only a key part but also an essential step for in vivo plaqueanalysis Due to the indistinct MR images it is very difficult to implement the automatic segmentation Two kinds of classificationmodels that is Bayes clustering and SSVM are introduced in this paper to segment the internal lumen wall of carotid artery Thecomparative experimental results show the segmentation performance of SSVM is better than Bayes

1 Introduction

Cardiovascular diseases (CVDs) are the leading cause ofdeath globally according to the recent statistics of the WorldHealth Organization Atherosclerosis a kind of systematicinflammatory disease is estimated to be responsible forCVDs to a great extent Therefore there are considerableinterests in characterizing atherosclerotic plaques for propertreatment planning Research in the past 20 years indicatesthat plaque vulnerability is very relative to its structure suchas the lumen condition atherosclerotic components withinthe plaque [1ndash5]

As the fundamental step artery wall should be segmentedaccurately Meanwhile explicit detection of wall is very im-portant to locate each component inside the plaque correctlywhich is also very significant for the subsequent proceduressuch as component analysis

Automated analysis of plaque composition in the carotidarteries has been presented by many researchers Differentimaging techniques always bring out distinct characteristicof image which will restrict different applicable approach toapproach of segmentation Among current standard imagingtechniques in clinical in vivo multicontrast MRI techniquehas been generally validated to be used to quantify the com-position of plaque effectively [6] Most segmentation meth-ods based on this kind of imaging technique are generally

based on manual extraction of numerous contours Auto-matic segmentation not only makes the combination ofdifferent multicontrast-weighted MR Image possible butalso can further make full use of the advantages of differentimage to improve the accurate rate of classification of com-ponent within lumen Other impressive experiments are alsocarried out by taking use of model-based clustering and fuzzyclustering [7] maximum-likelihood classifier and nearest-mean classifier [8] morphology-enhanced probability maps[9] and k-means clustering [10] Most of these methodsare based on voxel-wise statistical classification and themanual analysis cannot be completely replaced by themAn automatic method which was used to segment thecarotid artery plaques in CT angiography (CTA) [11] haspotential to replace the manual analysis Firstly the vessellumen was segmented Subsequently classifier was trainedto classify each pixel However this algorithm is needed tobe improved to deal with the multicontrast-weighted MRImage Furthermore in order to provide a more accurateand objective ground truth a simultaneous segmentationand registration model [12] is necessary in registration Thismethod is an active contour model based on simultaneoussegmentation and registration which is belong to mutual-information-based registration [13] Therefore researchesconcerning segmentation of plaques are essential


Image registration

Image acquisition

Components extraction

Preprocessing

Figure 1 Flow of operations

The paper is organized as follows Significance of study-ing carotid artery plaque and current research contributionsare briefly presented in Section 1 Section 2 is mainly focuson describing major and special preprocessing such as ill-illumination uniforming and image registration Two kindsof model used to segment the wall boundary are descried indetailed in Section 3 Section 4 focuses on two algorithms tosegment the lumen and a conclusion and further work arepresented in Section 5

2 Testing Image Set

The complete process of plaque analysis system is organizedas below which is composed of four modules Firstlycarotid artery region should be separated from the originalMRI image and then move on to the preprocessing partsincluding noise removal and illumination uniform Afterthat the lumen and the outer wall in the images are obtainedin turn The latter operations are related with extractingand modeling essential plaque components and mechanicalanalysis based on FSI (fluid-structure interaction) theory willbe also introduced to estimate the risk extent of a plaque Thesteps in Figure 1 will be discussed in detail in this paper

21 Acquisition of Testing Image Set Images used in ourresearch are acquired by a MRI scanner named GE SIGNATaking Figure 2(a) for instance it can be found that carotidarteries marked by two rectangles are closely surroundedby other tissues as muscles fat bones and other vesselsin the 512 mm times 512 mm MRI image In order to handlecarotid artery alone as shown in Figure 2(b) small ROI ofeach artery region should be firstly segmented from theoriginal scanning image by picking out the artery centroidwhich size is 81 mm times 81 mm The reduction of interestedregion effectively avoids disturbing from other tissues andalso improves the computing speed

The detail of MRI acquisition has already been publishedin [14] Briefly speaking patients undergo high resolutionMRI of their carotid arteries in a 15 Tesla MRI system(named as Signa HDx GE Healthcare Waukesha WI USA)with a 4-channel phased-array neck coil (named as PACCMachnet BV Elde The Netherlands) Artifact resulted frommovement is minimized by using a dedicated vacuum-based head restraint system (VAC-LOK Cushion OncologySystems Limited UK) It is used to fix the head and neckof patient in a comfortable position to avoid occurrence ofartefact After an initial coronal localizer sequence is sampledand tested 2-dimensional (2D) axial time-of-fight (TOF)MR angiography is performed to identify the location ofthe carotid bifurcation and the region of maximum stenosis

Axial images are acquired through the common carotidartery 12 mm (4 slices) below the carotid bifurcation to apoint 12 mm (4 slices) distal to the extent of the stenosisidentified on the TOF sequence This kind of method ensuresthat the whole region of carotid plaque is completely imaged

To describe the characteristic of different MRI sequencethe following parameters are used T1 weighted (repetitiontimeecho time 1 times RR78 ms) with fat saturation T2weighted (repetition timeecho time 2 times RR100 ms) withfat saturation proton density weighted (repetition timeechotime 2 times RR78 ms) with fat saturation and short-timeinversion recovery (repetition timeecho timeinversiontime 2 times RR46150 ms) The window of view of each MRimage is 10 cm times 10 cm and size of data matrix is 512 times 512The spatial resolution achieved of each pixel is 039 mm times039 mm

In Figure 2(a) two small ROIs marked by red rectanglesare carotid arteries each size of RIO is 81 mm times 81 mmFigure 2(b) is the amplified images of these two areas

22 Preprocessing Due to the inhomogeneity of coil theintensity of each image should be adjusted to be relativeuniform to obtain relative consistent gray scale for the sub-sequent segmentation based on clustering The region(14 mm times 14 mm) which lies in the center of the vessel isselected as the interesting region The contrast of the image isincreased by a linear transformation

u1 = u0 minusm

M minusmtimes 255 (1)

where u0 is the initial intensity u1 is adjusted intensityand M and m are the maximum intensity and minimumintensity of the original image The adjusted results ofintensity uniform are shown in Figure 3

23 Image Registration According to the characteristics ofMR image the contour of lumen is clearly presented inthe sequence of T1 which is blood suppressed for short InFigure 4 mark two feature points in images (a) and (b) asred points Normally the luminal bifurcation and narrowestlocation are selected as marking points for registration

Generally speaking the image is indistinct as shown inFigure 4 Therefore it is very difficult to mark feature pointsin some images In order to deal with this problem theregistration method proposed in this paper is based on prior-constrained segmentation of carotid artery under DOG scalespace As seen from the name the segmentation algorithmimplies two parts First inspired by SIFT algorithm theadvantage of difference of Gaussian (DOG) scale space isintroduced to catch the edges that seem ambiguous in theoriginal image scale which is the scale derivative of Gaussianscale space along the scale coordinate Second given a simpleprior knowledge that the artery wall is near round a giventhickness of carotid artery wall is set to restrict the searchingarea Prior shape is critical information for external wallsegmentation The steps to get the wall boundary are shownin Figure 5

Then through minimizing the energy function usinga gradient flow we can achieve the goal of simultaneous


(a) (b)

Figure 2 ROI extraction (a) original MRI image (b) extracted images

(a) (b)

Figure 3 Preprocessing of selected slices of MR images (a) a set of original images (b) resultant images after contrast normalization

segmentation and registration [12] On the one hard thisnew method can reduce the influence of noise on the originalimages and lead to improved registration on the other handit also can improve the precision segmentation especially forsegmentation the blurred images

Given two images I1 and I2 C1 is the object contour of I1and C2 is the object contour of I2 Establish mapping C2 =g(C1) The steps of simultaneous segmentation and registra-tion method are listed as follows

Step 1 Initialize C1 g and C2

Step 2 Optimize the registration parameters to obtain theoptimal mapping function g

Step 3 Evolute C1 to obtain the optimum partition line ofthe current image I1 and obtain the optimal split line of thecurrent image I by C2 = g(C1)

Step 4 Reach the maximum number of iterative steps orbefore and after the two results of the iteration are lessthan the threshold value then the algorithm stops endedotherwise turn to Step 2

3 Modelling

To compare the results of different algorithm of modelingtwo kinds of model which are based on Bayes classification

algorithm and SSVM (structural support vector machines)are carried out in this paper

31 Building of Training Set From MRI slices with matchinghistological slices slices 12 and 25 are selected to generatethe training set for segmentation Images of those two slicesare manually segmented based on registered histologicalresults and relative intensity A total of 549 pixels (eachpixel contains 4 densities representation with total 4 differentcontrast weight) are selected randomly in the investigationFrom these segmentation results each pixel is determined tobelong to one of the 4 issue types including lipid (denotedas Z1) normal issue (denoted as Z2) calcification (denotedas Z3) and others (including lumen or outer issue denotedas Z4) The training set is used to generate the probabilityfunction which is used to determine the probability of tissuetype of each pixel in the model based on Bayes classification

32 Model Based on Bayes Classification The most impor-tant part of the segmentation algorithms is to determine theprobabilities of each pixel These probabilities represent thelikelihood that the tissue of the pixel at the current locationis lipid calcification normal issue or others

Maximum classifier is used to determine which issue typethe pixel belongs to Figure 6 gives the flow-chart of our max-

imum decision probability functional classifier Where I isone pixel of multicontrast weighted MR images transformed


(a) (b) (c)

Figure 4 Handle marking points for registration (a) MR images (b) manual outline (c) result of registration

Give multiscale

images

Select the level with

the clearest boundary

Adapt active contour tosegment the lumen

Calculate the centroidand radius of lumen

Search the corresponding DOGimages for edges within the range

Optimize theregistration parameters

Get lumen boundary

Construct a

ring-like shape

Figure 5 Flowchart of multiscale PCA

g1(rarrI )

g2(rarrI )

g3(rarrI )

g4(rarrI )

rarrI

Maximumvalue Classification

label

Figure 6 Flowchart of maximum decision probability functionalclassifier

by preprocessing gi(I) is the decision function and P(Zi | I)is class-conditional probability density function (pdf) By

comparing values of four functions if gi(I) is the maximum

probability value of one pixel then pixel I belongs to Zi andis labeled i

33 Model Based on SSVM Recently structured predictionhas already attracted much attention and many approacheshave also been developed based on it Structured learning isone of the main approaches of structured prediction whichnot only studies the problems with well-structured inputs

Image featureSSVMtraining

Trainingmodel

Testing set

Training set

Results

Intensity value

Figure 7 Flowchart of SSVM to obtain gray information

Initializeweight

constraint

condition

Y

N

Solve the most violated

Increase constraints

Satisfaction

Solve for QP (quadraticprogramming) obtain newweight

Obtain model

Figure 8 Flowchart of the iterative training of SSVM

and outputs but also reveals strong internal correlations It isformulated as the learning of complex functional dependen-cies between multivariate input and output representationsStructured learning has significant impact in addressingimportant computer vision tasks Figure 7 gives the flowchartof SSVM to obtain gray information The flowchart of theiterative training of SSVM is given in Figure 8


20

40

60

80

100

20 40 60 80 100 120S28

20

40

60

80

20 40 60 80S34

(a)

20

40

60

80

100

20

40

60

80

20 40 60 80

20 40 60 80 100 120

(b)

20

40

60

80

100

20 40 60 80 100 120

20

40

60

80

20 40 60 80

(c)

Figure 9 Two segmentation results of selected slice using multicontrast MR images (a) testing MR images (b) automatic segmentationresults of Bayes classifier (c) automatic segmentation results of SSVM process

4 Comparison

The results of segmentation of slices 28 and 34 MR imagesbased on Bayes and SSVM are illustrated in Figure 9

As seen in Figure 9 the segmentation result in termof classification algorithm reveals that the performance ofSSVM is much better than that of Bayes due to the formerincluding structural information and smoothing effect ofsegmentation of SSVM is also obvious

The results presented by image are inadequate to makeevaluations Here a parameter named misclassification rateis defined to judge the accuracy of each algorithm

In the experiment of this paper a selected slice MRimage is corrupted by global intensity varying from 20to 40 and adding 1ndash9 noise Misclassification rate anevaluating criterion is defined as the ratio of misclassifiedpixels to total number of pixels of this class It is formulatedas (2) as follows

e(i) = f p + f n

n (2)

where e(i) is the misclassification rate of tissue i f p isthe false positive responses (pixel belongs to tissue i but isclassified as other tissues) f n is the false negative responses(pixel does not belong to tissue i but is classified as tissue typei) n is the total number of pixels of tissue type i

The misclassification rate of lumen obtained by Bayesand SSVM algorithm is listed in Table 1 From the statistics

Table 1 Misclassification rate of lumen for Bayes and SSVM

NoiseMisclassification rate

Bayes SSVM

1 35 26

3 53 48

5 65 63

7 106 85

9 169 96

shown in Table 1 it can be seen that the misclassificationrate caused by SSVM is much lower than that of Bayes Thatstands for the performance of SSVM outperforms that ofBayes especially while the level of noise is higher

5 Conclusion

To summarize the work in this paper is focus on the firstseveral steps of carotid artery plaque analysis includingpreprocessing of MR image model-based segmentation oflumen plaque and external wall Two kinds of model Bayesand SSVM are separately constructed and applied to thedetection of internal wall Receivable boundaries can be bothobtained by two algorithms the results of experiment shows


the segmentation performance of SSVM is better than that ofBayes especially while the level of noise in image is higher

But there are still some improvements need to be donein the future to break the limitations of the current workFirstly improve Bayes to better performance by increasingstructural information Secondly introduce sequence imagetracking technique in research to improve the performanceof human interaction to specify the center of lumen Furthereffort should focus on estimation of artery location in eachMRI slice and take advantage of information gained fromprevious slice to pick out the artery centroid of currentimage Moreover several other algorithms need to be testifiedand compared with them when dealing with plaques

Acknowledgments

The work was supported in part by the National ScienceFoundation of China (NSFC no 61173096 61103140 and51075367) Doctoral Fund of Ministry of Education ofChina (20113317110001) and Zhejiang Provincial S and TDepartment (2010R10006 2010C33095)

References

[1] Z Teng J He A J Degnan et al ldquoCritical mechanical con-ditions around neovessels in carotid atherosclerotic plaquemay promote intraplaque hemorrhagerdquo Atherosclerosis vol223 no 2 pp 321ndash326 2012

[2] Z Teng A J Degnan S Chen and J H Gillard ldquoCharac-terization of healing following atherosclerotic carotid plaquerupture in acutely symptomatic patients an exploratory studyusing in vivo cardiovascular magnetic resonancerdquo Journal ofCardiovascular Magnetic Resonance vol 13 no 1 article 642011


[4] S Y Chen J Zhang H Zhang et al ldquoMyocardial motionanalysis for determination of tei-index of human heartrdquoSensors vol 10 no 12 pp 11428ndash11439 2010

[5] S Y Chen J Zhang Q Guan and S Liu ldquoDetection andamendment of shape distortions based on moment invariantsfor active shape modelsrdquo IET Image Processing vol 5 no 3pp 273ndash285 2011

[6] R A Trivedi J U-King-Im M J Graves et al ldquoMulti-sequence in vivo MRI can quantify fibrous cap and lipid corecomponents in human carotid atherosclerotic plaquesrdquo Euro-pean Journal of Vascular and Endovascular Surgery vol 28 no2 pp 207ndash213 2004

[7] I M Adame R J van der Geest B A Wasserman M AMohamed J H C Reiber and B P F Lelieveldt ldquoAutomaticsegmentation and plaque characterization in atheroscleroticcarotid artery MR imagesrdquo Magnetic Resonance Materials inPhysics Biology and Medicine vol 16 no 5 pp 227ndash234 2004

[8] S E Clarke V Beletsky R R Hammond R A Hegele andB K Rutt ldquoValidation of automatically classifiedmagneticresonance images for carotid plaque compositional analysisrdquoStroke vol 37 no 1 pp 93ndash97 2006

[9] F Liu D Xu M S Ferguson et al ldquoAutomated in vivosegmentation of carotid plaque MRI with morphology-enhanced probability mapsrdquo Magnetic Resonance in Medicine

vol 55 no 3 pp 659ndash668 2006[10] C Karmonik P Basto K Vickers et al ldquoQuantitative segmen-

tation of principal carotid atherosclerotic lesion componentsby feature space analysis based on multicontrast MRI at 15 TrdquoIEEE Transactions on Biomedical Engineering vol 56 no 2 pp352ndash360 2009

[11] D Vukadinovic S Rozie M van Gils et al ldquoAutomatedversus manual segmentation of atherosclerotic carotid plaquevolume and components in CTA associations with cardio-vascular risk factorsrdquo International Journal of CardiovascularImaging vol 28 no 4 pp 877ndash887 2012

[12] Y Chen S Thiruvenkadam F Huang K S Gopinath andR W Brigg ldquoSimultaneous segmentation and registration forfunctional MR imagesrdquo in Proceedings of the 16th Interna-tional Conference on Pattern Recognition vol 1 pp 747ndash750Quebec Canada 2006

[13] J P W Pluim J B A Maintz and M A Viergever ldquoMutual-information-based registration of medical images a surveyrdquoIEEE Transactions on Medical Imaging vol 22 no 8 pp 986ndash1004 2003

[14] U Sadat R A Weerakkody D J Bowden et al ldquoUtility of highresolution MR imaging to assess carotid plaque morphologya comparison of acute symptomatic recently symptomaticand asymptomatic patients with carotid artery diseaserdquoAtherosclerosis vol 207 no 2 pp 434ndash439 2009


Research Article

Heavy-Tailed Prediction Error A Difficulty in PredictingBiomedical Signals of 1 f Noise Type

Ming Li1 Wei Zhao2 and Biao Chen2

1 School of Information Science amp Technology East China Normal University No 500 Dong-Chuan Road Shanghai 200241 China2 Department of Computer and Information Science University of Macau Padre Tomas Pereira Avenue Taipa Macau

Correspondence should be addressed to Ming Li ming lihkyahoocom



Copyright copy 2012 Ming Li et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A fractal signal x(t) in biomedical engineering may be characterized by 1 f noise that is the power spectrum density (PSD)divergences at f = 0 According the Taqqursquos law 1 f noise has the properties of long-range dependence and heavy-tailedprobability density function (PDF) The contribution of this paper is to exhibit that the prediction error of a biomedical signalof 1 f noise type is long-range dependent (LRD) Thus it is heavy-tailed and of 1 f noise Consequently the variance of theprediction error is usually large or may not exist making predicting biomedical signals of 1 f noise type difficult

1 Introduction

Signals of 1 f noise type are widely observed in biomedicalengineering ranging from heart rate to DNA and proteinsee for example [1ndash37] just to cite a few Predicting such atype of signals is desired in the field [38ndash43] A fundamentalissue in this regard is whether a biomedical signal of 1 fnoise type to be predicted is predicable or not

The predictability of signals of non-1 f noise type iswell studied [44ndash48] However the predictability of 1 fnoise is rarely reported to our best knowledge Since manyphenomena in biomedical engineering are characterized by1 f noise [1ndash37] the predictability issue of 1 f noise isworth investigating

Note that minimizing the mean square error (MSE) ofprediction is a commonly used criterion in both theory andpractical techniques of prediction see for example [49ndash68] Therefore a sufficient condition for a biomedical signalx(t) to be predictable is that the variance of its predicationerror exists If the variance of the predication error does notexist on the contrary it may be difficult to be predicted ifnot unpredictable In the case of a signal being bandlimitedthe variance of its predication error is generally finiteConsequently it may be minimized and it is predictableHowever that is not always the case for biomedical signalsof 1 f noise type

Let x(t) be a biomedical signal in the class of 1 f noiseThen its PDF is heavy-tailed and it is LRD see for exampleAdler et al [69] Samorodnitsky and Taqqu [70] Mandelbrot[71] Li and Zhao [72] Due to that here and below theterms 1 f noise LRD random function and heavy-tailedrandom function are interchangeable

Let p(x) be the PDF of a biomedical signal x(t) of 1 fnoise type Then its variance is expressed by

Var[x(t)] =intinfinminusinfin

(x minus μx

)2p(x)dx (1)

where μx is the mean of x(t) if it exists The term of heavytail in statistics implies that Var[x(t)] is large Theoreticallyspeaking in general we cannot assume that Var[x(t)] alwaysexists [72] In some cases such as the Pareto distribution theCauchy distribution α-stable distributions [72] Var[x(t)]may be infinite That Var[x(t)] does not exist is particularlytrue for signals in biomedical engineering and physiologysee Bassingthwaighte et al [33] for the interpretation of thispoint of view

Recall that a prediction error is a random function as weshall soon mention below Therefore whether the predictionerror is of 1 f noise or equivalently heavy-tailed turns to bea crucial issue we need studying We aim at in this researchexhibiting that prediction error of 1 f noise is heavy-tailed


and accordingly is of 1 f noise Thus generally speaking thevariance of a prediction error of a biomedical signal x(t) of1 f noise type may not exist or large That is a reason whypredicting biomedical signals of 1 f noise type is difficult

The rest of this paper is organized as follows Heavy-tailed prediction errors occurring in the prediction ofbiomedical signals of 1 f noise type are explained inSection 2 Discussions are in Section 3 which is followed bycon-clusions

2 Prediction Errors of 1 f Noise Type

We use x(n) to represent a biomedical signal in the discretecase for n isin N where N is the set of natural numbers LetxN (n) be a given sample of x(n) for n = 0 1 N minus 1Denote by xM(m) the predicted values of x(n) for m =N N + 1N + M minus 1 Then the prediction error denoted bye(m) is given by

e(m) =N+Mminus1summ=N

x(m)minus xM(m) (2)

If one uses the given sample of x(n) for n = N N +1 2N minus1 to obtain the predictions denoted by xM(m) form = 2N 2N + 1 2N + M minus 1 the error is usually differentfrom (2) which implies that the error e(m) is a randomvariable Denote by p(e) the PDF of e(m) Then its varianceis expressed by

Var[e(m)] =N+Mminus1summ=N

(e minus μe

)2p(e) (3)

where μe is the mean of e(m)Let P be the operator of a predictor Then

xM(m) = PxN (n) (4)

A natural requirement in terms of P is that Var[e(m)] shouldbe minimized Thus the premise that Var[e(m)] can beminimized is that it exists

It is obviously seen that Var[e(m)] may be large if p(e)is heavy tailed In a certain cases Var[e(m)] may not existTo explain the latter we assume that e(m) follows a type ofheavy-tailed distribution called the Pareto distribution

Denote by pPareto(e) the PDF of the Pareto distributionThen [73] it is in the form

pPareto(e) = aba

ea+1 (5)

where e ge b a gt 0 and b gt 0 The mean and variance ofe(m) are respectively expressed by

μe = ab

aminus 1

Var(e) = ab2

(aminus 1)2(aminus 2)

(6)

The above exhibits that Var[e(m)] does not exist if a = 1 ora = 2 and if e(m) follows the Pareto distribution

Note that the situation that Var[e(m)] does not exist maynot occur if e(m) is light-tailed Therefore the question inthis regard is whether e(m) is heavy-tailed if a biomedicalsignal x(n) is of 1 f noise The answer to that question isaffirmative We explain it below

Theorem 1 Let x(n) be a biomedical signal of 1 f noisetype to be predicted Then its prediction error is heavy-tailedConsequently it is of 1 f noise

Proof Let rxx(k) be the autocorrelation function (ACF) ofx(n) Then

rxx(k) = E[x(n)x(n + k)] (7)

where k is lag and E the mean operator Let rMM(k) be theACF of xM(m) Then

rMM(k) = E[xM(m)xM(m + k)] (8)

Let ree(k) be the ACF of e(m) Then

ree(k) = E[e(m)e(m + k)] (9)

Note that

ree(k) = E[e(m)e(m + k)]

= E[x(m)minus xM(m)][x(m + k)minus xM(m + k)]= E[x(m)x(m + k) + xM(m)xM(m + k)

minusxM(m)x(m + k)minus x(m)xM(m + k)]

= rxx(k) + rMM(k)minus rMx(k)minus rxM(k)

(10)

In the above expression rMx(k) is the cross-correlationbetween xM(m) and x(m) On the other side rxM(k) is thecross-correlation between x(m) and xM(m) Since rMx(k) =rxM(k) we have

ree(k) = rxx(k) + rMM(k)minus 2rxM(k) (11)

Recall that x(m) is 1 f noise Thus it is heavy-tailed andhence LRD Consequently for a constant c1 gt 0 we have

rxx(k) sim c1kminusα (k minusrarr infin) for 0 lt α lt 1 (12)

On the other hand the predicted series xM(m) is LRD Thusfor a constant c2 gt 0 the following holds

rMM(k) sim c2kminusβ (k minusrarr infin) for 0 lt β lt 1 (13)

In (11) if rxM(k) is summable that is it decays faster thanrx(k) or rM(k) it may be ignored for k rarr infin In this caseree(k) is still non-summable In fact one has

ree(k) sim

⎧⎪⎪⎨⎪⎪⎩c1kminusα 0 lt α lt β lt 1

c2kminusβ 0 lt β lt α lt 1

(c1 + c2)kminusβ α = β

(k minusrarr infin)

(14)


On the other side when rxM(k) is non-summable re(k) isnon-summable too In any case we may write ree(k) by

ree(k) sim ckminusγ (k minusrarr infin) for 0 lt γ lt 1 (15)

Therefore the prediction error e(m) is LRD Its PDF p(e)is heavy-tailed according to the Taqqursquos law Following [72]therefore e(m) is a 1 f noise This completes the proof

3 Discussions

The present result implies that cautions are needed fordealing with predication errors of biomedical signals of 1 fnoise type In fact if specific biomedical signals are in theclass of 1 f noise the variances of their prediction errors maynot exist or large [72] Tucker and Garway-Heath used tostate that their prediction errors with either prediction modelthey used are large [74] The result in this paper may in a wayprovide their research with an explanation

Due to the fact that a biomedical signal may be of 1 fnoise PDF estimation is suggested as a preparatory stagefor prediction As a matter of fact if a PDF estimation ofbiomedical signal is light-tailed its variance of predictionerror exists On the contrary the variance of the predictionerror may not exist In the latter case special techniques haveto be considered [75ndash78] For instance weighting predictionerror may be a technique necessarily to be taken into accountwhich is suggested in the domain of generalized functionsover the Schwartz distributions [79]

4 Conclusions

We have explained that the prediction error e(m) in pre-dicting biomedical signals of 1 f noise type is usually LRDThis implies that its PDF p(e) is heavy-tailed and 1 f noiseConsequently Var[e(m)] may in general be large In somecases [72] Var[e(m)] may not exist making the predictionof biomedical signals of 1 f noise type difficult with the wayof minimizing Var[e(m)]

Acknowledgments

This work was supported in part by the 973 plan underthe Project Grant no 2011CB302800 and by the NationalNatural Science Foundation of China under the ProjectGrant no 61272402 61070214 and 60873264

References

[1] N Aoyagi Z R Struzik K Kiyono and Y YamamotoldquoAutonomic imbalance induced breakdown of long-rangedependence in healthy heart raterdquo Methods of Information inMedicine vol 46 no 2 pp 174ndash178 2007

[2] S Tong D Jiang Z Wang Y Zhu R G Geocadin and N VThakor ldquoLong range correlations in the heart rate variabilityfollowing the injury of cardiac arrestrdquo Physica A vol 380 no1-2 pp 250ndash258 2007

[3] N V Sarlis E S Skordas and P A Varotsos ldquoHeart ratevariability in natural time and 1 f lsquonoisersquordquo Europhysics Lettersvol 87 no 1 Article ID 18003 2009

[4] Z R Struzik J Hayano R Soma S Kwak and Y YamamotoldquoAging of complex heart rate dynamicsrdquo IEEE Transactions onBiomedical Engineering vol 53 no 1 pp 89ndash94 2006

[5] U R Acharya K P Joseph N Kannathal C M Lim and J SSuri ldquoHeart rate variability a reviewrdquo Medical and BiologicalEngineering and Computing vol 44 no 12 pp 1031ndash10512006

[6] J H T Bates G N Maksym D Navajas and B SukildquoLung tissue rheology and 1 f noiserdquo Annals of BiomedicalEngineering vol 22 no 6 pp 674ndash681 1994

[7] J M Halley and W E Kunin ldquoExtinction risk and the 1 ffamily of noise modelsrdquo Theoretical Population Biology vol 56no 3 pp 215ndash230 1999

[8] M C Wichmann K Johst M Schwager B Blasius and FJeltsch ldquoExtinction risk coloured noise and the scaling ofvariancerdquo Theoretical Population Biology vol 68 no 1 pp 29ndash40 2005

[9] Z Yang L Hoang Q Zhao E Keefer and W Liu ldquo1 f neuralnoise reduction and spike feature extraction using a subset ofinformative samplesrdquo Annals of Biomedical Engineering vol39 no 4 pp 1264ndash1277 2011

[10] J Ruseckas and B Kaulakys ldquoTsallis distributions and 1 fnoise from nonlinear stochastic differential equationsrdquo Physi-cal Review E vol 84 no 5 Article ID 051125 7 pages 2011

[11] F Beckers B Verheyden and A E Aubert ldquoAging and non-linear heart rate control in a healthy populationrdquo AmericanJournal of Physiology vol 290 no 6 pp H2560ndashH2570 2006

[12] B Pilgram and D T Kaplan ldquoNonstationarity and 1 f noisecharacteristics in heart raterdquo American Journal of Physiologyvol 276 no 1 pp R1ndashR9 1999

[13] P Szendro G Vincze and A Szasz ldquoPink-noise behaviour ofbiosystemsrdquo European Biophysics Journal vol 30 no 3 pp227ndash231 2001

[14] G Massiera K M Van Citters P L Biancaniello and J CCrocker ldquoMechanics of single cells rheology time depend-ence and fluctuationsrdquo Biophysical Journal vol 93 no 10 pp3703ndash3713 2007

[15] Y Murase T Shimada N Ito and P A Rikvold ldquoEffects ofdemographic stochasticity on biological community assemblyon evolutionary time scalesrdquo Physical Review E vol 81 no 4Article ID 041908 14 pages 2010

[16] T Yokogawa and T Harada ldquoGenerality of a power-lawlong-term correlation in beat timings of single cardiac cellsrdquoBiochemical and Biophysical Research Communications vol387 no 1 pp 19ndash24 2009

[17] T Harada T Yokogawa T Miyaguchi and H Kori ldquoSingularbehavior of slow dynamics of single excitable cellsrdquo BiophysicalJournal vol 96 no 1 pp 255ndash267 2009

[18] A Eke P Herman J B Bassingthwaighte et al ldquoPhysiologicaltime series distinguishing fractal noises from motionsrdquoPflugers Archiv vol 439 no 4 pp 403ndash415 2000

[19] B J West ldquoFractal physiology and the fractional calculus aperspectiverdquo Frontiers in Fractal Physiology vol 1 article 122010

[20] P Grigolini G Aquino M Bologna M Lukovic and B JWest ldquoA theory of 1 f noise in human cognitionrdquo Physica Avol 388 no 19 pp 4192ndash4204 2009

[21] F Gruneis M Nakao Y Mizutani M Yamamoto MMeesmann and T Musha ldquoFurther study on 1 f fluctuationsobserved in central single neurons during REM sleeprdquo Biolog-ical Cybernetics vol 68 no 3 pp 193ndash198 1993

[22] H Sheng Y-Q Chen and T-S Qiu ldquoHeavy-tailed distribu-tion and local long memory in time series of molecular motion


on the cell membranerdquo Fluctuation and Noise Letters vol 10no 1 pp 93ndash119 2011

[23] B J West and W Deering ldquoFractal physiology for physicistsLevy statisticsrdquo Physics Report vol 246 no 1-2 pp 1ndash1001994

[24] W Deering and B J West ldquoFractal physiologyrdquo IEEE Engineer-ing in Medicine and Biology Magazine vol 11 no 2 pp 40ndash461992

[25] B J West ldquoPhysiology in fractal dimensions error tolerancerdquoAnnals of Biomedical Engineering vol 18 no 2 pp 135ndash1491990

[26] M Joyeux S Buyukdagli and M Sanrey ldquo1 f Fluctuations ofDNA temperature at thermal denaturationrdquo Physical ReviewE vol 75 no 6 Article ID 061914 9 pages 2007

[27] C Cattani ldquoFractals and hidden symmetries in DNArdquo Mathe-matical Problems in Engineering vol 2010 Article ID 50705631 pages 2010

[28] C Cattani E Laserra and I Bochicchio ldquoSimplicial approachto fractal structuresrdquo Mathematical Problems in Engineeringvol 2012 Article ID 958101 21 pages 2012

[29] P Herman and A Eke ldquoNonlinear analysis of blood cellflux fluctuations in the rat brain cortex during stepwisehypotension challengerdquo Journal of Cerebral Blood Flow ampMetabolism vol 26 no 9 pp 1189ndash1197 2006

[30] M Baumert V Baier and A Voss ldquoLong-term correlationsand fractal dimension of beat-to-beat blood pressure dynam-icsrdquo Fluctuation and Noise Letters vol 5 no 4 pp L549ndashL5552005


[32] S Y Ponomarev V Putkaradze and T C Bishop ldquoRelaxationdynamics of nucleosomal DNArdquo Physical Chemistry ChemicalPhysics vol 11 no 45 pp 10633ndash10643 2009

[33] J B Bassingthwaighte L S Liebovitch and B J West FractalPhysiology Oxford University Press 1994

[34] D Craciun A Isvoran and N M Avram ldquoLong rangecorrelation of hydrophilicity and flexibility along the calciumbinding protein chainsrdquo Physica A vol 388 no 21 pp 4609ndash4618 2009

[35] J Siodmiak J J Uher I Santamarıa-Holek N Kruszewskaand A Gadomski ldquoOn the protein crystal formation as aninterface-controlled process with prototype ion-channelingeffectrdquo Journal of Biological Physics vol 33 no 4 pp 313ndash3292007

[36] S C Kou and X S Xie ldquoGeneralized langevin equation withfractional gaussian noise subdiffusion within a single proteinmoleculerdquo Physical Review Letters vol 93 no 18 Article ID180603 4 pages 2004

[37] H Sheng Y-Q Chen and T-S Qiu Fractional Processes andFractional Order Signal Processing Springer 2012

[38] M Panella ldquoAdvances in biological time series prediction byneural networksrdquo Biomedical Signal Processing and Controlvol 6 no 2 pp 112ndash120 2011

[39] Y-R Cho and A Zhang ldquoPredicting protein function byfrequent functional association pattern mining in proteininteraction networksrdquo IEEE Transactions on Information Tech-nology in Biomedicine vol 14 no 1 pp 30ndash36 2010

[40] A Castro M A L Marques D Varsano F Sottile andA Rubio ldquoThe challenge of predicting optical propertiesof biomolecules what can we learn from time-dependentdensity-functional theoryrdquo Comptes Rendus Physique vol 10no 6 pp 469ndash490 2009

[41] Q Lu H J Wu J Z Wu et al ldquoA parallel ant coloniesapproach to de novo prediction of protein backbone inCASP89rdquo Science China Information Sciences In press

[42] B R Yang W Qu L J Wang and Y Zhou ldquoA new intelligentprediction system model-the compound pyramid modelrdquoScience China Information Sciences vol 55 no 3 pp 723ndash7362012

[43] J L Suo X Y Ji and Q H Dai ldquoAn overview of computa-tional photographyrdquo Science China Information Sciences vol55 no 6 pp 1229ndash1248 2012

[44] A Papoulis ldquoA note on the predictability of band-limitedprocessesrdquo Proceedings of the IEEE vol 73 no 8 pp 1332ndash1333 1985

[45] S Y Chen C Y Yao G Xiao Y S Ying and W L WangldquoFault detection and prediction of clocks and timers basedon computer audition and probabilistic neural networksrdquoin Proceedings of the 8th International Workshop on ArtificialNeural Networks IWANN 2005 Computational Intelligenceand Bioinspired Systems vol 3512 of Lecture Notes in ComputerScience pp 952ndash959 June 2005

[46] R J Lyman W W Edmonson S McCullough and MRao ldquoThe predictability of continuous-time bandlimitedprocessesrdquo IEEE Transactions on Signal Processing vol 48 no2 pp 311ndash316 2000

[47] R J Lyman and W W Edmonson ldquoLinear predictionof bandlimited processes with flat spectral densitiesrdquo IEEETransactions on Signal Processing vol 49 no 7 pp 1564ndash15692001

[48] N Dokuchaev ldquoThe predictability of band-limited high-frequency and mixed processes in the presence of ideal low-pass filtersrdquo Journal of Physics A vol 41 no 38 Article ID382002 7 pages 2008

[49] N Wiener Extrapolation Interpolation and Smoothing ofStationary Time Series John Wiley amp Sons 1964

[50] A N Kolmogorov ldquoInterpolation and extrapolation of sta-tionary random sequencesrdquo Izvestiya Akademii Nauk SSSRvol 5 pp 3ndash14 1941

[51] L A Zadeh and J R Ragazzini ldquoAn extension of Wienerrsquostheory of predictionrdquo Journal of Applied Physics vol 21 no7 pp 645ndash655 1950

[52] R J Bhansali ldquoAsymptotic properties of the Wiener-Kolmogorov predictor Irdquo Journal of the Royal StatisticalSociety B vol 36 no 1 pp 61ndash73 1974

[53] N Levinson ldquoA heuristic exposition of Wienerrsquos mathematicaltheory of prediction and filteringrdquo Journal of MathematicalPhysics vol 26 pp 110ndash119 1947

[54] N Levinson ldquoThe Wiener RMS (root mean squares) error cri-terion in filter design and predictionrdquo Journal of MathematicalPhysics vol 25 pp 261ndash278 1947

[55] R J Bhansali ldquoAsymptotic mean-square error of predictingmore than one-step ahead using the regression methodrdquoJournal of the Royal Statistical Society C vol 23 no 1 pp 35ndash42 1974

[56] J Makhoul ldquoLinear prediction a tutorial reviewrdquo Proceedingsof the IEEE vol 63 no 4 pp 561ndash580 1975

[57] D L Zimmerman and N Cressie ldquoMean squared predictionerror in the spatial linear model with estimated covarianceparametersrdquo Annals of the Institute of Statistical Mathematicsvol 44 no 1 pp 27ndash43 1992

[58] D Huang ldquoLevinson-type recursive algorithms for least-squares autoregressionrdquo Journal of Time Series Analysis vol11 no 4 pp 295ndash315 2008

[59] R S Deo ldquoImproved forecasting of autoregressive seriesby weighted least squares approximate REML estimationrdquo


International Journal of Forecasting vol 28 no 1 pp 39ndash432012

[60] A Rodrıguez and E Ruiz ldquoBootstrap prediction meansquared errors of unobserved states based on the Kalman filterwith estimated parametersrdquo Computational Statistics amp DataAnalysis vol 56 no 1 pp 62ndash74 2012

[61] M Abt ldquoEstimating the prediction mean squared error ingaussian stochastic processes with exponential correlationstructurerdquo Scandinavian Journal of Statistics vol 26 no 4 pp563ndash578 1999

[62] R Kohn and C F Ansley ldquoPrediction mean squared errorfor state space models with estimated parametersrdquo Biometrikavol 73 no 2 pp 467ndash473 1986

[63] R T Baillie ldquoAsymptotic prediction mean squared error forvector autoregressive modelsrdquo Biometrika vol 66 no 3 pp675ndash678 1979

[64] P Neelamegam A Jamaludeen and A Rajendran ldquoPredictionof calcium concentration in human blood serum using anartificial neural networkrdquo Measurement vol 44 no 2 pp312ndash319 2011

[65] E S G Carotti J C De Martin R Merletti and D FarinaldquoCompression of multidimensional biomedical signals withspatial and temporal codebook-excited linear predictionrdquoIEEE Transactions on Biomedical Engineering vol 56 no 11pp 2604ndash2610 2009

[66] W Bachta P Renaud L Cuvillon E Laroche A Forgioneand J Gangloff ldquoMotion prediction for computer-assistedbeating heart surgeryrdquo IEEE Transactions on Biomedical Engi-neering vol 56 no 11 pp 2551ndash2563 2009

[67] H-H Lin C L Beck and M J Bloom ldquoOn the use ofmultivariable piecewise-linear models for predicting humanresponse to anesthesiardquo IEEE Transactions on BiomedicalEngineering vol 51 no 11 pp 1876ndash1887 2004

[68] B S Atal ldquoThe history of linear predictionrdquo IEEE SignalProcessing Magazine vol 23 no 2 pp 154ndash161 2006

[69] R J Adler R E Feldman and M S Taqqu Eds A PracticalGuide to Heavy Tails Statistical Techniques and ApplicationsBirkhauser Boston Mass USA 1998

[70] G Samorodnitsky and M S Taqqu Stable Non-GaussianRandom Processes Chapman amp Hall New York NY USA1994

[71] B B Mandelbrot Multifractals and 1f Noise Springer 1998[72] M Li and W Zhao ldquoOn 1 f noiserdquo Mathematical Problems in

Engineering In press[73] G A Korn and T M Korn Mathematical Handbook for

Scientists and Engineers McGraw-Hill 1961[74] A Tucker and D Garway-Heath ldquoThe pseudotemporal

bootstrap for predicting glaucoma from cross-sectional visualfield datardquo IEEE Transactions on Information Technology inBiomedicine vol 14 no 1 pp 79ndash85 2010

[75] M Carlini and S Castellucci ldquoModelling the vertical heatexchanger in thermal basinrdquo in Proceedings of the InternationalConference on Computational Science and Its Applications(ICCSA rsquo11) vol 6785 of Lecture Notes in Computer Sciencepp 277ndash286 Springer

[76] M Carlini C Cattani and A Tucci ldquoOptical modelling ofsquare solar concentratorrdquo in Proceedings of the InternationalConference on Computational Science and Its Applications(ICCSA rsquo11) vol 6785 of Lecture Notes in Computer Sciencepp 287ndash295 Springer

[77] R J Bhansali and P S Kokoszka ldquoPrediction of long-memorytime series a tutorial reviewrdquo Lecture Notes in Physics vol 621pp 3ndash21 2003

[78] L Bisaglia and S Bordignon ldquoMean square prediction errorfor long-memory processesrdquo Statistical Papers vol 43 no 2pp 161ndash175 2002

[79] M Li and J-Y Li ldquoOn the predictability of long-rangedependent seriesrdquo Mathematical Problems in Engineering vol2010 Article ID 397454 9 pages 2010


Research Article

In Vitro Evaluation of Ferrule Effect and Depth of Post Insertionon Fracture Resistance of Fiber Posts

R Schiavetti and G Sannino

Department of Oral Health University of Rome Tor Vergata Viale Oxford 00100 Rome Italy

Correspondence should be addressed to G Sannino gianpaolosanninouniroma2it



Copyright copy 2012 R Schiavetti and G Sannino This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Purpose The analysis of the complex model of fiber post and ferrule is given and studied in this paper A novel approach and asolution to the evaluation of stress of post and core system within the ferrule effect are proposed Methods Sixty freshly extractedpremolars were selected for the study The following experimental groups were therefore defined (n = 10) (1) 5 mm (2) 7 mm (3)9 mm (4) ferrule-5 mm (5) ferrule-7 mm and (6) ferrule-9 mm Preshaping drills (C) were used to prepare the root canals at 57 and 9 mm in depth In specimens of groups 3ndash6 a circumferential collar of tooth structure of 2 mm in height Fluorocore 2 corebuild-up material (I) was used for fiber post luting With the same material a buildup of 2 mm in height was created A controlledcompressive load (crosshead speed 075 mmmin) was applied by means of a stainless steel stylus (Oslash 1 mm) at the coronal end ofthe post extruding out of the root Results In all the tests the level of significance was set at P lt 005 Significantly higher fracturestrengths were measured in the presence of a ferrule effect In groups 1 2 and 3 (ferrule group) the mean fracture values wererespectively 1638 N 2709 N and 2547 N These data are higher and statistically significantly different when compared with thethree groups 4 5 and 6 (no-ferrule group) in which the values obtained were respectively 405 N 417 N and 449 N ConclusionThe ferrule effect in the endodontically treated teeth positively affects the fracture strength of the fiber post Conversely post depthinsertion did not affect the resistance to fracture

1 Introduction

A persistent problem in clinical dentistry is represented bythe risk fracture of endodontically treated teeth [1] Theseteeth are considered to be less resistance because of theloss of tooth structure during conservative access cavitypreparation The influence of subsequent canal instrumen-tation and obturation leads to a reduction in the resistanceto fracture [2 3] To restore these teeth posts are oftenrequired in order to provide anchorage for the core-formingmaterial and coronoradicular stabilization [4 5] Cast postsand cores have been used for this purpose for many yearswhile more recently fiber posts showed to represent a validalternative The clinical success of fiber post restorationsis mainly related to their biomechanical properties thatbeing close to those of dentin reduce stress transmissionto the roots [6ndash9] The potential of fiber posts to reducethe incidence of nonretrievable root fractures in comparison

with cast posts was confirmed in several studies [10ndash12]Among the several parameters influencing the success ofa post-based rehabilitation preservation of coronal dentaltissue and particularly the presence of a ferrule effect havebeen advocated as favorable conditions to decrease stresstransmission to the root [13] Sorensen and Engelman [14]described the ferrule as the coronal-dentinal extension ofthe tooth structure occlusal to the shoulder preparationThe ferrule effect in association with cast post and coreshas been studied by many investigators [15ndash17] Converselylittle information is available if the ferrule is of additionalvalue in providing reinforcement in teeth restored withprefabricated post and composite cores and the advantagescoming from the presence of ferrule in prefabricated postand core are questioned by Al-Hazaimeh and Gutteridge[18]

The main task of this in vitro study is to evaluate theeffect of ferrule preparation on fracture resistance of fiber


post as a function of the presenceabsence of a ferrule andas a function of the depth of insertion of the fiber posts

The formulated null hypothesis was that neither depth ofpost insertion nor the presence of a 2 mm high ferrule hada significant influence on fracture resistance of a fiber post-retained restoration


Sixty freshly extracted premolars were selected for the studyTeeth had to be free of cracks caries and fractures andwere stored at room temperature in saline solution beforetesting The anatomic crowns of all teeth were sectionedperpendicularly to the tooth long axis at the cement-enameljunction (CEJ) Roots were endodontically treated using theldquostep-backrdquo technique [19] to a number 70 size file (A) (seeTable 2) and irrigated with 25 sodium hypochlorite

Each canal was obturated using the lateral condensationtechnique with gutta-percha points (B) and the resin sealerAH Plus Jet (C) (see Table 2) The endodontic access cavitieswere temporarily filled with a glass ionomer cement (D)(Fuji II GC corp Tokyo Japan) After 24 hours the coronalseal was removed by means of 240-grit abrasive SiC papersunder water cooling Roots were randomly divided intosix experimental groups that differed for the depth of theprepared post space and for the presence or absence ofa ferrule effect The following experimental groups weretherefore defined (n = 10) (1) 5 mm (Figure 1(a)) (2)7 mm (Figure 1(b)) (3) 9 mm (Figure 1(c)) (4) ferrule-5 mm (Figure 1(d)) (5) ferrule-7 mm (Figure 1(e)) (6)ferrule-9 mm (Figure 1(f)) Preshaping drills (C) were usedto prepare the root canals at 5 7 and 9 mm in depth Afterpreparation it was checked that a 3-mm long gutta-perchaapical seal In specimens of groups 3ndash6 a circumferentialcollar of tooth structure of 2 mm in height and 3 mm inwidth was realized with a diamond bur (Figure 2)

Translucent quartz fiber posts (E) consisting of unidirec-tional pretensed fibers bound in a translucent epoxy resinmatrix were used Each post was tried in into the root canaland the portion of the post extruding out the root was cutto a standardized length of 48 [20] Prior to cementation aprehydrolyzed silane coupling agent (F) was applied with amicrobrush on the post surface for 30 s The light cured self-priming adhesive Prime and Bond NT (G) was applied intothe root canal with a microbrush for 20 s and gently air-driedThe excess was removed using paper points The bondingagent was polymerized with a conventional quartz-tungsten-halogen light (750 mWcm2) (H) Fluorocore 2 core build-up material (I) was used for fiber post luting Base andcatalyst (1 1) were mixed for 30 s then the material wasapplied on the post The post was seated immediately intothe canal and sustained under finger pressure With the samematerial a buildup of 2 mm in height was created After thefirst 7-minute autocure period the material was light-curedfor 40 s After curing the specimens were prepared as for aprosthetic crown with a circumferential chamfer reductionof 15 mm of maximum thickness using a chamfer bur of2 mm in diameter (M) After post cementation each root

was embedded in a self-polymerizing acrylic resin (J) for halfof the root length with the long axis sloped at a 45-degreeangle to the base of the resin block During this procedurespecimens were continuously irrigated with water to avoidoverheating due to resin polymerization Before performingthe mechanical test samples were stored for 24 hours at 37Cand 100 relative humidity

Each sample was then mounted on a universal testingmachine (K) A controlled compressive load (cross-headspeed 075 mmmin) was applied by means of a stainlesssteel stylus (Oslash 1 mm) at the coronal end of the post extrudingout of the root (Figure 3) A software (L) connected to theloading machine recorded the load at failure of the post-retained restoration measured in Newton (N)

3 Results

Descriptive statistics of fracture strength data are reportedin Table 1 along with the significance of between-groupdifferences As the distribution of fracture strengths was notnormal according to the Kolmogorov-Smirnov test the useof the Two-Way Analysis of Variance to assess the influenceof depth ferrule effect and between-factor interaction wasprecluded Therefore the Kruskal-Wallis One-Way Analysisof Variance was applied with strength as the dependentvariable and experimental group as factor Consequentlythe Dunnrsquos multiple range test was used for post hoccomparisons In all the tests the level of significance wasset at P lt 005 Significantly higher fracture strengths weremeasured in the presence of a ferrule effect Neither in thepresence or in the absence of a ferrule effect had depth ofpost insertion a significant influence on fracture strength asno statistically significant differences emerged either amonggroups 1ndash3 or among groups 4ndash6

The results obtained from this in vitro study showed acorrelation between the presence of the ferrule and increasedresistance to fracture In groups 1 2 and 3 (with ferrule) themean fracture values were respectively 1638 N 2709 N and2547 N These data are higher and statistically significantlydifferent when compared with the three groups 4 5 and6 without ferrule effect in which the values obtained wererespectively 405 N 417 N and 449 N

The depth of post insertion did not show to be a param-eter affecting the results In fact no statistically significantdifferences were found between groups 1 2 and 3 as well asbetween groups 4 5 and 6

4 Discussion

Since in the presence of a ferrule significantly higher fracturestrengths were measured the null hypothesis has to berejected

Several factors determine the performances and thesuccess of a rehabilitation clinic in time types designand lengths of post bonding capacity [21] and ferruleLarge variations exist in regard to the physical and fatigueresistance of resin-fiber posts [22] The static or dynamicbehavior of resin-fiber posts depends on the composition


Table 1 Descriptive statistics of fiber post fracture strength data with the significance of between-group differences

Number group Name group N Mean Std Deviation Median 25ndash75 Significance P lt 005

1 Ferrule-5 mm 10 1638 725 1429 1327ndash1811 AB

2 Ferrule-7 mm 10 2709 1056 2449 2152ndash3503 A


4 No ferrule-5 mm 10 405 31 402 384ndash442 C


6 No ferrule-9 mm 10 449 67 445 405ndash517 BC

1

2

3

(a)

1

2

3

(b)

1

2

3

(c)

1

2

3

(d)

1

2

3

(e)

1

2

3

(f)

Figure 1 Experimental groups with different post depth (5 7 and 9 mm) and postspace with (groups a b c) and without (groups d e f) aferrule effect

(fiber type and density) as well as the fabrication processand in particular the quality of the resin-fiber interface Inan in vitro study examining physical properties of variousposts it was concluded that the ideal post design comprisesa cylindrical coronal portion and a conical apical portion[23] Much discussed is still the ideal post length if onepart provides greater stability to prosthetic rehabilitation atthe same time involves removal of dentin [24] and morebecause of the existing limitations of adhesive procedureswithin the root canal [25ndash27] It has been demonstrated thatthe loss of tooth vitality is not accompanied by significantchange in tissue moisture or collagen structure [28ndash30]The most important changes in tooth biomechanics areattributed to the loss of tissue either at radicular [2 31]

or coronal [31ndash34] levels pointing out the importanceof a highly conservative approach during endodontic andrestorative procedures The significance of remaining cervicaltissue known as the ferrule was also well documented[13 35] The incorporation of a ferrule is an importantfactor of tooth preparation when using a post-supportedrehabilitation technique [36ndash38] The effectiveness of theferrule has been evaluated with several laboratory tests asfracture resistance such as [39] impact [40] fatigue [41]and photoelastic analysis [42] According to these studies theferrule presence showed values of resistance to fracture muchhigher and statistically significant differences in groups 1 2and 3 than no-ferrule groups (groups 4 5 6) Concerningthe length of the ferrule some studies have reported that


Table 2 Classification of instruments used for collecting and meas-uring data during the tests

Class Type

(A) Flex R File Union Broach York PA USA

(B) Dentsply Maillefer Tulsa OK USA

(C) DeTrey Konstanz Germany

(D) Fuji II Gc corp Tokyo Japan

(E)ENDO LIGHT-POST number 3 Bisco SchaumburgIL USA

(F) Monobond S Ivoclar Vivadent Schaan Liechtenstein

(G)Prime and Bond NT Dentsply DeTrey KonstanzGermany

(H) Optilux 401 Kerr Danbury USA

(I) Fluorocore 2 Dentsply DeTrey Konstanz Germany

(J)ProBase Cold Ivoclar Vivadent Schaan FurstentumLiechtenstein

(K) Instron Corp Canton MA USA

(L) Digimax Plus Controls srl Cernusco sn Italy

1

2

32 mm

Figure 2 Ferrule effect A circumferential collar of tooth structureat least 2 mm in height was preserved at the gingival aspect of thepreparation

a tooth should have a minimum amount (2 mm) of coronalstructure above the cement-enamel junction (CEJ) to achievea proper resistance [43 44]

The results of the present study in which to assess themean fracture for each group the force was applied directlyon the post head in order to exclude other variables haveconfirmed these observations

About post insertion depth it is known that with castpost and core system the post length was an importantvariable because reducing post space can permit to savetooth structure positively affecting the tooth fracture resis-tance Some authors [45] in a recent study designed toobtain a biofaithful model of the maxillary incisor systemand to assess the effect of glass fiber post lengths usingFinite Element Analysis showed that the overall systemrsquos

Figure 3 Example of a sample mounted on the loading machineand prepared for the fracture test The tooth is oriented such as theload applied by means of the metallic stylus would have a 45-degreedirection

strain pattern did not appear to be influenced by post lengthThis could lead to the conclusion that a post inserted moredeeply could be more effective in a fiber post-supportedrehabilitation as the length of the post insertion has asignificant effect on retention the more apically the post isplaced in the root the more retentive is the system [46ndash48]This consideration should not be overestimated in clinicalpractice The adaptation of the canal shape to the post [49]and the overall length of the root should be in fact taken intoconsideration because it has been reported that a residualapical filling of less than 3 mm may result in an unpredictableseal [50 51]

From the results of the present study a tendency ofthe more deeply inserted post to have higher values ofresistance to fracture could be anyway observed particularlyin the no-ferrule groups This might be connected withthe use of tapered post considering that a post insertedmore deeply has a wider diameter at the breaking pointThe use of a cylindrical shaped post could have minimizedthis differences and this could be considered as a limit ofthe present study even if Lang et al [52] showed that ifan excessive amount of tooth structure is removed and thenatural geometry of the root canal is altered this will havea destabilizing effect on root-filled teeth For this reason inclinical practice the use of cylindrical-shaped post have beenprogressively abandoned and replaced with tapered post

As general consideration it should be noted that thisin vitro study does not reproduce the exact clinical condi-tions where lateral forces should be considered as well asaxial forces and fatigue loading ageing processes alternatethermal stress mechanical stress wear and water storageIn this in vitro study in fact lateral forces were appliedwith a 45 angle between the post and the loading tipMoreover stress applied to the teeth and dental restorationsis generally low and repetitive rather than being isolated andloading However because of a linear relationship betweenfatigue and static loading the compressive static test also


gives valuable information concerning load-bearing capacity[53 54] Based on this statement the results of this in vitrostudy showed that the ferrule effect positively affects theresistance to fracture of endodontically treated teeth restoredwith fiber posts Conversely post depth of insertion did notaffect the resistance to fracture

5 Conclusion

Within the limitation of this in vitro study the statisticalresults showed that the ferrule effect in the endodonticallytreated teeth positively affects the fracture strength ofthe fiber post Conversely post depth insertion did notaffect the resistance to fracture It could be advisable inthe rehabilitation of endodontically treated teeth preserveradicular tissue reducing the postspace preparation in orderto improve the fracture strength of the post with a ferrulelength of at least 2 mm

References

[1] S Belli A Erdemir and C Yildirim ldquoReinforcement effectof polyethylene fibre in root-filled teeth comparison of tworestoration techniquesrdquo International Endodontic Journal vol39 no 2 pp 136ndash142 2006

[2] M Trope and H L Ray ldquoResistance to fracture of endodon-tically treated rootsrdquo Oral Surgery Oral Medicine and OralPathology vol 73 no 1 pp 99ndash102 1992

[3] E S Reeh H H Messer and W H Douglas ldquoReductionin tooth stiffness as a result of endodontic and restorativeproceduresrdquo Journal of Endodontics vol 15 no 11 pp 512ndash516 1989

[4] O Pontius and J W Hutter ldquoSurvival rate and fracturestrength of incisors restored with different post and coresystems and endodontically treated incisors without corono-radicular reinforcementrdquo Journal of Endodontics vol 28 no10 pp 710ndash715 2002

[5] F H O Mitsui G M Marchi L A F Pimento and PM Ferraresi ldquoIn vitro study of fracture resistance of bovineroots using different intraradicular post systemsrdquo QuintessenceInternational vol 35 no 8 pp 612ndash616 2004

[6] M Hayashi Y Takahashi S Imazato and S Ebisu ldquoFractureresistance of pulpless teeth restored with post-cores andcrownsrdquo Dental Materials vol 22 no 5 pp 477ndash485 2006

[7] M Ferrari M C Cagidiaco C Goracci et al ldquoLong-termretrospective study of the clinical performance of fiber postsrdquoThe American Journal of Dentistry vol 20 no 5 pp 287ndash2912007

[8] M C Cagidiaco C Goracci F Garcia-Godoy and M FerrarildquoClinical studies of fiber posts a literature reviewrdquo Interna-tional Journal of Prosthodontics vol 21 no 4 pp 328ndash3362008

[9] M Ferrari A Vichi F Mannocci and P M Mason ldquoRetro-spective study of the clinical performance of fiber postsrdquo TheAmerican Journal of Dentistry vol 13 no 2 pp 9bndash13b 2000

[10] M Ferrari M C Cagidiaco S Grandini M De Sanctis andC Goracci ldquoPost placement affects survival of endodonticallytreated premolarsrdquo Journal of Dental Research vol 86 no 8pp 729ndash734 2007

[11] G Heydecke F Butz and J R Strub ldquoFracture strength andsurvival rate of endodontically treated maxillary incisors withapproximal cavities after restoration with different post and

core systems an in-vitro studyrdquo Journal of Dentistry vol 29no 6 pp 427ndash433 2001

[12] B Akkayan and T Gulmez ldquoResistance to fracture ofendodontically treated teeth restored with different postsystemsrdquo Journal of Prosthetic Dentistry vol 87 no 4 pp 431ndash437 2002

[13] A Martınez-Insua L da Silva B Rilo and U Santana ldquoCom-parison of the fracture resistances of pulpless teeth restoredwith a cast post and core or carbon-fiber post with a compositecorerdquo The Journal of Prosthetic Dentistry vol 80 no 5 pp527ndash532 1998

[14] J A Sorensen and M J Engelman ldquoFerrule design and frac-ture resistance of endodontically treated teethrdquo The Journal ofProsthetic Dentistry vol 63 no 5 pp 529ndash536 1990

[15] W J Libman and J I Nicholls ldquoLoad fatigue of teethrestored with cast posts and cores and complete crownsrdquo TheInternational Journal of Prosthodontics vol 8 no 2 pp 155ndash161 1995

[16] W A Saupe A H Gluskin and R A Radke ldquoA comparativestudy of fracture resistance between morphologic dowel andcores and a resin-reinforced dowel system in the intraradicularrestoration of structurally compromised rootsrdquo QuintessenceInternational vol 27 no 7 pp 483ndash491 1996

[17] R W Loney W E Kotowicz and G C Mcdowell ldquoThree-dimensional photoelastic stress analysis of the ferrule effect incast post and coresrdquo The Journal of Prosthetic Dentistry vol 63no 5 pp 506ndash512 1990

[18] N Al-Hazaimeh and D L Gutteridge ldquoAn in vitro studyinto the effect of the ferrule preparation on the fractureresistance of crowned teeth incorporating prefabricated postand composite core restorationsrdquo International EndodonticJournal vol 34 no 1 pp 40ndash46 2001

[19] C Dobo-Nagy T Serban J Szabo G Nagy and MMadlena ldquoA comparison of the shaping characteristics of twonickel-titanium endodontic hand instrumentsrdquo InternationalEndodontic Journal vol 35 no 3 pp 283ndash288 2002

[20] E Asmussen A Peutzfeldt and T Heitmann ldquoStiffness elasticlimit and strength of newer types of endodontic postsrdquoJournal of Dentistry vol 27 no 4 pp 275ndash278 1999

[21] A D Kececi B Ureyen Kaya and N Adanir ldquoMicro push-out bond strengths of four fiber-reinforced composite postsystems and 2 luting materialsrdquo Oral Surgery Oral MedicineOral Pathology Oral Radiology and Endodontology vol 105no 1 pp 121ndash128 2008

[22] S Grandini C Goracci F Monticelli F R Tay and MFerrari ldquoFatigue resistance and structural characteristics offiber posts three-point bending test and SEM evaluationrdquoDental Materials vol 21 no 2 pp 75ndash82 2005

[23] H Lambjerg-Hansen and E Asmussen ldquoMechanical proper-ties of endodontic postsrdquo Journal of Oral Rehabilitation vol24 no 12 pp 882ndash887 1997

[24] A H L Tjan and S B Whang ldquoResistance to root fractureof dowel channels with various thicknesses of buccal dentinwallsrdquo The Journal of Prosthetic Dentistry vol 53 no 4 pp496ndash500 1985

[25] D Dietschi S Ardu A Rossier-Gerber and I Krejci ldquoAdapta-tion of adhesive post and cores to dentin after in vitro occlusalloading evaluation of post material influencerdquo Journal ofAdhesive Dentistry vol 8 no 6 pp 409ndash419 2006

[26] S Bouillaguet S Troesch J C Wataha I Krejci J M Meyerand D H Pashley ldquoMicrotensile bond strength betweenadhesive cements and root canal dentinrdquo Dental Materials vol19 no 3 pp 199ndash205 2003


[27] F Mannocci M Sherriff M Ferrari and T F WatsonldquoMicrotensile bond strength and confocal microscopy ofdental adhesives bonded to root canal dentinrdquo The AmericanJournal of Dentistry vol 14 no 4 pp 200ndash204 2001

[28] A R Helfer S Melnick and H Schilder ldquoDetermination ofthe moisture content of vital and pulpless teethrdquo Oral SurgeryOral Medicine Oral Pathology vol 34 no 4 pp 661ndash6701972

[29] J L Gutmann ldquoThe dentin-root complex anatomic andbiologic considerations in restoring endodontically treatedteethrdquo The Journal of Prosthetic Dentistry vol 67 no 4 pp458ndash467 1992

[30] E M Rivera and M Yamauchi ldquoSite comparisons of dentinecollagen cross-links from extracted human teethrdquo Archives ofOral Biology vol 38 no 7 pp 541ndash546 1993


[32] W H Douglas ldquoMethods to improve fracture resistanceof teethrdquo in Proceedings of the International Symposium onPosterior Composite Resin Dental Restorative Materials GVanherle and D C Smith Eds pp 433ndash441 Peter SzulcPublishing Utrecht The Netherlands 1985

[33] J Linn and H H Messer ldquoEffect of restorative procedureson the strength of endodontically treated molarsrdquo Journal ofEndodontics vol 20 no 10 pp 479ndash485 1994

[34] P Pantvisai and H H Messer ldquoCuspal deflection in molars inrelation to endodontic and restorative proceduresrdquo Journal ofEndodontics vol 21 no 2 pp 57ndash61 1995

[35] P R Cathro N P Chandler and J A Hood ldquoImpactresistance of crowned endodontically treated central incisorswith internal composite coresrdquo Endodontics and Dental Trau-matology vol 12 no 3 pp 124ndash128 1996

[36] H Rosen ldquoOperative procedures on mutilated endodonticallytreated teethrdquo The Journal of Prosthetic Dentistry vol 11 no5 pp 973ndash986 1961

[37] A G Gegauff ldquoEffect of crown lengthening and ferruleplacement on static load failure of cemented cast post-coresand crownsrdquo Journal of Prosthetic Dentistry vol 84 no 2 pp169ndash179 2000

[38] J R Pereira F de Ornelas P C Conti and A L doValle ldquoEffect of a crown ferrule on the fracture resistanceof endodontically treated teeth restored with prefabricatedpostsrdquo Journal of Prosthetic Dentistry vol 95 no 1 pp 50ndash542006

[39] J R Pereira T M Neto V d C Porto L F Pegoraro and AL do Valle ldquoInfluence of the remaining coronal structure onthe resistance of teeth with intraradicular retainerrdquo BrazilianDental Journal vol 16 no 3 pp 197ndash201 2005

[40] P R Cathro N P Chandler and J A Hood ldquoImpact resist-ance of crowned endodontically treated central incisors withinternal composite coresrdquo Endodontics and Dental Traumatol-ogy vol 12 no 3 pp 124ndash128 1996

[41] F Isidor K Broslashndum and G Ravnholt ldquoThe influence ofpost length and crown ferrule length on the resistance to cyclicloading of bovine teeth with prefabricated titanium postsrdquoInternational Journal of Prosthodontics vol 12 no 1 pp 79ndash82 1999


[43] K C Trabert and J P Cooney ldquoThe endodontically treatedtooth restorative concepts and techniquesrdquo Dental Clinics ofNorth America vol 28 no 4 pp 923ndash951 1984

[44] G W Wagnild and K L Mueller ldquoRestoration of the endo-donticallytreated toothrdquo in Pathways of the Pulp S Cohen andR C Burns Eds pp 765ndash795 Elsevier Saunders St LouisMo USA 8th edition 2001

[45] M Ferrari R Sorrentino F Zarone D Apicella R Aversa andA Apicella ldquoNon-linear viscoelastic finite element analysis ofthe effect of the length of glass fiber posts on the biomechan-ical behaviour of directly restored incisors and surroundingalveolar bonerdquo Dental Materials Journal vol 27 no 4 pp485ndash498 2008

[46] J P Standlee A A Caputo and E C Hanson ldquoRetention ofendodontic dowels effects of cement dowel length diameterand designrdquo The Journal of Prosthetic Dentistry vol 39 no 4pp 400ndash405 1978

[47] J Nissan Y Dmitry and D Assif ldquoThe use of reinforcedcomposite resin cement as compensation for reduced postlengthrdquo Journal of Prosthetic Dentistry vol 86 no 3 pp 304ndash308 2001

[48] I Nergiz P Schmage M Ozcan and U Platzer ldquoEffect oflength and diameter of tapered posts on the retentionrdquo Journalof Oral Rehabilitation vol 29 no 1 pp 28ndash34 2002

[49] M K Wu A Rrsquooris D Barkis and P R Wesselink ldquoPreva-lence and extent of long oval canals in the apical thirdrdquo OralSurgery Oral Medicine Oral Pathology Oral Radiology andEndodontics vol 89 no 6 pp 739ndash743 2000

[50] L Abramovitz R Lev Z Fuss and Z Metzger ldquoThe unpre-dictability of seal after post space preparation a fluid transportstudyrdquo Journal of Endodontics vol 27 no 4 pp 292ndash2952001

[51] M K Wu Y Pehlivan E G Kontakiotis and P R WesselinkldquoMicroleakage along apical root fillings and cemented postsrdquoThe Journal of Prosthetic Dentistry vol 79 no 3 pp 264ndash2691998

[52] H Lang Y Korkmaz K Schneider and W H M RaabldquoImpact of endodontic treatments on the rigidity of the rootrdquoJournal of Dental Research vol 85 no 4 pp 364ndash368 2006

[53] S Garoushi L V J Lassila A Tezvergil and P K VallittuldquoStatic and fatigue compression test for particulate filler com-posite resin with fiber-reinforced composite substructurerdquoDental Materials vol 23 no 1 pp 17ndash23 2007

[54] M Naumann G Sterzenbach and P Proschel ldquoEvaluationof load testing of postendodontic restorations in vitro linearcompressive loading gradual cycling loading and chewingsimulationrdquo Journal of Biomedical Materials Research B vol74 no 2 pp 829ndash834 2005


Research Article

Optimization and Implementation of Scaling-FreeCORDIC-Based Direct Digital Frequency Synthesizer forBody Care Area Network Systems

Ying-Shen Juang1 Lu-Ting Ko2 Jwu-E Chen2 Tze-Yun Sung3 and Hsi-Chin Hsin4

1 Department of Business Administration Chung Hua University Hsinchu City 300-12 Taiwan2 Department of Electrical Engineering National Central University Chungli City 320-01 Taiwan3 Department of Microelectronics Engineering Chung Hua University Hsinchu City 300-12 Taiwan4 Department of Computer Science and Information Engineering National United University Miaoli 360-03 Taiwan

Correspondence should be addressed to Tze-Yun Sung bobsungchuedutw

Received 11 August 2012 Accepted 15 September 2012


Copyright copy 2012 Ying-Shen Juang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Coordinate rotation digital computer (CORDIC) is an efficient algorithm for computations of trigonometric functions Scaling-free-CORDIC is one of the famous CORDIC implementations with advantages of speed and area In this paper a novel directdigital frequency synthesizer (DDFS) based on scaling-free CORDIC is presented The proposed multiplier-less architecture withsmall ROM and pipeline data path has advantages of high data rate high precision high performance and less hardware cost Thedesign procedure with performance and hardware analysis for optimization has also been given It is verified by Matlab simulationsand then implemented with field programmable gate array (FPGA) by Verilog The spurious-free dynamic range (SFDR) is over8685 dBc and the signal-to-noise ratio (SNR) is more than 8112 dB The scaling-free CORDIC-based architecture is suitable forVLSI implementations for the DDFS applications in terms of hardware cost power consumption SNR and SFDR The proposedDDFS is very suitable for medical instruments and body care area network systems

1 Introduction

Direct digital frequency synthesizer (DDFS) has been widelyused in the modern communication systems DDFS is prefer-able to the classical phase-locked-loop- (PLL-) based synthe-sizer in terms of switching speed frequency resolution andphase noise which are beneficial to the high-performancecommunication systems Figure 1 depicts the conventionalDDFS architecture [1] which consists of a phase accumu-lator a sinecosine generator a digital-to-analog converter(DAC) and a low-pass filter (LPF) As noted two inputs thereference clock and the frequency control word (FCW) areused the phase accumulator integrates FCW to produce anangle in the interval of [0 2π) and the sinecosine generatorcomputes the sinusoidal values In practice the sinecosinegenerator is implemented digitally and thus followed by digi-tal-to-analog conversion and low-pass filtering for analogue

outputs Such systems can be applied in many fieldsespecially in industrial biological and medical applications[2ndash4]

The simplest way to implement the sinecosine generatoris to use ROM lookup table (LUT) However a large ROMis needed [5] Several efficient compression techniques havebeen proposed to reduce the lookup table size [5ndash10] Thequadrant compression technique can compress the lookuptable and then reduce the ROM size by 75 [6] The Sunder-land architecture splits the ROM into two smaller memories[7] and the Nicholas architecture improves the Sunderlandarchitecture to achieve a higher ROM-compression ratio(32 1) [8] The ROM size can be further reduced by usingthe polynomial approximations [11ndash18] or CORDIC algo-rithm [19ndash27] In the polynomial approximations-basedDDFSs the interval of [0π4] is divided into subintervalsand sinecosine functions are evaluated in each subinterval


PhaseFCW accumulator

Fclk

AA

θ Sinecosinegenerator

Digital toanalog

converterLow pass filter

cosθ

sinθ

Figure 1 The conventional DDFS architecture

The polynomial approximations-based DDFS requires aROM to store the coefficients of the polynomials and thepolynomial evaluation hardware with multipliers In thecircular mode of CORDIC which is an iterative algorithmto compute sinecosine functions an initial vector is rotatedwith a predetermined sequence of subangles such that thesummation of the rotations approaches the desired angle[28 29] CORDIC has been widely used for the sinecosinegenerator of DDFS [19ndash27] Compared to the lookup table-based DDFS the CORDIC-based DDFS has the advantageof avoiding the exponential growth of hardware complexitywhile the output word size increases [30ndash33]

In Figure 1 the word length of the phase accumulator isv bits thus the period of the output signal is as follows

To = 2vTs

FCW (1)

where FCW is the phase increment and Ts denotes the sampl-ing period It is noted that the output frequency can be writ-ten by

Fo = 1T0= Fs

2vmiddot FCW (2)

According to the equation above the minimum changeof output frequency is given by

ΔFomin = Fs2v

(FCW + 1)minus Fs2v

FCW = Fs2v (3)

Thus the frequency resolution of DDFS is dependent on theword length of the phase accumulator as follows

ΔFo ge Fs2v (4)

The bandwidth of DDFS is defined as the differencebetween the highest and the lowest output frequencies Thehighest frequency is determined by either the maximumclock rate or the speed of logic circuitries the lowest fre-quency is dependent on FCW Spurious-free dynamic range(SFDR) is defined as the ratio of the amplitude of the desiredfrequency component to that of the largest undesired one atthe output of DDFS which is often represented in dBc asfollows

SFDR = 20 log(Ap

As

)= 20 log

(Ap

)minus 20 log(As) (5)

where Ap is the amplitude of the desired frequency compo-nent and As is the amplitude of the largest undesired one

In this paper a novel DDFS architecture based on thescaling-free CORDIC algorithm [34] with ROM mapping ispresented The rest of the paper is organized as follows InSection 2 CORDIC is reviewed briefly In Section 3 theproposed DDFS architecture is presented In Section 4 thehardware implementation of DDFS is given Conclusion canbe found in Section 5

2 The CORDIC Algorithm

CORDIC is an efficient algorithm that evaluates variouselementary functions including sine and cosine functions Ashardware implementation might only require simple addersand shifters CORDIC has been widely used in the high speedapplications

21 The CORDIC Algorithm in the Circular Coordinate Sys-tem A rotation of angle θ in the circular coordinate systemcan be obtained by performing a sequence of micro-rotationsin the iterative manner Specifically a vector can be succes-sively rotated by the use of a sequence of pre-determinedstep-angles α(i) = tanminus1(2minusi) This methodology can beapplied to generate various elementary functions in whichonly simple adders and shifters are required The conven-tional CORDIC algorithm in the circular coordinate systemis as follows [28 29]

x(i + 1) = x(i)minus σ(i)2minusi y(i) (6)

y(i + 1) = y(i) + σ(i)2minus jx(i) (7)

z(i + 1) = z(i)minus σ(i)α(i) (8)

α(i) = tanminus12minusi (9)

where σ(i) isin minus1 +1 denotes the direction of the ith micro-rotation σi = sign(z(i)) with z(i) rarr 0 in the vector rotationmode [34] σi = minus sign(x(i))middotsign(y(i)) with y(i) rarr 0 in theangle accumulated mode [34] the corresponding scale factork(i) is equal to

radic1 + σ2(i)2minus2i and i = 0 1 n minus 1 The

product of the scale factors after n micro-rotations is givenby

K1 =nminus1prodi=0

k(i) =nminus1prodi=0

radic1 + 2minus2i (10)

In the vector rotation mode sin θ and cos θ can be ob-tained with the initial value (x(0) y(0)) = (1K1 0) More


specifically xout and yout are computed from the initial value(xin yin) = (x(0) y(0)) as follows

[xout

yout

]= K1

[cos θ minus sin θsin θ cos θ

][xin

yin

] (11)

22 Scaling-Free CORDIC Algorithm in the Circular Coordi-nate System Based on the following approximations of sineand cosine functions

sinα(i) sim= α(i) = 2minusi

cosα(i) sim= 1minus α2(i)2

= 1minus 2minus(2i+1)(12)

the scaling-free CORDIC algorithm is thus obtained by using(6) (7) and the above In which the iterative rotation is asfollows[

x(i + 1)y(i + 1)

]=[

1minus 2minus(2i+1) 2minusi

minus2minusi 1minus 2minus(2i+1)

][x(i)y(i)

]

z(i + 1) = z(i)minus 2minusi

(13)

For the word length of w bits it is noted that the im-plementation of scaling-free CORDIC algorithm utilizes fourshifters and four adders for each micro-rotation in the firstw2-microrotations it reduces two shifters and two addersfor each microrotation in the last w2-micro-rotations [2434 35]

3 Design and Optimization of the Scaling-FreeCORDIC-Based DDFS Architecture

In this section the architecture together with performanceanalysis of the proposed DDFS is presented It is a combi-nation of the scaling-free-CORDIC algorithm and LUT thishybrid approach takes advantage of both CORDIC and LUTto achieve high precision and high data rate respectively Theproposed DDFS architecture consists of phase accumulatorradian converter sinecosine generator and output stage

31 Phase Accumulator Figure 2 shows the phase accumu-lator which consists of a 32-bit adder to accumulate thephase angle by FCW recursively At time n the output ofphase accumulator is φ = (n middot FCW)232 and the sinecosinegenerator produces sin((n middot FCW)232) and cos((n middot FCW)232) The load control signal is used for FCW to be loadedinto the register and the reset signal is to initialize the contentof the phase accumulator to zero

32 Radian Converter In order to convert the output of thephase accumulator into its binary representation in radiansthe following strategy has been adopted Specifically anefficient ROM reduction scheme based on the symmetryproperty of sinusoidal wave can be obtained by simple logicoperations to reconstruct the sinusoidal wave from its firstquadrant part only In which the first two MSBs of an angle

RegFCW

Adder

(32-bit)

Reg

Load

Reset

φ

Figure 2 The phase accumulator in DDFS

π

2+ φ

φ

π + φ

3π2

+ φ

Figure 3 Symmetry-based map of an angle in either the secondthird or fourth quadrant to the corresponding angle in the firstquadrant

indicate the quadrant of the angle in the circular coordinateand the third MSB indicates the half portion of the quadrantthus the first three MSBs of an angle are used to controlthe interchangenegation operation in the output stage Asshown in Figure 3 the corresponding angles of φprime in the sec-ond third and fourth quadrants can be mapped into the firstquadrant by setting the first two MSBs to zero The radian ofφprime is therefore obtained by θ = (π4)φprime which can be imple-mented by using simple shifters and adders array shown inFigure 4 Note that the third MSB of any radian value in theupper half of a quadrant is 1 and the sinecosine of an angleγ in the upper half of a quadrant can be obtained from thecorresponding angle in the lower half as shown in Figure 5More specifically as cos γ = sin((π2) minus γ) and sin γ =cos((π2) minus γ) the normalized angle can be obtained byreplacing θ with θprime = 05minusθ while the third MSB is 1 In casethe third MSB is 0 there is no need to perform the replace-ment as θprime = θ

33 SineCosine Generator As the core of the DDFS archi-tecture the sinecosine generator produces sinusoidal wavesbased on the output of the radian converter Without lossof generality let the output resolution be of 16 bits for thesinecosine generator consisting of a cascade of w processorseach of which performs the sub-rotation by a fixed angle of2minusi radian as follows

x(i + 1) =(

1minus σ(i)2minus(2i+1))x(i) + σ(i)2minusi y(i)

y(i + 1) =(

1minus σ(i)2minus(2i+1))y(i)minus σ(i)2minusix(i)

(14)


Table 1 The hardware costs in 16-bit DDFS with respect to the number of the replaced CORDIC stages (m the number of the replacedCORDIC stages 16-bit adder 200 gates 16-bit shift 90 gates and 1-bit ROM 1 gate)

m 0 1 2 3 4 5 6 7

CORDIC processor requirement

CORDIC processor-A 7 5 4 3 2 1 0 0

CORDIC processor-B 9 9 9 9 9 9 9 8

Hardware cost

16-bit Adders 46 38 34 30 26 22 18 16

16-bit Shifters 46 38 34 30 26 22 18 16

ROM size (bits) 4 times 16 8 times 16 14 times 16 26 times 16 50 times 16 102 times 16 194 times 16 386 times 16

Total gate counts 13404 11148 10084 9116 8340 8012 8324 10816

Table 2 Control signals of the output stage

MSBrsquos of φ φ xinv yinv swap cos 2πφ sin 2πφ

0 0 0 0 lt 2πφ ltπ

40 0 0 cos θ sin θ

0 0 1π

4lt 2πφ lt

π

20 0 1 sin θ cos θ

0 1 0π

2lt 2πφ lt

3π4

0 1 1 minus sin θ cos θ

0 1 13π4

lt 2πφ lt π 1 0 0 minus cos θ sin θ

1 0 0 minusπ lt 2πφ lt minus3π4

1 1 0 minus cos θ minus sin θ

1 0 1 minus3π4

lt 2πφ lt minusπ

21 1 1 minus sin θ minus cos θ

1 1 0 minusπ

2lt 2πφ lt minusπ

41 0 1 sin θ minus cos θ

1 1 1 minusπ

4lt 2πφ lt 0 0 1 0 cos θ minus sin θ

Table 3 Comparisons of the proposed DDFS with other related works

DDFSKang and

Swartzlander2006 [23]

Sharma et al2009 [26]

Jafari et al 2005[17]

Ashrafi andAdhami 2007

[18]

Yi et al2006 [6]

De Caroet al 2009

[27]

This workJuang et al

2012

Process (μm) 013 mdash 05 035 035 025 018

Core area (mm2) 035 mdash mdash mdash mdash 051 0204

Maximum sampling rate(MHz)

1018 230 106 210 100 385 500

Power consumption (mW) 0343 mdash mdash 112 081 04 0302

SFDR (dBc) 90 54 mdash 722 80 90 8685

SNR (dB) mdash mdash mdash 67 mdash 70 8112

Output resolution (bit) 17 10 14 12 16 13 16

Tuning latency (clock) mdash mdash 33 mdash mdash mdash 11

For 8 le i lt 16

x(i + 1) = x(i) + σ(i)2minusi y(i)

y(i + 1) = y(i)minus σ(i)2minusix(i)(15)

where σ(i) isin 1 0 representing the positive or zero subrota-tion respectively Figure 6 depicts the CORDIC processor-Afor the first 7 microrotations which consists of four 16-bit

adders and four 16-bit shifters The CORDIC processor-Bwith two 16-bit adders and two 16-bit shifters for the last 9microrotations is shown in Figure 7

The first m CORDIC stages can be replaced by simpleLUT to reduce the data path at the cost of hardware com-plexity increasing exponentially Table 1 depicts the hardwarecosts in 16-bit DDFS with respect to the number of thereplaced CORDIC-stages where each 16-bit adder 16-bit


Input

1-bitshifter shifter shifter shifter shifter shifter

2-bit 5-bit 8-bit 12-bit 18-bit

CSA(32) CSA(32)

CSA(42)

CLA

Output

Figure 4 The constant (π4) multiplier

π

2π

4

π

2minus γ

γ

Figure 5 π4-mirror map of an angle γ above π4 to the corres-ponding angle π2minus γ below π4

xin

yin

+

+

+

+

+

minus

minus

minus

2i + 1-bitshifter

i-bitshifter

i-bit

shifter2i + 1-bit

shifter

x

y

xout

yout

Figure 6 The CORDIC processor-A

xoutxin

yin yout

+

+

+

minus

i-bitshifter

i-bitshifter

x

y

Figure 7 The CORDIC processor-B

0 1 2 3 4 5 6 706

07

08

09

1

11

12

13

14

15times104

m

Gat

es

Figure 8 Hardware requirements with respect to the replacedCORDIC stages

shifter and 1-bit memory require 200 gates 90 gates and 1gate [36] respectively Figure 8 shows the hardware require-ments with respect to the number of the replaced CORDIC-stages [24] Figure 9 shows the SFDRSNRs with respect to


75

80

85

90

95

m

SFD

RS

NR

(dB

)

SFDR (Fout = Fclk29)SNR (Fout = Fclk29)SFDR (Fout = Fclk27)

SNR (Fout = Fclk27)SFDR (Fout = Fclk25)SNR (Fout = Fclk25)

0 1 2 3 4 5

Figure 9 SFDRSNRs with respect to the replaced CORDIC-stages

xinv

yinv

Swap

sinθ

cosθ

sin2πφ

cos2πφ0

1

1

0

Figure 10 The output stage

32 3

1

Accumulator

FCW

Constant

multiplier

Quadrant

mirror

32

22 19 19

16

916

ROM CORDICprocessor

A

16

16

16

1616

16 16

16

CORDIC processor B array

I sim IXOutput

stage

cos output

sin outputbits102times 16

Figure 11 The proposed DDFS architecture

the replaced CORDIC-stages [25] As one can expect basedon the above figures there is a tradeoff between hardwarecomplexity and performance in the design of DDFS

34 Output Stage Figure 10 shows the architecture of outputstage which maps the computed sin θ and cos θ to the desired

sinφ and cosφ As mentioned previously the above mappingcan be accomplished by simple negation andor interchangeoperations The three control signals xinv yinv and swapderived from the first three MSBs of φ are shown in Table 2xinv and yinv are for the negation operation of the outputand swap for the interchange operation


minus140

minus120

minus100

minus80

minus60

minus40

minus20

0

Normalized frequencySF

DR

Figure 12 SFDR of the proposed DDFS architecture at output frequency Fclk25

PCUSB 2

MCU FPGA

Architecture evaluationboard

Figure 13 Block diagram and circuit board of the architecture development and verification platform

AlgorithmFunctionalsimulation(matlab)

Hardware codeimplementation

(verilog)

CKT tracing(debussy)

Comprehensivesimulation and

debug(modelsim)

Logic synthesis(design compiler)

Physicalcompilation

(astro)

CKT evaluation(DRCLVSPVS)

Tape out

Figure 14 Cell-based design flow

Figure 15 Layout view of the proposed scaling-free-CORDIC-based DDFS

4 Hardware Implementation ofthe Scaling-Free CORDIC-Based DDFS

In this section the proposed low-power and high-perfor-mance DDFS architecture (m = 5) is presented Figure 11depicts the system block diagram SFDR of the proposedDDFS architecture at output frequency Fclk25 is shown inFigure 12 As one can see the SFDR of the proposed archi-tecture is more than 8685 dBc

The platform for architecture development and verifi-cation has also been designed as well as implemented toevaluate the development cost [37ndash40] The proposed DDFSarchitecture has been implemented on the Xilinx FPGAemulation board [41] The Xilinx Spartan-3 FPGA has beenintegrated with the microcontroller (MCU) and IO inter-face circuit (USB 20) to form the architecture developmentand verification platform


Figure 13 depicts block diagram and circuit board of thearchitecture development and evaluation platform In whichthe microcontroller read data and commands from PC andwrites the results back to PC via USB 20 bus the XilinxSpartan-3 FPGA implements the proposed DDFS architec-ture The hardware code in Verilog runs on PC with theModelSim simulation tool [42] and Xilinx ISE smart com-piler [43] It is noted that the throughput can be improvedby using the proposed architecture while the computationaccuracy is the same as that obtained by using the conven-tional one with the same word length Thus the proposedDDFS architecture is able to improve the power consumptionand computation speed significantly Moreover all the con-trol signals are internally generated on-chip The proposedDDFS provides both high performance and less hardware

The chip has been synthesized by using the TSMC018 μm 1P6M CMOS cell libraries [44] The physical circuithas been synthesized by the Astro tool The circuit has beenevaluated by DRC LVS and PVS [45] Figure 14 shows thecell-based design flow

Figure 15 shows layout view of the proposed scaling-free CORDIC-based DDFS The core size obtained by theSynopsys design analyzer is 452 times 452μm2 The power con-sumption obtained by the PrimePower is 0302 mW withclock rate of 500 MHz at 18 V The tuning latency is 11 clockcycles All of the control signals are internally generated on-chip The chip provides both high throughput and low gatecount

5 Conclusion

In this paper we present a novel DDFS architecture-basedon the scaling-free CORDIC algorithm with small ROMand pipeline data path Circuit emulation shows that theproposed high performance architecture has the advantagesof high precision high data rate and simple hardware For16-bit DDFS the SFDR of the proposed architecture is morethan 8685 dBc As shown in Table 3 the proposed DDFSis superior to the previous works in terms of SFDR SNRoutput resolution and tuning latency [6 17 18 26 27]According to the high performance of the proposed DDFS itis very suited for medical instruments and body care networksystems [46ndash49] The proposed DDFS with the use of theportable Verilog is a reusable IP which can be implementedin various processes with tradeoffs of performance area andpower consumption

Acknowledgment

The National Science Council of Taiwan under GrantsNSC100-2628-E-239-002-MY2 and NSC100-2410-H-216-003 supported this work

References

[1] J Tierney C Rader and B Gold ldquoA digital frequency syn-thesizerrdquo IEEE Transactions on Audio and Electroacoustics vol19 no 1 pp 48ndash57 1971


[3] Z Teng A J Degnan U Sadat et al ldquoCharacterization ofhealing following atherosclerotic carotid plaque rupture inacutely symptomatic patients an exploratory study using invivo cardiovascular magnetic resonancerdquo Journal of Cardiovas-cular Magnetic Resonance vol 13 article 64 2011

[4] S Chen and X Li ldquoFunctional magnetic resonance imagingfor imaging neural activity in the human brain the annualprogressrdquo Computational and Mathematical Methods in Medi-cine vol 2012 Article ID 613465 9 pages 2012

[5] J Vankka ldquoMethods of mapping from phase to sine amplitudein direct digital synthesisrdquo in Proceedings of the 50th IEEEInternational Frequency Control Symposium pp 942ndash950 June1996

[6] S C Yi K T Lee J J Chen and C H Lin ldquoA low-powerefficient direct digital frequency synthesizer based on new two-level lookup tablerdquo in Proceedings of the Canadian Conferenceon Electrical and Computer Engineering (CCECE rsquo06) pp 963ndash966 May 2006

[7] D A Sunderland R A Strauch S S Wharfield H T Peter-son and C R Cole ldquoCMOSSOS frequency synthesizer LSIcircuit for spread spectrum communicationsrdquo IEEE Journal ofSolid-State Circuits vol 19 no 4 pp 497ndash506 1984

[8] H T Nicholas H Samueli and B Kim ldquoOptimization ofdirect digital frequency synthesizer performance in the pre-sence of finite word length effectsrdquo in Proceedings of the 42ndAnnual Frequency Control Symposium pp 357ndash363 June 1988

[9] L A Weaver and R J Kerr ldquoHigh resolution phase to sineamplitude conversionrdquo US Patent 4 905 177 1990

[10] A Bonfanti D De Caro A D Grasso S Pennisi C Samoriand A G M Strollo ldquoA 25-GHz DDFS-PLL with 18-MHzbandwidth in 035-μm CMOSrdquo IEEE Journal of Solid-StateCircuits vol 43 no 6 pp 1403ndash1413 2008

[11] A Bellaouar M S Orsquobrecht A M Fahim and M I ElmasryldquoLow-power direct digital frequency synthesis for wirelesscommunicationsrdquo IEEE Journal of Solid-State Circuits vol 35no 3 pp 385ndash390 2000

[12] A Bellaouar M S OrsquoBrecht and M I Elmasry ldquoLow-powerdirect digital frequency synthesizer architecturerdquo US Patent 5999 581 1999

[13] M M El Said and M I Elmasry ldquoAn improved ROM com-pression technique for direct digital frequency synthesizersrdquoin Proceedings of the IEEE International Symposium on Circuitsand Systems pp 437ndash440 May 2002

[14] G C Gielis R van de Plassche and J van Valburg ldquoA540-MHz 10-b polar-to-Cartesian converterrdquo IEEE Journal ofSolid-State Circuits vol 26 no 11 pp 1645ndash1650 1991

[15] D De Caro E Napoli and A G M Strollo ldquoDirect digitalfrequency synthesizers with polynomial hyperfolding tech-niquerdquo IEEE Transactions on Circuits and Systems II vol 51no 7 pp 337ndash344 2004

[16] Y H Chen and Y A Chau ldquoA direct digital frequency syn-thesizer based on a new form of polynomial approximationsrdquoIEEE Transactions on Consumer Electronics vol 56 no 2 pp436ndash440 2010

[17] H Jafari A Ayatollahi and S Mirzakuchaki ldquoA low powerhigh SFDR ROM-less direct digital frequency synthesizerrdquoin Proceedings of the IEEE Conference on Electron Devices andSolid-State Circuits (EDSSC rsquo05) pp 829ndash832 December 2005

[18] A Ashrafi and R Adhami ldquoTheoretical upperbound of thespurious-free dynamic range in direct digital frequency syn-thesizers realized by polynomial interpolation methodsrdquo IEEE


Transactions on Circuits and Systems I vol 54 no 10 pp2252ndash2261 2007

[19] S Nahm K Han and W Sung ldquoCORDIC-based digital quad-rature mixer comparison with a ROM-based architecturerdquo inProceedings of the IEEE International Symposium on Circuitsand Systems (ISCAS rsquo98) pp 385ndash388 June 1998

[20] A Madisetti A Y Kwentus and A N Willson ldquo100-MHz 16-b direct digital frequency synthesizer with a 100-dBc spuri-ous-free dynamic rangerdquo IEEE Journal of Solid-State Circuitsvol 34 no 8 pp 1034ndash1043 1999

[21] A Madisetti and A Y Kwentus ldquoMethod and apparatus fordirect digital frequency synthesizerrdquo US Patent 5 737 2531998

[22] E Grayver and B Daneshrad ldquoDirect digital frequency syn-thesis using a modified CORDICrdquo in Proceedings of the IEEEInternational Symposium on Circuits and Systems (ISCAS rsquo98)vol 5 pp 241ndash244 June 1998

[23] C Y Kang and E E Swartzlander Jr ldquoDigit-pipelined directdigital frequency synthesis based on differential CORDICrdquoIEEE Transactions on Circuits and Systems I vol 53 no 5 pp1035ndash1044 2006

[24] T Y Sung and H C Hsin ldquoDesign and simulation of reusableIP CORDIC core for special-purpose processorsrdquo IET Com-puters and Digital Techniques vol 1 no 5 pp 581ndash589 2007

[25] T Y Sung L T Ko and H C Hsin ldquoLow-power and high-SFDR direct digital frequency synthesizer based on hybridCORDIC algorithmrdquo in Proceedings of the IEEE InternationalSymposium on Circuits and Systems (ISCAS rsquo09) pp 249ndash252May 2009

[26] S Sharma P N Ravichandran S Kulkarni M Vanitha andP Lakshminarsimahan ldquoImplementation of Para-CORDICalgorithm and itrsquos applications in satellite communicationrdquoin Proceedings of the International Conference on Advances inRecent Technologies in Communication and Computing (ART-Com rsquo09) pp 266ndash270 October 2009

[27] D De Caro N Petra and A G M Strollo ldquoDigital syn-thesizermixer with hybrid CORDICmdashmultiplier architectureerror analysis and optimizationrdquo IEEE Transactions on Circuitsand Systems I vol 56 no 2 pp 364ndash373 2009

[28] J Volder ldquoThe CORDIC trigonometric computing tech-niquerdquo IRE Transactions on Electronic Computers vol 8 no3 pp 330ndash334 1959

[29] J S Walther ldquoA unified algorithm for elementary functionsrdquoin Proceedings of the Joint Computer Conference pp 379ndash3851971

[30] S Chen W Huang C Cattani and G Altieri ldquoTraffic dynam-ics on complex networks a surveyrdquo Mathematical Problems inEngineering vol 2012 Article ID 732698 23 pages 2012

[31] W Huang and S Y Chen ldquoEpidemic metapopulation modelwith traffic routing in scale-free networksrdquo Journal of Statisti-cal Mechanics vol 2011 no 12 Article ID P12004 19 pages2011

[32] H Shi W Wang N M Kwok and S Y Chen ldquoGame theoryfor wireless sensor networks a surveyrdquo Sensors vol 12 no 7pp 9055ndash9097 2012


[34] Y H Hu ldquoCORDIC-based VLSI architectures for digital signalprocessingrdquo IEEE Signal Processing Magazine vol 9 no 3 pp16ndash35 1992

[35] K Maharatna A S Dhar and S Banerjee ldquoA VLSI arrayarchitecture for realization of DFT DHT DCT and DSTrdquo Sig-nal Processing vol 81 no 9 pp 1813ndash1822 2001

[36] T Y Sung ldquoMemory-efficient and high-speed split-radix FFTIFFT processor based on pipelined CORDIC rotationsrdquo IEEProceedings vol 153 no 4 pp 405ndash410 2006

[37] C Cattani ldquoOn the existence of wavelet symmetries in archaeaDNArdquo Computational and Mathematical Methods in Medicinevol 2012 Article ID 673934 16 pages 2012

[38] M Li ldquoApproximating ideal filters by systems of fractionalorderrdquo Computational and Mathematical Methods in Medicinevol 2012 Article ID 365054 6 pages 2012

[39] S Chen Y Zheng C Cattani and W Wang ldquoModeling ofbiological intelligence for SCM system optimizationrdquo Com-putational and Mathematical Methods in Medicine vol 2012Article ID 769702 30 pages 2012

[40] C Cattani ldquoHarmonic wavelet approximation of randomfractal and high frequency signalsrdquo Telecommunication Sys-tems vol 2009 pp 207ndash217 2009

[41] SMIMS Technology Corp 2010 httpwwwsmimscom[42] ModelSimmdashSimulation and debug 2010 httpmodelcom

contentmodelsim-pe-simulation-and-debug[43] Xilinx FPGA products 2010 httpwwwxilinxcom

products[44] Taiwan Semiconductor Manufacturing Company (TSMC)

Hsinchu City Taiwan and National Chip ImplementationCenter (CIC) National Science Council Hsinchu City Tai-wan TSMC 018 CMOS Design Libraries and Technical Datav16 2010

[45] Cadence Design Systems 2010 httpwwwcadencecomproductspagesdefaultaspx

[46] D Prutchi and M Norris Design and Development of MedicalElectronic Instrumentation A Practical Perspective of the DesignConstruction and Test of Medical Devices John Wiley amp Sons2005

[47] N Li J Guo H S Nie W Yi H J Liu and H Xu ldquoDesignof embedded bio-impedance analyzer based on digital autobalancing bridge methodrdquo Applied Mechanics and Materialsvol 136 pp 396ndash401 2011

[48] K H Lin W H Chiu and J D Tseng ldquoLow-complexityarchitecture of carrier frequency offset estimation and com-pensation for body area network systemsrdquo Computer andMathematics with Applications vol 64 no 5 pp 1400ndash14082012

[49] J Guo and P Dong ldquoDesign of dual phase signals generatorbased on AD9833rdquo Lecture in Electrical Engineering vol 139pp 7ndash13 2012


Research Article

A Rate-Distortion-Based Merging Algorithm forCompressed Image Segmentation

Ying-Shen Juang1 Hsi-Chin Hsin2 Tze-Yun Sung3 Yaw-Shih Shieh3 and Carlo Cattani4

1 Department of Business Administration Chung Hua University Hsinchu City 30012 Taiwan2 Department of Computer Science and Information Engineering National United University Miaoli 36003 Taiwan3 Department of Electronics Engineering Chung Hua University Hsinchu City 30012 Taiwan4 Department of Mathematics University of Salerno Via Ponte Don Melillo 84084 Fisciano Italy





Original images are often compressed for the communication applications In order to avoid the burden of decompressingcomputations it is thus desirable to segment images in the compressed domain directly This paper presents a simple rate-distortion-based scheme to segment images in the JPEG2000 domain It is based on a binary arithmetic code table used in theJPEG2000 standard which is available at both encoder and decoder thus there is no need to transmit the segmentation resultExperimental results on the Berkeley image database show that the proposed algorithm is preferable in terms of the running timeand the quantitative measures probabilistic Rand index (PRI) and boundary displacement error (BDE)

1 Introduction

Data segmentation is important in many applications [1ndash6]Early research work on image segmentation is mainly ata single scale especially for medical images [7ndash9] Inthe human visual system (HVS) the perceived image isdecomposed into a set of band-pass subimages by meansof filtering with simple visual cortical cells which canbe well modeled by Gabor filters with suitable spatialfrequencies and orientations [10] Other state-of-the-artmultiscale techniques are based on wavelet transform (WT)which provides an efficient multiresolution representationin accord with the property of HVS [11] Specifically thehigher-detail information of an image is projected onto ashorter basis function with higher spatial resolution VariousWT-based features and algorithms were proposed in theliterature for image segmentation at multiple scales [12ndash14]

For the communication applications original images arecompressed in order to make good use of memory spaceand channel bandwidth Thus it is desirable to segment acompressed image directly The Joint Photographic ExpertGroup (JPEG) standard adopts discrete cosine transform for

subband image coding In order to improve the compressionperformance of JPEG with more coding advantages forexample embedded coding and progressive transmissionthe JPEG2000 standard adopts WT as the underlying trans-form algorithm Specifically embedding coding is to code animage into a single code stream from which the decodedimage at any bit rate can be obtained The embedded codestream of an image is organized in decreasing order ofsignificance for progressive transmission over band-limitedchannels This property is particularly desirable for theInternet streaming and database browsing applications [15ndash17] Zargari proposed an efficient method for JPEG2000image retrieval in the compressed domain [18] Pi proposeda simple scheme to estimate the probability mass function(PMF) of wavelet subbands by counting the number of 1-bitsand used the global PMF as features to retrieve similar imagesfrom a large database [19] For image segmentation howeverthe local PMF is needed In [20] we proposed a simplemethod to compute the local PMF of wavelet coefficientsbased on the MQ table It can be applied to a JPEG2000 codestream directly and the local PMF can be used as features tosegment a JPEG2000 image in the compressed domain


Motivated by the idea behind the postcompression ratedistortion (PCRD) algorithm [15] we propose a simplealgorithm called the rate-distortion-based merging (RDM)algorithm for JPEG2000 image segmentation It can beapplied to a JPEG2000 code stream instead of the decodedimage As a result the burden of decoding computationcan be saved In addition the RDM algorithm is basedon the MQ table which is available at both encoder anddecoder thus no overhead transmission is added froma segmentation viewpoint The remainder of the paperproceeds as follows In Section 2 the JPEG2000 standardis reviewed briefly In Section 3 the MQ-table-based ratedistortion slope (MQRDS) is proposed to examine thesignificance of wavelet segments based on which the RDMalgorithm is thus proposed to merge wavelet segments withsimilar characteristics Experimental results on the Berkeleycolor image database are given in Section 4 Conclusions canbe found in Section 5

2 Review of the JPEG2000 Standard

The core module of the JPEG2000 standard is the embeddedblock coding with optimized truncation (EBCOT) algorithm[15] which adopts wavelet transform (WT) as the under-lying method to decompose an image into multiresolutionsubbands WT has many desirable properties for examplethe self-similarity of wavelet coefficients across subbands ofthe same orientation the joint space-spatial frequency local-ization with orientation selectivity and the energy clusteringwithin each subband [11] The fundamental idea behindEBCOT is to take advantage of the energy clustering propertyof wavelet coefficients EBCOT is a two-tier algorithm tier-1 consists of bit plane coding (BPC) followed by arithmeticcoding (AC) tier-2 is primarily for optimal rate controlThree coding passes namely the significance propagation(SP) pass the magnitude refinement (MR) pass and theclean-up (CU) pass are involved with four primitive codingoperations namely the significance coding operation thesign coding operation the magnitude refinement codingoperation and the clean-up coding operation For a waveletcoefficient that is currently insignificant if any of the 8neighboring coefficients are already significant it is codedin the SP pass using the significance coding operationotherwise it is coded in the CU pass using the clean-upcoding operation If this coefficient becomes significant itssign is then coded using the sign coding operation Themagnitude of the significant wavelet coefficients that havebeen found in the previous coding passes is updated using themagnitude refinement coding operation in the MR pass Theresulting code streams of coding passes can be compressedfurther by using a context-based arithmetic coder knownas the MQ coder JPEG2000 defines 18 context labels forthe MQ coder and stores their respective probability modelsin the MQ table Specifically 10 context labels are used forthe significance coding operation and the clean-up codingoperation 5 context labels are used for the sign codingoperation and 3 context labels are used for the magnituderefinement coding operation

In JPEG2000 a large image can be partitioned intononoverlapped subimages called tiles for computationalsimplicity WT is then applied to the tiles of an imagefor subband decompositions and each wavelet subband isfurther divided into small blocks called code blocks Thecode blocks of an image are independently coded from themost significant bit plane (MSB) to the least significant bitplane (LSB) Based on the true rate-distortion slope (RDS)of code blocks JPEG2000 concatenates the significant codestreams with large RDS using the post compression ratedistortion (PCRD) algorithm for optimal rate control Morespecifically let Bi be a set of code blocks in the wholeimage The code stream of Bi can be terminated at the endof a coding pass say ni with the bit rate denoted by Rni

i all the end points of coding passes are possible truncationpoints The distortion incurred by discarding the codingpasses after ni is denoted by Dni

i PCRD selects the optimaltruncation points to minimize the overall distortion D =sum

i Dnii subject to the rate constraint R = sumi R

nii le Rc where

Rc is a given bitrate It is noted that the coding passes withnonincreasing RDS are candidates for the optimal truncationpoints Motivated by the idea of the above a new techniqueis proposed to segment JPEG2000 images in the JPEG2000domain the detail is given in the following section

3 Image Segmentation inthe JPEG2000 Domain

This section presents a simple merging algorithm forJPEG2000 image segmentation It merges wavelet segmentswith similar characteristics based on the change of theestimated RDS in the JPEG2000 domain Thus the proposedalgorithm can be applied to a JPEG2000 code stream withoutdecompressing complexity

31 MQ Table-Based Probability Mass Function InJPEG2000 the wavelet coefficients of an image are quant-ized with bit planes and binary wavelet variables arealmost independent across bit planes The probability massfunction (PMF) known as the wavelet histogram [19] can beapproximated by

P(|c| = x) =nminus1prodj=0

Pj

(xj)

x =nminus1sumj=0

xj middot 2 j xj isin 0 1(1)

where x is the magnitude of a wavelet coefficient c Pj()is the PMF of the binary wavelet variable xj on the jthbit plane and n is the number of bit planes For imagesegmentation the local PFM is needed We had proposed asimple method to estimate the local PMF based on the MQtable [20] Specifically the probability of 1-bitP j(xj = 1) isgiven by

Pj

(xj = 1

)=QeminusValue if MPS = 0

1minusQeminusValue if MPS = 1(2)


No

Yes

Initial superpixels

Segmentation result

JPEG2000 code stream

MQ table-based LPMF

Merge segments m and nmaxmn

ΔSmn gt Td

Figure 1 Flowchart of the RDM algorithm

whereQeminusValue is the probability of the less probable symbol(LPS) which is stored in the MQ table and MPS denotes themore probable symbol The set Pj(xj = 1) j = 0 nminus1obtained from the MQ table can be used to compute thelocal PMF As the MQ table is also available at decoderno overhead transmission is needed for the computation ofPMF In addition JPEG2000 defines only 18 context labels tomodel the binary wavelet variables thus the computation ofPMF is simple

32 MQ Table-Based Rate Distortion Slope and Merging Algo-rithm Motivated by the post compression rate distortion(PCRD) algorithm [15] we propose the MQ table-based ratedistortion slope (MQRDS) for image segmentation in theJPEG2000 domain as follows

Sm = E[Dm]E[Lm]

(3)

where Dm is the distortion of wavelet segment m defined as

Dm =Nmsumi=1

x2mi (4)

xmi is a wavelet coefficient at location i in wavelet segmentm represented by

xmi =nminus1sumj=0

xmi j middot 2 j xmi j isin 0 1 (5)

The estimate of Dm can be computed by

E[Dm] =Nmsumi=1

nminus1sumj=0

nminus1sumk=0

E[xmi j middot xmik

]middot 2 j+k

sim=Nmsumi=1

nminus1sumj=0

nminus1sumk=0

E[xmi j

]middot E[xmik

] middot 2 j+k

(6)

in which E[xmi j] can be obtained from the binary arithmeticcode table known as the MQ table as follows

E[xmi j

]= Pmi j

(xmi j = 1

) (7)

The estimate of code length E[Lm] can be efficiently obtainedby using [2]

E[Lm] = (D + Nm) middot E[Rm]minusNmlog2

(Nm

N

)(8)

E[Rm] =nminus1sumj=0

H(xm j

) (9)

H(xm j

)= minus Pm j

(xm j = 1

)middot log2

(Pm j

(xm j = 1

))

minus Pm j

(xm j = 0

)middot log2

(Pm j

(xm j = 0

))

(10)

Pm j

(xm j

)= 1

Nm

Nmsumi=1

middot Pmi j

(xmi j

) (11)

where j denotes the bit plane index xmi j is the binaryvariable of xmi on bit plane j which are independent acrossbit planes n is the number of bit planes D is the featurespace dimension Nm is the number of wavelet coefficientsin segment m N = sumK

m=1 Nm is the total number of waveletcoefficients and H() is an entropy operation After mergingtwo wavelet segments say m and n the change of MQRDS isgiven by

ΔSmn

= [Smn minus ((Nm(Nm + Nn ))Sm + (Nn(Nm + Nn ))Sn)]Smn

(12)

where Sm and Sn are the MQRDS of wavelet segments m andn with sizes Nm and Nn respectively and Smn is the MQRDSof the merged wavelet segment As one can see the changeof MQRDS is likely to be increased significantly for waveletsegments with similar characteristics Thus we propose asimple algorithm called the rate-distortion-based merging(RDM) algorithm for JPEG2000 image segmentation whichis presented in the steps below

The RDM Algorithm

Step 1 Given a JPEG2000 code stream compute theMQ table-based local PMF of wavelet coefficientsusing (2)


QWTImage Code stream

Local PMFRDMSegmentation result

MQ table

Bit-planeencoder

MQencoder

JPEG2000 encoder

(a)

DeQIWTImage

Local PMF

MQ table

RDMSegmentation result

Code streamBit-planedecoder

JPEG2000 decoder

MQencoder

(b)

Figure 2 Image segmentation using RDM in the JPEG2000 domain (a) encoder (b) decoder

Step 2 As mentioned in [2] a set of oversegmentedregions known as superpixels is in general neededfor any merging algorithms this low-level initialsegmentation can be obtained by coarsely clusteringthe local PMF as features

Step 3 For all pairs of superpixels compute theirrespective changes of MQRDS using (12) and mergethe one with maximum change of MQRDS

Step 4 Continue the merging process in step 3 untilthe change of MQRDS is insignificant

In order to reduce the computation time the followingequation can be used to approximate (6)

E[Dm] sim= Nm middot⎡⎣nminus1sum

j=0

nminus1sumk=0

⎛⎝ 1Nm

Nmsumi=1

Pmi j

(xmi j = 1

)⎞⎠

middot⎛⎝ 1Nm

Nmsumi=1

Pmik(xmik = 1

)⎞⎠ middot 2 j+k

⎤⎦

(13)

Moreover the cross terms of the previous equation arenot significant and can be discarded for computational

simplicity Figure 1 depicts flowchart of the RDM algorithmIt is noted that the MQ table defined in JPEG2000 is finitethus (10) can be obtained by look-up table (LUT) this surereduces the computation time further As shown in Figure 2RDM can be applied to a JPEG2000 code stream directly thisis one of the advantages of RDM


In the first experiment the potential of the MQ table-basedlocal PMF (LPMF) is shown by segmenting images withBrodatz textures As noted the essential characteristics oftextures are mainly contained in the middle-high-frequencywavelet subbands thus we applied a simple clusteringalgorithm known as K-means to the LPMF of waveletcoefficients to generate an initial segmentation The numberof superpixels was set to 30 which was then finely mergedusing the RDM algorithms Figure 3(a) shows the testimage with two Brodatz textures namely wood and grassThe segmentation result and error image with white pixelsrepresenting misclassifications are shown in Figure 3(b) andFigure 3(c) respectively Figure 3(d) shows the percentagesof errors at various rates of bits per pixel (bpp) It is noted


(a) (b) (c)

0 1 2 3 4 5 60

1

2

3

4

5

6

7

err

()

(bpp)

(d)

Figure 3 (a) Test image (b) the segmentation result and (c) error image at 1 bpp (d) error rates in percentage at various bpp rates

that the segmentation results even at low-middle bpp ratesare still satisfactory Hence a small portion of JPEG2000 codestream is sufficient for the segmentation task

The RDM algorithm has also been extensively evaluatedon the Berkeley image database [21] We adopted theWaveseg algorithm [14] to compute the initial superpixelsof a natural color image In order to avoid decoding aJPEG2000 code stream the Waveseg algorithm was appliedto the estimated wavelet coefficients instead of the decodedwavelet coefficients More specifically the estimated waveletcoefficient of xi using the MQ table-based LPMF is as follows

E[xi] =nminus1sumj=0

E[xi j]middot 2 j

=nminus1sumj=0

Pi j(xi j = 1

)middot 2 j

(14)

where Pi j(xi j = 1) is the probability of 1-bit on thejth bit plane which can be obtained from the MQ tableThe resulting superpixels were then merged by RDM withthreshold Td set to 01 We compared the RDM algorithmwith two other state-of-the-art algorithms known as Mean-shift [22] and CTM [2] In Mean-shift the parameters hs and

hr were set to 13 and 19 respectively in CTM the thresholdγ was set to 01 as suggested in [2] The original imagesshown at the top of Figure 4 are natural images contained inthe Berkeley database namely Pyramids Landscape Horsesand Giraffes Their respective segmentation results usingRDM CTM and Mean-shift are shown in the second thirdand fourth rows Visual inspection shows that RDM andMean-shift have similar performances for the first threeimages the performances of RDM and CTM are similar todetect the giraffes shown in the fourth image

In addition to visual inspection [23 24] two commonlyused measures namely the probabilistic Rand index (PRI)and the boundary displacement error (BDE) [25] wereadopted for quantitative comparisons Table 1 gives theaverage PRI performance on the Berkeley database PRIranges from 0 to 1 and higher is better BDE measuresthe average displacement error of boundaries betweensegmented images which is nonnegative and lower is betterThe average BDE performance is given in Table 2 It is notedthat RDM outperforms CTM and Mean-shift in terms of thePRI and BDE measures

The running times on a PC are given in Table 3 It showsthat RDM is faster than CTM and Mean-shift due largely tothe simple computations of (8) and (13) Moreover RDM


(a)

(b)

(c)

Figure 4 (a) Original images (b) segmentation using RDM (c) segmentation using CTM (d) segmentation using Mean-shift

Table 1 Average PRI on the Berkeley database

RDM CTM Mean-shift

0771 0762 0755

Table 2 Average BDE on the berkeley database

RDM CTM Mean-shift

87 94 97

Table 3 Execution times

Pyramids Landscape Horses Giraffes

RDM 89 s 87 s 107 s 68 s

Mean-shift 183 s 275 s 207 s 189 s

CTM 353 s 172 s 576 s 135 s

can be applied to a JPEG2000 code stream directly whilemost algorithms such as Mean-shift and CTM are primarilyapplied to the original or decoded image and it takes moretime to decode a compressed image

5 Conclusions

The MQ table defined in the JPEG2000 standard providesuseful information that can be used to compute the localprobability mass function (LPMF) of wavelet coefficients Asimple LPMF-based scheme has been proposed to estimatethe rate distortion slope (RDS) of a wavelet segment It isnoted that the RDS is increased significantly after merginga pair of wavelet segments with similar characteristics intoa single segment Similar ideas of the above can be used toimprove the rate control performance of JPEG2000 [26ndash28]In this paper we propose the rate-distortion-based merging(RDM) algorithm to segment images in the framework ofJPEG2000 RDM has been evaluated on images with Brodatztextures and the Berkeley color image database Experimentalresults show that the segmentation performance even at low-middle bpp rates is rather promising For natural imageswith high-detail contents RDM is preferable in terms ofthe average PRI and BDE measures In addition the totalrunning time of RDM which includes the computation ofsuperpixels and the merging process is faster than Mean-shift and CTM

As RDM is based on the MQ table which is availableat both encoder and decoder no overhead transmission isneeded to compute the LPMF of wavelet coefficients RDMcan be applied to a JPEG2000 code stream directly thus


the burden of decompressing computation can be avoidedand memory space that is required to store the decompressedimage is no longer necessary from the segmentation point ofview

Acknowledgments

The authors are grateful to the maintainers of the Berkeleyimage database The National Science Council of Taiwanunder Grants NSC100-2628-E-239-002-MY2 and NSC100-2410-H-216-003 supported this work

References

[1] Y Xia D Feng and R Zhao ldquoAdaptive segmentation oftextured images by using the coupled Markov random fieldModelrdquo IEEE Transactions on Image Processing vol 15 no 11pp 3559ndash3566 2006

[2] A Y Yang J Wright Y Ma and S Shankar SastryldquoUnsupervised segmentation of natural images via lossy datacompressionrdquo Computer Vision and Image Understanding vol110 no 2 pp 212ndash225 2008

[3] N A M Isa S A Salamah and U K Ngah ldquoAdaptive fuzzymoving K-means clustering algorithm for image segmenta-tionrdquo IEEE Transactions on Consumer Electronics vol 55 no4 pp 2145ndash2153 2009

[4] S Xiang C Pan F Nie and C Zhang ldquoTurbopixel seg-mentation using eigen-imagesrdquo IEEE Transactions on ImageProcessing vol 19 no 11 pp 3024ndash3034 2010

[5] M Li and W Zhao ldquoQuantitatively investigating locallyweak stationarity of modified multifractional gaussian noiserdquoPhysica A vol 391 no 24 pp 6268ndash6278 2012

[6] M Li and W Zhao ldquoVariance bound of ACF estimationof one block of fGn with LRDrdquo Mathematical Problems inEngineering vol 2010 Article ID 560429 14 pages 2010

[7] S Chen and X Li ldquoFunctional magnetic resonance imag-ing for imaging neural activity in the human brain theannual progressrdquo Computational and Mathematical Methodsin Medicine vol 2012 Article ID 613465 9 pages 2012

[8] Z Teng J He A J Degnan et al ldquoCritical mechanical condi-tions around neovessels in carotid atherosclerotic plaque maypromote intraplaque hemorrhagerdquo Arteriosclerosis Thrombo-sis and Vascular Biology vol 223 no 2 pp 321ndash326 2012


[10] D E Ilea and P F Whelan ldquoCTexmdashan adaptive unsupervisedsegmentation algorithm based on color-texture coherencerdquoIEEE Transactions on Image Processing vol 17 no 10 pp1926ndash1939 2008

[11] S Mallat A Wavelet Tour of Signal Processing Academic PressSan Diego Calif USA 1999

[12] M K Bashar N Ohnishi and K Agusa ldquoA new texturerepresentation approach based on local feature saliencyrdquoPattern Recognition and Image Analysis vol 17 no 1 pp 11ndash24 2007

[13] C M Pun and M C Lee ldquoExtraction of shift invariant waveletfeatures for classification of images with different sizesrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol26 no 9 pp 1228ndash1233 2004

[14] C R Jung ldquoUnsupervised multiscale segmentation of colorimagesrdquo Pattern Recognition Letters vol 28 no 4 pp 523ndash533 2007

[15] T Acharya and P S Tsai JPEG2000 Standard for ImageCompression Concepts Algorithms and VLSI ArchitecturesJohn Wiley amp Sons New York NY USA 2005

[16] C Cattani ldquoHarmonic wavelet approximation of randomfractal and high frequency signalsrdquo Telecommunication Sys-tems vol 43 no 3-4 pp 207ndash217 2010

[17] S Y Chen and Z J Wang ldquoAcceleration strategies in gen-eralized belief propagationrdquo IEEE Transactions on IndustrialInformatics vol 8 no 1 pp 41ndash48 2012

[18] F Zargari A Mosleh and M Ghanbari ldquoA fast and efficientcompressed domain JPEG2000 image retrieval methodrdquo IEEETransactions on Consumer Electronics vol 54 no 4 pp 1886ndash1893 2008

[19] M H Pi C S Tong S K Choy and H Zhang ldquoA fastand effective model for wavelet subband histograms and itsapplication in texture image retrievalrdquo IEEE Transactions onImage Processing vol 15 no 10 pp 3078ndash3088 2006

[20] H C Hsin ldquoTexture segmentation in the joint photographicexpert group 2000 domainrdquo IET Image Processing vol 5 no6 pp 554ndash559 2011

[21] httpwwweecsberkeleyedusimyangsoftwarelossy segmen-tation

[22] D Comaniciu and P Meer ldquoMean shift a robust approachtoward feature space analysisrdquo IEEE Transactions on PatternAnalysis and Machine Intelligence vol 24 no 5 pp 603ndash6192002

[23] H C Hsin T-Y Sung Y-S Shieh and C Cattani ldquoMQ Coderbased image feature and segmentation in the compresseddomainrdquo Mathematical Problems in Engineering vol 2012Article ID 490840 14 pages 2012


[25] R Unnikrishnan C Pantofaru and M Hebert ldquoTowardobjective evaluation of image segmentation algorithmsrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol29 no 6 pp 929ndash944 2007

[26] H C Hsin and T Y Sung ldquoContext-based rate distortionestimation and its application to wavelet image codingrdquoWSEAS Transactions on Information Science and Applicationsvol 6 no 6 pp 988ndash993 2009

[27] H-C Hsin and T-Y Sung ldquoImage segmentation in theJPEG2000 domainrdquo in Proceedings of the InternationalConference on Wavelet Analysis and Pattern Recognition(ICWAPRrsquo11) pp 24ndash28 2011

[28] H-C Hsin T-Y Sung Y-S Shieh and C Cattani ldquoAdaptivebinary arithmetic coder-based image feature and segmenta-tion in the compressed domainrdquo Mathematical Problems inEngineering vol 2012 Article ID 490840 14 pages 2012







Editorial Board




Contents














































Acknowledgments













1 Introduction





ATP ATP ATP

ATP ATP

ADP

ADP

ADP

ADP ADP


ATP + AMP 2ADP

v1

v2

v3

v4 v

5

v6

v7

v8

Fruc16P2






119889119909119894

119889119905=

119898

sum

119895=1

119888119894119895119903119895 for 119894 = 1 119896 (1)


119895



119895is




119894119895]119896times119898

Let 119883 = [1199091 1199092 119909

119896]119879 and r =

[1199031 1199032 119903

119898]119879 and let 120573 = [120573

1 1205732 120573



119889119883

119889119905= Cr (119883120573) (2)





119889

119889119905Gluc6P = 119903

1minus 1199032minus 1199033

119889

119889119905Fruc6P = 119903

3minus 1199034

119889

119889119905Fruc1 6P

2= 1199034minus 1199035


119889

119889119905ATP = minus119903


119889

119889119905ADP = 119903

1+ 1199032+ 1199034minus 1199036+ 1199037+ 21199038

119889

119889119905AMP = minus119903

8

(3)


1199031=

119881max2ATP (119905)

119870ATP1 + ATP (119905)

1199032= 1198962ATP (119905) sdot Gluc6P (119905)

1199033= (

119881119891

max3

119870Gluc6P3Gluc6P (119905)

minus119881119903

max3

119870Fruc6P3Fruc6P (119905))

times (1 + (Gluc6P (119905)

119870Gluc6P3)

+Fruc6P (119905)

119870Fruc6P3)

minus1

1199034=

119881max4(Fruc6P (119905))2


2

1199035= 1198965Fruc1 6P

2 (119905)

1199036= 1198966ADP (119905)

1199037= 1198967ATP (119905)


8119903(ADP (119905))2

(4)




metric matrix

C =

[[[[[[[

[


0 0 1 minus1 0 0 0 0

0 0 0 1 minus1 0 0 0


1 1 0 1 0 minus1 1 2

0 0 0 0 0 0 0 minus1

]]]]]]]

]

(5)






119889119883

119889119905= Cr (119883120573) = C

119903r119903(119883120573) + C

119901r119901(119883120573) (6)









C119903= [1198881 1198883 1198884] =

[[[[[[[

[

1 minus1 0

0 1 minus1

0 0 1

minus1 0 minus1

1 0 1

0 0 0

]]]]]]]

]

C119901

= [1198882 1198885 1198886 1198887 1198888] =

[[[[[[[

[

minus1 0 0 0 0

0 0 0 0 0

0 minus1 0 0 0


1 0 minus1 1 2

0 0 0 0 minus1

]]]]]]]

]

(7)

and r119903

= [1199031 1199033 1199034] and r

119901= [1199032 1199035 1199036 1199037 1199038] The rank of


rates



Cminus119903C119903= 119868 (8)


119903satisfying





Cminus119903

= [

[

1 1 1 0 0 0

0 1 1 0 0 0

0 0 1 0 0 0

]

]

(9)


Cminus119903

119889119883

119889119905= Cminus119903C119903r119903(119883120573) + Cminus

119903C119901r119901(119883120573)

= r119903(119883120573) + Cminus

119903C119901r119901(119883120573)

(10)


or

r119903(119883120573) + Cminus

119903C119901r119901(119883120573) = Cminus

119903

119889119883

119889119905 (11)



1199031minus 1199032minus 1199035=

119889


2)

1199033minus 1199035=

119889

119889119905(Fruc6P + Fruc1 6P

2)

1199034minus 1199035=

119889

119889119905Fruc1 6119875

2

(12)


Cperp119903C119903= 0 (13)



119903) =





Cperp119903

119889119883

119889119905= Cperp119903C119903r119903(119883120573) + Cperp

119903C119901r119901(119883120573) = Cperp

119903C119901r119901(119883120573)

(14)or

Cperp119903C119901r119901(119883120573) = Cperp

119903

119889119883

119889119905 (15)


Cperp119903

= [

[

1 1 2 1 0 0

0 0 0 1 1 0

0 0 0 0 0 1

]

]

Cperp119903C119901

= [

[


0 0 0 0 1

0 0 0 0 minus1

]

]

(16)



r119901(119883120573) = (119863

119879119863)minus1

119863119879Cperp119903

119889119883

119889119905 (17)



such that

119863r119901(119883120573) = 119863r

119901(119883120573) = Cperp

119903C119901r119901(119883120573) = Cperp

119903

119889119883

119889119905 (18)


r119901(119883120573) = (119863

119879

119863)119863119879Cperp119903

119889119883

119889119905 (19)



we have

119863 = [

[

1 minus1

0 1

0 minus1

]

]

119863119879Cperp119903

= [1 1 2 1 0 0


(20)



=119889

119889119905(Gluc6P + Fruc6P


1199038= minus

119889

119889119905AMP

(21)





120578 (X120573) =1198730 (X) + sum

119901119873

119894=1119873119894 (X) 120573119873119894

1198630 (X) + sum

119901119863

119895=1119863119895 (X) 120573119863119895

+

119901119875

sum

119896=1

119875119896 (X) 120573119875119896

(22)



119873119894(119894 = 1 119901



(119895 = 1 119901119863) and those in the

polynomial 120573119875119896


119863+119901119873+

119901119875

= 119901 119873119894(X) (119894 = 0 1 119901

119873) 119863119895(X) (119895 = 0 1 119901

119863)

and 119875119896(X) (119896 = 1 119901



0(X) or 119863




120578 (X120573) = (1198730 (X) +

119901119873

sum

119894=1

119873119894 (X) 120573119873119894

+ (

119901119875

sum

119896=1

119875119896 (X) 120573119875119896

)

times(1198630 (X) +

119901119863

sum

119895=1

119863119895 (X) 120573119863119895

))

times (1198630(X) +

119901119863

sum

119895=1

119863119895(X)120573119863119895

)

minus1

(23)


+ 119901119873


119863+ 119901119873

+






119905and X

119905(119905 = 1 2 119899) we introduce the

following notation

120573119873

= [1205731198731

1205731198732

120573119873119901119873

]119879

isin 119877119901119873

120573119863

= [1205731198631

1205731198632

120573119863119901119863

]119879

isin 119877119901119863

120573119875

= [1205731198751

1205731198752

120573119875119901119863

]119879

isin 119877119901119875

120573 = [ 120573119879119875120573119879119873120573119879119863]119879

120593119873

(X119905) = [119873

1(X119905) 1198732(X119905) 119873

119901119873(X119905)] isin 119877

119901119873

120593119863

(X119905) = [119863

1(X119905) 1198632(X119905) 119863

119901119863(X119905)] isin 119877

119901119863

120593119875(X119905) = [119875

1(X119905) 1198752(X119905) 119875

119901119875(X119905)] isin 119877

119901119875

Y = [119910(1) 119910(2) 119910(119899)]119879

isin 119877119899

Φ1198730

= [1198730(X1) 1198730(X2) 119873

0(X119899)]119879

isin 119877119899

Φ1198630

= [1198630(X1) 1198630(X2) 119863

0(X119899)]119879

isin 119877119899

Φ119873

=

[[[[[

[

120593119873

(X1)

120593119873

(X2)

120593119873

(X119899)

]]]]]

]

isin 119877119899times119901119873

Φ119863

=

[[[[[

[

120593119863

(X1)

120593119863

(X2)

120593119863

(X119899)

]]]]]

]

isin 119877119899times119901119863

Φ119875

=

[[[[[

[

120593119875(X1)

120593119875(X2)

120593119875(X119899)

]]]]]

]

isin 119877119899times119901119875

Ψ (120573119863) = diag

[[[[[

[

1198630(X1) + 120593119863

(X1)120573119863

1198630(X2) + 120593119863

(X2)120573119863

1198630(X119899) + 120593119863

(X119899)120573119863

]]]]]

]

isin 119877119899times119899

(24)


119869 (120573) = 119869 (120573119875120573119873120573119863)

= sum(1198630(X119905) + 120593119863

(X119905)120573119863)2

times (1198730(X119905) + 120593119873

(X119905)120573119873

1198630(X119905) + 120593119863

(X119905)120573119863

+ Φ119875120573119875minus 119910119905)

2

(25)



119875

120573119873 and120573


119869 (120573) = sum[(1198630(X119905) + 120593119863

(X119905)120573119863)Φ119875120573119875+ 120593119873

(X119905)120573119873

minus120593119863

(X119905) 119910119905120573119863

minus 1198630(X119905) 119910119905+ 1198730(X119905)]2

(26)




119881119891



1198966(minminus1) 6848 684837 00054

1198967(minminus1) 321 320797 00078

1198968119891




119869 (120573) = 119869 (120573119875120573119873120573119863120573119863)

= [A (120573119863)120573 minus b]

119879

[A (120573119863)120573 minus b]

(27)

where

119860(120573119863) =

[[[

[

Ψ(120573119863)Φ119879

119875

Φ119879

119873

minus diag (119884)Φ119879

119863

]]]

]

isin 119877119899times119901

(28)

b = (Φ1198630

diag (119884) minus Φ1198730

) isin 119877119899 (29)


eters 120573 = [120573119879119875120573119879119873120573119879119863]119879


120573 = [A119879 (120573119863)A (120573

119863)]minus1

A119879 (120573119863) b (30)





119869 (120573119904+1

) = [A (120573119904

119863)120573119904+1

minus b]119879

[A (120573119904

119863)120573119904+1

minus b] (31)


120573119904+1

= [A119879 (120573119904119863)A (120573

119904

119863)]minus1

A119879 (120573119904119863) b (32)


120573119904119879119873

120573119904119879119863




10038171003817100381710038171003817120573119896 minus 120573119896minus1

1003817100381710038171003817100381710038171003817100381710038171003817120573119896minus1

10038171003817100381710038171003817+ 1

le 120576 (33)


4 Application


2(0) = 0mM ATP(0) = 21mM ADP(0) =




0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6

Time (min)

Gluc6PFruc6P

ATPADPAMP

Con

cent

ratio

ns

Fruc16P2



119909(119905119899) =

1

12Δ119905[119909 (119905119899minus2

) minus 8119909 (119905119899minus1

) + 8119909 (119905119899+1

) minus 119909 (119905119899+2

)]

(34)



true value (35)





Acknowledgments


References



























1 Introduction






02 04 06 08 1 12 14 16 18 2

0500

1000150020002500

Time (ms) times105

minus500

minus1000

minus1500

minus2000

minus2500

EEG

vol

tage

(120583V

)














Skin


Elec

trode

Elec

trode

gel

Rp

Ep

Cp

RuR

e

Ese

Rs

Rd

Ehe

Cd

Ce














119885 (119904) asymp (119877119889

119904119877119889119862119889+ 1

+119877119890

119904119877119890119862119890+ 1

119877119901

119904119877119901119862119901+ 1

) (1)


119885 (119904) asymp1199041198611+ 1198610

11990421198602+ 1199041198601+ 1

(2)


1


119901


119864119898= 119883in

1199041198611+ 1198610

11990421198602+ 1199041198601+ 1

+ 119864 +119882noise (3)

0 5 10 15 200

10

20

30

40

50

60

70

80

90

100

EEG channels

Fit p

erce

ntag

e


where 119864119898


119864lowast

119898= 119883in

1199041198611+ 1198610

11990421198602+ 1199041198601+ 1

(4)





lowast

119898(119905))2

(sum (119864119898 (119905) minusmean(119864

119898 (119905))2))

) (5)


119885 (119904) = 119870119901

1 + 119904119879119911

11990421198792119908+ 2119904120577 sdot 119879

119908+ 1

(6)

with 119870119901

= minus40921 119879119908



0 10 20 30 40 50 60 700

102030405060708090

100


Fit p

erce

ntag

e

(a)

0 5 10 15 20 25 30 350

102030405060708090

100


Fit p

erce

ntag

e

(b)

1 2 3 4 5 6 7 8 9 10 11 12 13 140

102030405060708090

100


Fit p

erce

ntag

e

(c)

1 2 3 4 5 6 7 8 9 100

102030405060708090

100


Fit p

erce

ntag

e

(d)

1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

90

100


Fit p

erce

ntag

e

(e)

1 2 3 4 50

10

20

30

40

50

60

70

80

90

100


Fit p

erce

ntag

e

(f)









119860 (119902) 119910 (119905) =119861 (119902)

119865 (119902)119906 (119905) +

119862 (119902)

119863 (119902)119890 (119905) (7)








119898(119899) as a





119890 (119899) = 119864119898 (119899) minus 119864GVS (119899) = 119864

119905 (119899) minus [119911 (119899) minus 119864GVS (119899)] (8)

where

119864GVS (119899) =119872

sum

119898=1

ℎ119898sdot 119894GVS (119899 + 1 minus 119898) (9)


119864 [1198902(119899)] = 119864 [(119864

119898 (119899) minus 119864GVS (119899))2

] (10)

or

119864 [1198902(119899)] = 119864 [119864

2

119905(119899)] minus 119864 [(119911 (119899) minus 119864GVS (119899))

2

] (11)











0 50 100 150 200 250 300 350 400 450 500Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)


minus55

minus60

minus65

minus70

minus75

minus80

minus85

2 4 6 8 10 12 14Frequency (Hz)

minus52

minus53

minus54

minus55

minus56

minus57

Pow

erfr

eque

ncy

(dB

Hz)



120595119895119896 (119905) = 2






1(119905) 119890



1(119905) 119904

119873(119905))

119864 (119905) = 119872119878 (119905) (13)



0 02 04 06 08 1 12 14 16 18 2

0

5

10

15

Time (ms)

minus5

minus10

minus15

ICA

com

pone

nt (120583

V)

times105





119864 (119905) = 119872119878 (119905) (14)



0 02 04 06 08 1 12 14 16 18 2

00102030405

Time (ms) times105

ICA

com

pone

nt (120583

V)

minus01

minus02

minus03

minus04

minus05





Corr (119906 119910) =Cov (119906 119910)120590119906sdot 120590119910

(15)














Correlation 09776 09769 09899 09899

GVS current



L1

L2

L3

L4

L5

L6

L7

L8

L9

L10

L12

L11




Regression analysis


EEG




RSS119873=

sum (119864119900 (119905) minus 119864

119900 (119905))2

sum(119864119900 (119905) minusmean (119864

119900 (119905)))2 (16)










Corr 09932 09933 09933 09932 09932 09933 09933 09932RSS119873

01710 01700 01705 01714 01710 01700 01705 01714



01700 01701 01704 02267 01711SS2 SS3 SS4 NLHW3 NLHW4

Corr 09933 08105 07466 09926 09851RSS119873

01704 07628 09174 01230 01725









component


component



Corr 06445 06171 09933 09934RSS119873

09567 10241 01700 01711



component


component



Corr 06859 06858 08743 08743
















0 05 1 15 2 25 3 35

065

07

075

08

085

09

095

1

GVS (mA)

Cor

rela

tion





3 Results




1 2 3 4 5 6 7 8 9 10 11 120

10

20

30

40

50

60

70

80

90

100

Frequency bands

Fit p

erce

ntag

e


1 2 3 4 5 6 7 8 9 10 11 120

01

02

03

04

05

06

07

08

09

1

Frequency bands

Cor

relat

ion

coeffi

cien

t





0 02 04 06 08 1 12 14 16 18 2

0

100

200

300

Time (ms)

minus100

minus200

minus300

minus400

EEG

vol

tage

(120583V

)

times105


0 02 04 06 08 1 12 14 16 18 2

050

100150200250

Time (ms)

minus50

minus100

minus150

minus200

minus250

EEG

vol

tage

(120583V

)

times105






0

50

100

150

minus50

minus100

minus150

0 02 04 06 08 1 12 14 16 18 2Time (ms)

EEG

vol

tage

(120583V

)

times105



4 Discussion









Acknowledgments


References











































1 Introduction







2 Methods







119909and



RRI1015840 (119894) =RRI (119894)SD119909

PTT1015840 (119895) =PTT (119895)

SD119910

(1)





ECG

PPG

RRI(1) RRI(2) RRI(1000)






RRI1015840(119906)(120591) = 1

120591

119906120591

sum

119894=(119906minus1)120591+1

RRI1015840 (119894) 1 le 119906 le1000

120591

PTT1015840(119906)(120591) = 1

120591

119906120591

sum

119895=(119906minus1)120591+1

PTT1015840 (119895) 1 le 119906 le1000

120591

(2)




119894 = 1 119873 minus 119898 + 1

y (119895)


119895 = 1 119873 minus 119898 + 1

(3)


119889 [x (119894) y (119895)]

=119898max119896=1


10038161003816100381610038161003816]

(4)



119862119898

RRI1015840(120591)PTT1015840(120591) (119894) =119873119898

RRI1015840(120591)PTT1015840(120591) (119894)

119873 minus 119898 + 1 (5)




119898


120601119898

RRI1015840(120591)PTT1015840(120591) (119903) =1

119873 minus 119898 + 1

119873minus119898+1

sum

119894=1

ln119862119898RRI1015840(120591)PTT1015840(120591) (119894) (6)


RRI1015840(120591)PTT1015840(120591)(119894) 120601119898+1


119873rarrinfin

[120601119898

RRI1015840(120591)PTT1015840(120591)(119903) minus 120601119898+1


Co ApEnRRI1015840(120591)PTT1015840(120591) (119898 119903119873) = 120601119898

RRI1015840(120591)PTT1015840(120591) (119903)

minus 120601119898+1

RRI1015840(120591)PTT1015840(120591) (119903) (7)




MCEISS =5

sum

120591=1

Co ApEnRRI1015840(120591)PTT1015840(120591) (120591) (8)

MCEILS =20

sum

120591=6

Co ApEnRRI1015840(120591)PTT1015840(120591) (120591) (9)






3 Results


32 MCEI119871119878


119864(RRI) and 119878






4 Discussion









16156 plusmn 897 16117 plusmn 728





9746 plusmn 377


12846 plusmn 1636



5025 plusmn 1312








764 plusmn 081





2106 plusmn 492







0 5 10 15 2008

1

12

14

16

18

2

Scale

Sam

ple e

ntro

py (R

RI)

Group 1Group 2

Group 3Group 4

(a)

Scale

Group 1Group 2

Group 3Group 4

0 5 10 15 201

12

14

16

18

2

22

24

Sam

ple e

ntro

py (P

TT)

(b)




0 2 4 6 8 10 12 14 16 18 20

12

14

16

18

2

22

Group 1Group 2

Group 3Group 4

120591

Co

ApEn

RRI998400(120591)PT

T998400(120591)(120591)





5 Conclusions






Acknowledgments


References






































1 Introduction




















GMM-FJ

Lesion detection

lesions


Train images

Test image

Likelihood lesions

RGB lesions

Overall score

Multiple expert

Baseline

trainingBaseline

Score



RGB image


fusion

annotationfusion

annotationsExpert


Expert





























































True finding area










(a) (b) (c)




perf 119868exp119894119895119899

119892119905119894119895

997888rarr R (1)






119894119895119899


perf (119868exp119894119895119899

119892119905119894119895

)

=1

119873sum

119899


119894119895119899

) 119868mask119894119895 (119909 119910 120591))

(2)



(a) (b)





120591119895larr997888 argmin

120591119895

1

119873sum

119899

EER (sdot sdot) (3)








SN =TP

TP + FN(4)


SP =TN

TN + FP(5)






1 + =


1 + (7)







(8) else(9) FN = FN + 1


(14) else(15) FP = FP + 1


TPTP + FN

(Sensitivity)

(20) SP =TN






im1

120577im119899


im1

120596im119899

where each 120596

im119894





pix1

120577pix119899


pix1

120596pix119899






TPTP + FN

(Sensitivity)

(22) SP =TN











1 x

119872 where each


1 x





SCOREsummax = sum

119898isin119873119884

119901 (x119898

| abnormal) (8)




0 10

02

04

06

08

1Se

nsiti

vity

05



1minus specificity

(a)

0 05 10

02

04

06

08

1

Sens

itivi

ty



1minus specificity

(b)




In [9] 0233 0333 0273 0200 0220 0216 0476 0625 0593 0250 0333 0317 0349In [8] (min) 0263 0476 0322 0250 0250 0250 0286 0574 0338 0333 0333 0333 0311In [8] ( max) 0263 0476 0322 0250 0250 0250 0386 0574 0338 0200 0268 0241 0288








1

09

08

07

06

05

04

03

02

01

010908070605040302010

HAHA-orig

(a) Haemorrhage

1

09

08

07

06

05

04

03

02

01

010908070605040302010

HEHE-orig

(b) Hard exudate

1

09

08

07

06

05

04

03

02

01

010908070605040302010

MAMA-orig

(c) Microaneurysm

1

09

08

07

06

05

04

03

02

01

010908070605040302010

SESE-orig

(d) Soft exudate





6 Conclusions



(a) (b)

(c) (d)



Acknowledgments


References


















































1 Introduction
















(3)

(A)

Lead-inbevel

empty35 11

(1) D36-L55-T030-ST-SM

(2) D36-L55-T1030-ST-SM

(3) D43-L55-T1030-ST-SM

(4) D43-L9-T1030-DT-SM

(5) D43-L9-T1030-DT-LM

(6) D43-L9-T1030-ST-LM

(7) D36-L9-T030-DT-SM

(8) D36-L9-T1030-DT-SM

(9) D36-L9-T1030-DT-LM

(10) D36-L9-T1030-ST-LM

(A) D35-L11 Ankylos

empty36 empty3655

empty36 55

55empty43

empty43 9

empty43 9

empty43 9

9

empty36 9

empty36 9

empty36 9







(a)

xy

z

(b)

(c)

x

z

7 mm

250 N

100 N

(d)


1 mm

P0

P1

05 mm



02 mm

P05














0119863 = 01 and

ℎ119894119863 = 001 ℎ

0and ℎ




119894 with 119894 = 1 2 3) [44 47 53 63 64]


120590119862 (119875) = min 120590

1 (119875) 1205902 (119875) 1205903 (119875) 0

120590119879 (119875) = max 120590

1 (119875) 1205902 (119875) 1205903 (119875) 0

(1)

120590119862and 120590



119877 =

10038161003816100381610038161205901198621003816100381610038161003816

1205901198620

+120590119879

1205901198790

le 1 (2)


1198790 1205901198620


1198790= 180MPa and 120590





D 120575

Ωa

t

Ωt

i

Ωt

c

Ωt

Ωc



119888and Ω

119905(such that





119905(apex


119888 Ω119888119905 Ω119894119905 Ω119886119905 These


3 Results


119888and




119888and Ω

119905 and








119888and Ω

119905(resp

20 in Ω119888and 30 in Ω













(MPa)

z

x

0 10 15 20 25 30 50 60 70 Above






(MPa)

x

z

0 05 1 15 2 25 3 35 45 Above








(MPa

)

1 2 3 4 5 6 7 8 9 10 AImplant type

120590VM

0

10

20

30

40

50

60

70

0

1

2

3

4

5

(MPa

)

1 2 3 4 5 6 7 8 9 10 AImplant type

120590VM

Ωc

t

Ωi

t

Ωa

t

(a)

minus50

minus40

minus30

minus20

minus10

0

10

20

(MPa

)

1 2 3 4 5 6 7 8 9 10 AImplant type

1 2 3 4 5 6 7 8 9 10 AImplant type

120590T

120590C

120590T

120590C

minus4

minus3

minus2

minus1

0

1

2

3(M

Pa)

Ωc

t

Ωi

t

Ωa

t

(b)







119888andΩ




00

01

02

03

04

05

06

07

R

1 2 3 4 5 6 7 8 9 10 AImplant type



(8) D36-L9-T1030-DT-SM


z

x

P0 P05 P1

0 10 15 20 25 30 50 60 70 Above

(a)

(8) D36-L9-T1030-DT-SM

(A) D35-L11 Ankylos

(MPa)x

z

P0 P05 P1

0 05 1 15 2 25 3 35 45 Above

(b)



(MPa

)

P0 P05 P1

Implant 8Implant A

0

10

20

30

40

50

60

70120590VM

00

05

10

15

20

25

30

35

(MPa

)

P0 P05 P1 P0 P05 P1


Ωc

t

Ωi

t

Ωa

t

(a)


P0 P05 P1 P0 P05 P1 P0 P05 P1 P0 P05 P1

(MPa

)

120590T

120590T

120590C

120590C

minus40

minus30

minus20

minus10

0

10

20

minus2

minus1

0

1

2

3(M

Pa)

Ωc

t

Ωi

t

Ωa

t

(b)








00

01

02

03

04

R

P0 P05 P1 P0 P05 P1

Implant 8 Implant A





119888and Ω




4 Discussion







0

20

40

60

80

100

120

140

(MPa

)


Implant 8Implant A

120590VM

(a)

0

1

2

3

4

5

6

(MPa

)0 25 50 0 25 50


Implant 8 Implant A

120590VM

Ωc

t

Ωi

t

Ωa

t

(b)

Implant 8 Implant A


00

02

04

06

08

10

R

CorticalTrabecular

(c)












References















































































1 Introduction



2 Methods










FPzFP2FP1

Fz

Cz

Pz

OzO1 O2

T7 T8

F7 F8

P7 P8

F3 F4

C3 C4

P3 P4

AF3 AF4

F5 F1 F2 F6

FCzFT7 FT8


CPzTP7 TP8


POz PO8PO7

P5 P2 P6

PO4 PO6PO3PO5

C2 C6C1C5

CB1 CB2

P1

1

2 3 4

5






119885 = 119911119894 (119899) (119894 = 1 119872 119899 = 1 119879)

119909119894 (119899) =

(119911119894 (119899) minus ⟨119885

119894⟩)

120590119894

119883 = 119909119894 (119899)

(1)



119909119894(119899) and ⟨119885

119894⟩ and 120590


119911119894(119899) respectively



PersonsChanges









Δ120593119908

119909119894119909119896(119904 120591) = 120593

119908

119909119894(119904 120591) minus 120593

119908

119909119896(119904 120591) (119896 = 1 119872) (2)


120574119894119896

=100381610038161003816100381610038161003816⟨119890119895Δ120593119908

119909119894119909119896(119904120591)

⟩119879

100381610038161003816100381610038161003816isin [0 1] (3)



119894(119899) and


written as C = 120574119894119896


follows

Ck119894

= 120582119894k119894 (4)


le 1205822




119904

1le 120582119904

2le




120582119892

119894=

120582119894120582119904119894

sum119872

119894=1120582119894120582119904119894

(119894 = 1 119872)

GSI = 1 +sum119872

119894=1120582119892

119894log (120582

119892

119894)

log (119872)

(5)




119903(119896)

119895119894=

119910(119896)

119895119894minus 119910(119896)

1198951

119910(119896)

1198951

(119894 = 1 119873 119873 = 6 119895 = 1 119870 119870 = 5 119896 = 1 2 3)

(6)



(119896)

119895119894is the








119895119894will






3 Results





Fron

tal r

atio

Righ

t tem

pora

l rat

io

Left

tem

pora

l rat

io

Cen

tral

ratio

Occ

ipita

l rat

io

Glo

bal r

atio

0

1

2

3

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6N test N test

minus1

0

1

2

3

minus1

0

1

2

3

minus1

0

1

2

3

minus1

0

1

2

3

minus1

0

1

2

3

minus1

N test



minus02

minus01

0

01

minus02

minus01

0

01

minus02

minus01

0

01

minus02

minus01

01

minus02

minus01

01

minus02

minus01

0 0 0

01

Fron

tal r

atio

Righ

t tem

pora

l rat

io

Left

tem

pora

l rat

io

Cen

tral

ratio

Occ

ipita

l rat

io

Glo

bal r

atio






minus05

0

05

minus05

0

05

minus05

0

05

minus05

0

05

minus05

0

05

minus05

0

05

Fron

tal r

atio

Righ

t tem

pora

l rat

io

Left

tem

pora

l rat

io

Cen

tral

ratio

Occ

ipita

l rat

io

Glo

bal r

atio








4 Discussions






Acknowledgments


References










































1 Introduction













X = x11 x1

1198731 x21 x2

1198732 x119862

1 x119862

119873119862 (1)






119897(x119894) andNM




119894119895is given by

119901119894119895=

exp (minus119889211989411989521205822)

sum119905isin119867119898

exp (minus119889211989811990521205822)

forall119895 isin 119867119894

exp (minus119889211989411989521205822)

sum119905isin119872119898

exp (minus119889211989811990521205822)

forall119895 isin 119872119894

0 otherwise

(2)





119894119895 119867119894= 119895 | 1 le 119895 le 119873 1 le 119894 le 119873

x119895= NH

119896(x119894) and 1 le 119896 le 119870

1 119867119898= 119905 | 1 le 119905 le 119873 1 le

119898 le 119873 x119905= NH

119896(x119898) and 1 le 119896 le 119870

1 119872119894= 119895 | 1 le

119895 le 119873 1 le 119894 le 119873 x119895= NH

119896(x119894) and 1 le 119896 le 119870

2 and

119872119898= 119905 | 1 le 119905 le 119873 1 le 119898 le 119873 x

119905= NH

119896(x119898) and



119894119895




119894and




119902119894119895=

(1 + 1198892

119894119895(A))minus1

sum119905isin119867119898

(1 + 1198892119898119905(A))minus1

forall119895 isin 119867119894

(1 + 1198892

119894119895(A))minus1

sum119905isin119872119898

(1 + 1198892119898119905(A))minus1

forall119895 isin 119872119894

0 otherwise

(3)



119894119895(A) = y

119894minus

y119895 = Ax


119894minus x119895)119879A119879A(x



119902119894119895

=

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119905isin119867119898

(1 + (x119898minus x119905)119879A119879A (x


forall119895 isin 119867119894

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119905isin119872119898

(1 + (x119898minus x119905)119879A119879A (x


forall119895 isin 119872119894

0 otherwise(4)


min119862 (A) = sum

forall119895isin119867119894

119901119894119895log

119901119894119895

119902119894119895

+ sum

forall119895isin119872119894

119901119894119895log

119901119894119895

119902119894119895

(5)


119894119895 119906119894119895 119906119867

119894119895 and 119906119872

119894119895

as

119908119894119895= [1 + (x

119894minus x119895)119879

A119879A (x119894minus x119895)]

minus1

119906119894119895= (119901119894119895minus 119902119894119895)119908119894119895

119906119867

119894119895=

119906119894119895

forall119895 isin 119867119894

0 otherwise

119906119872

119894119895=

119906119894119895

forall119895 isin 119872119894

0 otherwise

(6)


119889119862 (A)119889 (A)

= sum

forall119895isin119867119894

119901119894119895

119902119894119895

(119902119894119895)1015840

+ sum

forall119895isin119872119894

119901119894119895

119902119894119895

(119902119894119895)1015840

= 2A[

[

sum

forall119895isin119867119894

119901119894119895

(x119894minus x119895) (x119894minus x119895)119879

1 + (x119894minus x119895)119879

A119879A (x119894minus x119895)

]

]

minus 2A[

[

sum

forall119895isin119867119894

119901119894119895( sum

119905isin119867119898

(1 + (x119898minus x119905)119879A119879A (x



times( sum

119905isin119867119898

(1 + (x119898minus x119905)119879A119879A (x


)

minus1

]

]

+ 2A[

[

sum

forall119895isin119872119894

119901119894119895

(x119894minus x119895) (x119894minus x119895)119879

1 + (x119894minus x119895)119879

A119879A (x119894minus x119895)

]

]

minus 2A[

[

sum

forall119895isin119872119894

119901119894119895( sum

119905isin119872119898

(1 + (x119898minus x119905)119879A119879A (x



times( sum

119905isin119872119898

(1 + (x119898minus x119905)119879A119879A (x


)

minus1

]

]

= 2A[

[

sum

forall119895isin119867119894

119901119894119895119908119894119895(x119894minus x119895) (x119894minus x119895)119879

minus sum

119905isin119867119898

119902119898119905119908119898119905(x119898minus x119905) (x119898minus x119905)119879]

+ 2A[

[

sum

forall119895isin119872119894

119901119894119895119908119894119895(x119894minus x119895) (x119894minus x119895)119879

minus sum

119905isin119872119898

119902119898119905119908119898119905(x119898minus x119905) (x119898minus x119905)119879]

= 2A[

[

sum

forall119895isin119867119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879

+ sum

forall119895isin119872119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879]

]

(7)





119894119894= sum119895U119867119894119895and D119872

119894119894=


be reduced to

119889119862 (A)119889 (A)

= 2A

sum

forall119895isin119867119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879

+ sum

forall119895isin119872119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879

= 2A

( sum

forall119895isin119867119894

119906119894119895x119894x119879119894+ sum

forall119895isin119867119894

119906119894119895x119895x119879119895

minus sum

forall119895isin119867119894

119906119894119895x119894x119879119895minus sum

forall119895isin119867119894

119906119894119895x119895x119879119894)

+ ( sum

forall119895isin119872119894

119906119894119895x119894x119879119894+ sum

forall119895isin119872119894

119906119894119895x119895x119879119895

minus sum

forall119895isin119872119894

119906119894119895x119894x119879119895minus sum

forall119895isin119872119894

119906119894119895x119895x119879119894)

= 4A (XD119867X119879 minus XU119867X119879)

+ (XD119872X119879 minus XU119872X119879)


(8)







class labels












119901119894119895=

exp (minus119863geo1198941198952)

sum119896 = 119894

exp (minus119863geo1198941198962)

119902119894119895=

[1205742+ (x119894minus x119895)119879

A119879A (x119894minus x119895)]

minus1

sum119896 = 119897

[1205742 + (x119896minus x119897)119879A119879A(x


min119862 (A) = sum119894119895

119901119894119895log

119901119894119895

119902119894119895

(9)

where 119863geo119894119895




119901119894119895=


10038171003817100381710038171003817

2

21205822)

sum119888119896=119888119897


1003817100381710038171003817221205822)

if 119888119894= 119888119895


10038171003817100381710038171003817

2

21205822)

sum119888119896 =119888119898


1003817100381710038171003817221205822)

else


119902119894119895=

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119888119896=119888119897

(1 + (x119896minus x119897)119879A119879A (x


if 119888119894= 119888119895

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119888119896 =119888119898

(1 + (x119896minus x119898)119879A119879A (x


else

min119862 (A) = sum

119888119894=119888119895

119901119894119895log

119901119894119895

119902119894119895

+ sum

119888119894 =119888119896

119901119894119896log

119901119894119896

119902119894119896

(10)



119894







4 Kernel FDSNE




120581 (x119894 x119895) = ⟨120593 (x

119894) 120593 (x

119895)⟩ (11)



119894) for


A = [

119873

sum

119894=1

119887(1)

119894120593119894

119873

sum

119894=1

119887(119903)

119894120593119894]

119879

(12)

We define B = [119887(1) 119887

(119903)]119879

and Φ = [1205931 120593

119873]119879



119889119865

119894119895(A) = 10038171003817100381710038171003817A (120593

119894minus 120593119895)10038171003817100381710038171003817=10038171003817100381710038171003817BΦ (120593

119894minus 120593119895)10038171003817100381710038171003817

=10038171003817100381710038171003817B (119870119894minus 119870119895)10038171003817100381710038171003817= radic(119870

119894minus 119870119895)119879

B119879B (119870119894minus 119870119895)

(13)

where 119870119894= [120581(x

1 x119894) 120581(x




119894119895(A) with 119889119865

119894119895(A)



1199011

119894119895

=

exp (minus (119870119894119894+ 119870119895119895minus 2119870119894119895) 21205822)

sum119905isin119867119898

exp (minus (119870119898119898

+119870119905119905minus2119870119898119905) 21205822)

forall119895 isin 119867119894

exp (minus (119870119894119894+ 119870119895119895minus 2119870119894119895) 21205822)

sum119905isin119872119898

exp (minus (119870119898119898

+119870119905119905minus2119870119898119905) 21205822)

forall119895 isin 119872119894

0 otherwise

1199021

119894119895

=

(1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895))

minus1

sum119905isin119867119898

(1+(119870119898minus119870119905)119879B119879B (119870

119898minus119870119905))minus1

forall119895 isin 119867119894

(1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895))

minus1

sum119905isin119872119898

(1+(119870119898minus119870119905)119879B119879B (119870

119898minus119870119905))minus1

forall119895 isin 119872119894

0 otherwise(14)






119889119862 (B)119889 (B)

= sum

forall119895isin119872119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

+ sum

forall119895isin119867119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

= 2B[[

sum

forall119895isin119867119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879

+ sum

forall119895isin119872119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879]

]

(15)


119894119895 1199061119894119895 1199061119867119894119895 and 1199061119872


1199081

119894119895= [1 + (119870

119894minus 119870119895)119879

B119879B (119870119894minus 119870119895)]

minus1

1199061

119894119895= (119901119894119895minus 119902119894119895)1199081

119894119895

1199061119867

119894119895=

1199061

119894119895forall119895 isin 119867

119894

0 otherwise

1199061119872

119894119895=

1199061

119894119895forall119895 isin 119872

119894

0 otherwise

(16)


119889119862 (B)119889 (B)

= 2B

sum

forall119895isin119867119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879

+ sum

forall119895isin119872119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879


= 4B (KD1119867K119879 minus KU1119867K119879)

+ (KD1119872K119879 minus KU1119872K119879)





119894119894= sum119895U1119867119894119895

andD1119872119894119894

= sum119895U1119872119894119895




119889119862119865(A)

119889 (A)

= sum

forall119895isin119872119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

+ sum

forall119895isin119867119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

= 2[[

[

sum

forall119895isin119867119894

1199011

119894119895

B (119870119894minus 119870119895) (120593119894minus 120593119895)119879

(1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895))

]]

]

minus 2[

[

sum

forall119895isin119867119894

1199011

119894119895( sum

119905isin119867119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus2


times( sum

119905isin119867119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus1

)

minus1

]

]

+ 2[

[

sum

forall119895isin119872119894

1199011

119894119895

B (119870119894minus 119870119895) (120593119894minus 120593119895)119879

1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895)

]

]

minus 2[

[

sum

forall119895isin119872119894

1199011

119894119895( sum

119905isin119872119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus2






times( sum

119905isin119872119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus1

)

minus1

]

]

= 2[

[

sum

forall119895isin119867119894

1199011

1198941198951199081

119894119895B119876(119870119894minus119870119895)119894119895

minus sum

119905isin119867119898

1199021

1198981199051199081

119898119905B119876(119870119898minus119870119905)119898119905

]

]

Φ

+ 2[

[

sum

forall119895isin119872119894

1199011

1198941198951199081

119894119895B119876(119870119894minus119870119895)119894119895

minus sum

119905isin119872119898

1199021

1198981199051199081

119898119905B119876(119870119898minus119870119905)119898119905

]

]

Φ

= 2[

[

sum

forall119895isin119867119894

1199061

119894119895B119876(119870119894minus119870119895)119894119895

+ sum

forall119895isin119872119894

1199061

119894119895B119876(119870119894minus119870119895)119894119895

]

]

Φ

(18)




119895minus 119870119894in the






5 Experiments






















10 20 30 40 50 6007

075

08

085

Dimensionality

Reco

gniti

on ra

te (

)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(a) ℎ = 5

10 20 30 40 50 60075

08

085

09

095

Dimensionality

Reco

gniti

on ra

te (

)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(b) ℎ = 10



FKDSNE2FKDSNE1FDSNE

DSNEMSNP

10 20 30 40 50 60065

07

075

08

085

Dimensionality

Reco

gniti

on ra

te (

)

(a) ℎ = 14

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

Reco

gniti

on ra

te (

)

10 20 30 40 50 6007

075

08

085

09

Dimensionality

(b) ℎ = 25


10 20 30 40 50 6006

065

07

075

08

085

Dimensionality

Reco

gniti

on ra

te (

)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(a) ℎ = 3

Reco

gniti

on ra

te (

)

10 20 30 40 50 6006

065

07

075

08

085

09

Dimensionality

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(b) ℎ = 5






10 20 30 40 50 60

10

20

30

40

50

Dimensionality

Elap

sed

time (

s)

FKDSNE2FKDSNE1

FDSNEDSNE

(a) ℎ = 5


Elap

sed

time (

s)

20

40

60

80

FKDSNE2FKDSNE1

FDSNEDSNE

(b) ℎ = 10


10 20 30 40 50 60

6

8

10

12

14

16

18

Dimensionality

Elap

sed

time (

s)

FKDSNE2FKDSNE1

FDSNEDSNE

(a) ℎ = 14

Elap

sed

time (

s)

10 20 30 40 50 60

25

30

35

40


FDSNEDSNE

(b) ℎ = 25





2= 40 for DSNE





Elap

sed

time (

s)

10 20 30 40 50 60

5

10

15

20

25

30

35

40

Dimensionality

FKDSNE2FKDSNE1

FDSNEDSNE

(a) ℎ = 3

10 20 30 40 50 60

10

20

30

40

50

60

Dimensionality

FKDSNE2FKDSNE1

FDSNEDSNE

Elap

sed

time (

s)

(b) ℎ = 5




0 200 400 600 800 1000

Iteration number

Obj

ectiv

e fun

ctio

n va

lue (

log)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

minus7

minus6

minus4

minus5








6 Conclusion


Acknowledgment


References








































1 Introduction

















119863 =1

119873

119873

sum

119899=2

log 119901119909 (119899)

log 119899 (1)


119873


120583119903 (119896) =

119896+119903minus1

sum

119904=119896

Vlowastsh (2)





119901119903 (119896) =1

119903

119896+119903minus1

sum

119904=119896

Vlowastsh (3)


119901119903 (119896)119896=1119873 (4)


3 Results












4 Discussion










5 Conclusion




References
















































1 Introduction











119875 (119903 120579) = 119877 (119903 120579) 119891 (119909 119910)

= ∬

infin

minusinfin

119891 (119909 119910) 120575 (1199031199021 minus 119879 (120595 (119909 119910) 120579)) 119889119909 119889119910

(1)

where 120595(119909 119910) isin 1198712(119863) 119902



119879 (120595 (119909 119910) 120579) minus 1199031199021 = 0 (2)





1= 1 119879(120595(119909 119910) 120579) =




119875 (119903 120579) = 119875 (119903 120579 plusmn 2119896120587) (3)


2(119909 119910) are two images


1(119909 119910) and 119891


10038161003816100381610038161198751 (119903 120579) minus 1198752 (119903 120579)1003816100381610038161003816

le ∬119863

100381610038161003816100381610038161003816100381610038161198911 (119903 120579)minus1198912 (119903 120579)

1003816100381610038161003816 120575 (1199031199021minus119879 (120595 (119909 119910) 120579))

1003816100381610038161003816 119889119909 119889119910

(4)



a distance 119889 = 1199090cos 120579 + 119910







119875 (119903 120579) 997888rarr 119875 (119903 120579 + 1205790) (6)


119891 (119886119909 119886119910) 997888rarr1

1198862119875 (119886119903 120579) (7)


119885119901119902=(119901 + 1)

120587int

2120587

0

int

1

0

119877119901119902 (119903) 119890

minus119902120579119891 (119903 120579) 119903119889119903 119889120579 (8)


119877119901119902 (119903) =

119901

sum

119896=119902


119861119901|119902|119896

119903119896 (9)

With

119861119901|119902|119896

=

(minus1)((119901minus119896)2)

((119901+119896) 2)


0 119901minus119896 = odd(10)




Line Radontransform






(119903 120579) = 120582119875(119903

120582 120579 + 120573) (11)


119885119901119902=119901 + 1

120587int

2120587

0

int

1

0

(119903 120579) 119877119901119902 (120582119903) 119890(minus119902120579)

119903119889119903 119889120579

=119901 + 1

120587int

2120587

0

int

1

0

120582119875(119903

120582 120579 + 120573)119877

119901119902 (120582119903) 119890(minus119902120579)

119903119889119903 119889120579

(12)



119877119901119902 (120582119903) =

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

120582119894119861119901119902119894119863119901119894119896 (13)

Image



Zernikemoment NRZM




119885119901119902=119901 + 1

120587

times int

2120587

0

int

1

0

120582119875(119903

120582 120579+120573)

times

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

120582119894119861119901119902119894119863119901119894119896119890(minus119902120579)

119903119889119903 119889120579

(14)



119885119901119902=119901 + 1

120587

times int

2120587

0

int

1

0

120582119875 (120591 120593)

119901

sum

119896=119902

119877119901119896 (119903)

times

119896

sum

119894=119902

(120582119894119861119901119902119894119863119901119894119896) 119890(minus119902(120593minus120573))

1205822120591119889120591 119889120593

=119901 + 1

120587119890119902120573

times int

2120587

0

int

1

0

119875 (120591 120593)

times

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

(120582119894+3119861119901119902119894119863119901119894119896) 119890minus119902120593

120591119889120591 119889120593

=119901 + 1

120587119890119902120573

times

119901

sum

119896=119902

119896

sum

119894=119902

(120582119894+3119861119901119902119894119863119901119894119896)

times int

2120587

0

int

1

0

119875 (120591 120593) 119877119901119896 (119903) 119890

minus119902120593120591119889120591 119889120593

= 119890119902120573

119901

sum

119896=119902

119896

sum

119894=119902

(120582119894+3119861119901119902119894119863119901119894119896)119885119901119896

(15)



119868119901119902= exp (119895119902119886119903119892 (119885

11))

119901

sum

119896=119902

(

119896

sum

119894=119902

11988500

minus((119894+3)3)119861119901119902119894119863119901119894119896)119885119901119896

(16)

Then 119868119901119902




119877119885119872 = [119868119891 (1 0) 119868119891 (1 1) 119868119891 (119872119872)] (17)




1199021


PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

Chongrsquos method







Bird

Bone

Bric

k

Cam

el

Car

Ch

ildre

nCl

assic

El

epha

ntFa

ce

Fo

rk

Gla

ss

Ham

mer

H

eart

Ke

y

M

isk

Ra

y

Tu

rtle

0

2

4

6

8

10

12


PRZ

Foun

tain

The n

umbe

r of r

etrie

ved

rele

vant

imag

e













4 Conclusion




09

08

07

06

05

04

03

02

01

0090807060504030201 1

(a) SNR = 16

09

08

07

06

05

04

03

02

01

0090807060504030201 1

(b) SNR = 14

09

08

07

06

05

04

03

02

01

0090807060504030201 1

(c) SNR=12

09

08

07

06

05

04

03

02

01

0090807060504030201 1

(d) SNR=10

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0090807060504030201 1

Chongrsquos method

(e) SNR = 8

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0090807060504030201 1

Chongrsquos method

(f) SNR = 6

Figure 4 Continued


PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0090807060504030201 1

Chongrsquos method

(g) SNR =4

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0

1

0 090807060504030201

Chongrsquos method



PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

010 08060402 1

1

Chongrsquos method




Appendix


(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)

=(

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)(

119903119902

119903119902+1

119903119901

)

(A1)



(

119903119902

119903119902+1

119903119901

) = (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

minus1

times(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)


= (

119863119901119902119902

119863119901119902119902+1

sdot sdot sdot 119863119901119902119901

119863119901119902+1119902+1

sdot sdot sdot 119863119901119902+1119901

d

119863119901119901119901

)

times(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)

(

119877119901119902 (120582119903)

119877119901119902+1 (120582119903)

119877119901119901 (120582119903)

) = (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

times(

(120582119903)119902

(120582119903)119902+1

(120582119903)119901

)

= (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

times(

120582119902

120582119902+1

d120582119901

)(

119903119902

119903119902+1

119903119901

)

= (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

times(

120582119902

120582119902+1

d120582119901

)

times(

119863119901119902119902

119863119901119902119902+1

sdot sdot sdot 119863119901119902119901

119863119901119902+1119902+1

sdot sdot sdot 119863119901119902+1119901

d

119863119901119901119901

)

times(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)

=

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

119903119894sdot 119861119901119902119894sdot 119863119901119894119896

(A2)

Acknowledgments


References

































1 Introduction










ECGsignal

Signalprocessing

Featureextraction

IEMMCalgorithm

Resultcompare


ClearECGAdaptive

Filter


noise 1198641

RawECGsignal


1198642

Referenceinput

Wavelettransform





21 Preprocessing






119877119877119899(s) 119877119877

1015840

119899(s) 119876119877119878

119899(s) 119875119877

119899(s) 119876119879

119899(s) 119878119879

119899(s) 119877

119899(mv) 119875

119899(mv) 119879

119899(mv)

08477 08692 00742 01663 02930 02188 18149 00570 0681709023 08931 00742 01445 02891 02148 16339 00142 0592608594 08916 00781 01406 02852 02070 23085 00579 0612508281 08034 00742 01663 02931 02109 21007 00469 06247



1which contain














119899)


119899)




119899)






119899and 119877119877

1015840







119899 and

their labels 119910 = 1199101 119910





min119908119887120585119894

1

21199082+ 119862

119899

sum

119894=1

120585119894

st 119910119894(119908119879120601 (119909) + 119887) ge 1 minus 120585

119894

120585119894ge 0 119894 = 1 119899

(1)








119899min119908119887120585119894

1

21199082+ 119862

119899

sum

119894=1

120585119894

st 119910119894(119908119879120601 (119909) + 119887) ge 1 minus 120585

119894

120585119894ge 0 119894 = 1 119899 119862 ge 0

(2)


minusℓ le 119890119879119910 le ℓ (3)





inf119891isin119867

1

119899

119899

sum

119894=1

119871 (119910119894 119891 (119909119894)) + 120582

100381710038171003817100381711989110038171003817100381710038172

119867 (4)


2






2 leading to

min119908119887120578

1

21199082+119862

2

119899

sum

119894=1

1205782

st 119910i ((119908119879120601 (119909119894)) + 119887) = 1 minus 120578 119894 = 1 119899

(5)


minyisinminus1+1119899119908119887

119869 (119910 119908 119887) =1

21199082+119862

2

119899

sum

119894=1

1205782

st 119910i ((119908119879120601 (119909119894)) + 119887) = 1 minus 120578

119894 = 1 119899 minus119897 le

119899

sum

119894=1

119910119894le 119897

(6)







119910119898+119903


119875119898


119898+ 119875119903) 119875 should















lowast

119898is generated


119888and 119875

lowast

119898to








1 119910

119898+119903 sube minus1 +1



119875119903(119875 = 119875



119865 (119910) = exp (minusmin 119869 (119910 119908 119887)) (7)



would be returned


min119910119887

119899

sum

119894=1

(119908 sdot 120601 (119909119894) + 119887 minus 119910

119894)2


119894 = 1 119899 minusℓ le 119890119879119910 le ℓ

(8)
















sensitivity =TP

(TP + FN)

specificity =TN

(FP + TN)

accuracy =(TP + TN)

(TP + FN + FP + TN)

(9)








10158401205902) is used




100

90

80

70

60

50

40

30

200 1 2 3 4 5 6 7 8 9 10

Sens

itivi

ty (

)




(a) Sensitivity



Spec

ifici

ty (

)

100

95

90

85

80

75

70

65

600 1 2 3 4 5 6 7 8 9 10


(b) Specificity



Accu

racy

()

100

95

90

85

80

75

70

65

60


55

50

(c) Accuracy



4 Conclusions





Acknowledgments


References





































1 Introduction










A C T G














[ 119865[minus ]

[ 119865[minus ]

[ 119865[minus ]

[119865][119865]

[+119865]

[+119865]

[+119865]







119866 = (119881 120596 119875) (1)

where

(i) 119881 = 1199041 1199042 119904
















119875 997888rarr 119871119877 (2)


119871and 119877


119875 rarr 119871119877 and 119877 rarr 119877119871119877119877


119875 997888rarr [minus119865119871] [+119865119877]



(3)


119877119871rdquo and ldquo119877



119875

119871 119871119877 119877

119875

119877119871 119877119877

119875 rarr 119871119877 119875 rarr 119871119877

119877 rarr 119877119871119877119877




119875 997888rarr [minus119865119879119871] [+119865119879

119877]

119879119871997888rarr [minus119865] [+119865]

119879119877997888rarr [minus119865] [+119865119879119877119877

]

119879119877119877

997888rarr [minus119865] [+119865119879119877119877119877]

119879119877119877119877

997888rarr [minus119865]

(4)


119877rarr

[minus119865][+119865119879119877119877] and 119879

119877119877rarr [minus119865][+119865119879






119875119875

119879119871

119879119871119879119877

119879119877

119879119877119877

119879119877119871


119879119877 rarr [minus119865119879119877119871][+119865119879119877119877

]

119879119877 rarr null


119879119877119871rarr null

119879119877119877rarr null


119875

119879119871 119879119877

119875

119879119871 119879119877

119879119877119877119879119877119871


119879119877 rarr [minus119865119879119877119871][+119865119879119877119877

]




119877rarr

[minus119865][+119865119879119877119877] and 119879

119877119877rarr [minus119865][+119865119879





2are homomorphic



2in DNA


1and rule119877

2generate




2are isomorphic on



119875 997888rarr [minus119865119879119871] [+119865119879

119877] 997888rarr [minus119865] [+119865]


119879119877997888rarr [minus119865] [+119865119879119877119877

] 997888rarr [minus119865] [+119865]

119879119877119877


119879119877119877119877


(5)

We find that 119875 119879119871 119879119877 and 119879







3rarr





rarr [minus119865][+119865] and119879119877119877119877119871119871

rarr [minus119865][+119865] and 119879119877119871119877119871119877




119877] 119879119877119871119871119871

rarr

[minus119865][+119865] and 119879119877119877119877119877

rarr [minus119865][+119865119879119877119877119877119877119877









119875 rarr [minus119865119879119871] [+119865119879

119877]

119879119871rarr [minus119865119879

119871119871] [+119865119879

119871119877]

119879119871119871

rarr [minus119865119879119871119871119871

] [+119865119879119871119871119877

]

119879119871119871119871

rarr [minus119865119879119871119871119871119871

] [+119865119879119871119871119871119877

]

119879119871119871119871119871

rarr [minus119865] [+119865]

119879119871119871119871119877

rarr [minus119865] [+119865]

119879119871119871119877

rarr [minus119865119879119871119871119877119871

] [+119865119879119871119871119877119877

]

119879119871119871119877119871

rarr [minus119865] [+119865119879119871119871119877119871119877]

119879119871119871119877119871119877

rarr [minus119865] [+119865]

119879119871119871119877119877

rarr [minus119865] [+119865119879119871119871119877119877119877]

119879119871119871119877119877119877

rarr [minus119865] [+119865]

119879119871119877

rarr [minus119865119879119871119877119871

] [+119865119879119871119877119877

]

119879119871119877119871

rarr [minus119865119879119871119877119871119871

] [+119865119879119871119877119871119877

]

119879119871119877119871119871

rarr [minus119865119879119871119877119871119871119871

] [+119865]

119879119871119877119871119871119871

rarr [minus119865] [+119865]

119879119871119877119871119877

rarr [minus119865119879119871119877119871119877119871

] [+119865]

119879119871119877119871119877119871

rarr [minus119865] [+119865]

119879119871119877119877

rarr [minus119865119879119871119877119877119871

] [+119865119879119871119877119877119877

]

119879119871119877119877119871

rarr [minus119865119879119871119877119877119871119871

] [+119865119879119871119877119877119871119877

]

119879119871119877119877119871119871

rarr [minus119865] [+119865]

119879119871119877119877119871119877

rarr [minus119865] [+119865]

119879119871119877119877119877

rarr [minus119865119879119871119877119877119877119871

] [+119865119879119871119877119877119877119877

]

119879119871119877119877119877119871

rarr [minus119865] [+119865]

119879119871119877119877119877119877

rarr [minus119865] [+119865]

119879119877rarr [minus119865119879

119877119871] [+119865119879

119877119877]

119879119877119871

rarr [minus119865119879119877119871119871

] [+119865119879119877119871119877

]

Table 1 Continued

119879119877119871119871

rarr [minus119865119879119877119871119871119871

] [+119865119879119877119871119871119877

]

119879119877119871119871119871

rarr [minus119865] [+119865]

119879119877119871119871119877

rarr [minus119865119879119877119871119871119877119871

] [+119865]

119879119877119871119871119877119871

rarr [minus119865][+119865]

119879119877119871119877

rarr [minus119865119879119877119871119877119871

] [+119865119879119877119871119877119877

]

119879119877119871119877119871

rarr [minus119865] [+119865119879119877119871119877119871119877]

119879119877119871119877119871119877

rarr [minus119865][+119865]

119879119877119871119877119877

rarr [minus119865119879119877119871119877119877119871

] [+119865119879119877119871119877119877119877

]

119879119877119871119877119877119871

rarr [minus119865][+119865]

119879119877119871119877119877119877

rarr [minus119865] [+119865]

119879119877119877

rarr [minus119865119879119877119877119871

] [+119865119879119877119877119877

]

119879119877119877119871

rarr [minus119865119879119877119877119871119871

] [+119865119879119877119877119871119877

]

119879119877119877119871119871

rarr [minus119865119879119877119877119871119871119871

] [+119865]

119879119877119877119871119871119871

rarr [minus119865] [+119865]

119879119877119877119871119877

rarr [minus119865][+119865]

119879119877119877119877

rarr [minus119865119879119877119877119877119871

] [+119865119879119877119877119877119877

]

119879119877119877119877119871

rarr [minus119865119879119877119877119877119871119871

] [+119865119879119877119877119877119871119877

]

119879119877119877119877119871119871

rarr [minus119865][+119865]

119879119877119877119877119871119877

rarr [minus119865][+119865]

119879119877119877119877119877

rarr [minus119865] [+119865119879119877119877119877119877119877]

119879119877119877119877119877119877

rarr [minus119865][+119865]


form)

119881119894997888rarr 11990511989411198801198941 11990511989421198801198942 119905

119894119896119894119880119894119896119894 (6)

where 1199051198941 1199051198942 119905


1198941 1198801198942



119881119894=

119896119894

sum

119895=1

119905119894119895119880119894119895 (7)



119881119894 (119911) =

infin

sum

119899=1

119873119894 (119899) 119911

119899 (8)








Class 1(19) 119862

1rarr 11986211198621

(4) 1198621rarr 11986211198622

(4) 1198621rarr 11986221198621

(20) 1198621rarr 11986221198622

(8) 1198621rarr 11986211198621

(3) 1198621rarr 11986211198621

(1) 1198621rarr 11986211198621

(1) 1198621rarr 11986211198623

(1) 1198621rarr 11986241198622

(1) 1198621rarr 11986241198623

(1) 1198621rarr 11986221198622

(1) 1198621rarr 11986271198625

(1) 1198621rarr 11986251198622

(1) 1198621rarr 11986221198624

(1) 1198621rarr 11986281198628

(1) 1198621rarr 11986231198621

(1) 1198621rarr 11986231198621

(1) 1198621rarr 11986231198623

(1) 1198621rarr 11986281198626

(1) 1198621rarr 11986241198622

(5) 1198621rarr 11986241198624

Class 2 (48) 1198622rarr null (4) 119862

2rarr 11986241198625

(1) 1198622rarr 119862811986210

(1) 1198622rarr 11986281198626

Class 3 (4) 1198623rarr 11986251198624

(1) 1198623rarr 11986291198629

(1) 1198623rarr 11986291198627

Class 4 (20) 1198624rarr 11986251198625

(1) 1198624rarr 119862911986211

(1) 1198624rarr 1198621211986210

Class 5 (48) 1198625rarr null (1) 119862

5rarr 119862101198628

(1) 1198625rarr 1198621311986211

Class 6 (1) 1198626rarr 1198621011986210

(1) 1198626rarr 1198621311986213

Class 7 (1) 1198627rarr 119862111198629

(1) 1198627rarr 1198621311986215

Class 8 (5) 1198628rarr 1198621111986211

(1) 1198628rarr 1198621411986214

Class 9 (4) 1198629rarr 1198621111986212

(1) 1198629rarr 1198621411986216

Class 10 (4) 11986210

rarr 1198621211986211

(1) 11986210

rarr 1198621511986213

Class 11 (20) 11986211

rarr 1198621211986212

(1) 11986211

rarr 1198621511986215

Class 12 (48) 11986212

rarr null (1) 11986212

rarr 1198621611986214

Class 13 (5) 11986213

rarr 1198621611986216

Class 14 (4) 11986214

rarr 1198621611986217

Class 15 (4) 11986215

rarr 1198621711986216

Class 16 (20) 11986216

rarr 1198621711986217

Class 17 (48) 11986217

rarr null



1198700= minus ln119877 (9)




119894contains 119899

119894rules Let 119881

119894isin 1198621 1198622 119862

119899

119880119894119895isin 119877119894119895 119894 = 1 2 119899 119895 = 1 2 119899

119894 and 119886

119894119895119896isin


form

1198801198941997888rarr 119881

1198861198941111988111988611989412

1198801198942997888rarr 119881

1198861198942111988111988611989422


119880119894119899119894

997888rarr 1198811198861198941198991198941

1198811198861198941198991198942

(10)


follows

119881119894 (119911) =

sum119899119894

119901=11198991198941199011199111198811198861198941199011

(119911) 1198811198861198941199012(119911)

sum119899119894

119902=1119899119894119902

(11)


119881119894(119911) = 1




1to denote the



1(119911) we set 119877 = 119911




1198700= minus ln119877 (12)



1198815(1199111015840) = 1 (by definition)

1198814(1199111015840) =

sum1198994

119901=11198994119901119911101584011988111988641199011

(1199111015840)11988111988641199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=1199111015840times (20 times 119881

5(1199111015840) times 1198815(1199111015840))

20= 1199111015840

1198813(1199111015840) =

sum1198993

119901=11198993119901119911101584011988111988631199011

(1199111015840)11988111988631199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=1199111015840times (4 times 119881

5(1199111015840) times 1198814(1199111015840))

4= 11991110158402

1198812(1199111015840) =

sum1198992

119901=11198992119901119911101584011988111988621199011

(1199111015840)11988111988621199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=1199111015840times (4 times 119881

4(1199111015840) times 1198815(1199111015840))

4= 11991110158402

1198811(1199111015840) =

sum1198991

119901=11198991119901119911101584011988111988611199011

(1199111015840)11988111988611199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=81199111015840times 1198811(1199111015840)2

+ 2(1199111015840)3

times 1198811(1199111015840)

19

+

(2(1199111015840)5

+ 2(1199111015840)4

+ 5(1199111015840)3

)

19

(13)


a quadratic for 1198811(1199111015840)

8

19(1199111015840) times 1198811(1199111015840) + (1 minus

2

19(1199111015840)3

) times 1198811(1199111015840)

+1

19(2(1199111015840)5

+ 2(1199111015840)4

+ 5(1199111015840)3

) = 0

(14)


1198811(1199111015840) = (

(1199111015840)2

4minus

19

81199111015840) plusmn

19

81199111015840radic1198612 minus 119860 (15)



119899111

119899112

(8) 1198621rarr 11986211198621

11989912

119899121

119899122

(1) 1198621rarr 11986211198623

11989913

119899131

119899132

(1) 1198621rarr 11986221198622

11989914

119899141

119899142

(119899 = 5) Class 1 (1198991= 8)

(1) 1198621rarr 11986221198624

11989915

119899151

119899152

(1) 1198621rarr 11986231198621

11989916

119899161

119899162

(4) 1198621rarr 11986231198623

11989917

119899171

119899172

(1) 1198621rarr 11986241198622

11989918

119899181

119899182

(5) 1198621rarr 11986241198624

Class 2 (1198992= 1)

11989921

119899211

119899212

(4) 1198622rarr 11986241198625

Class 3 (1198993= 1)

11989931

119899311

119899312

(4) 1198623rarr 11986251198624

Class 4 (1198994= 1)

11989941

119899411

119899412

(20) 1198624rarr 11986251198625

Class 5 (1198995= 1)

11989951

119899511

119899512

(48) 1198625rarr null






where

119860 =32

361(2(1199111015840)6

+ 2(1199111015840)5

+ 5(1199111015840)4

)

119861 = 1 minus2

19(1199111015840)3

(16)


B

D

A C


04

06

08

1

1 101 201 301 401 501 601 701 801 901

234





119881119898

119894(1199111015840) =

sum119899119894

119901=11198991198941199011199111015840119881119898minus1

1198861198941199011(1199111015840)119881119898minus1

1198861198941199012(1199111015840)

sum119899119894

119902=1119899119894119902

1198810

119894(1199111015840) = 1

(17)


119894(1199111015840) to 119881

119898

119894(1199111015840) When 119881

119898minus1

119894(1199111015840) =

119881119898


119894(1199111015840) reach the








4 Results


0

02

04

06

08

1

12

1 11 21 31 41 51 61 71 81 91

0

02

04

06

08

1

12

1 51 101 151 201 251

TEIso 1

Iso 2Iso 3


002040608

11214

1 101 201







0

02

04

06

08

1

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3


0

02

04

06

08

1

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3


0

02

04

06

08

1

12

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3


0

02

04

06

08

1

12

14

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3











0

02

04

06

08

1 101 201 301 401 501 601 701 801 901

1632

64128

(a) Koslicki method

0

02

04

06

08

1

12

14

1 101 201 301 401 501 601 701 801 901

1632

64128


0

02

04

06

08

1

12

14

1 101 201 301 401 501 601 701 801 901

1632

64128


0

02

04

06

08

1

12

1 101 201 301 401 501 601 701 801 901

1632

64128





5 Summary




Acknowledgment


References
































1 Introduction

















2 Backgrounds






119903119894= minus ln [ 119873 (119894 120572)

1198730 (119894 120572)

] (1)



119873(119894 120572) = 1198730 (119894 120572) exp (minus119903119894) (2)



1205902

119894(120583119894) = 119891119894exp(

120583119894

120574) (3)








119894=

1

119862 (119894)sum

119895isin119861(119894 119903)

119910119895120596 (119894 119895) (4)



sum119895isin119861(119894 119903)


119895isin119861(119894 119903)120596(119894 119895) = 1


1198892(119894 119895) =

1

(2119891 + 1)2

sum

119896isin119861(0 119891)

(119910119894+119896minus 119910119895+119896)2

(5)


120596 (119894 119895) = 119890minusmax(1198892minus21205902

119873 0)ℎ2

(6)





dim (119878) = lim120576rarr0

log119873(120576)

log (1120576) (7)


119899120576= 120580 minus 120581 + 1 (8)


119873120576= sum

119895

119899120576(119895) (9)




3 The New Method







119899120576 (119894) = 120580 minus 120581 + 1 (10)


window is

119873120576 (119894) = sum

119895

119899120576(119895) (11)







(a) (b) (c)

(d) (e) (f)




120596 (119894 119895) = 119890minusmax(1198892minus21205902

119873 0)ℎ2

1minus(119896(119894)minus119896(119895))

2ℎ2

2 (12)




1198892(119894 119895) =

1

(2119891 + 1)2

sum

119896isin119861(0 119891)

(119910119894+119896minus 119910119895+119896)2

(13)



119894=

1

119862 (119894)sum

119895isin119861(119894 119903)

119910119895120596 (119894 119895) (14)




119895isin119861(119894 119903)120596(119894 119895) = 1



119899 119899 isin 119885 and
























1= 15 for the






119891119894= 35 119879 = 2119890 + 4 2188 3379 3459

119891119894= 4 119879 = 2119890 + 4 2130 3345 3416












119873= 15 the size





5 Conclusions




Acknowledgments


References











































1 Introduction








2 Theory



minusinfin

119906 (x) ℎ (x minus r) 119889x (1)



minusinfin






nabla2119906 (r) + 412058721198962119906 (r) = 0 (3)


119906 (r) = 119860 exp (1198952120587k sdot r) (4)



minusinfin

119880 (k) exp (1198952120587k sdot r) 119889k (5)



minusinfin



119906 (119903119909 119903119910 119903119911)

=∭infin

119880(119896119909 119896119910 119896119911) exp (1198952120587 (119896

119909119903119909+ 119896119910119903119910+ 119896119911119903119911)) 120575


1

1205822minus 1198962119909minus 1198962119910)119889119896119909119889119896119910119889119896119911

= ∬infin

119880(119896119909 119896119910 plusmnradic

1

1205822minus 1198962119909minus 1198962119910)

times exp(1198952120587(119896119909119903119909+ 119896119910119903119910

∓119903119911radic1

1205822minus 1198962119909minus 1198962119910))119889119896

119909119889119896119910

(7)




119911(119896119909 119896119910)


such that

119880119911(119896119909 119896119910) = 119880(119896

119909 119896119910 radic

1

1205822minus 1198962119909minus 1198962119910) (8)


119911= 119885

we have

119906119885(119903119909 119903119910)

= ∬infin

119880119885(119896119909 119896119910) exp(1198952120587119885radic 1

1205822minus 1198962119909minus 1198962119910)

times exp (1198952120587 (119896119909119903119909+ 119896119910119903119910)) 119889119896119909119889119896119910

(9)


119880119885(119896119909 119896119910)

= exp(minus1198952120587119885radic 1

1205822minus 1198962119909minus 1198962119910)

times∬infin

119906119885(119903119909 119903119910) exp (minus1198952120587 (119896

119909119903119909+ 119896119910119903119910)) 119889119903119909119889119903119910

(10)



119877119885(119903119909 119903119910) = int

+infin

minusinfin

119880119885(119896119909 119896119910)119867lowast

119911(119896119909 119896119910)

times exp(1198952120587119885radic 1

1205822minus 1198962119909minus 1198962119910)

times exp (1198952120587 (119903119909119896119909+ 119903119909119896119910)) 119889119896119909119889119896119910

(11)


119911=

119885 and

119867119885(119896119909 119896119910) = 119867(119896

119909 119896119910 radic

1

1205822minus 1198962119909minus 1198962119910) (12)


119877119885(119903119909 119903119910) = int

+infin

minusinfin

119906119885 (119906 V) ℎ119885 (119906 minus 119903119909 V minus 119903119910) 119889119906 119889V

(13)

Object beam

Sample

Microscope lens

CCD



120572 (3∘)



where

ℎ119885(119903119909 119903119910) = int

+infin

minusinfin

119867119885(119896119909 119896119910)

times exp (minus1198952120587 (119903119909119896119909+ 119903119909119896119910)) 119889119896119909119889119896119910

(14)



119885(119903119909 119903119910) with an






[1199091 1199092 119909



1 ℎ2 ℎ


x =119899

sum

119894=1

ℎlowast

119894minus119899+1119909119894 (15)


ℎ119899+119886

= ℎ119886 (16)


x = [11988611990931+ 1198871199092

1+ 1198881199091+ 119889 119886119909

3

2+ 1198871199092

2+ 1198881199092

+119889 1198861199093

119899+ 1198871199092

119899+ 119888119909119899+ 119889]119879

(17)


x = [10038161003816100381610038161199091100381610038161003816100381621003816100381610038161003816119909210038161003816100381610038162

100381610038161003816100381611990911989910038161003816100381610038162] (18)


= 119894119894 (19)



1 s2 s



R = S (20)


119864 =

119899119898

sum

119894=1 119895=1

(119877119894119895minus 119874119894119895)2

+ 119899

119898

sum

119895=1

(1198771119895minus 1198741119895)2

(21)

40

35

30

25

20

15

10

5

0

119885po

sitio

ns (120583

)

8070

6050

4030

2010

0

119884 positions (120583) 0 10 20 30 40 50 60 70 80

119883 positions (120583)

7060

5040

3020

10

119884 positions 20 30 40 50 60 70

itions (120583)


where119877119894119895and119874




3 Experiment




(a) (b)








40

35

30

25

20

15

10

5

0

119885po

sitio

ns (120583

)

8070

6050

4030

2010






4 Conclusion


Acknowledgment


References





























1 Introduction














1 1199092 119909



119910 = 11988611199091+ 11988621199092+ sdot sdot sdot + 119886

119899119909119899 (1)




119910 = 119883119860 (2)




119879119883 + 120583119868)

minus1







followed

119890119894=1003817100381710038171003817119910 minus 119886

119894119909119894

10038171003817100381710038172 (3)
















119910 = 11988711199091+ sdot sdot sdot + 119887

119872119909119872 (4)



119910 = 119861 (5)




119861 = ()minus1

119910 (6)


119861 = (119879

+ 120574119868)minus1

119879

119910 (7)






119892119903= 119887119904119909119904+ sdot sdot sdot + 119887

119905119909119905 (8)



119863119903=1003817100381710038171003817119910 minus 119892

119903

10038171003817100381710038172 119903 isin 119862 (9)



119863119896= min119863
















1 1199092 119909



119894isin 119877119897


119906119894= 119882119879119909119894 (119894 = 1 2 119899) (11)



119878119879=

119899

sum

119894=1

(119909119894minus 120583) (119909

119894minus 120583)119879 (12)




1 1199062 119906

119899is



119882119898= arg max

119882

119882119879119878119879119882

= [1199081 1199082sdot sdot sdot 119908119897]

(13)



119863119894=10038171003817100381710038171003817119882119879

119898119910 minus119882

119879

119898119909119894

10038171003817100381710038171003817

2

=10038171003817100381710038171003817119882119879

119898(119910 minus 119909

119894)10038171003817100381710038171003817

2

(119894 = 1 2 119899)

(14)



119879 such that

119863119896= min119863

119894lt 119879 (119896 119894 = 1 2 119899 119879 isin [0 +infin)) (15)




119896






119878119887=

119871

sum

119894=1

119873119894(120583119894minus 120583) (120583

119894minus 120583)119879 (16)


119878119908=

119871

sum

119894=1

119873119894

sum

119895=1

(119909119895minus 120583119894) (119909119895minus 120583119894)119879

(17)





119908 such

that

119882119898= argmax

119882

1003816100381610038161003816100381611988211987911987811988711988210038161003816100381610038161003816

119882119879119878119908119882

= [11990811199082sdot sdot sdot 119908119897]

(18)




eigenvalues such as

119878119887119908119894= 120582119894119878119908119908119894 (119894 = 1 2 119897) (19)





is calculated as

119863119894=10038171003817100381710038171003817119882119879

119898119910 minus119882

119879

119898119909119894

10038171003817100381710038171003817

2

=10038171003817100381710038171003817119882119879

119898(119910 minus 119909

119894)10038171003817100381710038171003817

2

(119894 = 1 2 119899)

(20)



119863119896= min119863

119894lt 119879 (119896 119894 = 1 2 119899 119879 isin [0 +infin))

(21)






119896lt
















(24)






(25)












01 02 03 04 05 06 07 08 09 10

102030405060708090

100


Clas

sifica

tion

erro

r rat

e (

)

(a) T-TPTSR

0 01 02 03 04 05 06 07 08 09 10

102030405060708090

100


Clas

sifica

tion

erro

r rat

e (

)

(b) T-GR

0 005 01 015 02 0250

102030405060708090

100

Clas

sifica

tion

erro

r rat

e (

)



(c) T-PCA

005 01 015 02 025 030

102030405060708090

100

Clas

sifica

tion

erro

r rat

e (

)



(d) T-LDA







0 01 02 03 04 05 06 070

102030405060708090

100

Det

ectio

n ra

te (

)


(a) T-TPTSR

01 02 03 04 05 06 07 080

102030405060708090

100

Det

ectio

n ra

te (

)


(b) T-GR

005 01 015 02 025 030

102030405060708090

100

Det

ectio

n ra

te (

)


TPRoutlier

ERRFA

119863119874-119865

(c) T-PCA

0 005 01 015 02 025 03 035 04

0

20

40

60

80

100

Det

ectio

n ra

te (

)


minus20

TPRoutlier

ERRFA

119863119874-119865

(d) T-LDA






















5 Conclusion




Acknowledgment


References













































1 Introduction








2 Related Work











(a) (b)









119894119895(119905) The force


119886119894119895 (119905 + Δ119905) =

1

120583119894119895

119865119894119895 (119905)

V119894119895 (119905 + Δ119905) = V119894119895 (119905) + Δ119905 sdot 119886119894119895 (119905 + Δ119905)

119875119894119895 (119905 + Δ119905) = 119875119894119895 (119905) + Δ119905 sdot V119894119895 (119905 + Δ119905)

(1)












119875119906V (119905 + Δ119905) =

1003816100381610038161003816119875119906V (119905) + 119881119906V (119905 + Δ119905) sdot Δ1199051003816100381610038161003816 le (1 + 120591119888) sdot 119871

(2)


(a) (b)











119898 = 05 gray = 0ln (gray + 1) gray = 0

(3)
















119875119894119894(119890 119905)

119875 119894119895(119890 119905)

119875119894119896(119890 119905)State 119878119894

State 119878119895

State 119878119896

larr997892











119894 119878119895 and 119878




119895






119875119894119894 (119890 119905) = 119890

minus120582119894(119890)119905 0 le 119894 le 119899 (4)

120582119894 (119890) =

ln 2120591119894 (119890) (5)



denoted as 1 minus 119875119894119894(119890 119905) 119875



119895 and it is


119875119894119895 (119890 119905) = (1 minus 119875119894119894 (119890 119905))119883119894119895 (119890) 0 le 119894 ≺ 119899 119894 =119895 (6)






Begin

End


shapes


user interaction



probabilities








6 Results



7 Conclusion






Acknowledgments


References














































1 Introduction








2 Outlier Rejection




(1)





Number of matches

Bucket

Random

Variable

0 1

0

2 3

1

119871 minus 1







0 1 2 3 4 5 6

1

2

3

4

5

6

7

7

0





119873



matrixH or F


















(a) 51140

(b) 47140




5 Conclusion


50100150200250300350

100 200 300 400 500 600 700 800


50100150200250300350

100 200 300 400 500 600 700 800


50100150200250300350

100 200 300 400 500 600 700 800



0

200

400

600

800

1000

02 03 04 05 06 07 08 09120593

119879

RANSAC(P)RANSAC(E)





Acknowledgments


References



























1 Introduction













119888119888out =11989911989911989911989910055761005576119894119894=119894119888119888 (119894119894)

11989411989411989911989910055771005577119895119895=119894

119899 119899 119886119886 1007649100764911989511989510076651007665

= 119888119888119894 + 119888119888119899 10076491007649119899 119899 11988611988611989410076651007665 + 1198881198882 10076491007649119899 119899 11988611988611989910076651007665 10076491007649119899 119899 11988611988611989410076651007665 + ⋯

(1)




Image plane


0




119894119894 = 10077161007716119878119878Δ119878119878

10077321007732 119878 119895119895 = 10077171007717119878119878Δ119878119878

10077331007733 119878 119894119894 = 10077161007716119878119878Δ119878119878

10077321007732 119878

119878119878119894119894 = 119894119894 119894 Δ119878119878119878 119878119878119895119895 = 119895119895 119894 Δ119878119878119878 119878119878119894119894 = 119894119894 119894 Δ119878119878119878

119878119878119899119899 =119878119878 119899 119878119878119894119894Δ119878119878

119878 119878119878119899119899 =119878119878 119899 119878119878119895119895Δ119878119878

119878 119878119878119899119899 =119878119878 119899 119878119878119894119894Δ119878119878

119878

(2)



119865119865119899 = 119868119868119894 + 119878119878119899119899 119894 100764910076491198681198683 119899 11986811986811989410076651007665 119878 1198651198652 = 119868119868119899 + 119878119878119899119899 119894 100764910076491198681198682 119899 11986811986811989910076651007665 119878

1198651198653 = 1198681198685 + 119878119878119899119899 119894 100764910076491198681198686 119899 119868119868510076651007665 119878 1198651198654 = 1198681198684 + 119878119878119899119899 119894 100764910076491198681198687 119899 119868119868410076651007665 119878

1198651198655 = 119865119865119899 + 119878119878119899119899 119894 100764910076491198651198652 119899 11986511986511989910076651007665 119878 1198651198656 = 1198651198654 + 119878119878119899119899 119894 100764910076491198651198653 119899 119865119865410076651007665 119878

119865119865 = 1198651198655 + 119878119878119899119899 119894 100764910076491198651198656 119899 119865119865510076651007665 (3)






119883119883119894119894 120577 119894119894Δ119864119864 120577119894119894 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 119894120577 120577

119884119884119895119895 120577 119895119895Δ119864119864 10076491007649119895119895 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 11989410076651007665 120577

119885119885119896119896 120577 119896119896Δ119864119864 120577119896119896 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 119894120577

(4)


119864119864119895119895 120577 119864119864119900119900 + 120577120577 119864 119898119898119895119895 120577 119895119895Δ119864119864 10076491007649119895119895 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 11989410076651007665 120577 (5)


119895119895 120577 10077171007717119864119864Δ119864119864

10077331007733 (6)

erefore

119898119898119895119895 120577119895119895Δ119864119864 119894 119864119864119900119900

120577120577120577 (7)


119864119864119894119894 120577 119864119864119900119900 + 120577120577 119864 119898119898119895119895 119864119864119896119896 120577 119864119864119900119900 + 120577120577 119864 119898119898119895119895 (8)


119894119894 120577 10077171007717119864119864119894119894Δ119864119864

10077331007733 120577

119896119896 120577 10077171007717119864119864119896119896Δ119864119864

10077331007733 (9)




119868119868119864119864 120577 119868119868119894 + 10076491007649119868119868119894 119894 11986811986811989410076651007665 10076651007665119864119864119894119894Δ119864119864

119894 11989411989410076681007668 + 100764910076491198681198683 119894 11986811986811989410076651007665 10076651007665119864119864119896119896Δ119864119864

119894 11989611989610076681007668 (10)



Heart512 119864 512 119864 41


0486 119864 0486 1198640700

0318 119864 0318 1198642000



119868119868119878119878 120577 119868119868119864119864 +119898119898 119894 119898119898119895119895

119898119898119895119895+119894 119894 11989811989811989511989510076501007650119868119868119876119876 119894 11986811986811986411986410076661007666 (11)

















4 Conclusion



Acknowledgments


References


















Research Article









1 Introduction





Dim Light

(a)

(b)












ΔρT = 0530υmax

radicln cNp minus 1

2ln[Np + σ2

D

] (1)





light intensity



Lens 2

Lens 1

Target scene

DMDgenerates

themeasurement


min∥θ∥1

subject to

^λJ

^λJ asymp λJ

λJ = XN

^XN =




Lens N

XN

XN

ΦXN

YM =YM =ΦΨθ

=Ψθ

=Ψθlowast

Ψθlowast





rang+ ODC (2)



Xi = XiC + XiS (3)



XN = Ψθ (4)






⎡⎢⎢⎢⎢⎣Y1

Y2

YM

⎤⎥⎥⎥⎥⎦ =

⎡⎢⎢⎢⎢⎣Φ1 0

Φ2

0 ΦM

⎤⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎣X1

X2

XN

⎤⎥⎥⎥⎥⎦ (6)





(a) (b)

(c) (d)




for k = J to 1


(γkminus1

)


)


(8)






) = λk




(a) (b)

(c) (d)







02 03 04 05 06 07 0820

25

30

35

40

45

50

55

60

Sampling rate

PSN

R







4 Conclusion




Acknowledgments


References








































Research Article









1 Introduction






Image registration

Image acquisition


Preprocessing



2 Testing Image Set








u1 = u0 minusm







(a) (b)


(a) (b)








3 Modelling








(a) (b) (c)


Give multiscale

images







Get lumen boundary

Construct a

ring-like shape


g1(rarrI )

g2(rarrI )

g3(rarrI )

g4(rarrI )

rarrI


label







Trainingmodel

Testing set

Training set

Results

Intensity value


Initializeweight

constraint

condition

Y

N



Satisfaction


Obtain model




20

40

60

80

100

20 40 60 80 100 120S28

20

40

60

80

20 40 60 80S34

(a)

20

40

60

80

100

20

40

60

80

20 40 60 80

20 40 60 80 100 120

(b)

20

40

60

80

100

20 40 60 80 100 120

20

40

60

80

20 40 60 80

(c)


4 Comparison





e(i) = f p + f n

n (2)





Bayes SSVM

1 35 26

3 53 48

5 65 63

7 106 85

9 169 96


5 Conclusion





Acknowledgments


References

















Research Article









1 Introduction







(x minus μx

)2p(x)dx (1)









x(m)minus xM(m) (2)



(e minus μe

)2p(e) (3)


xM(m) = PxN (n) (4)




pPareto(e) = aba

ea+1 (5)


μe = ab

aminus 1

Var(e) = ab2


(6)





rxx(k) = E[x(n)x(n + k)] (7)




ree(k) = E[e(m)e(m + k)] (9)

Note that





(10)








ree(k) sim




(k minusrarr infin)

(14)





3 Discussions



4 Conclusions


Acknowledgments


References





















































































Research Article









1 Introduction













3 Results




4 Discussion












1

2

3

(a)

1

2

3

(b)

1

2

3

(c)

1

2

3

(d)

1

2

3

(e)

1

2

3

(f)






Class Type













1

2

32 mm











5 Conclusion


References


























































Research Article









1 Introduction






Fclk

AA


Digital toanalog


cosθ

sinθ




To = 2vTs

FCW (1)


Fo = 1T0= Fs

2vmiddot FCW (2)


ΔFomin = Fs2v

(FCW + 1)minus Fs2v

FCW = Fs2v (3)


ΔFo ge Fs2v (4)


SFDR = 20 log(Ap

As

)= 20 log

(Ap








y(i + 1) = y(i) + σ(i)2minus jx(i) (7)

z(i + 1) = z(i)minus σ(i)α(i) (8)





K1 =nminus1prodi=0






[xout

yout

]= K1


][xin

yin

] (11)






x(i + 1)y(i + 1)

]=[



][x(i)y(i)

]


(13)






RegFCW

Adder

(32-bit)

Reg

Load

Reset

φ


π

2+ φ

φ

π + φ

3π2

+ φ




x(i + 1) =(


y(i + 1) =(


(14)



m 0 1 2 3 4 5 6 7




Hardware cost

16-bit Adders 46 38 34 30 26 22 18 16

16-bit Shifters 46 38 34 30 26 22 18 16





0 0 0 0 lt 2πφ ltπ


0 0 1π

4lt 2πφ lt

π


0 1 0π

2lt 2πφ lt

3π4


0 1 13π4




1 0 1 minus3π4

lt 2πφ lt minusπ


1 1 0 minusπ



1 1 1 minusπ



DDFSKang and





[18]

Yi et al2006 [6]

De Caroet al 2009

[27]


2012

Process (μm) 013 mdash 05 035 035 025 018



1018 230 106 210 100 385 500


SFDR (dBc) 90 54 mdash 722 80 90 8685




For 8 le i lt 16







Input



CSA(32) CSA(32)

CSA(42)

CLA

Output


π

2π

4

π

2minus γ

γ


xin

yin

+

+

+

+

+

minus

minus

minus

2i + 1-bitshifter

i-bitshifter

i-bit

shifter2i + 1-bit

shifter

x

y

xout

yout


xoutxin

yin yout

+

+

+

minus

i-bitshifter

i-bitshifter

x

y


0 1 2 3 4 5 6 706

07

08

09

1

11

12

13

14

15times104

m

Gat

es




75

80

85

90

95

m

SFD

RS

NR

(dB

)



0 1 2 3 4 5


xinv

yinv

Swap

sinθ

cosθ

sin2πφ

cos2πφ0

1

1

0


32 3

1

Accumulator

FCW

Constant

multiplier

Quadrant

mirror

32

22 19 19

16

916

ROM CORDICprocessor

A

16

16

16

1616

16 16

16


I sim IXOutput

stage

cos output







minus140

minus120

minus100

minus80

minus60

minus40

minus20

0


DR


PCUSB 2

MCU FPGA





(verilog)



debug(modelsim)


Physicalcompilation

(astro)


Tape out










5 Conclusion


Acknowledgment


References





















































Research Article









1 Introduction












nii le Rc where






Pj

(xj)

x =nminus1sumj=0



Pj

(xj = 1




No

Yes

Initial superpixels

Segmentation result


MQ table-based LPMF


ΔSmn gt Td




Sm = E[Dm]E[Lm]

(3)


Dm =Nmsumi=1

x2mi (4)


xmi =nminus1sumj=0



E[Dm] =Nmsumi=1

nminus1sumj=0

nminus1sumk=0

E[xmi j middot xmik

]middot 2 j+k

sim=Nmsumi=1

nminus1sumj=0

nminus1sumk=0

E[xmi j

]middot E[xmik

] middot 2 j+k

(6)


E[xmi j

]= Pmi j

(xmi j = 1

) (7)



(Nm

N

)(8)


H(xm j

) (9)

H(xm j

)= minus Pm j

(xm j = 1

)middot log2

(Pm j

(xm j = 1

))

minus Pm j

(xm j = 0

)middot log2

(Pm j

(xm j = 0

))

(10)

Pm j

(xm j

)= 1

Nm

Nmsumi=1

middot Pmi j

(xmi j

) (11)



ΔSmn


(12)


The RDM Algorithm





MQ table

Bit-planeencoder

MQencoder

JPEG2000 encoder

(a)

DeQIWTImage

Local PMF

MQ table



JPEG2000 decoder

MQencoder

(b)







j=0

nminus1sumk=0

⎛⎝ 1Nm

Nmsumi=1

Pmi j

(xmi j = 1

)⎞⎠

middot⎛⎝ 1Nm

Nmsumi=1

Pmik(xmik = 1


⎤⎦

(13)






(a) (b) (c)

0 1 2 3 4 5 60

1

2

3

4

5

6

7

err

()

(bpp)

(d)





E[xi j]middot 2 j

=nminus1sumj=0

Pi j(xi j = 1

)middot 2 j

(14)






(a)

(b)

(c)



RDM CTM Mean-shift

0771 0762 0755


RDM CTM Mean-shift

87 94 97



RDM 89 s 87 s 107 s 68 s

Mean-shift 183 s 275 s 207 s 189 s

CTM 353 s 172 s 576 s 135 s


5 Conclusions





Acknowledgments


References


































Editorial Board




Contents














































Acknowledgments













1 Introduction





ATP ATP ATP

ATP ATP

ADP

ADP

ADP

ADP ADP


ATP + AMP 2ADP

v1

v2

v3

v4 v

5

v6

v7

v8

Fruc16P2






119889119909119894

119889119905=

119898

sum

119895=1

119888119894119895119903119895 for 119894 = 1 119896 (1)


119895



119895is




119894119895]119896times119898

Let 119883 = [1199091 1199092 119909

119896]119879 and r =

[1199031 1199032 119903

119898]119879 and let 120573 = [120573

1 1205732 120573



119889119883

119889119905= Cr (119883120573) (2)





119889

119889119905Gluc6P = 119903

1minus 1199032minus 1199033

119889

119889119905Fruc6P = 119903

3minus 1199034

119889

119889119905Fruc1 6P

2= 1199034minus 1199035


119889

119889119905ATP = minus119903


119889

119889119905ADP = 119903

1+ 1199032+ 1199034minus 1199036+ 1199037+ 21199038

119889

119889119905AMP = minus119903

8

(3)


1199031=

119881max2ATP (119905)

119870ATP1 + ATP (119905)

1199032= 1198962ATP (119905) sdot Gluc6P (119905)

1199033= (

119881119891

max3

119870Gluc6P3Gluc6P (119905)

minus119881119903

max3

119870Fruc6P3Fruc6P (119905))

times (1 + (Gluc6P (119905)

119870Gluc6P3)

+Fruc6P (119905)

119870Fruc6P3)

minus1

1199034=

119881max4(Fruc6P (119905))2


2

1199035= 1198965Fruc1 6P

2 (119905)

1199036= 1198966ADP (119905)

1199037= 1198967ATP (119905)


8119903(ADP (119905))2

(4)




metric matrix

C =

[[[[[[[

[


0 0 1 minus1 0 0 0 0

0 0 0 1 minus1 0 0 0


1 1 0 1 0 minus1 1 2

0 0 0 0 0 0 0 minus1

]]]]]]]

]

(5)






119889119883

119889119905= Cr (119883120573) = C

119903r119903(119883120573) + C

119901r119901(119883120573) (6)









C119903= [1198881 1198883 1198884] =

[[[[[[[

[

1 minus1 0

0 1 minus1

0 0 1

minus1 0 minus1

1 0 1

0 0 0

]]]]]]]

]

C119901

= [1198882 1198885 1198886 1198887 1198888] =

[[[[[[[

[

minus1 0 0 0 0

0 0 0 0 0

0 minus1 0 0 0


1 0 minus1 1 2

0 0 0 0 minus1

]]]]]]]

]

(7)

and r119903

= [1199031 1199033 1199034] and r

119901= [1199032 1199035 1199036 1199037 1199038] The rank of


rates



Cminus119903C119903= 119868 (8)


119903satisfying





Cminus119903

= [

[

1 1 1 0 0 0

0 1 1 0 0 0

0 0 1 0 0 0

]

]

(9)


Cminus119903

119889119883

119889119905= Cminus119903C119903r119903(119883120573) + Cminus

119903C119901r119901(119883120573)

= r119903(119883120573) + Cminus

119903C119901r119901(119883120573)

(10)


or

r119903(119883120573) + Cminus

119903C119901r119901(119883120573) = Cminus

119903

119889119883

119889119905 (11)



1199031minus 1199032minus 1199035=

119889


2)

1199033minus 1199035=

119889

119889119905(Fruc6P + Fruc1 6P

2)

1199034minus 1199035=

119889

119889119905Fruc1 6119875

2

(12)


Cperp119903C119903= 0 (13)



119903) =





Cperp119903

119889119883

119889119905= Cperp119903C119903r119903(119883120573) + Cperp

119903C119901r119901(119883120573) = Cperp

119903C119901r119901(119883120573)

(14)or

Cperp119903C119901r119901(119883120573) = Cperp

119903

119889119883

119889119905 (15)


Cperp119903

= [

[

1 1 2 1 0 0

0 0 0 1 1 0

0 0 0 0 0 1

]

]

Cperp119903C119901

= [

[


0 0 0 0 1

0 0 0 0 minus1

]

]

(16)



r119901(119883120573) = (119863

119879119863)minus1

119863119879Cperp119903

119889119883

119889119905 (17)



such that

119863r119901(119883120573) = 119863r

119901(119883120573) = Cperp

119903C119901r119901(119883120573) = Cperp

119903

119889119883

119889119905 (18)


r119901(119883120573) = (119863

119879

119863)119863119879Cperp119903

119889119883

119889119905 (19)



we have

119863 = [

[

1 minus1

0 1

0 minus1

]

]

119863119879Cperp119903

= [1 1 2 1 0 0


(20)



=119889

119889119905(Gluc6P + Fruc6P


1199038= minus

119889

119889119905AMP

(21)





120578 (X120573) =1198730 (X) + sum

119901119873

119894=1119873119894 (X) 120573119873119894

1198630 (X) + sum

119901119863

119895=1119863119895 (X) 120573119863119895

+

119901119875

sum

119896=1

119875119896 (X) 120573119875119896

(22)



119873119894(119894 = 1 119901



(119895 = 1 119901119863) and those in the

polynomial 120573119875119896


119863+119901119873+

119901119875

= 119901 119873119894(X) (119894 = 0 1 119901

119873) 119863119895(X) (119895 = 0 1 119901

119863)

and 119875119896(X) (119896 = 1 119901



0(X) or 119863




120578 (X120573) = (1198730 (X) +

119901119873

sum

119894=1

119873119894 (X) 120573119873119894

+ (

119901119875

sum

119896=1

119875119896 (X) 120573119875119896

)

times(1198630 (X) +

119901119863

sum

119895=1

119863119895 (X) 120573119863119895

))

times (1198630(X) +

119901119863

sum

119895=1

119863119895(X)120573119863119895

)

minus1

(23)


+ 119901119873


119863+ 119901119873

+






119905and X

119905(119905 = 1 2 119899) we introduce the

following notation

120573119873

= [1205731198731

1205731198732

120573119873119901119873

]119879

isin 119877119901119873

120573119863

= [1205731198631

1205731198632

120573119863119901119863

]119879

isin 119877119901119863

120573119875

= [1205731198751

1205731198752

120573119875119901119863

]119879

isin 119877119901119875

120573 = [ 120573119879119875120573119879119873120573119879119863]119879

120593119873

(X119905) = [119873

1(X119905) 1198732(X119905) 119873

119901119873(X119905)] isin 119877

119901119873

120593119863

(X119905) = [119863

1(X119905) 1198632(X119905) 119863

119901119863(X119905)] isin 119877

119901119863

120593119875(X119905) = [119875

1(X119905) 1198752(X119905) 119875

119901119875(X119905)] isin 119877

119901119875

Y = [119910(1) 119910(2) 119910(119899)]119879

isin 119877119899

Φ1198730

= [1198730(X1) 1198730(X2) 119873

0(X119899)]119879

isin 119877119899

Φ1198630

= [1198630(X1) 1198630(X2) 119863

0(X119899)]119879

isin 119877119899

Φ119873

=

[[[[[

[

120593119873

(X1)

120593119873

(X2)

120593119873

(X119899)

]]]]]

]

isin 119877119899times119901119873

Φ119863

=

[[[[[

[

120593119863

(X1)

120593119863

(X2)

120593119863

(X119899)

]]]]]

]

isin 119877119899times119901119863

Φ119875

=

[[[[[

[

120593119875(X1)

120593119875(X2)

120593119875(X119899)

]]]]]

]

isin 119877119899times119901119875

Ψ (120573119863) = diag

[[[[[

[

1198630(X1) + 120593119863

(X1)120573119863

1198630(X2) + 120593119863

(X2)120573119863

1198630(X119899) + 120593119863

(X119899)120573119863

]]]]]

]

isin 119877119899times119899

(24)


119869 (120573) = 119869 (120573119875120573119873120573119863)

= sum(1198630(X119905) + 120593119863

(X119905)120573119863)2

times (1198730(X119905) + 120593119873

(X119905)120573119873

1198630(X119905) + 120593119863

(X119905)120573119863

+ Φ119875120573119875minus 119910119905)

2

(25)



119875

120573119873 and120573


119869 (120573) = sum[(1198630(X119905) + 120593119863

(X119905)120573119863)Φ119875120573119875+ 120593119873

(X119905)120573119873

minus120593119863

(X119905) 119910119905120573119863

minus 1198630(X119905) 119910119905+ 1198730(X119905)]2

(26)




119881119891



1198966(minminus1) 6848 684837 00054

1198967(minminus1) 321 320797 00078

1198968119891




119869 (120573) = 119869 (120573119875120573119873120573119863120573119863)

= [A (120573119863)120573 minus b]

119879

[A (120573119863)120573 minus b]

(27)

where

119860(120573119863) =

[[[

[

Ψ(120573119863)Φ119879

119875

Φ119879

119873

minus diag (119884)Φ119879

119863

]]]

]

isin 119877119899times119901

(28)

b = (Φ1198630

diag (119884) minus Φ1198730

) isin 119877119899 (29)


eters 120573 = [120573119879119875120573119879119873120573119879119863]119879


120573 = [A119879 (120573119863)A (120573

119863)]minus1

A119879 (120573119863) b (30)





119869 (120573119904+1

) = [A (120573119904

119863)120573119904+1

minus b]119879

[A (120573119904

119863)120573119904+1

minus b] (31)


120573119904+1

= [A119879 (120573119904119863)A (120573

119904

119863)]minus1

A119879 (120573119904119863) b (32)


120573119904119879119873

120573119904119879119863




10038171003817100381710038171003817120573119896 minus 120573119896minus1

1003817100381710038171003817100381710038171003817100381710038171003817120573119896minus1

10038171003817100381710038171003817+ 1

le 120576 (33)


4 Application


2(0) = 0mM ATP(0) = 21mM ADP(0) =




0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6

Time (min)

Gluc6PFruc6P

ATPADPAMP

Con

cent

ratio

ns

Fruc16P2



119909(119905119899) =

1

12Δ119905[119909 (119905119899minus2

) minus 8119909 (119905119899minus1

) + 8119909 (119905119899+1

) minus 119909 (119905119899+2

)]

(34)



true value (35)





Acknowledgments


References



























1 Introduction






02 04 06 08 1 12 14 16 18 2

0500

1000150020002500

Time (ms) times105

minus500

minus1000

minus1500

minus2000

minus2500

EEG

vol

tage

(120583V

)














Skin


Elec

trode

Elec

trode

gel

Rp

Ep

Cp

RuR

e

Ese

Rs

Rd

Ehe

Cd

Ce














119885 (119904) asymp (119877119889

119904119877119889119862119889+ 1

+119877119890

119904119877119890119862119890+ 1

119877119901

119904119877119901119862119901+ 1

) (1)


119885 (119904) asymp1199041198611+ 1198610

11990421198602+ 1199041198601+ 1

(2)


1


119901


119864119898= 119883in

1199041198611+ 1198610

11990421198602+ 1199041198601+ 1

+ 119864 +119882noise (3)

0 5 10 15 200

10

20

30

40

50

60

70

80

90

100

EEG channels

Fit p

erce

ntag

e


where 119864119898


119864lowast

119898= 119883in

1199041198611+ 1198610

11990421198602+ 1199041198601+ 1

(4)





lowast

119898(119905))2

(sum (119864119898 (119905) minusmean(119864

119898 (119905))2))

) (5)


119885 (119904) = 119870119901

1 + 119904119879119911

11990421198792119908+ 2119904120577 sdot 119879

119908+ 1

(6)

with 119870119901

= minus40921 119879119908



0 10 20 30 40 50 60 700

102030405060708090

100


Fit p

erce

ntag

e

(a)

0 5 10 15 20 25 30 350

102030405060708090

100


Fit p

erce

ntag

e

(b)

1 2 3 4 5 6 7 8 9 10 11 12 13 140

102030405060708090

100


Fit p

erce

ntag

e

(c)

1 2 3 4 5 6 7 8 9 100

102030405060708090

100


Fit p

erce

ntag

e

(d)

1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

90

100


Fit p

erce

ntag

e

(e)

1 2 3 4 50

10

20

30

40

50

60

70

80

90

100


Fit p

erce

ntag

e

(f)









119860 (119902) 119910 (119905) =119861 (119902)

119865 (119902)119906 (119905) +

119862 (119902)

119863 (119902)119890 (119905) (7)








119898(119899) as a





119890 (119899) = 119864119898 (119899) minus 119864GVS (119899) = 119864

119905 (119899) minus [119911 (119899) minus 119864GVS (119899)] (8)

where

119864GVS (119899) =119872

sum

119898=1

ℎ119898sdot 119894GVS (119899 + 1 minus 119898) (9)


119864 [1198902(119899)] = 119864 [(119864

119898 (119899) minus 119864GVS (119899))2

] (10)

or

119864 [1198902(119899)] = 119864 [119864

2

119905(119899)] minus 119864 [(119911 (119899) minus 119864GVS (119899))

2

] (11)











0 50 100 150 200 250 300 350 400 450 500Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)


minus55

minus60

minus65

minus70

minus75

minus80

minus85

2 4 6 8 10 12 14Frequency (Hz)

minus52

minus53

minus54

minus55

minus56

minus57

Pow

erfr

eque

ncy

(dB

Hz)



120595119895119896 (119905) = 2






1(119905) 119890



1(119905) 119904

119873(119905))

119864 (119905) = 119872119878 (119905) (13)



0 02 04 06 08 1 12 14 16 18 2

0

5

10

15

Time (ms)

minus5

minus10

minus15

ICA

com

pone

nt (120583

V)

times105





119864 (119905) = 119872119878 (119905) (14)



0 02 04 06 08 1 12 14 16 18 2

00102030405

Time (ms) times105

ICA

com

pone

nt (120583

V)

minus01

minus02

minus03

minus04

minus05





Corr (119906 119910) =Cov (119906 119910)120590119906sdot 120590119910

(15)














Correlation 09776 09769 09899 09899

GVS current



L1

L2

L3

L4

L5

L6

L7

L8

L9

L10

L12

L11




Regression analysis


EEG




RSS119873=

sum (119864119900 (119905) minus 119864

119900 (119905))2

sum(119864119900 (119905) minusmean (119864

119900 (119905)))2 (16)










Corr 09932 09933 09933 09932 09932 09933 09933 09932RSS119873

01710 01700 01705 01714 01710 01700 01705 01714



01700 01701 01704 02267 01711SS2 SS3 SS4 NLHW3 NLHW4

Corr 09933 08105 07466 09926 09851RSS119873

01704 07628 09174 01230 01725









component


component



Corr 06445 06171 09933 09934RSS119873

09567 10241 01700 01711



component


component



Corr 06859 06858 08743 08743
















0 05 1 15 2 25 3 35

065

07

075

08

085

09

095

1

GVS (mA)

Cor

rela

tion





3 Results




1 2 3 4 5 6 7 8 9 10 11 120

10

20

30

40

50

60

70

80

90

100

Frequency bands

Fit p

erce

ntag

e


1 2 3 4 5 6 7 8 9 10 11 120

01

02

03

04

05

06

07

08

09

1

Frequency bands

Cor

relat

ion

coeffi

cien

t





0 02 04 06 08 1 12 14 16 18 2

0

100

200

300

Time (ms)

minus100

minus200

minus300

minus400

EEG

vol

tage

(120583V

)

times105


0 02 04 06 08 1 12 14 16 18 2

050

100150200250

Time (ms)

minus50

minus100

minus150

minus200

minus250

EEG

vol

tage

(120583V

)

times105






0

50

100

150

minus50

minus100

minus150

0 02 04 06 08 1 12 14 16 18 2Time (ms)

EEG

vol

tage

(120583V

)

times105



4 Discussion









Acknowledgments


References











































1 Introduction







2 Methods







119909and



RRI1015840 (119894) =RRI (119894)SD119909

PTT1015840 (119895) =PTT (119895)

SD119910

(1)





ECG

PPG

RRI(1) RRI(2) RRI(1000)






RRI1015840(119906)(120591) = 1

120591

119906120591

sum

119894=(119906minus1)120591+1

RRI1015840 (119894) 1 le 119906 le1000

120591

PTT1015840(119906)(120591) = 1

120591

119906120591

sum

119895=(119906minus1)120591+1

PTT1015840 (119895) 1 le 119906 le1000

120591

(2)




119894 = 1 119873 minus 119898 + 1

y (119895)


119895 = 1 119873 minus 119898 + 1

(3)


119889 [x (119894) y (119895)]

=119898max119896=1


10038161003816100381610038161003816]

(4)



119862119898

RRI1015840(120591)PTT1015840(120591) (119894) =119873119898

RRI1015840(120591)PTT1015840(120591) (119894)

119873 minus 119898 + 1 (5)




119898


120601119898

RRI1015840(120591)PTT1015840(120591) (119903) =1

119873 minus 119898 + 1

119873minus119898+1

sum

119894=1

ln119862119898RRI1015840(120591)PTT1015840(120591) (119894) (6)


RRI1015840(120591)PTT1015840(120591)(119894) 120601119898+1


119873rarrinfin

[120601119898

RRI1015840(120591)PTT1015840(120591)(119903) minus 120601119898+1


Co ApEnRRI1015840(120591)PTT1015840(120591) (119898 119903119873) = 120601119898

RRI1015840(120591)PTT1015840(120591) (119903)

minus 120601119898+1

RRI1015840(120591)PTT1015840(120591) (119903) (7)




MCEISS =5

sum

120591=1

Co ApEnRRI1015840(120591)PTT1015840(120591) (120591) (8)

MCEILS =20

sum

120591=6

Co ApEnRRI1015840(120591)PTT1015840(120591) (120591) (9)






3 Results


32 MCEI119871119878


119864(RRI) and 119878






4 Discussion









16156 plusmn 897 16117 plusmn 728





9746 plusmn 377


12846 plusmn 1636



5025 plusmn 1312








764 plusmn 081





2106 plusmn 492







0 5 10 15 2008

1

12

14

16

18

2

Scale

Sam

ple e

ntro

py (R

RI)

Group 1Group 2

Group 3Group 4

(a)

Scale

Group 1Group 2

Group 3Group 4

0 5 10 15 201

12

14

16

18

2

22

24

Sam

ple e

ntro

py (P

TT)

(b)




0 2 4 6 8 10 12 14 16 18 20

12

14

16

18

2

22

Group 1Group 2

Group 3Group 4

120591

Co

ApEn

RRI998400(120591)PT

T998400(120591)(120591)





5 Conclusions






Acknowledgments


References






































1 Introduction




















GMM-FJ

Lesion detection

lesions


Train images

Test image

Likelihood lesions

RGB lesions

Overall score

Multiple expert

Baseline

trainingBaseline

Score



RGB image


fusion

annotationfusion

annotationsExpert


Expert





























































True finding area










(a) (b) (c)




perf 119868exp119894119895119899

119892119905119894119895

997888rarr R (1)






119894119895119899


perf (119868exp119894119895119899

119892119905119894119895

)

=1

119873sum

119899


119894119895119899

) 119868mask119894119895 (119909 119910 120591))

(2)



(a) (b)





120591119895larr997888 argmin

120591119895

1

119873sum

119899

EER (sdot sdot) (3)








SN =TP

TP + FN(4)


SP =TN

TN + FP(5)






1 + =


1 + (7)







(8) else(9) FN = FN + 1


(14) else(15) FP = FP + 1


TPTP + FN

(Sensitivity)

(20) SP =TN






im1

120577im119899


im1

120596im119899

where each 120596

im119894





pix1

120577pix119899


pix1

120596pix119899






TPTP + FN

(Sensitivity)

(22) SP =TN











1 x

119872 where each


1 x





SCOREsummax = sum

119898isin119873119884

119901 (x119898

| abnormal) (8)




0 10

02

04

06

08

1Se

nsiti

vity

05



1minus specificity

(a)

0 05 10

02

04

06

08

1

Sens

itivi

ty



1minus specificity

(b)




In [9] 0233 0333 0273 0200 0220 0216 0476 0625 0593 0250 0333 0317 0349In [8] (min) 0263 0476 0322 0250 0250 0250 0286 0574 0338 0333 0333 0333 0311In [8] ( max) 0263 0476 0322 0250 0250 0250 0386 0574 0338 0200 0268 0241 0288








1

09

08

07

06

05

04

03

02

01

010908070605040302010

HAHA-orig

(a) Haemorrhage

1

09

08

07

06

05

04

03

02

01

010908070605040302010

HEHE-orig

(b) Hard exudate

1

09

08

07

06

05

04

03

02

01

010908070605040302010

MAMA-orig

(c) Microaneurysm

1

09

08

07

06

05

04

03

02

01

010908070605040302010

SESE-orig

(d) Soft exudate





6 Conclusions



(a) (b)

(c) (d)



Acknowledgments


References


















































1 Introduction
















(3)

(A)

Lead-inbevel

empty35 11

(1) D36-L55-T030-ST-SM

(2) D36-L55-T1030-ST-SM

(3) D43-L55-T1030-ST-SM

(4) D43-L9-T1030-DT-SM

(5) D43-L9-T1030-DT-LM

(6) D43-L9-T1030-ST-LM

(7) D36-L9-T030-DT-SM

(8) D36-L9-T1030-DT-SM

(9) D36-L9-T1030-DT-LM

(10) D36-L9-T1030-ST-LM

(A) D35-L11 Ankylos

empty36 empty3655

empty36 55

55empty43

empty43 9

empty43 9

empty43 9

9

empty36 9

empty36 9

empty36 9







(a)

xy

z

(b)

(c)

x

z

7 mm

250 N

100 N

(d)


1 mm

P0

P1

05 mm



02 mm

P05














0119863 = 01 and

ℎ119894119863 = 001 ℎ

0and ℎ




119894 with 119894 = 1 2 3) [44 47 53 63 64]


120590119862 (119875) = min 120590

1 (119875) 1205902 (119875) 1205903 (119875) 0

120590119879 (119875) = max 120590

1 (119875) 1205902 (119875) 1205903 (119875) 0

(1)

120590119862and 120590



119877 =

10038161003816100381610038161205901198621003816100381610038161003816

1205901198620

+120590119879

1205901198790

le 1 (2)


1198790 1205901198620


1198790= 180MPa and 120590





D 120575

Ωa

t

Ωt

i

Ωt

c

Ωt

Ωc



119888and Ω

119905(such that





119905(apex


119888 Ω119888119905 Ω119894119905 Ω119886119905 These


3 Results


119888and




119888and Ω

119905 and








119888and Ω

119905(resp

20 in Ω119888and 30 in Ω













(MPa)

z

x

0 10 15 20 25 30 50 60 70 Above






(MPa)

x

z

0 05 1 15 2 25 3 35 45 Above








(MPa

)

1 2 3 4 5 6 7 8 9 10 AImplant type

120590VM

0

10

20

30

40

50

60

70

0

1

2

3

4

5

(MPa

)

1 2 3 4 5 6 7 8 9 10 AImplant type

120590VM

Ωc

t

Ωi

t

Ωa

t

(a)

minus50

minus40

minus30

minus20

minus10

0

10

20

(MPa

)

1 2 3 4 5 6 7 8 9 10 AImplant type

1 2 3 4 5 6 7 8 9 10 AImplant type

120590T

120590C

120590T

120590C

minus4

minus3

minus2

minus1

0

1

2

3(M

Pa)

Ωc

t

Ωi

t

Ωa

t

(b)







119888andΩ




00

01

02

03

04

05

06

07

R

1 2 3 4 5 6 7 8 9 10 AImplant type



(8) D36-L9-T1030-DT-SM


z

x

P0 P05 P1

0 10 15 20 25 30 50 60 70 Above

(a)

(8) D36-L9-T1030-DT-SM

(A) D35-L11 Ankylos

(MPa)x

z

P0 P05 P1

0 05 1 15 2 25 3 35 45 Above

(b)



(MPa

)

P0 P05 P1

Implant 8Implant A

0

10

20

30

40

50

60

70120590VM

00

05

10

15

20

25

30

35

(MPa

)

P0 P05 P1 P0 P05 P1


Ωc

t

Ωi

t

Ωa

t

(a)


P0 P05 P1 P0 P05 P1 P0 P05 P1 P0 P05 P1

(MPa

)

120590T

120590T

120590C

120590C

minus40

minus30

minus20

minus10

0

10

20

minus2

minus1

0

1

2

3(M

Pa)

Ωc

t

Ωi

t

Ωa

t

(b)








00

01

02

03

04

R

P0 P05 P1 P0 P05 P1

Implant 8 Implant A





119888and Ω




4 Discussion







0

20

40

60

80

100

120

140

(MPa

)


Implant 8Implant A

120590VM

(a)

0

1

2

3

4

5

6

(MPa

)0 25 50 0 25 50


Implant 8 Implant A

120590VM

Ωc

t

Ωi

t

Ωa

t

(b)

Implant 8 Implant A


00

02

04

06

08

10

R

CorticalTrabecular

(c)












References















































































1 Introduction



2 Methods










FPzFP2FP1

Fz

Cz

Pz

OzO1 O2

T7 T8

F7 F8

P7 P8

F3 F4

C3 C4

P3 P4

AF3 AF4

F5 F1 F2 F6

FCzFT7 FT8


CPzTP7 TP8


POz PO8PO7

P5 P2 P6

PO4 PO6PO3PO5

C2 C6C1C5

CB1 CB2

P1

1

2 3 4

5






119885 = 119911119894 (119899) (119894 = 1 119872 119899 = 1 119879)

119909119894 (119899) =

(119911119894 (119899) minus ⟨119885

119894⟩)

120590119894

119883 = 119909119894 (119899)

(1)



119909119894(119899) and ⟨119885

119894⟩ and 120590


119911119894(119899) respectively



PersonsChanges









Δ120593119908

119909119894119909119896(119904 120591) = 120593

119908

119909119894(119904 120591) minus 120593

119908

119909119896(119904 120591) (119896 = 1 119872) (2)


120574119894119896

=100381610038161003816100381610038161003816⟨119890119895Δ120593119908

119909119894119909119896(119904120591)

⟩119879

100381610038161003816100381610038161003816isin [0 1] (3)



119894(119899) and


written as C = 120574119894119896


follows

Ck119894

= 120582119894k119894 (4)


le 1205822




119904

1le 120582119904

2le




120582119892

119894=

120582119894120582119904119894

sum119872

119894=1120582119894120582119904119894

(119894 = 1 119872)

GSI = 1 +sum119872

119894=1120582119892

119894log (120582

119892

119894)

log (119872)

(5)




119903(119896)

119895119894=

119910(119896)

119895119894minus 119910(119896)

1198951

119910(119896)

1198951

(119894 = 1 119873 119873 = 6 119895 = 1 119870 119870 = 5 119896 = 1 2 3)

(6)



(119896)

119895119894is the








119895119894will






3 Results





Fron

tal r

atio

Righ

t tem

pora

l rat

io

Left

tem

pora

l rat

io

Cen

tral

ratio

Occ

ipita

l rat

io

Glo

bal r

atio

0

1

2

3

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6N test N test

minus1

0

1

2

3

minus1

0

1

2

3

minus1

0

1

2

3

minus1

0

1

2

3

minus1

0

1

2

3

minus1

N test



minus02

minus01

0

01

minus02

minus01

0

01

minus02

minus01

0

01

minus02

minus01

01

minus02

minus01

01

minus02

minus01

0 0 0

01

Fron

tal r

atio

Righ

t tem

pora

l rat

io

Left

tem

pora

l rat

io

Cen

tral

ratio

Occ

ipita

l rat

io

Glo

bal r

atio






minus05

0

05

minus05

0

05

minus05

0

05

minus05

0

05

minus05

0

05

minus05

0

05

Fron

tal r

atio

Righ

t tem

pora

l rat

io

Left

tem

pora

l rat

io

Cen

tral

ratio

Occ

ipita

l rat

io

Glo

bal r

atio








4 Discussions






Acknowledgments


References










































1 Introduction













X = x11 x1

1198731 x21 x2

1198732 x119862

1 x119862

119873119862 (1)






119897(x119894) andNM




119894119895is given by

119901119894119895=

exp (minus119889211989411989521205822)

sum119905isin119867119898

exp (minus119889211989811990521205822)

forall119895 isin 119867119894

exp (minus119889211989411989521205822)

sum119905isin119872119898

exp (minus119889211989811990521205822)

forall119895 isin 119872119894

0 otherwise

(2)





119894119895 119867119894= 119895 | 1 le 119895 le 119873 1 le 119894 le 119873

x119895= NH

119896(x119894) and 1 le 119896 le 119870

1 119867119898= 119905 | 1 le 119905 le 119873 1 le

119898 le 119873 x119905= NH

119896(x119898) and 1 le 119896 le 119870

1 119872119894= 119895 | 1 le

119895 le 119873 1 le 119894 le 119873 x119895= NH

119896(x119894) and 1 le 119896 le 119870

2 and

119872119898= 119905 | 1 le 119905 le 119873 1 le 119898 le 119873 x

119905= NH

119896(x119898) and



119894119895




119894and




119902119894119895=

(1 + 1198892

119894119895(A))minus1

sum119905isin119867119898

(1 + 1198892119898119905(A))minus1

forall119895 isin 119867119894

(1 + 1198892

119894119895(A))minus1

sum119905isin119872119898

(1 + 1198892119898119905(A))minus1

forall119895 isin 119872119894

0 otherwise

(3)



119894119895(A) = y

119894minus

y119895 = Ax


119894minus x119895)119879A119879A(x



119902119894119895

=

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119905isin119867119898

(1 + (x119898minus x119905)119879A119879A (x


forall119895 isin 119867119894

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119905isin119872119898

(1 + (x119898minus x119905)119879A119879A (x


forall119895 isin 119872119894

0 otherwise(4)


min119862 (A) = sum

forall119895isin119867119894

119901119894119895log

119901119894119895

119902119894119895

+ sum

forall119895isin119872119894

119901119894119895log

119901119894119895

119902119894119895

(5)


119894119895 119906119894119895 119906119867

119894119895 and 119906119872

119894119895

as

119908119894119895= [1 + (x

119894minus x119895)119879

A119879A (x119894minus x119895)]

minus1

119906119894119895= (119901119894119895minus 119902119894119895)119908119894119895

119906119867

119894119895=

119906119894119895

forall119895 isin 119867119894

0 otherwise

119906119872

119894119895=

119906119894119895

forall119895 isin 119872119894

0 otherwise

(6)


119889119862 (A)119889 (A)

= sum

forall119895isin119867119894

119901119894119895

119902119894119895

(119902119894119895)1015840

+ sum

forall119895isin119872119894

119901119894119895

119902119894119895

(119902119894119895)1015840

= 2A[

[

sum

forall119895isin119867119894

119901119894119895

(x119894minus x119895) (x119894minus x119895)119879

1 + (x119894minus x119895)119879

A119879A (x119894minus x119895)

]

]

minus 2A[

[

sum

forall119895isin119867119894

119901119894119895( sum

119905isin119867119898

(1 + (x119898minus x119905)119879A119879A (x



times( sum

119905isin119867119898

(1 + (x119898minus x119905)119879A119879A (x


)

minus1

]

]

+ 2A[

[

sum

forall119895isin119872119894

119901119894119895

(x119894minus x119895) (x119894minus x119895)119879

1 + (x119894minus x119895)119879

A119879A (x119894minus x119895)

]

]

minus 2A[

[

sum

forall119895isin119872119894

119901119894119895( sum

119905isin119872119898

(1 + (x119898minus x119905)119879A119879A (x



times( sum

119905isin119872119898

(1 + (x119898minus x119905)119879A119879A (x


)

minus1

]

]

= 2A[

[

sum

forall119895isin119867119894

119901119894119895119908119894119895(x119894minus x119895) (x119894minus x119895)119879

minus sum

119905isin119867119898

119902119898119905119908119898119905(x119898minus x119905) (x119898minus x119905)119879]

+ 2A[

[

sum

forall119895isin119872119894

119901119894119895119908119894119895(x119894minus x119895) (x119894minus x119895)119879

minus sum

119905isin119872119898

119902119898119905119908119898119905(x119898minus x119905) (x119898minus x119905)119879]

= 2A[

[

sum

forall119895isin119867119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879

+ sum

forall119895isin119872119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879]

]

(7)





119894119894= sum119895U119867119894119895and D119872

119894119894=


be reduced to

119889119862 (A)119889 (A)

= 2A

sum

forall119895isin119867119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879

+ sum

forall119895isin119872119894

119906119894119895(x119894minus x119895) (x119894minus x119895)119879

= 2A

( sum

forall119895isin119867119894

119906119894119895x119894x119879119894+ sum

forall119895isin119867119894

119906119894119895x119895x119879119895

minus sum

forall119895isin119867119894

119906119894119895x119894x119879119895minus sum

forall119895isin119867119894

119906119894119895x119895x119879119894)

+ ( sum

forall119895isin119872119894

119906119894119895x119894x119879119894+ sum

forall119895isin119872119894

119906119894119895x119895x119879119895

minus sum

forall119895isin119872119894

119906119894119895x119894x119879119895minus sum

forall119895isin119872119894

119906119894119895x119895x119879119894)

= 4A (XD119867X119879 minus XU119867X119879)

+ (XD119872X119879 minus XU119872X119879)


(8)







class labels












119901119894119895=

exp (minus119863geo1198941198952)

sum119896 = 119894

exp (minus119863geo1198941198962)

119902119894119895=

[1205742+ (x119894minus x119895)119879

A119879A (x119894minus x119895)]

minus1

sum119896 = 119897

[1205742 + (x119896minus x119897)119879A119879A(x


min119862 (A) = sum119894119895

119901119894119895log

119901119894119895

119902119894119895

(9)

where 119863geo119894119895




119901119894119895=


10038171003817100381710038171003817

2

21205822)

sum119888119896=119888119897


1003817100381710038171003817221205822)

if 119888119894= 119888119895


10038171003817100381710038171003817

2

21205822)

sum119888119896 =119888119898


1003817100381710038171003817221205822)

else


119902119894119895=

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119888119896=119888119897

(1 + (x119896minus x119897)119879A119879A (x


if 119888119894= 119888119895

(1 + (x119894minus x119895)119879

A119879A (x119894minus x119895))

minus1

sum119888119896 =119888119898

(1 + (x119896minus x119898)119879A119879A (x


else

min119862 (A) = sum

119888119894=119888119895

119901119894119895log

119901119894119895

119902119894119895

+ sum

119888119894 =119888119896

119901119894119896log

119901119894119896

119902119894119896

(10)



119894







4 Kernel FDSNE




120581 (x119894 x119895) = ⟨120593 (x

119894) 120593 (x

119895)⟩ (11)



119894) for


A = [

119873

sum

119894=1

119887(1)

119894120593119894

119873

sum

119894=1

119887(119903)

119894120593119894]

119879

(12)

We define B = [119887(1) 119887

(119903)]119879

and Φ = [1205931 120593

119873]119879



119889119865

119894119895(A) = 10038171003817100381710038171003817A (120593

119894minus 120593119895)10038171003817100381710038171003817=10038171003817100381710038171003817BΦ (120593

119894minus 120593119895)10038171003817100381710038171003817

=10038171003817100381710038171003817B (119870119894minus 119870119895)10038171003817100381710038171003817= radic(119870

119894minus 119870119895)119879

B119879B (119870119894minus 119870119895)

(13)

where 119870119894= [120581(x

1 x119894) 120581(x




119894119895(A) with 119889119865

119894119895(A)



1199011

119894119895

=

exp (minus (119870119894119894+ 119870119895119895minus 2119870119894119895) 21205822)

sum119905isin119867119898

exp (minus (119870119898119898

+119870119905119905minus2119870119898119905) 21205822)

forall119895 isin 119867119894

exp (minus (119870119894119894+ 119870119895119895minus 2119870119894119895) 21205822)

sum119905isin119872119898

exp (minus (119870119898119898

+119870119905119905minus2119870119898119905) 21205822)

forall119895 isin 119872119894

0 otherwise

1199021

119894119895

=

(1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895))

minus1

sum119905isin119867119898

(1+(119870119898minus119870119905)119879B119879B (119870

119898minus119870119905))minus1

forall119895 isin 119867119894

(1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895))

minus1

sum119905isin119872119898

(1+(119870119898minus119870119905)119879B119879B (119870

119898minus119870119905))minus1

forall119895 isin 119872119894

0 otherwise(14)






119889119862 (B)119889 (B)

= sum

forall119895isin119872119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

+ sum

forall119895isin119867119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

= 2B[[

sum

forall119895isin119867119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879

+ sum

forall119895isin119872119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879]

]

(15)


119894119895 1199061119894119895 1199061119867119894119895 and 1199061119872


1199081

119894119895= [1 + (119870

119894minus 119870119895)119879

B119879B (119870119894minus 119870119895)]

minus1

1199061

119894119895= (119901119894119895minus 119902119894119895)1199081

119894119895

1199061119867

119894119895=

1199061

119894119895forall119895 isin 119867

119894

0 otherwise

1199061119872

119894119895=

1199061

119894119895forall119895 isin 119872

119894

0 otherwise

(16)


119889119862 (B)119889 (B)

= 2B

sum

forall119895isin119867119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879

+ sum

forall119895isin119872119894

1199061

119894119895(119870119894minus 119870119895) (119870119894minus 119870119895)119879


= 4B (KD1119867K119879 minus KU1119867K119879)

+ (KD1119872K119879 minus KU1119872K119879)





119894119894= sum119895U1119867119894119895

andD1119872119894119894

= sum119895U1119872119894119895




119889119862119865(A)

119889 (A)

= sum

forall119895isin119872119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

+ sum

forall119895isin119867119894

1199011

119894119895

1199021119894119895

(1199021

119894119895)1015840

= 2[[

[

sum

forall119895isin119867119894

1199011

119894119895

B (119870119894minus 119870119895) (120593119894minus 120593119895)119879

(1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895))

]]

]

minus 2[

[

sum

forall119895isin119867119894

1199011

119894119895( sum

119905isin119867119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus2


times( sum

119905isin119867119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus1

)

minus1

]

]

+ 2[

[

sum

forall119895isin119872119894

1199011

119894119895

B (119870119894minus 119870119895) (120593119894minus 120593119895)119879

1 + (119870119894minus 119870119895)119879

B119879B (119870119894minus 119870119895)

]

]

minus 2[

[

sum

forall119895isin119872119894

1199011

119894119895( sum

119905isin119872119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus2






times( sum

119905isin119872119898

(1 + (119870119898minus 119870119905)119879B119879B (119870

119898minus 119870119905))minus1

)

minus1

]

]

= 2[

[

sum

forall119895isin119867119894

1199011

1198941198951199081

119894119895B119876(119870119894minus119870119895)119894119895

minus sum

119905isin119867119898

1199021

1198981199051199081

119898119905B119876(119870119898minus119870119905)119898119905

]

]

Φ

+ 2[

[

sum

forall119895isin119872119894

1199011

1198941198951199081

119894119895B119876(119870119894minus119870119895)119894119895

minus sum

119905isin119872119898

1199021

1198981199051199081

119898119905B119876(119870119898minus119870119905)119898119905

]

]

Φ

= 2[

[

sum

forall119895isin119867119894

1199061

119894119895B119876(119870119894minus119870119895)119894119895

+ sum

forall119895isin119872119894

1199061

119894119895B119876(119870119894minus119870119895)119894119895

]

]

Φ

(18)




119895minus 119870119894in the






5 Experiments






















10 20 30 40 50 6007

075

08

085

Dimensionality

Reco

gniti

on ra

te (

)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(a) ℎ = 5

10 20 30 40 50 60075

08

085

09

095

Dimensionality

Reco

gniti

on ra

te (

)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(b) ℎ = 10



FKDSNE2FKDSNE1FDSNE

DSNEMSNP

10 20 30 40 50 60065

07

075

08

085

Dimensionality

Reco

gniti

on ra

te (

)

(a) ℎ = 14

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

Reco

gniti

on ra

te (

)

10 20 30 40 50 6007

075

08

085

09

Dimensionality

(b) ℎ = 25


10 20 30 40 50 6006

065

07

075

08

085

Dimensionality

Reco

gniti

on ra

te (

)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(a) ℎ = 3

Reco

gniti

on ra

te (

)

10 20 30 40 50 6006

065

07

075

08

085

09

Dimensionality

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

(b) ℎ = 5






10 20 30 40 50 60

10

20

30

40

50

Dimensionality

Elap

sed

time (

s)

FKDSNE2FKDSNE1

FDSNEDSNE

(a) ℎ = 5


Elap

sed

time (

s)

20

40

60

80

FKDSNE2FKDSNE1

FDSNEDSNE

(b) ℎ = 10


10 20 30 40 50 60

6

8

10

12

14

16

18

Dimensionality

Elap

sed

time (

s)

FKDSNE2FKDSNE1

FDSNEDSNE

(a) ℎ = 14

Elap

sed

time (

s)

10 20 30 40 50 60

25

30

35

40


FDSNEDSNE

(b) ℎ = 25





2= 40 for DSNE





Elap

sed

time (

s)

10 20 30 40 50 60

5

10

15

20

25

30

35

40

Dimensionality

FKDSNE2FKDSNE1

FDSNEDSNE

(a) ℎ = 3

10 20 30 40 50 60

10

20

30

40

50

60

Dimensionality

FKDSNE2FKDSNE1

FDSNEDSNE

Elap

sed

time (

s)

(b) ℎ = 5




0 200 400 600 800 1000

Iteration number

Obj

ectiv

e fun

ctio

n va

lue (

log)

FKDSNE2FKDSNE1FDSNE

DSNEMSNP

minus7

minus6

minus4

minus5








6 Conclusion


Acknowledgment


References








































1 Introduction

















119863 =1

119873

119873

sum

119899=2

log 119901119909 (119899)

log 119899 (1)


119873


120583119903 (119896) =

119896+119903minus1

sum

119904=119896

Vlowastsh (2)





119901119903 (119896) =1

119903

119896+119903minus1

sum

119904=119896

Vlowastsh (3)


119901119903 (119896)119896=1119873 (4)


3 Results












4 Discussion










5 Conclusion




References
















































1 Introduction











119875 (119903 120579) = 119877 (119903 120579) 119891 (119909 119910)

= ∬

infin

minusinfin

119891 (119909 119910) 120575 (1199031199021 minus 119879 (120595 (119909 119910) 120579)) 119889119909 119889119910

(1)

where 120595(119909 119910) isin 1198712(119863) 119902



119879 (120595 (119909 119910) 120579) minus 1199031199021 = 0 (2)





1= 1 119879(120595(119909 119910) 120579) =




119875 (119903 120579) = 119875 (119903 120579 plusmn 2119896120587) (3)


2(119909 119910) are two images


1(119909 119910) and 119891


10038161003816100381610038161198751 (119903 120579) minus 1198752 (119903 120579)1003816100381610038161003816

le ∬119863

100381610038161003816100381610038161003816100381610038161198911 (119903 120579)minus1198912 (119903 120579)

1003816100381610038161003816 120575 (1199031199021minus119879 (120595 (119909 119910) 120579))

1003816100381610038161003816 119889119909 119889119910

(4)



a distance 119889 = 1199090cos 120579 + 119910







119875 (119903 120579) 997888rarr 119875 (119903 120579 + 1205790) (6)


119891 (119886119909 119886119910) 997888rarr1

1198862119875 (119886119903 120579) (7)


119885119901119902=(119901 + 1)

120587int

2120587

0

int

1

0

119877119901119902 (119903) 119890

minus119902120579119891 (119903 120579) 119903119889119903 119889120579 (8)


119877119901119902 (119903) =

119901

sum

119896=119902


119861119901|119902|119896

119903119896 (9)

With

119861119901|119902|119896

=

(minus1)((119901minus119896)2)

((119901+119896) 2)


0 119901minus119896 = odd(10)




Line Radontransform






(119903 120579) = 120582119875(119903

120582 120579 + 120573) (11)


119885119901119902=119901 + 1

120587int

2120587

0

int

1

0

(119903 120579) 119877119901119902 (120582119903) 119890(minus119902120579)

119903119889119903 119889120579

=119901 + 1

120587int

2120587

0

int

1

0

120582119875(119903

120582 120579 + 120573)119877

119901119902 (120582119903) 119890(minus119902120579)

119903119889119903 119889120579

(12)



119877119901119902 (120582119903) =

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

120582119894119861119901119902119894119863119901119894119896 (13)

Image



Zernikemoment NRZM




119885119901119902=119901 + 1

120587

times int

2120587

0

int

1

0

120582119875(119903

120582 120579+120573)

times

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

120582119894119861119901119902119894119863119901119894119896119890(minus119902120579)

119903119889119903 119889120579

(14)



119885119901119902=119901 + 1

120587

times int

2120587

0

int

1

0

120582119875 (120591 120593)

119901

sum

119896=119902

119877119901119896 (119903)

times

119896

sum

119894=119902

(120582119894119861119901119902119894119863119901119894119896) 119890(minus119902(120593minus120573))

1205822120591119889120591 119889120593

=119901 + 1

120587119890119902120573

times int

2120587

0

int

1

0

119875 (120591 120593)

times

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

(120582119894+3119861119901119902119894119863119901119894119896) 119890minus119902120593

120591119889120591 119889120593

=119901 + 1

120587119890119902120573

times

119901

sum

119896=119902

119896

sum

119894=119902

(120582119894+3119861119901119902119894119863119901119894119896)

times int

2120587

0

int

1

0

119875 (120591 120593) 119877119901119896 (119903) 119890

minus119902120593120591119889120591 119889120593

= 119890119902120573

119901

sum

119896=119902

119896

sum

119894=119902

(120582119894+3119861119901119902119894119863119901119894119896)119885119901119896

(15)



119868119901119902= exp (119895119902119886119903119892 (119885

11))

119901

sum

119896=119902

(

119896

sum

119894=119902

11988500

minus((119894+3)3)119861119901119902119894119863119901119894119896)119885119901119896

(16)

Then 119868119901119902




119877119885119872 = [119868119891 (1 0) 119868119891 (1 1) 119868119891 (119872119872)] (17)




1199021


PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

Chongrsquos method







Bird

Bone

Bric

k

Cam

el

Car

Ch

ildre

nCl

assic

El

epha

ntFa

ce

Fo

rk

Gla

ss

Ham

mer

H

eart

Ke

y

M

isk

Ra

y

Tu

rtle

0

2

4

6

8

10

12


PRZ

Foun

tain

The n

umbe

r of r

etrie

ved

rele

vant

imag

e













4 Conclusion




09

08

07

06

05

04

03

02

01

0090807060504030201 1

(a) SNR = 16

09

08

07

06

05

04

03

02

01

0090807060504030201 1

(b) SNR = 14

09

08

07

06

05

04

03

02

01

0090807060504030201 1

(c) SNR=12

09

08

07

06

05

04

03

02

01

0090807060504030201 1

(d) SNR=10

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0090807060504030201 1

Chongrsquos method

(e) SNR = 8

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0090807060504030201 1

Chongrsquos method

(f) SNR = 6

Figure 4 Continued


PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0090807060504030201 1

Chongrsquos method

(g) SNR =4

PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

01

0

1

0 090807060504030201

Chongrsquos method



PRZRZERZ

HRZHu moment

09

08

07

06

05

04

03

02

010 08060402 1

1

Chongrsquos method




Appendix


(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)

=(

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)(

119903119902

119903119902+1

119903119901

)

(A1)



(

119903119902

119903119902+1

119903119901

) = (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

minus1

times(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)


= (

119863119901119902119902

119863119901119902119902+1

sdot sdot sdot 119863119901119902119901

119863119901119902+1119902+1

sdot sdot sdot 119863119901119902+1119901

d

119863119901119901119901

)

times(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)

(

119877119901119902 (120582119903)

119877119901119902+1 (120582119903)

119877119901119901 (120582119903)

) = (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

times(

(120582119903)119902

(120582119903)119902+1

(120582119903)119901

)

= (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

times(

120582119902

120582119902+1

d120582119901

)(

119903119902

119903119902+1

119903119901

)

= (

119861119901119902119902

119861119901119902119902+1

sdot sdot sdot 119861119901119902119901

119861119901119902+1119902+1

sdot sdot sdot 119861119901119902+1119901

d

119861119901119901119901

)

times(

120582119902

120582119902+1

d120582119901

)

times(

119863119901119902119902

119863119901119902119902+1

sdot sdot sdot 119863119901119902119901

119863119901119902+1119902+1

sdot sdot sdot 119863119901119902+1119901

d

119863119901119901119901

)

times(

119877119901119902 (119903)

119877119901119902+1 (119903)

119877119901119901 (119903)

)

=

119901

sum

119896=119902

119877119901119896 (119903)

119896

sum

119894=119902

119903119894sdot 119861119901119902119894sdot 119863119901119894119896

(A2)

Acknowledgments


References

































1 Introduction










ECGsignal

Signalprocessing

Featureextraction

IEMMCalgorithm

Resultcompare


ClearECGAdaptive

Filter


noise 1198641

RawECGsignal


1198642

Referenceinput

Wavelettransform





21 Preprocessing






119877119877119899(s) 119877119877

1015840

119899(s) 119876119877119878

119899(s) 119875119877

119899(s) 119876119879

119899(s) 119878119879

119899(s) 119877

119899(mv) 119875

119899(mv) 119879

119899(mv)

08477 08692 00742 01663 02930 02188 18149 00570 0681709023 08931 00742 01445 02891 02148 16339 00142 0592608594 08916 00781 01406 02852 02070 23085 00579 0612508281 08034 00742 01663 02931 02109 21007 00469 06247



1which contain














119899)


119899)




119899)






119899and 119877119877

1015840







119899 and

their labels 119910 = 1199101 119910





min119908119887120585119894

1

21199082+ 119862

119899

sum

119894=1

120585119894

st 119910119894(119908119879120601 (119909) + 119887) ge 1 minus 120585

119894

120585119894ge 0 119894 = 1 119899

(1)








119899min119908119887120585119894

1

21199082+ 119862

119899

sum

119894=1

120585119894

st 119910119894(119908119879120601 (119909) + 119887) ge 1 minus 120585

119894

120585119894ge 0 119894 = 1 119899 119862 ge 0

(2)


minusℓ le 119890119879119910 le ℓ (3)





inf119891isin119867

1

119899

119899

sum

119894=1

119871 (119910119894 119891 (119909119894)) + 120582

100381710038171003817100381711989110038171003817100381710038172

119867 (4)


2






2 leading to

min119908119887120578

1

21199082+119862

2

119899

sum

119894=1

1205782

st 119910i ((119908119879120601 (119909119894)) + 119887) = 1 minus 120578 119894 = 1 119899

(5)


minyisinminus1+1119899119908119887

119869 (119910 119908 119887) =1

21199082+119862

2

119899

sum

119894=1

1205782

st 119910i ((119908119879120601 (119909119894)) + 119887) = 1 minus 120578

119894 = 1 119899 minus119897 le

119899

sum

119894=1

119910119894le 119897

(6)







119910119898+119903


119875119898


119898+ 119875119903) 119875 should















lowast

119898is generated


119888and 119875

lowast

119898to








1 119910

119898+119903 sube minus1 +1



119875119903(119875 = 119875



119865 (119910) = exp (minusmin 119869 (119910 119908 119887)) (7)



would be returned


min119910119887

119899

sum

119894=1

(119908 sdot 120601 (119909119894) + 119887 minus 119910

119894)2


119894 = 1 119899 minusℓ le 119890119879119910 le ℓ

(8)
















sensitivity =TP

(TP + FN)

specificity =TN

(FP + TN)

accuracy =(TP + TN)

(TP + FN + FP + TN)

(9)








10158401205902) is used




100

90

80

70

60

50

40

30

200 1 2 3 4 5 6 7 8 9 10

Sens

itivi

ty (

)




(a) Sensitivity



Spec

ifici

ty (

)

100

95

90

85

80

75

70

65

600 1 2 3 4 5 6 7 8 9 10


(b) Specificity



Accu

racy

()

100

95

90

85

80

75

70

65

60


55

50

(c) Accuracy



4 Conclusions





Acknowledgments


References





































1 Introduction










A C T G














[ 119865[minus ]

[ 119865[minus ]

[ 119865[minus ]

[119865][119865]

[+119865]

[+119865]

[+119865]







119866 = (119881 120596 119875) (1)

where

(i) 119881 = 1199041 1199042 119904
















119875 997888rarr 119871119877 (2)


119871and 119877


119875 rarr 119871119877 and 119877 rarr 119877119871119877119877


119875 997888rarr [minus119865119871] [+119865119877]



(3)


119877119871rdquo and ldquo119877



119875

119871 119871119877 119877

119875

119877119871 119877119877

119875 rarr 119871119877 119875 rarr 119871119877

119877 rarr 119877119871119877119877




119875 997888rarr [minus119865119879119871] [+119865119879

119877]

119879119871997888rarr [minus119865] [+119865]

119879119877997888rarr [minus119865] [+119865119879119877119877

]

119879119877119877

997888rarr [minus119865] [+119865119879119877119877119877]

119879119877119877119877

997888rarr [minus119865]

(4)


119877rarr

[minus119865][+119865119879119877119877] and 119879

119877119877rarr [minus119865][+119865119879






119875119875

119879119871

119879119871119879119877

119879119877

119879119877119877

119879119877119871


119879119877 rarr [minus119865119879119877119871][+119865119879119877119877

]

119879119877 rarr null


119879119877119871rarr null

119879119877119877rarr null


119875

119879119871 119879119877

119875

119879119871 119879119877

119879119877119877119879119877119871


119879119877 rarr [minus119865119879119877119871][+119865119879119877119877

]




119877rarr

[minus119865][+119865119879119877119877] and 119879

119877119877rarr [minus119865][+119865119879





2are homomorphic



2in DNA


1and rule119877

2generate




2are isomorphic on



119875 997888rarr [minus119865119879119871] [+119865119879

119877] 997888rarr [minus119865] [+119865]


119879119877997888rarr [minus119865] [+119865119879119877119877

] 997888rarr [minus119865] [+119865]

119879119877119877


119879119877119877119877


(5)

We find that 119875 119879119871 119879119877 and 119879







3rarr





rarr [minus119865][+119865] and119879119877119877119877119871119871

rarr [minus119865][+119865] and 119879119877119871119877119871119877




119877] 119879119877119871119871119871

rarr

[minus119865][+119865] and 119879119877119877119877119877

rarr [minus119865][+119865119879119877119877119877119877119877









119875 rarr [minus119865119879119871] [+119865119879

119877]

119879119871rarr [minus119865119879

119871119871] [+119865119879

119871119877]

119879119871119871

rarr [minus119865119879119871119871119871

] [+119865119879119871119871119877

]

119879119871119871119871

rarr [minus119865119879119871119871119871119871

] [+119865119879119871119871119871119877

]

119879119871119871119871119871

rarr [minus119865] [+119865]

119879119871119871119871119877

rarr [minus119865] [+119865]

119879119871119871119877

rarr [minus119865119879119871119871119877119871

] [+119865119879119871119871119877119877

]

119879119871119871119877119871

rarr [minus119865] [+119865119879119871119871119877119871119877]

119879119871119871119877119871119877

rarr [minus119865] [+119865]

119879119871119871119877119877

rarr [minus119865] [+119865119879119871119871119877119877119877]

119879119871119871119877119877119877

rarr [minus119865] [+119865]

119879119871119877

rarr [minus119865119879119871119877119871

] [+119865119879119871119877119877

]

119879119871119877119871

rarr [minus119865119879119871119877119871119871

] [+119865119879119871119877119871119877

]

119879119871119877119871119871

rarr [minus119865119879119871119877119871119871119871

] [+119865]

119879119871119877119871119871119871

rarr [minus119865] [+119865]

119879119871119877119871119877

rarr [minus119865119879119871119877119871119877119871

] [+119865]

119879119871119877119871119877119871

rarr [minus119865] [+119865]

119879119871119877119877

rarr [minus119865119879119871119877119877119871

] [+119865119879119871119877119877119877

]

119879119871119877119877119871

rarr [minus119865119879119871119877119877119871119871

] [+119865119879119871119877119877119871119877

]

119879119871119877119877119871119871

rarr [minus119865] [+119865]

119879119871119877119877119871119877

rarr [minus119865] [+119865]

119879119871119877119877119877

rarr [minus119865119879119871119877119877119877119871

] [+119865119879119871119877119877119877119877

]

119879119871119877119877119877119871

rarr [minus119865] [+119865]

119879119871119877119877119877119877

rarr [minus119865] [+119865]

119879119877rarr [minus119865119879

119877119871] [+119865119879

119877119877]

119879119877119871

rarr [minus119865119879119877119871119871

] [+119865119879119877119871119877

]

Table 1 Continued

119879119877119871119871

rarr [minus119865119879119877119871119871119871

] [+119865119879119877119871119871119877

]

119879119877119871119871119871

rarr [minus119865] [+119865]

119879119877119871119871119877

rarr [minus119865119879119877119871119871119877119871

] [+119865]

119879119877119871119871119877119871

rarr [minus119865][+119865]

119879119877119871119877

rarr [minus119865119879119877119871119877119871

] [+119865119879119877119871119877119877

]

119879119877119871119877119871

rarr [minus119865] [+119865119879119877119871119877119871119877]

119879119877119871119877119871119877

rarr [minus119865][+119865]

119879119877119871119877119877

rarr [minus119865119879119877119871119877119877119871

] [+119865119879119877119871119877119877119877

]

119879119877119871119877119877119871

rarr [minus119865][+119865]

119879119877119871119877119877119877

rarr [minus119865] [+119865]

119879119877119877

rarr [minus119865119879119877119877119871

] [+119865119879119877119877119877

]

119879119877119877119871

rarr [minus119865119879119877119877119871119871

] [+119865119879119877119877119871119877

]

119879119877119877119871119871

rarr [minus119865119879119877119877119871119871119871

] [+119865]

119879119877119877119871119871119871

rarr [minus119865] [+119865]

119879119877119877119871119877

rarr [minus119865][+119865]

119879119877119877119877

rarr [minus119865119879119877119877119877119871

] [+119865119879119877119877119877119877

]

119879119877119877119877119871

rarr [minus119865119879119877119877119877119871119871

] [+119865119879119877119877119877119871119877

]

119879119877119877119877119871119871

rarr [minus119865][+119865]

119879119877119877119877119871119877

rarr [minus119865][+119865]

119879119877119877119877119877

rarr [minus119865] [+119865119879119877119877119877119877119877]

119879119877119877119877119877119877

rarr [minus119865][+119865]


form)

119881119894997888rarr 11990511989411198801198941 11990511989421198801198942 119905

119894119896119894119880119894119896119894 (6)

where 1199051198941 1199051198942 119905


1198941 1198801198942



119881119894=

119896119894

sum

119895=1

119905119894119895119880119894119895 (7)



119881119894 (119911) =

infin

sum

119899=1

119873119894 (119899) 119911

119899 (8)








Class 1(19) 119862

1rarr 11986211198621

(4) 1198621rarr 11986211198622

(4) 1198621rarr 11986221198621

(20) 1198621rarr 11986221198622

(8) 1198621rarr 11986211198621

(3) 1198621rarr 11986211198621

(1) 1198621rarr 11986211198621

(1) 1198621rarr 11986211198623

(1) 1198621rarr 11986241198622

(1) 1198621rarr 11986241198623

(1) 1198621rarr 11986221198622

(1) 1198621rarr 11986271198625

(1) 1198621rarr 11986251198622

(1) 1198621rarr 11986221198624

(1) 1198621rarr 11986281198628

(1) 1198621rarr 11986231198621

(1) 1198621rarr 11986231198621

(1) 1198621rarr 11986231198623

(1) 1198621rarr 11986281198626

(1) 1198621rarr 11986241198622

(5) 1198621rarr 11986241198624

Class 2 (48) 1198622rarr null (4) 119862

2rarr 11986241198625

(1) 1198622rarr 119862811986210

(1) 1198622rarr 11986281198626

Class 3 (4) 1198623rarr 11986251198624

(1) 1198623rarr 11986291198629

(1) 1198623rarr 11986291198627

Class 4 (20) 1198624rarr 11986251198625

(1) 1198624rarr 119862911986211

(1) 1198624rarr 1198621211986210

Class 5 (48) 1198625rarr null (1) 119862

5rarr 119862101198628

(1) 1198625rarr 1198621311986211

Class 6 (1) 1198626rarr 1198621011986210

(1) 1198626rarr 1198621311986213

Class 7 (1) 1198627rarr 119862111198629

(1) 1198627rarr 1198621311986215

Class 8 (5) 1198628rarr 1198621111986211

(1) 1198628rarr 1198621411986214

Class 9 (4) 1198629rarr 1198621111986212

(1) 1198629rarr 1198621411986216

Class 10 (4) 11986210

rarr 1198621211986211

(1) 11986210

rarr 1198621511986213

Class 11 (20) 11986211

rarr 1198621211986212

(1) 11986211

rarr 1198621511986215

Class 12 (48) 11986212

rarr null (1) 11986212

rarr 1198621611986214

Class 13 (5) 11986213

rarr 1198621611986216

Class 14 (4) 11986214

rarr 1198621611986217

Class 15 (4) 11986215

rarr 1198621711986216

Class 16 (20) 11986216

rarr 1198621711986217

Class 17 (48) 11986217

rarr null



1198700= minus ln119877 (9)




119894contains 119899

119894rules Let 119881

119894isin 1198621 1198622 119862

119899

119880119894119895isin 119877119894119895 119894 = 1 2 119899 119895 = 1 2 119899

119894 and 119886

119894119895119896isin


form

1198801198941997888rarr 119881

1198861198941111988111988611989412

1198801198942997888rarr 119881

1198861198942111988111988611989422


119880119894119899119894

997888rarr 1198811198861198941198991198941

1198811198861198941198991198942

(10)


follows

119881119894 (119911) =

sum119899119894

119901=11198991198941199011199111198811198861198941199011

(119911) 1198811198861198941199012(119911)

sum119899119894

119902=1119899119894119902

(11)


119881119894(119911) = 1




1to denote the



1(119911) we set 119877 = 119911




1198700= minus ln119877 (12)



1198815(1199111015840) = 1 (by definition)

1198814(1199111015840) =

sum1198994

119901=11198994119901119911101584011988111988641199011

(1199111015840)11988111988641199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=1199111015840times (20 times 119881

5(1199111015840) times 1198815(1199111015840))

20= 1199111015840

1198813(1199111015840) =

sum1198993

119901=11198993119901119911101584011988111988631199011

(1199111015840)11988111988631199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=1199111015840times (4 times 119881

5(1199111015840) times 1198814(1199111015840))

4= 11991110158402

1198812(1199111015840) =

sum1198992

119901=11198992119901119911101584011988111988621199011

(1199111015840)11988111988621199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=1199111015840times (4 times 119881

4(1199111015840) times 1198815(1199111015840))

4= 11991110158402

1198811(1199111015840) =

sum1198991

119901=11198991119901119911101584011988111988611199011

(1199111015840)11988111988611199012

(1199111015840)

sum119899119894

119902=1119899119894119902

=81199111015840times 1198811(1199111015840)2

+ 2(1199111015840)3

times 1198811(1199111015840)

19

+

(2(1199111015840)5

+ 2(1199111015840)4

+ 5(1199111015840)3

)

19

(13)


a quadratic for 1198811(1199111015840)

8

19(1199111015840) times 1198811(1199111015840) + (1 minus

2

19(1199111015840)3

) times 1198811(1199111015840)

+1

19(2(1199111015840)5

+ 2(1199111015840)4

+ 5(1199111015840)3

) = 0

(14)


1198811(1199111015840) = (

(1199111015840)2

4minus

19

81199111015840) plusmn

19

81199111015840radic1198612 minus 119860 (15)



119899111

119899112

(8) 1198621rarr 11986211198621

11989912

119899121

119899122

(1) 1198621rarr 11986211198623

11989913

119899131

119899132

(1) 1198621rarr 11986221198622

11989914

119899141

119899142

(119899 = 5) Class 1 (1198991= 8)

(1) 1198621rarr 11986221198624

11989915

119899151

119899152

(1) 1198621rarr 11986231198621

11989916

119899161

119899162

(4) 1198621rarr 11986231198623

11989917

119899171

119899172

(1) 1198621rarr 11986241198622

11989918

119899181

119899182

(5) 1198621rarr 11986241198624

Class 2 (1198992= 1)

11989921

119899211

119899212

(4) 1198622rarr 11986241198625

Class 3 (1198993= 1)

11989931

119899311

119899312

(4) 1198623rarr 11986251198624

Class 4 (1198994= 1)

11989941

119899411

119899412

(20) 1198624rarr 11986251198625

Class 5 (1198995= 1)

11989951

119899511

119899512

(48) 1198625rarr null






where

119860 =32

361(2(1199111015840)6

+ 2(1199111015840)5

+ 5(1199111015840)4

)

119861 = 1 minus2

19(1199111015840)3

(16)


B

D

A C


04

06

08

1

1 101 201 301 401 501 601 701 801 901

234





119881119898

119894(1199111015840) =

sum119899119894

119901=11198991198941199011199111015840119881119898minus1

1198861198941199011(1199111015840)119881119898minus1

1198861198941199012(1199111015840)

sum119899119894

119902=1119899119894119902

1198810

119894(1199111015840) = 1

(17)


119894(1199111015840) to 119881

119898

119894(1199111015840) When 119881

119898minus1

119894(1199111015840) =

119881119898


119894(1199111015840) reach the








4 Results


0

02

04

06

08

1

12

1 11 21 31 41 51 61 71 81 91

0

02

04

06

08

1

12

1 51 101 151 201 251

TEIso 1

Iso 2Iso 3


002040608

11214

1 101 201







0

02

04

06

08

1

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3


0

02

04

06

08

1

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3


0

02

04

06

08

1

12

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3


0

02

04

06

08

1

12

14

1 101 201 301 401 501 601 701 801 901

TEIso 1

Iso 2Iso 3











0

02

04

06

08

1 101 201 301 401 501 601 701 801 901

1632

64128

(a) Koslicki method

0

02

04

06

08

1

12

14

1 101 201 301 401 501 601 701 801 901

1632

64128


0

02

04

06

08

1

12

14

1 101 201 301 401 501 601 701 801 901

1632

64128


0

02

04

06

08

1

12

1 101 201 301 401 501 601 701 801 901

1632

64128





5 Summary




Acknowledgment


References
































1 Introduction

















2 Backgrounds






119903119894= minus ln [ 119873 (119894 120572)

1198730 (119894 120572)

] (1)



119873(119894 120572) = 1198730 (119894 120572) exp (minus119903119894) (2)



1205902

119894(120583119894) = 119891119894exp(

120583119894

120574) (3)








119894=

1

119862 (119894)sum

119895isin119861(119894 119903)

119910119895120596 (119894 119895) (4)



sum119895isin119861(119894 119903)


119895isin119861(119894 119903)120596(119894 119895) = 1


1198892(119894 119895) =

1

(2119891 + 1)2

sum

119896isin119861(0 119891)

(119910119894+119896minus 119910119895+119896)2

(5)


120596 (119894 119895) = 119890minusmax(1198892minus21205902

119873 0)ℎ2

(6)





dim (119878) = lim120576rarr0

log119873(120576)

log (1120576) (7)


119899120576= 120580 minus 120581 + 1 (8)


119873120576= sum

119895

119899120576(119895) (9)




3 The New Method







119899120576 (119894) = 120580 minus 120581 + 1 (10)


window is

119873120576 (119894) = sum

119895

119899120576(119895) (11)







(a) (b) (c)

(d) (e) (f)




120596 (119894 119895) = 119890minusmax(1198892minus21205902

119873 0)ℎ2

1minus(119896(119894)minus119896(119895))

2ℎ2

2 (12)




1198892(119894 119895) =

1

(2119891 + 1)2

sum

119896isin119861(0 119891)

(119910119894+119896minus 119910119895+119896)2

(13)



119894=

1

119862 (119894)sum

119895isin119861(119894 119903)

119910119895120596 (119894 119895) (14)




119895isin119861(119894 119903)120596(119894 119895) = 1



119899 119899 isin 119885 and
























1= 15 for the






119891119894= 35 119879 = 2119890 + 4 2188 3379 3459

119891119894= 4 119879 = 2119890 + 4 2130 3345 3416












119873= 15 the size





5 Conclusions




Acknowledgments


References











































1 Introduction








2 Theory



minusinfin

119906 (x) ℎ (x minus r) 119889x (1)



minusinfin






nabla2119906 (r) + 412058721198962119906 (r) = 0 (3)


119906 (r) = 119860 exp (1198952120587k sdot r) (4)



minusinfin

119880 (k) exp (1198952120587k sdot r) 119889k (5)



minusinfin



119906 (119903119909 119903119910 119903119911)

=∭infin

119880(119896119909 119896119910 119896119911) exp (1198952120587 (119896

119909119903119909+ 119896119910119903119910+ 119896119911119903119911)) 120575


1

1205822minus 1198962119909minus 1198962119910)119889119896119909119889119896119910119889119896119911

= ∬infin

119880(119896119909 119896119910 plusmnradic

1

1205822minus 1198962119909minus 1198962119910)

times exp(1198952120587(119896119909119903119909+ 119896119910119903119910

∓119903119911radic1

1205822minus 1198962119909minus 1198962119910))119889119896

119909119889119896119910

(7)




119911(119896119909 119896119910)


such that

119880119911(119896119909 119896119910) = 119880(119896

119909 119896119910 radic

1

1205822minus 1198962119909minus 1198962119910) (8)


119911= 119885

we have

119906119885(119903119909 119903119910)

= ∬infin

119880119885(119896119909 119896119910) exp(1198952120587119885radic 1

1205822minus 1198962119909minus 1198962119910)

times exp (1198952120587 (119896119909119903119909+ 119896119910119903119910)) 119889119896119909119889119896119910

(9)


119880119885(119896119909 119896119910)

= exp(minus1198952120587119885radic 1

1205822minus 1198962119909minus 1198962119910)

times∬infin

119906119885(119903119909 119903119910) exp (minus1198952120587 (119896

119909119903119909+ 119896119910119903119910)) 119889119903119909119889119903119910

(10)



119877119885(119903119909 119903119910) = int

+infin

minusinfin

119880119885(119896119909 119896119910)119867lowast

119911(119896119909 119896119910)

times exp(1198952120587119885radic 1

1205822minus 1198962119909minus 1198962119910)

times exp (1198952120587 (119903119909119896119909+ 119903119909119896119910)) 119889119896119909119889119896119910

(11)


119911=

119885 and

119867119885(119896119909 119896119910) = 119867(119896

119909 119896119910 radic

1

1205822minus 1198962119909minus 1198962119910) (12)


119877119885(119903119909 119903119910) = int

+infin

minusinfin

119906119885 (119906 V) ℎ119885 (119906 minus 119903119909 V minus 119903119910) 119889119906 119889V

(13)

Object beam

Sample

Microscope lens

CCD



120572 (3∘)



where

ℎ119885(119903119909 119903119910) = int

+infin

minusinfin

119867119885(119896119909 119896119910)

times exp (minus1198952120587 (119903119909119896119909+ 119903119909119896119910)) 119889119896119909119889119896119910

(14)



119885(119903119909 119903119910) with an






[1199091 1199092 119909



1 ℎ2 ℎ


x =119899

sum

119894=1

ℎlowast

119894minus119899+1119909119894 (15)


ℎ119899+119886

= ℎ119886 (16)


x = [11988611990931+ 1198871199092

1+ 1198881199091+ 119889 119886119909

3

2+ 1198871199092

2+ 1198881199092

+119889 1198861199093

119899+ 1198871199092

119899+ 119888119909119899+ 119889]119879

(17)


x = [10038161003816100381610038161199091100381610038161003816100381621003816100381610038161003816119909210038161003816100381610038162

100381610038161003816100381611990911989910038161003816100381610038162] (18)


= 119894119894 (19)



1 s2 s



R = S (20)


119864 =

119899119898

sum

119894=1 119895=1

(119877119894119895minus 119874119894119895)2

+ 119899

119898

sum

119895=1

(1198771119895minus 1198741119895)2

(21)

40

35

30

25

20

15

10

5

0

119885po

sitio

ns (120583

)

8070

6050

4030

2010

0

119884 positions (120583) 0 10 20 30 40 50 60 70 80

119883 positions (120583)

7060

5040

3020

10

119884 positions 20 30 40 50 60 70

itions (120583)


where119877119894119895and119874




3 Experiment




(a) (b)








40

35

30

25

20

15

10

5

0

119885po

sitio

ns (120583

)

8070

6050

4030

2010






4 Conclusion


Acknowledgment


References





























1 Introduction














1 1199092 119909



119910 = 11988611199091+ 11988621199092+ sdot sdot sdot + 119886

119899119909119899 (1)




119910 = 119883119860 (2)




119879119883 + 120583119868)

minus1







followed

119890119894=1003817100381710038171003817119910 minus 119886

119894119909119894

10038171003817100381710038172 (3)
















119910 = 11988711199091+ sdot sdot sdot + 119887

119872119909119872 (4)



119910 = 119861 (5)




119861 = ()minus1

119910 (6)


119861 = (119879

+ 120574119868)minus1

119879

119910 (7)






119892119903= 119887119904119909119904+ sdot sdot sdot + 119887

119905119909119905 (8)



119863119903=1003817100381710038171003817119910 minus 119892

119903

10038171003817100381710038172 119903 isin 119862 (9)



119863119896= min119863
















1 1199092 119909



119894isin 119877119897


119906119894= 119882119879119909119894 (119894 = 1 2 119899) (11)



119878119879=

119899

sum

119894=1

(119909119894minus 120583) (119909

119894minus 120583)119879 (12)




1 1199062 119906

119899is



119882119898= arg max

119882

119882119879119878119879119882

= [1199081 1199082sdot sdot sdot 119908119897]

(13)



119863119894=10038171003817100381710038171003817119882119879

119898119910 minus119882

119879

119898119909119894

10038171003817100381710038171003817

2

=10038171003817100381710038171003817119882119879

119898(119910 minus 119909

119894)10038171003817100381710038171003817

2

(119894 = 1 2 119899)

(14)



119879 such that

119863119896= min119863

119894lt 119879 (119896 119894 = 1 2 119899 119879 isin [0 +infin)) (15)




119896






119878119887=

119871

sum

119894=1

119873119894(120583119894minus 120583) (120583

119894minus 120583)119879 (16)


119878119908=

119871

sum

119894=1

119873119894

sum

119895=1

(119909119895minus 120583119894) (119909119895minus 120583119894)119879

(17)





119908 such

that

119882119898= argmax

119882

1003816100381610038161003816100381611988211987911987811988711988210038161003816100381610038161003816

119882119879119878119908119882

= [11990811199082sdot sdot sdot 119908119897]

(18)




eigenvalues such as

119878119887119908119894= 120582119894119878119908119908119894 (119894 = 1 2 119897) (19)





is calculated as

119863119894=10038171003817100381710038171003817119882119879

119898119910 minus119882

119879

119898119909119894

10038171003817100381710038171003817

2

=10038171003817100381710038171003817119882119879

119898(119910 minus 119909

119894)10038171003817100381710038171003817

2

(119894 = 1 2 119899)

(20)



119863119896= min119863

119894lt 119879 (119896 119894 = 1 2 119899 119879 isin [0 +infin))

(21)






119896lt
















(24)






(25)












01 02 03 04 05 06 07 08 09 10

102030405060708090

100


Clas

sifica

tion

erro

r rat

e (

)

(a) T-TPTSR

0 01 02 03 04 05 06 07 08 09 10

102030405060708090

100


Clas

sifica

tion

erro

r rat

e (

)

(b) T-GR

0 005 01 015 02 0250

102030405060708090

100

Clas

sifica

tion

erro

r rat

e (

)



(c) T-PCA

005 01 015 02 025 030

102030405060708090

100

Clas

sifica

tion

erro

r rat

e (

)



(d) T-LDA







0 01 02 03 04 05 06 070

102030405060708090

100

Det

ectio

n ra

te (

)


(a) T-TPTSR

01 02 03 04 05 06 07 080

102030405060708090

100

Det

ectio

n ra

te (

)


(b) T-GR

005 01 015 02 025 030

102030405060708090

100

Det

ectio

n ra

te (

)


TPRoutlier

ERRFA

119863119874-119865

(c) T-PCA

0 005 01 015 02 025 03 035 04

0

20

40

60

80

100

Det

ectio

n ra

te (

)


minus20

TPRoutlier

ERRFA

119863119874-119865

(d) T-LDA






















5 Conclusion




Acknowledgment


References













































1 Introduction








2 Related Work











(a) (b)









119894119895(119905) The force


119886119894119895 (119905 + Δ119905) =

1

120583119894119895

119865119894119895 (119905)

V119894119895 (119905 + Δ119905) = V119894119895 (119905) + Δ119905 sdot 119886119894119895 (119905 + Δ119905)

119875119894119895 (119905 + Δ119905) = 119875119894119895 (119905) + Δ119905 sdot V119894119895 (119905 + Δ119905)

(1)












119875119906V (119905 + Δ119905) =

1003816100381610038161003816119875119906V (119905) + 119881119906V (119905 + Δ119905) sdot Δ1199051003816100381610038161003816 le (1 + 120591119888) sdot 119871

(2)


(a) (b)











119898 = 05 gray = 0ln (gray + 1) gray = 0

(3)
















119875119894119894(119890 119905)

119875 119894119895(119890 119905)

119875119894119896(119890 119905)State 119878119894

State 119878119895

State 119878119896

larr997892











119894 119878119895 and 119878




119895






119875119894119894 (119890 119905) = 119890

minus120582119894(119890)119905 0 le 119894 le 119899 (4)

120582119894 (119890) =

ln 2120591119894 (119890) (5)



denoted as 1 minus 119875119894119894(119890 119905) 119875



119895 and it is


119875119894119895 (119890 119905) = (1 minus 119875119894119894 (119890 119905))119883119894119895 (119890) 0 le 119894 ≺ 119899 119894 =119895 (6)






Begin

End


shapes


user interaction



probabilities








6 Results



7 Conclusion






Acknowledgments


References














































1 Introduction








2 Outlier Rejection




(1)





Number of matches

Bucket

Random

Variable

0 1

0

2 3

1

119871 minus 1







0 1 2 3 4 5 6

1

2

3

4

5

6

7

7

0





119873



matrixH or F


















(a) 51140

(b) 47140




5 Conclusion


50100150200250300350

100 200 300 400 500 600 700 800


50100150200250300350

100 200 300 400 500 600 700 800


50100150200250300350

100 200 300 400 500 600 700 800



0

200

400

600

800

1000

02 03 04 05 06 07 08 09120593

119879

RANSAC(P)RANSAC(E)





Acknowledgments


References



























1 Introduction













119888119888out =11989911989911989911989910055761005576119894119894=119894119888119888 (119894119894)

11989411989411989911989910055771005577119895119895=119894

119899 119899 119886119886 1007649100764911989511989510076651007665

= 119888119888119894 + 119888119888119899 10076491007649119899 119899 11988611988611989410076651007665 + 1198881198882 10076491007649119899 119899 11988611988611989910076651007665 10076491007649119899 119899 11988611988611989410076651007665 + ⋯

(1)




Image plane


0




119894119894 = 10077161007716119878119878Δ119878119878

10077321007732 119878 119895119895 = 10077171007717119878119878Δ119878119878

10077331007733 119878 119894119894 = 10077161007716119878119878Δ119878119878

10077321007732 119878

119878119878119894119894 = 119894119894 119894 Δ119878119878119878 119878119878119895119895 = 119895119895 119894 Δ119878119878119878 119878119878119894119894 = 119894119894 119894 Δ119878119878119878

119878119878119899119899 =119878119878 119899 119878119878119894119894Δ119878119878

119878 119878119878119899119899 =119878119878 119899 119878119878119895119895Δ119878119878

119878 119878119878119899119899 =119878119878 119899 119878119878119894119894Δ119878119878

119878

(2)



119865119865119899 = 119868119868119894 + 119878119878119899119899 119894 100764910076491198681198683 119899 11986811986811989410076651007665 119878 1198651198652 = 119868119868119899 + 119878119878119899119899 119894 100764910076491198681198682 119899 11986811986811989910076651007665 119878

1198651198653 = 1198681198685 + 119878119878119899119899 119894 100764910076491198681198686 119899 119868119868510076651007665 119878 1198651198654 = 1198681198684 + 119878119878119899119899 119894 100764910076491198681198687 119899 119868119868410076651007665 119878

1198651198655 = 119865119865119899 + 119878119878119899119899 119894 100764910076491198651198652 119899 11986511986511989910076651007665 119878 1198651198656 = 1198651198654 + 119878119878119899119899 119894 100764910076491198651198653 119899 119865119865410076651007665 119878

119865119865 = 1198651198655 + 119878119878119899119899 119894 100764910076491198651198656 119899 119865119865510076651007665 (3)






119883119883119894119894 120577 119894119894Δ119864119864 120577119894119894 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 119894120577 120577

119884119884119895119895 120577 119895119895Δ119864119864 10076491007649119895119895 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 11989410076651007665 120577

119885119885119896119896 120577 119896119896Δ119864119864 120577119896119896 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 119894120577

(4)


119864119864119895119895 120577 119864119864119900119900 + 120577120577 119864 119898119898119895119895 120577 119895119895Δ119864119864 10076491007649119895119895 120577 119894120577 119894120577 119894120577119894 120577 119864119864119864119864 119894 11989410076651007665 120577 (5)


119895119895 120577 10077171007717119864119864Δ119864119864

10077331007733 (6)

erefore

119898119898119895119895 120577119895119895Δ119864119864 119894 119864119864119900119900

120577120577120577 (7)


119864119864119894119894 120577 119864119864119900119900 + 120577120577 119864 119898119898119895119895 119864119864119896119896 120577 119864119864119900119900 + 120577120577 119864 119898119898119895119895 (8)


119894119894 120577 10077171007717119864119864119894119894Δ119864119864

10077331007733 120577

119896119896 120577 10077171007717119864119864119896119896Δ119864119864

10077331007733 (9)




119868119868119864119864 120577 119868119868119894 + 10076491007649119868119868119894 119894 11986811986811989410076651007665 10076651007665119864119864119894119894Δ119864119864

119894 11989411989410076681007668 + 100764910076491198681198683 119894 11986811986811989410076651007665 10076651007665119864119864119896119896Δ119864119864

119894 11989611989610076681007668 (10)



Heart512 119864 512 119864 41


0486 119864 0486 1198640700

0318 119864 0318 1198642000



119868119868119878119878 120577 119868119868119864119864 +119898119898 119894 119898119898119895119895

119898119898119895119895+119894 119894 11989811989811989511989510076501007650119868119868119876119876 119894 11986811986811986411986410076661007666 (11)

















4 Conclusion



Acknowledgments


References


















Research Article









1 Introduction





Dim Light

(a)

(b)












ΔρT = 0530υmax

radicln cNp minus 1

2ln[Np + σ2

D

] (1)





light intensity



Lens 2

Lens 1

Target scene

DMDgenerates

themeasurement


min∥θ∥1

subject to

^λJ

^λJ asymp λJ

λJ = XN

^XN =




Lens N

XN

XN

ΦXN

YM =YM =ΦΨθ

=Ψθ

=Ψθlowast

Ψθlowast





rang+ ODC (2)



Xi = XiC + XiS (3)



XN = Ψθ (4)






⎡⎢⎢⎢⎢⎣Y1

Y2

YM

⎤⎥⎥⎥⎥⎦ =

⎡⎢⎢⎢⎢⎣Φ1 0

Φ2

0 ΦM

⎤⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎣X1

X2

XN

⎤⎥⎥⎥⎥⎦ (6)





(a) (b)

(c) (d)




for k = J to 1


(γkminus1

)


)


(8)






) = λk




(a) (b)

(c) (d)







02 03 04 05 06 07 0820

25

30

35

40

45

50

55

60

Sampling rate

PSN

R







4 Conclusion




Acknowledgments


References








































Research Article









1 Introduction






Image registration

Image acquisition


Preprocessing



2 Testing Image Set








u1 = u0 minusm







(a) (b)


(a) (b)








3 Modelling








(a) (b) (c)


Give multiscale

images







Get lumen boundary

Construct a

ring-like shape


g1(rarrI )

g2(rarrI )

g3(rarrI )

g4(rarrI )

rarrI


label







Trainingmodel

Testing set

Training set

Results

Intensity value


Initializeweight

constraint

condition

Y

N



Satisfaction


Obtain model




20

40

60

80

100

20 40 60 80 100 120S28

20

40

60

80

20 40 60 80S34

(a)

20

40

60

80

100

20

40

60

80

20 40 60 80

20 40 60 80 100 120

(b)

20

40

60

80

100

20 40 60 80 100 120

20

40

60

80

20 40 60 80

(c)


4 Comparison





e(i) = f p + f n

n (2)





Bayes SSVM

1 35 26

3 53 48

5 65 63

7 106 85

9 169 96


5 Conclusion





Acknowledgments


References

















Research Article









1 Introduction







(x minus μx

)2p(x)dx (1)









x(m)minus xM(m) (2)



(e minus μe

)2p(e) (3)


xM(m) = PxN (n) (4)




pPareto(e) = aba

ea+1 (5)


μe = ab

aminus 1

Var(e) = ab2


(6)





rxx(k) = E[x(n)x(n + k)] (7)




ree(k) = E[e(m)e(m + k)] (9)

Note that





(10)








ree(k) sim




(k minusrarr infin)

(14)





3 Discussions



4 Conclusions


Acknowledgments


References





















































































Research Article









1 Introduction













3 Results




4 Discussion












1

2

3

(a)

1

2

3

(b)

1

2

3

(c)

1

2

3

(d)

1

2

3

(e)

1

2

3

(f)






Class Type













1

2

32 mm











5 Conclusion


References


























































Research Article









1 Introduction






Fclk

AA


Digital toanalog


cosθ

sinθ




To = 2vTs

FCW (1)


Fo = 1T0= Fs

2vmiddot FCW (2)


ΔFomin = Fs2v

(FCW + 1)minus Fs2v

FCW = Fs2v (3)


ΔFo ge Fs2v (4)


SFDR = 20 log(Ap

As

)= 20 log

(Ap








y(i + 1) = y(i) + σ(i)2minus jx(i) (7)

z(i + 1) = z(i)minus σ(i)α(i) (8)





K1 =nminus1prodi=0






[xout

yout

]= K1


][xin

yin

] (11)






x(i + 1)y(i + 1)

]=[



][x(i)y(i)

]


(13)






RegFCW

Adder

(32-bit)

Reg

Load

Reset

φ


π

2+ φ

φ

π + φ

3π2

+ φ




x(i + 1) =(


y(i + 1) =(


(14)



m 0 1 2 3 4 5 6 7




Hardware cost

16-bit Adders 46 38 34 30 26 22 18 16

16-bit Shifters 46 38 34 30 26 22 18 16





0 0 0 0 lt 2πφ ltπ


0 0 1π

4lt 2πφ lt

π


0 1 0π

2lt 2πφ lt

3π4


0 1 13π4




1 0 1 minus3π4

lt 2πφ lt minusπ


1 1 0 minusπ



1 1 1 minusπ



DDFSKang and





[18]

Yi et al2006 [6]

De Caroet al 2009

[27]


2012

Process (μm) 013 mdash 05 035 035 025 018



1018 230 106 210 100 385 500


SFDR (dBc) 90 54 mdash 722 80 90 8685




For 8 le i lt 16







Input



CSA(32) CSA(32)

CSA(42)

CLA

Output


π

2π

4

π

2minus γ

γ


xin

yin

+

+

+

+

+

minus

minus

minus

2i + 1-bitshifter

i-bitshifter

i-bit

shifter2i + 1-bit

shifter

x

y

xout

yout


xoutxin

yin yout

+

+

+

minus

i-bitshifter

i-bitshifter

x

y


0 1 2 3 4 5 6 706

07

08

09

1

11

12

13

14

15times104

m

Gat

es




75

80

85

90

95

m

SFD

RS

NR

(dB

)



0 1 2 3 4 5


xinv

yinv

Swap

sinθ

cosθ

sin2πφ

cos2πφ0

1

1

0


32 3

1

Accumulator

FCW

Constant

multiplier

Quadrant

mirror

32

22 19 19

16

916

ROM CORDICprocessor

A

16

16

16

1616

16 16

16


I sim IXOutput

stage

cos output







minus140

minus120

minus100

minus80

minus60

minus40

minus20

0


DR


PCUSB 2

MCU FPGA





(verilog)



debug(modelsim)


Physicalcompilation

(astro)


Tape out










5 Conclusion


Acknowledgment


References





















































Research Article









1 Introduction












nii le Rc where






Pj

(xj)

x =nminus1sumj=0



Pj

(xj = 1




No

Yes

Initial superpixels

Segmentation result


MQ table-based LPMF


ΔSmn gt Td




Sm = E[Dm]E[Lm]

(3)


Dm =Nmsumi=1

x2mi (4)


xmi =nminus1sumj=0



E[Dm] =Nmsumi=1

nminus1sumj=0

nminus1sumk=0

E[xmi j middot xmik

]middot 2 j+k

sim=Nmsumi=1

nminus1sumj=0

nminus1sumk=0

E[xmi j

]middot E[xmik

] middot 2 j+k

(6)


E[xmi j

]= Pmi j

(xmi j = 1

) (7)



(Nm

N

)(8)


H(xm j

) (9)

H(xm j

)= minus Pm j

(xm j = 1

)middot log2

(Pm j

(xm j = 1

))

minus Pm j

(xm j = 0

)middot log2

(Pm j

(xm j = 0

))

(10)

Pm j

(xm j

)= 1

Nm

Nmsumi=1

middot Pmi j

(xmi j

) (11)



ΔSmn


(12)


The RDM Algorithm





MQ table

Bit-planeencoder

MQencoder

JPEG2000 encoder

(a)

DeQIWTImage

Local PMF

MQ table



JPEG2000 decoder

MQencoder

(b)







j=0

nminus1sumk=0

⎛⎝ 1Nm

Nmsumi=1

Pmi j

(xmi j = 1

)⎞⎠

middot⎛⎝ 1Nm

Nmsumi=1

Pmik(xmik = 1


⎤⎦

(13)






(a) (b) (c)

0 1 2 3 4 5 60

1

2

3

4

5

6

7

err

()

(bpp)

(d)





E[xi j]middot 2 j

=nminus1sumj=0

Pi j(xi j = 1

)middot 2 j

(14)






(a)

(b)

(c)



RDM CTM Mean-shift

0771 0762 0755


RDM CTM Mean-shift

87 94 97



RDM 89 s 87 s 107 s 68 s

Mean-shift 183 s 275 s 207 s 189 s

CTM 353 s 172 s 576 s 135 s


5 Conclusions





Acknowledgments


References





























Date post:	11-Sep-2021
Category:	Documents
Upload:	others
View:	2 times
Download:	0 times

Biomedical Signal Processing and Modeling Complexity of Living Systems 2013

Documents