Research Article Center Symmetric Local Multilevel Pattern...

Research ArticleCenter Symmetric Local Multilevel Pattern BasedDescriptor and Its Application in Image Matching

Hui Zeng1 Xiuqing Wang2 and Yu Gu1

1School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing 100083 China2Vocational amp Technical Institute Hebei Normal University Shijiazhuang 050031 China

Correspondence should be addressed to Yu Gu guyuustbeducn

Received 10 December 2015 Revised 14 April 2016 Accepted 17 April 2016

Academic Editor Fortunato Tito Arecchi

Copyright copy 2016 Hui Zeng et alThis is an open access article distributed under theCreative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents an effective local image region description method called CS-LMP (Center Symmetric Local MultilevelPattern) descriptor and its application in image matching The CS-LMP operator has no exponential computations so the CS-LMP descriptor can encode the differences of the local intensity values using multiply quantization levels without increasingthe dimension of the descriptor Compared with the binaryternary pattern based descriptors the CS-LMP descriptor has betterdescriptive ability and computational efficiency Extensive image matching experimental results testified the effectiveness of theproposed CS-LMP descriptor compared with other existing state-of-the-art descriptors

1 Introduction

Image matching is one of the fundamental research areasin the fields of computer vision and it can be used in 3Dreconstruction panoramic image stitching image registra-tion robot localization and so forth The task of imagematching is to search the corresponding points between twoimages that are projected by the same 3D point Generallythe image matching has the following three steps At first theinterest points are detected and their local support regionsare determinedThen the descriptors of the feature points areconstructed Finally the corresponding points are determinedthrough matching their descriptors In the above three stepsthe descriptor construction is the key factor that can influencethe performance of the image matching [1] In this paperwe focus on the effective local image descriptor constructionmethod and its application in image matching

For an ideal local image descriptor it should havehigh discriminative power and be robust to many kinds ofimage transformations such as illumination changes imagegeometric distortion and partial occlusion [2 3] Manyresearch efforts have been made for local image descriptorconstruction and several comparative studies have shownthat the SIFT-like descriptors perform best [4] The SIFT

(Scale Invariant Feature Transform) descriptor is built by a3D histogram of gradient locations and orientations wherethe contribution to bins is weighted by the gradient mag-nitude and a Gaussian window overlaid over the region[5] Its dimension is 128 and is invariant to image scaleand rotation transforms and robust to affine distortionschanges in 3D viewpoint addition of noise and changesin illumination Because of the good performance of SIFTdescriptor many varieties of SIFT descriptor have beenproposed For example the PCA-SIFT descriptor is a 36-dimensional vector by applying PCA (Principal ComponentAnalysis) on gradient maps and it can be fast for imagematching [6] The SURF (Speeded Up Robust Features)descriptor uses integral image to compute the gradienthistograms and it can speed up the computations effectivelywhile preserving the quality of SIFT [7] Furthermore GLOH(Gradient Location-Orientation Histogram) [4] Rank-SIFT[8] and RIFT (Rotation-Invariant Feature Transform) [9] arealso proposed based on the construction method of SIFTdescriptor

The LBP (Local Binary Pattern) operator has been proveda powerful image texture feature which has been successfullyused in face recognition image retrieval texture segmen-tation and facial expression recognition [10] It has several

Hindawi Publishing CorporationInternational Journal of OpticsVolume 2016 Article ID 1584514 9 pageshttpdxdoiorg10115520161584514

2 International Journal of Optics

advantages which are suitable for local image descriptor con-struction such as computational simplicity and invariance tolinear illumination But the LBP operator tends to producea rather long histogram especially when the number ofneighboring pixels increases So it is not suitable for imagematching The CS-LBP (Center Symmetric Local BinaryPattern) descriptor can address the dimension problemwhileretaining the powerful ability of texture description [11] Itcombines the advantages of the SIFT descriptor and LBPoperator and performs better than the SIFT descriptor inthe field of image matching To improve the descriptionability and the robustness to image transformation severalgeneralized descriptors have been proposed such as the CS-LTP (Center Symmetric Local Ternary Pattern) descriptor[12] the IWCS-LTP (Improved Weighted Center SymmetricLocal Ternary Pattern) descriptor [13] and the WOS-LTP(Weighted Orthogonal Symmetric Local Ternary Pattern)descriptor [14] Among the above descriptors the WOS-LTPdescriptor has better performance than the SIFT descriptorand IWCS-LTP descriptor It divides the neighboring pixelsinto several orthogonal groups to reduce the dimension ofthe histogram and an adaptive weight is used to adjust thecontribution of the code in histogram calculation For theWOS-LTP descriptor the quantization level of the intensityvalues is three The image intensity variant informationof the local neighborhood has not been fully investigatedFurthermore LDTP (Local Directional Texture Pattern) isanother kind of local texture pattern which includes bothdirectional and intensity information [15] Although theLDTP descriptor is consistent against noise and illuminationchanges its dimension is high To solve this problem CLDTP(Compact Local Directional Texture Pattern) is a proposeddescriptor [16] which not only reduces the dimension ofLDTP descriptor but also retains the advantages of LDTPdescriptor

Vector quantization is an effective method for texturedescription and it is robust to noise and illuminationvariation [17 18] The number of quantization levels isan important parameter The lower the quantization levelthe less the discriminative information the descriptor hasHowever if the quantization level is increased the descriptorrsquosrobustness to noise and illumination variety will degradeFor LBP or LTP operator based descriptor the differencesof the local intensity values are quantized in two or threelevelsThey have better robustness to illumination variety buttheir discriminative abilities are degraded If we increase thequantization level directly according to the encodingmode ofthe LBP or LTP operator the dimension of the descriptor willincrease dramatically LQP (Local Quantized Pattern) wasproposed to solve these problems It uses large local neighbor-hoods and deeper quantization with domain-adaptive vectorquantization But it uses visual word quantization to separatelocal patterns and uses a precompiled lookup table to cachethe final coding for speed Its main constraint is the sizeof the lookup table and it is not suitable to be used forimage matching So for the multiply quantization level baseddescriptor the effective encoding method is the key problemto balance the relationship between the discriminative abilityand the dimension of the descriptor

In this paper we present a novel encoding method forlocal image descriptor named as CS-LMP (Center SymmetricLocal Multilevel Pattern) operator which can encode thedifferences of the local intensity values using multiply quan-tization levels The CS-LMP descriptor is constructed basedon the CS-LMP operator and it can describe the local imageregion more detailedly without increasing the dimensionof the descriptor To make the descriptor containing morespatial structural information we use a SIFT-like grid todivide the interest region Compared with binaryternarypattern based descriptor it not only has better discriminativeability but also has higher computational efficiency Theperformance of the CS-LMP descriptor is evaluated forimage matching and the experimental results demonstrate itsrobustness and distinctiveness

The rest of the paper is organized as follows In Sec-tion 2 the CS-LBP CS-LTP and the WOS-LTP operatorand descriptor construction methods are reviewed Section 3gives the CS-LMP operator the CS-LMP histogram and theconstruction method of the CS-LMP descriptor The imagematching experiments are conducted and their experimentalresults are presented in Section 4 Some concluding remarksare listed in Section 5

2 Related Work

Before presenting in detail the CS-LMP operator and the CS-LMPdescriptor we give a brief review of theCS-LBP CS-LTPand WOS-LTP methods that form the basis for our work

21 CS-LBP and CS-LTP TheCS-LBP operator is a modifiedversion of the well-known LBP operator which comparescenter symmetric pairs of pixels in the neighborhood [11]Formally the CS-LBP operator can be represented as

CS-LBP119877119873 (119906 V) =

(1198732)minus1

sum119894=0

119904 (119899119894minus 119899119894+(1198732)

) 2119894

119904 (119909) =

1 119909 gt 119879

0 otherwise

(1)

where 119899119894and 119899

119894+(1198732)correspond to the gray values of center

symmetric pairs of pixels of119873 equally spaced pixels on a circlewith radius 119877 Obviously the CS-LBP operator can produce21198732 distinct values resulting in 21198732-dimensional histogramIt should be noticed that the CS-LBP descriptor is obtainedby the binary codes which is computed from the differencesof the intensity value between pairs of the opposite pixels ina neighborhood For the CS-LBP descriptor its dimension is21198732 and the quantization level of the intensity values is two

The CS-LTP operator is powerful texture operator [12]It uses the encoding method similar to the CS-LBP operatorand extends the quantization level of the intensity values from

International Journal of Optics 3

two to three The encoding method of the CS-LTP operatorcan be formulated as

CS-LTP119877119873 (119906 V) =

(1198732)minus1

sum119894=0

119904 (119899119894minus 119899119894+(1198732)

) 3119894

119904 (119909) =

2 119909 ge 119879

1 minus119879 lt 119909 lt 119879

0 119909 le minus119879

(2)

From (2) we can see that the dimension of the CS-LTP his-togram is 31198732 Compared with CS-LBP descriptor the CS-LTP descriptor has better descriptive ability for local texturalvariants but its dimension is higher and its computationalamount is larger

22 WOS-LTP The WOS-LTP descriptor is constructedbased on the OS-LTP (Orthogonal Symmetric Local TernaryPattern) operator [14] The OS-LTP operator is an improvedversion of the LTP operator to reduce the dimension ofthe histogram It takes only orthogonal symmetric fourneighboring pixels into account At first the neighboringpixels are divided into1198734 orthogonal groups Then the OS-LTP code is computed separately for each group Given 119873

neighboring pixels equally located in a circle of radius 119877around a central pixel at (119906 V) the encoding method of theOS-LTP operator can be formulated as

OS-LTP(119894)119877119873

(119906 V) = 119904 (119899119894minus1

minus 119899(119894minus1)+2[1198734]

) 30

+ 119904 (119899(119894minus1)+[1198734]

minus 119899(119894minus1)+3[1198734]

) 31

119904 (119909) =

2 119909 ge 119879

1 minus119879 lt 119909 lt 119879

0 119909 le minus119879

119894 = 1 2 119873

4

(3)

From (3) we can see that there are 1198734 different 4-orthogonal-symmetric neighbor operators each of whichconsists of turning the four orthogonal neighbors by oneposition in a clockwise direction Existing research workhas shown that compared with the LTP CS-LTP and ICS-LTP operator the OS-LTP operator has better discriminativeability for describing local texture structure and could achievebetter robustness against noise interference

The WOS-LTP descriptor is built by concatenating theweighted histograms of the subregions together which usesthe OS-LTP variance of the local region as an adaptive weightto adjust its contribution to the histogram [14] Suppose thesize of the image patch is 119882 times 119867 the WOS-LTP histogramcan be computed as

119867119894 (119896) =

119882

sum119906=1

119867

sumV=1119891119894(OS-LTP(119894)

119877119873(119906 V) 119896)

119891119894(119909 119910)

=

1003816100381610038161003816119899119894minus1 minus 119899(119894minus1)+2[1198734]1003816100381610038161003816 +

1003816100381610038161003816119899(119894minus1)+[1198734] minus 119899(119894minus1)+3[1198734]1003816100381610038161003816 119909 = 119910

0 119909 = 119910

119894 = 1 2 [119873

4]

(4)

where 119896 isin [0 119870] and 119870 is the maximal value of the OS-LTP operator Existing experimental results have shown thatcompared with SIFT and IWCS-LTP descriptor the WOS-LTP descriptor can not only better characterize the imagetexture but also achieve higher computational efficiency Butits quantization level of the intensity values is three and theintensity variant information has not been fully used

3 Center Symmetric Local Multilevel Pattern

31 CS-LMP Operator Although the local binary or ternarypattern based descriptors have good performance they arelimited to very coarse quantization and increasing the sizeof local neighborhood increases the histogram dimensionsexponentiallyThese shortcomings limit the local descriptorsrsquodescriptive ability and prevent them from leveraging all theavailable information To solve these problemswe proposed anovel encodingmethod namedCS-LMP operator It encodesthe differences of the local intensity values according tothe thresholds and a pixel has 1198732 encoding values Theselection method of pixels is the same as the LBP operatorThe readers can find the detailed selection steps in [10]

At first we define the thresholds 119879 = [minus119889119898 minus119889

2

minus1198891 0 1198891 1198892 119889

119898] to divide the differences of the local

intensity values into multiply intervals

1198921= (minusinfin minus119889

119898]

1198922= (minus119889

119898 minus119889119898minus1

]

1198922119898

= (119889119898minus1

minus119889119898]

1198922119898+1

= (119889119898 +infin)

(5)

Then the CS-LMP code of the pixel at (119906 V) is illustrated as

CS-LMP(119894)119877119873

(119906 V) = 119902 (119899119894minus 119899119894+(1198732)

)

119894 = 0 1 119873

2

119902 (119909) = 119905 119909 isin 119892119905 119905 = 1 2 2119898 + 1

(6)

From (6) we can see that the CS-LMP operator has noexponential computations and its maximum value is 2119898 +

1 Furthermore the difference of the local intensity valueis quantized 2119898 + 1 levels Compared with the localbinaryternary patterns the CS-LMP can describe the localtexture more flexibly and detailedly Figure 1 shows an exam-ple of calculating the CS-LMP operator with 8 neighboring


nc n0

n1n2

n3

n4

n5

n6n7 CS-LMP(1)

(u ) = q(n0 minus n4)

CS-LMP(2)(u ) = q(n1 minus n5)



Figure 1 Calculation of the CS-LMP operator with 8 neighboring pixels

Local image region CS-LBP CS-LTP OS-LTP CS-LMP

80

8080

80

8080

80

80

80

Flat image area

00

0

01

1

1

11

1

1

13

3

3

3

[3333]

24

3031

28

3225

29

33

28

Texture variance image area

00

0

01

1

1

11

1

1

15

5

4

2

[4552]

[0000]2

[0000]2 [1111]3

[1111]3

[11]3[11]3

[11]3[11]3

Figure 2 Examples of four encoding methods (119879 = 5119873 = 8 1198891= 3 and 119889

2= 26)

pixels and the CS-LMP code has 4 values Figure 2 givesexamples of four encoding methods As shown in Figure 2for the flat image area and the texture variance image area thecode of the CS-LBP CS-LTP and OS-LTP operator remainsunchanged But there exist distinct differences between theCS-LMP code of the flat image area and that of the texturevariance image area So we can conclude that our CS-LMPoperator appears to have better discriminative ability fordescribing local image texture

32 CS-LMP Histogram For the local image region the CS-LMP histogram can be obtained using the CS-LMP code ofeach pixel For the CS-LBP CS-LTP andWOS-LTP operatorthe final code of a pixel has one value by performing binaryor ternary computation Their corresponding histogram canbe obtained by computing the number of each kind of codeDifferent from the above three kinds of operators the CS-LMP code of a pixel has N2 values the occurrences of eachkind of value should be computed The CS-LMP histogramcan be represented as

119867119894 (119896) =

119882

sum119906=1

119867

sumV=1119891 (CS-LMP(119894)

119877119873(119906 V) 119896)

119894 = 0 1 119873

2

119891 (119909 119910) = 1 119909 = 119910

0 119909 = 119910

(7)

Figure 3 The normalization and division of a detected region

where 119896 isin [0 2119898 + 1] 2119898 + 1 is the maximal value of theCS-LMP operator Based on (7) the CS-LMP descriptor ofthe local image region can be obtained by concatenating1198732

histograms together

33 CS-LMP Descriptor To construct the CS-LMP descrip-tor the interest regions are firstly detected by the Hessian-Affine detector [19] which are used to compute the descrip-torsThen the detected regions are normalized to the circularregions with the same size 41 times 41 As shown in Figure 3 thedetected ellipse region is rotated in order that the long axisof the ellipse is aligned to the positive v-axis of the local u-v image coordinate system and the rotated elliptical regionis geometrically mapped to a canonical circular region by anaffine transformation The normalized regions are invariantto scale rotation and affine transformation In the rest ofthis paper the normalized regions are used for local imagedescriptor construction


(a) Bikes (blur changes) (b) Trees (blur changes)

(c) Wall (viewpoint changes) (d) Graffiti (viewpoint changes)

(e) Bark (scale + rotation changes) (f) Boat (scale + rotation changes)

(g) Leuven (illumination changes) (h) Ubc (JPEG compression)

Figure 4 Testing image pairs

In order to integrate the spatial information into thedescriptor we divide the normalized region into 16 (4 times

4) subregions using the grid division method of the SIFTdescriptor For each subregion we firstly compute the CS-LMP codes of each pixel respectively Then the CS-LMPhistograms are obtained using (7) For a single subregion thedimension of the CS-LMP descriptor is (1198732) times (2119898 + 1)Finally we connect all the histograms of different subregionstogether to obtain the final CS-LMPdescriptor for the interestregion So the dimension of the CS-LMP descriptor is 16 times(1198732) times (2119898 + 1) For example we compare the dimensionsof three descriptors based on the CS-LTP method WOS-LTP method and the CS-LMP method respectively whosequantization levels are all three Assume the number ofthe neighboring pixels is 12 then the variable 119898 is 1 andthe dimensions of the CS-LTP WOS-LTP and CS-LMPdescriptor are 16 times 729 16 times 27 and 16 times 18 respectively Wecan conclude that the dimension of the CS-LMP descriptor issignificantly reduced

Furthermore two normalization steps are performedon the CS-LMP descriptor to reduce the effects of theillumination At first the descriptor vector is normalizedto unit length to remove the linear illumination changesThen the elements of the normalized descriptor vector aretruncated by 02 in order to reduce the impact of thenonlinear illumination changes Finally the descriptor vectoris renormalized to unit length and truncated by 02 again

4 Experimental Results

In this paper we use the Mikolajczyk et al dataset [20] toevaluate the performance of the SIFT WOS-LTP and CS-LMP descriptor by imagematching experimentsThis datasetincludes eight types of scene images with different illumi-nation and geometric distortion transformations and it hasthe ground-truth matches through estimated homographymatrix As shown in Figure 4 we randomly select one imagepair in each category from the dataset In the imagematching


m = 1m = 2m = 3

0

01

02

03

04

05Re

call

04 06 08 1021 minus precision

(a) 119873 = 8 119877 = 2 1198891 = 001 1198892 = 01 and 1198893 = 02

04 06 08 1020

01

02

03

04

05

Reca

ll

d1 = 001 d2 = 004

d1 = 001 d2 = 006

d1 = 001 d2 = 008

d1 = 001 d2 = 010

d1 = 001 d2 = 012

1 minus precision

(b) 119873 = 8 119877 = 2 and119898 = 2

0

01

02

03

04

05

Reca

ll


d1 = 001 d2 = 010

d1 = 0006 d2 = 010

d1 = 0014 d2 = 010d1 = 0008 d2 = 010

d1 = 0012 d2 = 010

(c) 119873 = 8 119877 = 2 and119898 = 2

N = 8 R = 1N = 8 R = 2N = 12 R = 2

N = 16 R = 2N = 12 R = 3N = 20 R = 3

0

01

02

03

04

05Re

call


(d) 119898 = 2 1198891 = 001 and 1198892 = 01

Figure 5 The results of the CS-LMP descriptor with different parameter settings

experiments we firstly use the Hessian-Affine detector toobtain the interest regions Then the interest regions arenormalized to the circular regions and the gray values ofthe regions are transformed to lie between 0 and 1 Finallythe descriptor of each interest region is constructed and thenearest neighbor distance ratio (NNDR) matching algorithmis performed to obtain the matching points Here we selectthe Euclidean distance as similarity measure The parametersettings of the SIFT descriptor and WOS-LTP descriptor arethe same as the original proposed papers [5 14]

The Recall-Precision criterion is used to evaluate thematching results which is computed from the number ofthe correct matches and the number of the false matches

between a pair of images Two interest regions are matchedif the distance between their descriptors is below a threshold119905 and a match is correct if the overlap error is smaller than05 The Recall-Precision curve can be obtained by changingthe distance threshold 119905 So a perfect descriptor would give arecall equal to 1 for any precision

41 Parameter Evaluation There are four parameters in theproposed CS-LMP descriptor the number of neighboringpixels 119873 the radius of neighboring pixels 119877 the thresholds119879 = [minus119889

119898 minus119889

2 minus1198891 0 1198891 1198892 119889

119898] and the variable

119898 We conducted image matching experiments to investigatethe effects of different parameters on the performance of


02 04 06 0800

02

04

06

08

1Re

call

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision

(a) Bikes (blur changes)

0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision

(b) Trees (blur changes)

0

01

02

03

04

05

06

07

08

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision

(c) Wall (viewpoint changes)

0

01

02

03

04

05Re

call

04 06 08 102

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision

(d) Graffiti (viewpoint changes)

0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision

(e) Bark (scale + rotation changes)

0

01

02

03

04

05

06

07

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision

(f) Boat (scale + rotation changes)

Figure 6 Continued


0

01

02

03

04

05

06

07

08Re

call

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision

(g) Leuven (illumination changes)

0

02

04

06

08

1

Reca

ll

005 01 015 02 0250

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision

(h) Ubc (JPEG compression)

Figure 6 The matching results of the testing image pairs

the proposed descriptor The matching results are shownin Figure 5 and only one parameter was varied in oneexperiment For simplicity the parameters 119873 and 119877 wereevaluated in pairs such as (8 1) (8 2) (12 2) (16 2) and(12 3)

Figure 5(a) shows the results with different variable 119898From Figure 5(a) we can see that the performances of imagematching are similar when 119898 = 2 and 119898 = 3 andthey are better than the performance when 119898 = 1 Asthe dimension of the CS-LMP descriptor with 119898 = 3 ismuch larger than that with 119898 = 2 the variable 119898 is fixedto 2 in the following experiments to obtain higher com-putational efficiency Figures 5(b) and 5(c) show the resultswith different thresholds 119879 = [minus119889

2 minus1198891 0 1198891 1198892] We can

see that the CS-LMP descriptor performs similarly underdifferent thresholds and the best performance is achievedwhen 119879 = [minus01 minus001 0 001 01] Figure 5(d) shows theresults with different (119873 119877) From the results we can observethat our proposed descriptor is not sensitive to small changesTo achieve the balance between the computation amountand matching performance the optimal parameter settingof (119873 119877) is selected as (8 2) Based on the above analysiswe select the following parameter settings for the followingimage matching experiments 119873 = 8 119877 = 2 119879 =

[minus01 minus001 0 001 01] and119898 = 2

42 Matching Evaluation In this section we compare theperformance of the proposed CS-LMP descriptor withthe SIFT descriptor the LDTP descriptor the WOS-LTPdescriptor and the CLDTP descriptor using the Recall-Precision criterionThe image matching results of the testingimages are shown in Figure 6 Figures 6(a) and 6(b) showthe results for blur changes Figure 6(a) is the results forthe structured scene and Figure 6(b) for the textured sceneWe can see that the SIFT descriptor obtained the lowest

score The CL-LMP descriptor performs best than otherdescriptors for the structured scene and the performanceof the WOS-LTP and CS-LMP descriptor is similar for thetextured scene Figures 6(c) and 6(d) show the performanceof descriptors for viewpoint changes Figure 6(c) is the resultsfor the structured scene and Figure 6(d) for the texturedscene Figures 6(e) and 6(f) show the results to evaluate thedescriptors for combined image rotation and scale changesFigure 6(g) shows the results for illumination changes FromFigure 6(c) we can see that the SIFT descriptor obtains worseresults and the performances of the other four descriptorsare similar From Figures 6(d)ndash6(g) we can see that the CS-LMP descriptor obtains the best matching score and theCLDTP descriptor obtains the second good matching scoreFigure 6(h) shows the results to evaluate the influence ofJPEG compression From Figure 6(h) we can see that the fivekinds of descriptors perform better than other cases and theperformance of the CS-LMP descriptor is slightly better thanthe other four descriptors Based on the above analysis wecan conclude that the CS-LMP descriptor performs betterthan the well-known state-of-the-art SIFT descriptor theLDTP descriptor the WOS-LTP descriptor and the CLDTPdescriptor

5 Conclusions

This paper presents a novel CS-LMP descriptor and itsapplication in image matching The CS-LMP descriptor isconstructed based on the CS-LMP operator and the CS-LMP histogram which can describe the local image regionusing multiply quantization levels The constructed CS-LMPdescriptor not only contains the gradient orientation infor-mation but also contains the spatial structural informationof the local image region Furthermore the dimension of theCS-LMP descriptor is much lower than the binaryternary


pattern based descriptor when they use the same quanti-zation level Our experimental results show that the CS-LMP descriptor performs better than the SIFT descriptor theLDTP descriptor the WOS-LTP descriptor and the CLDTPdescriptor So the CS-LMP descriptor is effective for localimage description In the futureworkwewill further improveits performance and apply it in object recognition

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This paper is supported by the National Natural ScienceFoundation of China (Grants no 61375010 no 61175059and no 61472031) and Beijing Higher Education Young EliteTeacher Project (Grant no YETP0375)

References

[1] X Yang and K-T T Cheng ldquoLocal difference binary forultrafast and distinctive feature descriptionrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 36 no 1 pp188ndash194 2014

[2] K Liao G Liu and Y Hui ldquoAn improvement to the SIFTdescriptor for image representation and matchingrdquo PatternRecognition Letters vol 34 no 11 pp 1211ndash1220 2013

[3] C Zhu C-E Bichot and L Chen ldquoImage region descrip-tion using orthogonal combination of local binary patternsenhanced with color informationrdquo Pattern Recognition vol 46no 7 pp 1949ndash1963 2013

[4] K Mikolajczyk and C Schmid ldquoA performance evaluation oflocal descriptorsrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 27 no 10 pp 1615ndash1630 2005

[5] D G Lowe ldquoDistinctive image features from scale-invariantkeypointsrdquo International Journal of Computer Vision vol 60 no2 pp 91ndash110 2004

[6] Y Ke and R Sukthankar ldquoPCA-SIFT a more distinctiverepresentation for local image descriptorsrdquo in Proceedings of theConference on Computer Vision and Pattern Recognition (CVPRrsquo04) pp 506ndash513 2004

[7] H Bay T Tuytelaars and L Van ldquoSURF speeded up robustfeaturesrdquo in Computer VisionmdashECCV 2006 9th European Con-ference on Computer Vision Graz Austria May 7ndash13 2006Proceedings Part I vol 3951 of Lecture Notes in ComputerScience pp 404ndash417 Springer Berlin Germany 2006

[8] B Li R Xiao Z Li R Cai B-L Lu and L Zhang ldquoRank-SIFT learning to rank repeatable local interest pointsrdquo inProceedings of the IEEE Conference on Computer Vision andPattern Recognition (CVPR rsquo11) pp 1737ndash1744 Providence RIUSA June 2011

[9] S Lazebnik C Schmid and J Ponce ldquoA sparse texture represen-tation using local affine regionsrdquo IEEE Transactions on PatternAnalysis and Machine Intelligence vol 27 no 8 pp 1265ndash12782005

[10] T Ojala M Pietikainen and T Maenpaa ldquoMultiresolutiongray-scale and rotation invariant texture classificationwith localbinary patternsrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 24 no 7 pp 971ndash987 2002

[11] M Heikkila M Pietikainen and C Schmid ldquoDescription ofinterest regions with local binary patternsrdquo Pattern Recognitionvol 42 no 3 pp 425ndash436 2009

[12] R Gupta H Patil and A Mittal ldquoRobust order-based methodsfor feature descriptionrdquo inProceedings of the IEEEConference onComputer Vision and Pattern Recogntion (CVPR rsquo10) pp 334ndash341 San Francisco Calif USA June 2010

[13] H Zeng Z-CMu and X-QWang ldquoA robust method for localimage feature region descriptionrdquo Acta Automatica Sinica vol37 no 6 pp 658ndash664 2011

[14] M Huang Z Mu H Zeng and S Huang ldquoLocal image regiondescription using orthogonal symmetric local ternary patternrdquoPattern Recognition Letters vol 54 pp 56ndash62 2015

[15] A R Rivera J R Castillo and O Chae ldquoLocal directionaltexture pattern image descriptorrdquo Pattern Recognition Lettersvol 51 pp 94ndash100 2015

[16] H Zeng R Zhang M Huang and X Wang ldquoCompactlocal directional texture pattern for local image descriptionrdquoAdvances in Multimedia vol 2015 Article ID 360186 10 pages2015

[17] S Hussain and B Triggs ldquoVisual recognition using local quan-tized patternsrdquo inComputer VisionmdashECCV 2012 12th EuropeanConference on Computer Vision Florence Italy October 7ndash132012 Proceedings Part II vol 7573 of Lecture Notes in ComputerScience pp 716ndash729 Springer Berlin Germany 2012

[18] V Ojansivu and J Heikkila ldquoBlur insensitive texture classifica-tion using local phase quantizationrdquo in Proceedings of the 3rdInternational Conference on Image and Signal Processing (ICISPrsquo08) A Elmoataz O Lezoray F Nouboud and D MammassEds vol 5099 of Lecture Notes in Computer Science pp 236ndash243 Cherbourg-Octeville France July 2008

[19] KMikolajczyk and C Schmid ldquoScale amp affine invariant interestpoint detectorsrdquo International Journal of Computer Vision vol60 no 1 pp 63ndash86 2004

[20] K Mikolajczyk T Tuytelaars C Schmid et al ldquoA comparisonof affine region detectorsrdquo International Journal of ComputerVision vol 65 no 1-2 pp 43ndash72 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


advantages which are suitable for local image descriptor con-struction such as computational simplicity and invariance tolinear illumination But the LBP operator tends to producea rather long histogram especially when the number ofneighboring pixels increases So it is not suitable for imagematching The CS-LBP (Center Symmetric Local BinaryPattern) descriptor can address the dimension problemwhileretaining the powerful ability of texture description [11] Itcombines the advantages of the SIFT descriptor and LBPoperator and performs better than the SIFT descriptor inthe field of image matching To improve the descriptionability and the robustness to image transformation severalgeneralized descriptors have been proposed such as the CS-LTP (Center Symmetric Local Ternary Pattern) descriptor[12] the IWCS-LTP (Improved Weighted Center SymmetricLocal Ternary Pattern) descriptor [13] and the WOS-LTP(Weighted Orthogonal Symmetric Local Ternary Pattern)descriptor [14] Among the above descriptors the WOS-LTPdescriptor has better performance than the SIFT descriptorand IWCS-LTP descriptor It divides the neighboring pixelsinto several orthogonal groups to reduce the dimension ofthe histogram and an adaptive weight is used to adjust thecontribution of the code in histogram calculation For theWOS-LTP descriptor the quantization level of the intensityvalues is three The image intensity variant informationof the local neighborhood has not been fully investigatedFurthermore LDTP (Local Directional Texture Pattern) isanother kind of local texture pattern which includes bothdirectional and intensity information [15] Although theLDTP descriptor is consistent against noise and illuminationchanges its dimension is high To solve this problem CLDTP(Compact Local Directional Texture Pattern) is a proposeddescriptor [16] which not only reduces the dimension ofLDTP descriptor but also retains the advantages of LDTPdescriptor

Vector quantization is an effective method for texturedescription and it is robust to noise and illuminationvariation [17 18] The number of quantization levels isan important parameter The lower the quantization levelthe less the discriminative information the descriptor hasHowever if the quantization level is increased the descriptorrsquosrobustness to noise and illumination variety will degradeFor LBP or LTP operator based descriptor the differencesof the local intensity values are quantized in two or threelevelsThey have better robustness to illumination variety buttheir discriminative abilities are degraded If we increase thequantization level directly according to the encodingmode ofthe LBP or LTP operator the dimension of the descriptor willincrease dramatically LQP (Local Quantized Pattern) wasproposed to solve these problems It uses large local neighbor-hoods and deeper quantization with domain-adaptive vectorquantization But it uses visual word quantization to separatelocal patterns and uses a precompiled lookup table to cachethe final coding for speed Its main constraint is the sizeof the lookup table and it is not suitable to be used forimage matching So for the multiply quantization level baseddescriptor the effective encoding method is the key problemto balance the relationship between the discriminative abilityand the dimension of the descriptor

In this paper we present a novel encoding method forlocal image descriptor named as CS-LMP (Center SymmetricLocal Multilevel Pattern) operator which can encode thedifferences of the local intensity values using multiply quan-tization levels The CS-LMP descriptor is constructed basedon the CS-LMP operator and it can describe the local imageregion more detailedly without increasing the dimensionof the descriptor To make the descriptor containing morespatial structural information we use a SIFT-like grid todivide the interest region Compared with binaryternarypattern based descriptor it not only has better discriminativeability but also has higher computational efficiency Theperformance of the CS-LMP descriptor is evaluated forimage matching and the experimental results demonstrate itsrobustness and distinctiveness

The rest of the paper is organized as follows In Sec-tion 2 the CS-LBP CS-LTP and the WOS-LTP operatorand descriptor construction methods are reviewed Section 3gives the CS-LMP operator the CS-LMP histogram and theconstruction method of the CS-LMP descriptor The imagematching experiments are conducted and their experimentalresults are presented in Section 4 Some concluding remarksare listed in Section 5

2 Related Work

Before presenting in detail the CS-LMP operator and the CS-LMPdescriptor we give a brief review of theCS-LBP CS-LTPand WOS-LTP methods that form the basis for our work

21 CS-LBP and CS-LTP TheCS-LBP operator is a modifiedversion of the well-known LBP operator which comparescenter symmetric pairs of pixels in the neighborhood [11]Formally the CS-LBP operator can be represented as

CS-LBP119877119873 (119906 V) =

(1198732)minus1

sum119894=0

119904 (119899119894minus 119899119894+(1198732)

) 2119894

119904 (119909) =

1 119909 gt 119879

0 otherwise

(1)

where 119899119894and 119899

119894+(1198732)correspond to the gray values of center

symmetric pairs of pixels of119873 equally spaced pixels on a circlewith radius 119877 Obviously the CS-LBP operator can produce21198732 distinct values resulting in 21198732-dimensional histogramIt should be noticed that the CS-LBP descriptor is obtainedby the binary codes which is computed from the differencesof the intensity value between pairs of the opposite pixels ina neighborhood For the CS-LBP descriptor its dimension is21198732 and the quantization level of the intensity values is two

The CS-LTP operator is powerful texture operator [12]It uses the encoding method similar to the CS-LBP operatorand extends the quantization level of the intensity values from



CS-LTP119877119873 (119906 V) =

(1198732)minus1

sum119894=0

119904 (119899119894minus 119899119894+(1198732)

) 3119894

119904 (119909) =

2 119909 ge 119879

1 minus119879 lt 119909 lt 119879

0 119909 le minus119879

(2)




OS-LTP(119894)119877119873

(119906 V) = 119904 (119899119894minus1

minus 119899(119894minus1)+2[1198734]

) 30

+ 119904 (119899(119894minus1)+[1198734]

minus 119899(119894minus1)+3[1198734]

) 31

119904 (119909) =

2 119909 ge 119879

1 minus119879 lt 119909 lt 119879

0 119909 le minus119879

119894 = 1 2 119873

4

(3)



119867119894 (119896) =

119882

sum119906=1

119867

sumV=1119891119894(OS-LTP(119894)

119877119873(119906 V) 119896)

119891119894(119909 119910)

=



0 119909 = 119910

119894 = 1 2 [119873

4]

(4)





2

minus1198891 0 1198891 1198892 119889




119898]

1198922= (minus119889

119898 minus119889119898minus1

]

1198922119898

= (119889119898minus1

minus119889119898]

1198922119898+1

= (119889119898 +infin)

(5)


CS-LMP(119894)119877119873

(119906 V) = 119902 (119899119894minus 119899119894+(1198732)

)

119894 = 0 1 119873

2

119902 (119909) = 119905 119909 isin 119892119905 119905 = 1 2 2119898 + 1

(6)




nc n0

n1n2

n3

n4

n5

n6n7 CS-LMP(1)







80

8080

80

8080

80

80

80

Flat image area

00

0

01

1

1

11

1

1

13

3

3

3

[3333]

24

3031

28

3225

29

33

28


00

0

01

1

1

11

1

1

15

5

4

2

[4552]

[0000]2

[0000]2 [1111]3

[1111]3

[11]3[11]3

[11]3[11]3


2= 26)



119867119894 (119896) =

119882

sum119906=1

119867

sumV=1119891 (CS-LMP(119894)

119877119873(119906 V) 119896)

119894 = 0 1 119873

2

119891 (119909 119910) = 1 119909 = 119910

0 119909 = 119910

(7)



histograms together














m = 1m = 2m = 3

0

01

02

03

04

05Re

call


(a) 119873 = 8 119877 = 2 1198891 = 001 1198892 = 01 and 1198893 = 02

04 06 08 1020

01

02

03

04

05

Reca

ll

d1 = 001 d2 = 004

d1 = 001 d2 = 006

d1 = 001 d2 = 008

d1 = 001 d2 = 010

d1 = 001 d2 = 012

1 minus precision

(b) 119873 = 8 119877 = 2 and119898 = 2

0

01

02

03

04

05

Reca

ll


d1 = 001 d2 = 010

d1 = 0006 d2 = 010

d1 = 0014 d2 = 010d1 = 0008 d2 = 010

d1 = 0012 d2 = 010

(c) 119873 = 8 119877 = 2 and119898 = 2

N = 8 R = 1N = 8 R = 2N = 12 R = 2

N = 16 R = 2N = 12 R = 3N = 20 R = 3

0

01

02

03

04

05Re

call


(d) 119898 = 2 1198891 = 001 and 1198892 = 01






119898 minus119889

2 minus1198891 0 1198891 1198892 119889




02 04 06 0800

02

04

06

08

1Re

call

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

08

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05Re

call

04 06 08 102

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


Figure 6 Continued


0

01

02

03

04

05

06

07

08Re

call

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

02

04

06

08

1

Reca

ll

005 01 015 02 0250

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision





2 minus1198891 0 1198891 1198892] We can


[minus01 minus001 0 001 01] and119898 = 2



5 Conclusions




Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





CS-LTP119877119873 (119906 V) =

(1198732)minus1

sum119894=0

119904 (119899119894minus 119899119894+(1198732)

) 3119894

119904 (119909) =

2 119909 ge 119879

1 minus119879 lt 119909 lt 119879

0 119909 le minus119879

(2)




OS-LTP(119894)119877119873

(119906 V) = 119904 (119899119894minus1

minus 119899(119894minus1)+2[1198734]

) 30

+ 119904 (119899(119894minus1)+[1198734]

minus 119899(119894minus1)+3[1198734]

) 31

119904 (119909) =

2 119909 ge 119879

1 minus119879 lt 119909 lt 119879

0 119909 le minus119879

119894 = 1 2 119873

4

(3)



119867119894 (119896) =

119882

sum119906=1

119867

sumV=1119891119894(OS-LTP(119894)

119877119873(119906 V) 119896)

119891119894(119909 119910)

=



0 119909 = 119910

119894 = 1 2 [119873

4]

(4)





2

minus1198891 0 1198891 1198892 119889




119898]

1198922= (minus119889

119898 minus119889119898minus1

]

1198922119898

= (119889119898minus1

minus119889119898]

1198922119898+1

= (119889119898 +infin)

(5)


CS-LMP(119894)119877119873

(119906 V) = 119902 (119899119894minus 119899119894+(1198732)

)

119894 = 0 1 119873

2

119902 (119909) = 119905 119909 isin 119892119905 119905 = 1 2 2119898 + 1

(6)




nc n0

n1n2

n3

n4

n5

n6n7 CS-LMP(1)







80

8080

80

8080

80

80

80

Flat image area

00

0

01

1

1

11

1

1

13

3

3

3

[3333]

24

3031

28

3225

29

33

28


00

0

01

1

1

11

1

1

15

5

4

2

[4552]

[0000]2

[0000]2 [1111]3

[1111]3

[11]3[11]3

[11]3[11]3


2= 26)



119867119894 (119896) =

119882

sum119906=1

119867

sumV=1119891 (CS-LMP(119894)

119877119873(119906 V) 119896)

119894 = 0 1 119873

2

119891 (119909 119910) = 1 119909 = 119910

0 119909 = 119910

(7)



histograms together














m = 1m = 2m = 3

0

01

02

03

04

05Re

call


(a) 119873 = 8 119877 = 2 1198891 = 001 1198892 = 01 and 1198893 = 02

04 06 08 1020

01

02

03

04

05

Reca

ll

d1 = 001 d2 = 004

d1 = 001 d2 = 006

d1 = 001 d2 = 008

d1 = 001 d2 = 010

d1 = 001 d2 = 012

1 minus precision

(b) 119873 = 8 119877 = 2 and119898 = 2

0

01

02

03

04

05

Reca

ll


d1 = 001 d2 = 010

d1 = 0006 d2 = 010

d1 = 0014 d2 = 010d1 = 0008 d2 = 010

d1 = 0012 d2 = 010

(c) 119873 = 8 119877 = 2 and119898 = 2

N = 8 R = 1N = 8 R = 2N = 12 R = 2

N = 16 R = 2N = 12 R = 3N = 20 R = 3

0

01

02

03

04

05Re

call


(d) 119898 = 2 1198891 = 001 and 1198892 = 01






119898 minus119889

2 minus1198891 0 1198891 1198892 119889




02 04 06 0800

02

04

06

08

1Re

call

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

08

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05Re

call

04 06 08 102

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


Figure 6 Continued


0

01

02

03

04

05

06

07

08Re

call

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

02

04

06

08

1

Reca

ll

005 01 015 02 0250

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision





2 minus1198891 0 1198891 1198892] We can


[minus01 minus001 0 001 01] and119898 = 2



5 Conclusions




Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




nc n0

n1n2

n3

n4

n5

n6n7 CS-LMP(1)







80

8080

80

8080

80

80

80

Flat image area

00

0

01

1

1

11

1

1

13

3

3

3

[3333]

24

3031

28

3225

29

33

28


00

0

01

1

1

11

1

1

15

5

4

2

[4552]

[0000]2

[0000]2 [1111]3

[1111]3

[11]3[11]3

[11]3[11]3


2= 26)



119867119894 (119896) =

119882

sum119906=1

119867

sumV=1119891 (CS-LMP(119894)

119877119873(119906 V) 119896)

119894 = 0 1 119873

2

119891 (119909 119910) = 1 119909 = 119910

0 119909 = 119910

(7)



histograms together














m = 1m = 2m = 3

0

01

02

03

04

05Re

call


(a) 119873 = 8 119877 = 2 1198891 = 001 1198892 = 01 and 1198893 = 02

04 06 08 1020

01

02

03

04

05

Reca

ll

d1 = 001 d2 = 004

d1 = 001 d2 = 006

d1 = 001 d2 = 008

d1 = 001 d2 = 010

d1 = 001 d2 = 012

1 minus precision

(b) 119873 = 8 119877 = 2 and119898 = 2

0

01

02

03

04

05

Reca

ll


d1 = 001 d2 = 010

d1 = 0006 d2 = 010

d1 = 0014 d2 = 010d1 = 0008 d2 = 010

d1 = 0012 d2 = 010

(c) 119873 = 8 119877 = 2 and119898 = 2

N = 8 R = 1N = 8 R = 2N = 12 R = 2

N = 16 R = 2N = 12 R = 3N = 20 R = 3

0

01

02

03

04

05Re

call


(d) 119898 = 2 1198891 = 001 and 1198892 = 01






119898 minus119889

2 minus1198891 0 1198891 1198892 119889




02 04 06 0800

02

04

06

08

1Re

call

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

08

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05Re

call

04 06 08 102

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


Figure 6 Continued


0

01

02

03

04

05

06

07

08Re

call

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

02

04

06

08

1

Reca

ll

005 01 015 02 0250

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision





2 minus1198891 0 1198891 1198892] We can


[minus01 minus001 0 001 01] and119898 = 2



5 Conclusions




Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics















m = 1m = 2m = 3

0

01

02

03

04

05Re

call


(a) 119873 = 8 119877 = 2 1198891 = 001 1198892 = 01 and 1198893 = 02

04 06 08 1020

01

02

03

04

05

Reca

ll

d1 = 001 d2 = 004

d1 = 001 d2 = 006

d1 = 001 d2 = 008

d1 = 001 d2 = 010

d1 = 001 d2 = 012

1 minus precision

(b) 119873 = 8 119877 = 2 and119898 = 2

0

01

02

03

04

05

Reca

ll


d1 = 001 d2 = 010

d1 = 0006 d2 = 010

d1 = 0014 d2 = 010d1 = 0008 d2 = 010

d1 = 0012 d2 = 010

(c) 119873 = 8 119877 = 2 and119898 = 2

N = 8 R = 1N = 8 R = 2N = 12 R = 2

N = 16 R = 2N = 12 R = 3N = 20 R = 3

0

01

02

03

04

05Re

call


(d) 119898 = 2 1198891 = 001 and 1198892 = 01






119898 minus119889

2 minus1198891 0 1198891 1198892 119889




02 04 06 0800

02

04

06

08

1Re

call

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

08

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05Re

call

04 06 08 102

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


Figure 6 Continued


0

01

02

03

04

05

06

07

08Re

call

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

02

04

06

08

1

Reca

ll

005 01 015 02 0250

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision





2 minus1198891 0 1198891 1198892] We can


[minus01 minus001 0 001 01] and119898 = 2



5 Conclusions




Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




m = 1m = 2m = 3

0

01

02

03

04

05Re

call


(a) 119873 = 8 119877 = 2 1198891 = 001 1198892 = 01 and 1198893 = 02

04 06 08 1020

01

02

03

04

05

Reca

ll

d1 = 001 d2 = 004

d1 = 001 d2 = 006

d1 = 001 d2 = 008

d1 = 001 d2 = 010

d1 = 001 d2 = 012

1 minus precision

(b) 119873 = 8 119877 = 2 and119898 = 2

0

01

02

03

04

05

Reca

ll


d1 = 001 d2 = 010

d1 = 0006 d2 = 010

d1 = 0014 d2 = 010d1 = 0008 d2 = 010

d1 = 0012 d2 = 010

(c) 119873 = 8 119877 = 2 and119898 = 2

N = 8 R = 1N = 8 R = 2N = 12 R = 2

N = 16 R = 2N = 12 R = 3N = 20 R = 3

0

01

02

03

04

05Re

call


(d) 119898 = 2 1198891 = 001 and 1198892 = 01






119898 minus119889

2 minus1198891 0 1198891 1198892 119889




02 04 06 0800

02

04

06

08

1Re

call

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

08

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05Re

call

04 06 08 102

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


Figure 6 Continued


0

01

02

03

04

05

06

07

08Re

call

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

02

04

06

08

1

Reca

ll

005 01 015 02 0250

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision





2 minus1198891 0 1198891 1198892] We can


[minus01 minus001 0 001 01] and119898 = 2



5 Conclusions




Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




02 04 06 0800

02

04

06

08

1Re

call

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

08

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05Re

call

04 06 08 102

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

Reca

ll

02 04 06 08 10

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

01

02

03

04

05

06

07

Reca

ll

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


Figure 6 Continued


0

01

02

03

04

05

06

07

08Re

call

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

02

04

06

08

1

Reca

ll

005 01 015 02 0250

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision





2 minus1198891 0 1198891 1198892] We can


[minus01 minus001 0 001 01] and119898 = 2



5 Conclusions




Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

01

02

03

04

05

06

07

08Re

call

02 04 06 080

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision


0

02

04

06

08

1

Reca

ll

005 01 015 02 0250

SIFTLDTPWOS-LTP

CLDTPCS-LMP

1 minus precision





2 minus1198891 0 1198891 1198892] We can


[minus01 minus001 0 001 01] and119898 = 2



5 Conclusions




Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



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