Hand shape identification on multirange images

Information Sciences xxx (2014) xxx–xxx

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Information Sciences

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Hand shape identification on multirange images

http://dx.doi.org/10.1016/j.ins.2014.02.0310020-0255/� 2014 Elsevier Inc. All rights reserved.

⇑ Corresponding author. Tel.: +34 928452864.E-mail addresses: [email protected] (C.M. Travieso), [email protected] (J.R. Ticay-Rivas), [email protected] (J.C. Briceño), mpozo@

(M. del Pozo-Baños), [email protected] (J.B. Alonso).

Please cite this article in press as: C.M. Travieso et al., Hand shape identification on multirange images, Inform. Sci. (2014),dx.doi.org/10.1016/j.ins.2014.02.031

Carlos M. Travieso a,⇑, Jaime R. Ticay-Rivas a, Juan C. Briceño b, Marcos del Pozo-Baños a,Jesús B. Alonso a

a Signals and Communications Department, Institute for Technological Development and Innovation in Communications (IDETIC),University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spainb Computer Science Department, University of Costa Rica, San Jose, Costa Rica

a r t i c l e i n f o

Article history:Received 1 July 2012Received in revised form 3 February 2014Accepted 9 February 2014Available online xxxx

Keywords:Hand-based BiometricsMulti-range imagesDHMM kernelEdge detection

a b s t r a c t

A hand-shape based biometric identification system which is independent of the imagespectrum range is proposed here. Two different spectrum ranges; visible and mid-rangeinfrared, were used to validated the architecture, which maintained the accuracy and sta-bility levels between ranges. In particular, three public databases were tested, obtainingaccuracies over 99.9% using a 40% hold-out cross-validation approach. Discrete HiddenMarkov Models (DHMM) representing each target identification class was trained withangular chain descriptors. A kernel was then extracted from the trained DHMM andapplied as a feature extraction method. Finally, supervised Support Vector Machines wereused to classify the extracted features.

� 2014 Elsevier Inc. All rights reserved.

1. Introduction

The usage of different biometric systems on security applications has become increasingly common nowadays [6,8,44].Mainly because their advantages over other methods such as carrying magnetic cards or reminding passports or PIN num-bers, which can be forgotten or used by non-authorized persons. Identification systems based on human body measures arewell accepted and perceived naturally by both men and women. This is driving biometric methods to achieve outstandingresults in the security market.

An example of this is hand based identification systems, which have proven to be simple in architecture and capable ofachieving a high degree of discrimination [24]. In addition, the hand requires a medium–low precision data representationand its usage is highly accepted in social term. Most of the research published so far on hand biometry has focused on visiblerange images, geometry features and the application of statistical models, Artificial Neural Networks and linear classifiers[20,40,41]. Other, more complex techniques, such as fuzzy pattern recognition algorithms based on Lattice Similarity Degree,have also been used satisfactorily, reaching success rates above 96% [46].

One dimensional centroid distances have been used as hand geometric descriptors [43]. In this study, a centroid distanceseries was computed from each finger. A Gaussian mixture model (GMM) for each finger series was then built to carry outhand shape classification and verification. The testing database, collected by the authors, included fifty subject and fiveimages per subject. The proposed system achieved a success rate of 99.8%.

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2 C.M. Travieso et al. / Information Sciences xxx (2014) xxx–xxx

In [34], a scheme based on the Radon Transform; the line integral of an object on the image plane along all the lines from0� to 360�, was proposed. The maximum distance between the hand palm center of mass and its boundary points, whichcoincided with the distance to the middle finger, was used for optimization. Therefore, one dimensional position invariantfeatures were extracted from binarized hand silhouettes. The proposed scheme was tested on a data set of 136 images withan Euclidian norm match score, obtaining an Equal Error Rate (EER) of 5.1%.

Two methods based on the overall hand shape were compared on [45] for person identification and verification. On oneside, features from the hand contour were classified with a modified Hausdorff distance, achieving a success rate of 98.75%.On the other, features from the Independent Component Analysis of the hand shape were passed to an Euclidean distancebased classifier, achieving 99.48% of success rate. The database was composed of 1374 images extracted from 458 subjects(three images per subject).

A Support Vector Machine was applied over hand geometrical information for classification in [16]. An IIT-Delhi databasewith 100 users and 10 samples per user was used for testing. The system achieved a 98% of identification accuracy, a FalseAcceptance Rate (FAR) lower than 0.04% and a False Rejection Rate (FRR) under 2%. A similar result was reported in [14] usingprobabilistic Neural Network.

In [28], palm print and hand geometry information were combined to rise the system’s performance to 90% of accuracywith 50-users database.

Abductive learning and hand geometric features were used in [15]. In this case, the used database contained 200 images,collected from 20 subjects using a digital camera and peg-free mode. The applied system achieved 98% of overall accuracy,1.67% of FRR and 0.088% of FAR.

An infrared illumination device was used in [21]. 34 geometric features were extracted from the users’ hands and clas-sified by an SVM. The system achieved a 96.23% of Correct Identification Rate and 1.85% of FAR on a 100-users database (60images per subject).

Geometric features such as the length and width of fingers, the length and width of the palm, deviations and angles wereapplied in [12]. Pegs were not used for the acquisition of images. Euclidian distances were computed for classification. Thearchitecture was tested with a real time database as well as with a standard database. An FAR of 0.48% and an FRR of 1% werefinally achieved. In turn, experiments with geometric features obtained an EER of 93% with 30 users [10].

Texture descriptors were included alongside geometric features in [9]. A 100-users database was used for testing (8images per user). A similarity measure classification was applied to each source of information independently, and the re-sponses were then fused (decision level fusion). The Genuine Acceptance Rate reached was 99.5%. When noise was added tothe system, in the form of a 10� rotation of the hands, the performance dropped to 98.5%. In both experiments the EER was1.11%.

A method based on HMM was proposed in [13]. The problem was divided in 5 sub-problems; the five fingers. In otherwords, each finger was verified independently and a final result was computed from the fusion of each independent sub-sys-tem. Each point of the contour was characterized by two parameters: the radius-contour point and the curvature at the con-tour point. Continuous and discrete HMM classification was used. A data set of 300 images from 26 subjects was collected(between 9 and 15 images per user). The success rate achieved was 90%.

Other modalities for hand biometry include palm-print, veins and knuckle [27,33]. These are sometimes combined withhand-shape features. Palm texture and hand shape were fused at feature-level on [27]. This combination was evaluated ondifferent classification schemes of naive Bayes (normal, estimated, multinomial), decision trees (LMT), NN, SVM and FFN. Thefeature selection strategy was able to find the best features, which gave 96% (89%) of accuracy using the SVM classifier. Theimage database was collected from 100 subjects, with 10 images per subject, obtained with a digital camera using uncon-strained peg-free setup in an indoor environment.

The usage of new sensors has also been explored. There are a number of studies in multirange images but only a few ofthem focused on hand identification. These works used the veins distribution as a source of information and its combinationwith geometrical parameters. It is important to note that the using of the hand contour extracted from mid-infrared imagesis a novel approach that has not been covered so far, to the best of the authors’ knowledge.

A scheme based on vascular and geometrical information extracted from the dorsum of the hand captured in the infraredrange was proposed in [18]. A matcher based on Hamming distance was used as a classifier. An averaged EER of 1.43% wasachieved on a database with 150 users.

Dorsal hand vein near-infrared images were also used in [29]. In this case, a new segmentation based on local threshold-ing using grayscale morphology was presented. In contrast, thermal images were used in [25] to extract vein patterns. Thebranch points and box approach for representing the vein patterns were used. A success rate of 99.6% was obtained with a100-users database and 3 samples per subject.

Two approaches of contact-free biometric identification systems based on geometric hand features were presented in[31]. Two preliminary databases with 500 images were used. The results reported an EER of 6.3% and 4.2% respectively.

Finally, shape-hand features have also been used for gesture identification. Two problems were covered in [7]. One con-cerned the identification of users through the shape of their hand. Invariant geometrical features and similarity measureswere applied in this case. The second problem included the recognition of gestures and signs made by hands. The proposedapproach used gesture blob from texture and moment invariant features. When tested over a 300 samples database, the sys-tem correctly detected 282 hand gestures (94%).

Please cite this article in press as: C.M. Travieso et al., Hand shape identification on multirange images, Inform. Sci. (2014), http://dx.doi.org/10.1016/j.ins.2014.02.031



C.M. Travieso et al. / Information Sciences xxx (2014) xxx–xxx 3

The usage of HMM and the Fisher kernel can be found on the literature mainly as scores extractors. A scheme applying amulti-classifier on each Fisher score space which are extracted from the HMM was presented in [3]. In [22], the approachproposed is based on HMM modeling and has two main steps. First, one HMM was fit to each of the N individual sequences.For each fitted model, log-likelihood of each sequence is evaluated. This resulted in an N � N log-likelihood similarity matrixthat was adapted to work as the kernel of an SVM classifier. A hybrid HMM-based speech recognition system was proposedin [2]. The speech recognition was achieved by translating the outputs of the kernel-based classifier into class-conditionalprobabilities and using them instead of Gaussian mixtures as production probabilities of a HMM-based decoder.

On contrast, the approach proposed in the present work uses a new kernel based on the Fisher kernel to transform theinformation given by the HMM states. In this case, the system has been designed to work only with edge features. In par-ticular, a system based on hand-shape features has been implemented (see Fig. 1). The hand identification approach has beendeveloped based on a DHMM kernel [4] and classified with a Support Vector Machine (SVM) [5]. The behavior shown by SVMwith little training data was of special interest on the proposed scenario, where data is generated by the DHMM Kernel.

Therefore, the main contributions and innovations of this work are: (1) the usage of edge coding for hand-shape featuresextracted from multirange images and (2) its DHMMK transformation (see Fig. 1). This presented architecture has shown arobust behavior regardless of the image range. Moreover, the method has been tested with three public databases achievingencouraging results.

The remaining of this paper is organized as follows. Section 2 presents the proposed approach based on HMM transfor-mation and SVM classification. Section 3 introduces the databases used and the experimental procedure. Results and discus-sions are given in Section 4, and the concluding remarks are presented in Section 5.

2. Proposal method

In this section, the proposed method is described in detail. First, the shape coding used to represent the hand’s contour isexplained. Then, the Hidden Markov Model theory is introduced briefly in order to extend the model as a kernel which pro-duces a hyperdimensional transformation. Finally, the classification system is described.

2.1. Shape coding

As stated before, only information extracted from the shape of the hands has been used in this study. To extract thisshape, images were binarized by the Otsu’s method [35] and the hands contour was found by edge detection. This contourwas then characterized by a string of coordinates (x,y) representing the position of some of its pixels. This was achieved byapplying a process of shadowing (black shape over white background), filtering isolated points and automatically detecting

Fig. 1. Approach of the proposal.





perimeter point locations (x = line, y = row) by a point to point continuous flow procedure. The result was a perimeterdescription of {(xi,yi) |i = 1, . . .,n} location points representing a single pixel stroke of a closed contour of a hand shape.

Data compression, size regularization and critical control point selection of perimeters description was achieved by astructuring procedure. This procedure was based on the idea that a single pixel stroke on a black and white image maybe described as a graph Gf of a one dimensional trajectory application f if we have preservation of a correct sequencing def-inition or monotonic behavior on the x ordinate. That is Gf = {(xi,yi) |yi = f(xi), i = 1, . . .,n}, where ordinate points xi of the fstroke must be such that: xi < xi+1 or xi+1 < xi for i = 1, . . .,n � 1.

Afterwards, considering the complete perimeter G, the description relation F can be defined as the partial definition ofpiece like 1-D trajectory applications fj (with graphs Gj) preserving a monotonic behavior. That is G ¼ [j2JGj, where Gj is aset of positional points; i.e. a piece of border Gj = {(xa, ya) |ya = fj(xa), a 2 Jj} for a convenient set of indices J and Jj. The restrict-ing trajectory applications (or coded pieces of border) fj ¼ F jfxa ja2Jjg are such that the next point following the last of Gj is thefirst of Gj+1.

Accordingly, Gj graphs are correct descriptions of fj trajectory applications. To avoid Gj reducing to a single pixel, only thefirst point of constant x ordinate series was preserved. Note that the structure of G bordered by partial graph descriptions Gj

accounts for abrupt direction changes on the perimeter description. After building up the Gj, all the n first points of each Gj,j = 1, . . .,n were selected. For an arbitrary constant number p P n, the perimeter points description was completed byk = n � p points uniformly distributed for each Gj and proportionally to its size.

In order to perform a rotational, scale size and origin reference free coding, an angle transformation for the positionalpoint border coded was applied as before. For a given coded border of n positional control points G = {Xi = (xi,yi)|i = 1, . . .,n}, let C0 be its central point, and let bi and ai be the angles referred by C0 and Xi, bi = angle(C0,Xi,Xi+1) andai = angle(Xi,C0,Xi+1). Then the sequence of (xi,yi) i = 1, . . .,n positional points are transformed in a sequence of (ai,bi)i = 1, . . .,n � 1 angular origin free representation points. Note that the choice of the start point X1 and the C0 point accountfor scale and hand shape rotation, and geometrical properties of triangular similarities make such sequence of hand shapecoding size and location free (see Fig. 2).

2.2. Hidden Markov Model (HMM)

An HMM can be defined as a system that can be found in one and only one state (of the N possible) at each instant t, andprovides an output value. Furthermore, an HMM has two associated stochastic processes: one hidden process associatedwith the probability of transition between states (non-directly observable), and one observable process associated withthe probability of obtaining each of the possible values at the output depending on the actual state. In particular, a DiscreteHMM (DHMM) defined by [37] was used. This DHMM can be characterized by:

� The number of states N and the number of different observations M.� The transition probability matrix A from one state to another.� The probability vector of the starting state p.� The probability matrix B of each of the possible states at each of the observations.

The model used is called ‘‘Left to Right’’ or ‘‘Bakis’’ HMM, which is particularly appropriate for the evaluation of sequencesand, in turn, for the evaluation of hand contours. This is due the fact that the transitions between states are made in a singledirection and therefore these transitions can be seen as movements on the contours. This, in fact, provides the ability to keepa certain order with respect to the observations produced on the temporary distance among the more representativechanges.

In the DHMM approach, the conventional technique for quantifying features is applied. For each input data, the quantifiertoke the decision about which was the most convenient value from the information of the previous input vector. To avoidtaking a software decision, a fixed decision on the value quantified was made. Multi-labeling was used in order to expand

Fig. 2. An example of a fragment of an image border, decomposed in Gj graphs.





the possible values that the quantifier was going to acquire, so that the possible quantified values were controlled varyingthis parameter. Note that the number of labels in a DHMM is related to the number of symbols per state.

DHMM algorithms should be generalized to be adjusted to the multi-labeling output ({vk} k = 1, . . .,C), where C is the sizeof the vector values codebook, in order to generate the output vector ({w(xt,vk)} k = 1, . . .,C). Therefore, for a given state j ofthe DHMM, the probability that a vector xt is observed in the instant t can be written as:

Pleasedx.doi

bjðxtÞ ¼XC

k¼1

wðxt;vkÞbjðkÞ ð1Þ

where bj(k) is the output discrete probability associated with the value vk and the state j.This approach models a DHMM from contour features. This system has proven to be inappropriate for a discriminative

identification system. Therefore, an improvement is proposed by the transformation of the HMM kernel.

2.3. HMM transformation

The Fisher evaluator transforms the Discrete Hidden Markov Model (DHMM) states to a hyperdimensional space [37].Only the gradients of the transmitted DHMM’s probabilities are considered, as described in the equation: UX ¼ r log PðX kj Þ:

1. The probability of transmitting a residual x (from the observed chain X = (x1, . . .,xn)) from the alphabet, while it is in thestate s 2 {s1, . . ., sn}, is defined by Pðx s; hj Þ ¼ hx sj :

a. Note that:

hx sj ¼ Pðx s; kj Þ ¼ bsðxÞ ð2Þ

b. With the property:

8sX

x

hx sj ¼X

x

Pðx s; kj Þ ¼X

x

bsðxÞ ¼ 1 ð3Þ

By the implementation of the DHMM
i. Where bs ¼ Pðx ¼ vk sj Þ1 6 k 6 L is defined with vk the labels of the DHMM quantization.
2. The probability of transition from the state s to the state s0 is defined as: Pðs0 s; sj Þ ¼ ss0 sj :

a. Note that:

ss0 sj ¼ Pðs0 sj Þ ¼ as0s: ð4Þ

To simplify, a unique initial state s0 is assumed, i.e. ps0 ¼ 1. Note that, in terms of the derivative oX; where x is char-
acterized by hx sj ¼ bsðxÞ (depending on the descriptors x), psi
are constants (�).
3. The defined k DHMM assigns a probability for each sequence X = (x1, x2, . . ., xT) given by:
PðX h; sj Þ ¼ PðX kj Þ ¼X

s1 ;...;sm

Yi

Pðxi si; kj ÞPðsi si�1; sj Þ ¼X

s1 ;...;sm

Yi

hxi sij ssi si�1j : ð5Þ

4. And according to (1.a) and (2.a):

PðX h; sj Þ ¼ PðX kj Þ ¼X

s1 ;...sn

Yi

bsiðxiÞasi ;si�1

¼X

s1 ;...;sn

bs1 ðx1Þas1s2 bs2 ðx2Þ . . . asn�1sn bsn ðxnÞ: ð6Þ

where the sum is applied over all possible states’ sequences.

The interest falls in the derivatives of log PðX h; sj Þ ¼ log PðX kj Þ with respect to the emission probabilities hx sj ¼ bsðxÞ ascommented in (�), as they are the components of the evaluator vector UX.

By (1.b.), the vectors hx sj are linked by the fact that the sum must be 1 for any fixed state s. In order to be able to imple-ment independent derivations, an independent description must be implemented. To achieve this, the terms hx sj must bewritten in terms of a set of independent parameters:

5. hx sj ¼ hx;sPx0

hx0 ;s, with the values hx,s such that: !
X
x0hx0 ;s ¼ 1 ) hx;s ¼ hx sj :ð�Þ ð7Þ

Therefore, the HMM kernel (HMMK) can be defined as:

ddPðx; qÞ logPðx=q; kÞ ¼ nðx; qÞ

bqðxÞ � nðqÞ ð8Þ

cite this article in press as: C.M. Travieso et al., Hand shape identification on multirange images, Inform. Sci. (2014), http://.org/10.1016/j.ins.2014.02.031




where n(x,q) represents the number of times the model is located in a state q during the generation of a sequence emitting acertain symbol x, and n(q) represents the number of times the model has been in q during the process of sequence generation[37]. These values were directly obtained from the forward backward algorithm applied to the DHMM by [37]. The applica-tion of this score UX to the SVM is given by the following expression, using the technique of the natural gradient:

Pleasedx.doi

UX ¼ rPðx; qÞlogPðx=q; kÞ ð9Þ

where UX defines the direction of maximum slope of the logarithm of the probability of having a certain symbol in a givenstate.

Therefore, the proposed HMM Kernel (HMMK) is defined as the calculation of the natural distance between the scores oftwo sequences X and Y:

D2ðX;YÞ ¼ 12ðUX � UY ÞT F�1ðUX � UY Þ ð10Þ

where F is the HMM information matrix. Note that Eq. (10) is equivalent to the covariance matrix of vectors UX and UY.

2.4. Support Vector Machine

The basic idea of SVM is to train the system to obtain two sets of vectors (two dimensions corresponding with points) thatrepresent the classes to identify. Subsequently, the separating hyperplane H (a lineal classifier in two dimensions) betweenthese two sets is calculated. The pertinent points within the hyperplane have to satisfy the following equation given by [5]:

x � xþ w ¼ 0 ð11Þ

where x is normal to the hyperplane, w/||x|| is the perpendicular distance from the hyperplane to the origin, ||x|| is theEuclidean norm of x, x is the independent term, and x is a point in the hyperplane.

Furthermore, other two hyperplanes defined as H1: xi �x + w = 1 and H2: xi �x + w = �1 contain the so called Support Vec-tors (SVs). The distance between planes H1 and H2 is known as the margin of the model. In short, the aim of the SVM trainingalgorithm is to find a hyperplane H that maximizes the aforementioned margin while minimizing the classification error.

Once the system is trained and the separation hyperplane has been obtained, this can be shifted based on further valida-tion probes in order to further adjust the classification results. In accordance with the final decision, the corresponding classlabel of the test vector x is assigned as a decision of two states. This means that only two labels (‘‘+1’’ and ‘‘�1’’) are possibleas this is a bi-class algorithm. In order to obtain a multiclass classifier, the proposed method implements a one-versus-allstrategy to allocate one model for each class.

SVM calculates the separation between classes by means of the calculation of the natural distance between the scores oftwo sequences X and Y:

D2ðX;YÞ ¼ 12ðUX � UY ÞT F�1ðUX � UY Þ ð12Þ

where F is the HMM information matrix, and is equivalent to the matrix of covariance of the vectors UX and UY.Finally, different types of functions, which can be used on SVM, are lineal and Gaussian (RBF) kernels. These are used for

establishing the decision limit. The RBF kernel is shown in the following equation:

kðX;YÞ ¼ e�D2ðx;yÞ ð13Þ

3. Experimental settings

This section introduces the databases used and the experimental methodology, which is based on three experiments. It isimportant to note that only results from the combination of DHMMK and SVM have been included, as the DHMM approachonly reaches accuracy rates up to 80%.

3.1. Databases

Three databases have been used in this work: the public GPDS database, the UST Hand Image database and the mid-rangeinfrared GPDS database.

The public GPDS database contains 10 images from each of the 144 users [23]. For each subject, images were acquired inthree different sessions. An HP scanner was used to acquire the images, which minimized the environment effects. A detaileddescription of this database can be found in Table 1.

The UST Hand Image public database was created by the Hong Kong University of Science and Technology [26]. It contains10 images of the right hand and 10 images of the left hand from 287 people. These hands have been acquired in a contactlessscenario with an Olympus C-3020 digital camera (1280 � 960 pixels), employing neither special illumination nor pegs.Table 1 shows the most important characteristics of this database.

cite this article in press as: C.M. Travieso et al., Hand shape identification on multirange images, Inform. Sci. (2014), http://.org/10.1016/j.ins.2014.02.031



Table 1Characteristics of the visible spectrum databases.

Parameters Details from GPDS database Details from UST database

Number of classes 144 287Number of samples per classes 10 right hand samples 10 left and 10 right hand samplesAcquisition and quantification Gray scale (8 bits, 256 levels) Gray scale (8 bits, 256 levels)Resolution 150 dpi 500 dpiSize 1403 � 1021 pixels 1280 � 960 pixelsExample

Table 2Characteristics of mid-infrared GPDS database.

Parameters Details from mid-infrared GPDS database

Number of classes 100Number of samples per classes 10 right hand samplesAcquisition and quantification Gray scale (8 bits, 256 levels)Resolution 150 dpiSize 320 � 256 pixelsExample


Finally, the third database was acquired on the mid-range infrared spectrum [23]. This database consists of 10 acquisi-tions from each of the 100 subjects between 23 and 40 years old mostly. Images of the right hand were taken in the rangeof 1470 nm (mid-range infrared) with a resolution of 320 � 256 pixels by a camera sensor XENICS XEVA 1.7-320 InGaAs sen-sitive in the range of 900–1700 nm with a band pass filter centered on 1470 and a bandwidth of 250 nm. An incandescentbulb with a radiation pattern from 400 nm to 2500 nm was used for lightning. Table 2 shows the details of this database.

3.2. Experiments for the visible range

This section includes two experiments. Both experiments implemented a hold-out cross-validation procedure, using be-tween 50% and 10% of the database for testing. Results are shown as mean and standard deviation based on identification,using a supervised classification procedure.

The GPDS database was used on the first experiment in order to tune up the variables of the proposed approach. In par-ticular, the tuned parameters were the number of HMM states (between 20 and 140 states), the kernel used on the SVM (lin-ear and Gaussian kernels) and its corresponding parameters.

In the second experiment, the resulting optimal configuration was used to train and test the system with the public USTdatabase in order to check the scalability and stability of the method. In this case, the robustness of the system when thenumber of training samples fell was tested.

Note that this procedure based on two experiments using two different databases to optimize, train and evaluate the sys-tem shows the robustness of the proposal. Moreover, two different experimental branches have been executed. One based onhand contour classified with the DHMM (such results have not be shown because they were lower than 80%), and anotherwhere the contours have been parameterized with the DHMMK and classified with the SVM.

3.3. Experiments for the mid-infrared range

Finally, the third experiment was developed with the mid-infrared GPDS Database (see Table 2), aiming to prove thevalidity of the proposed system and to show the independency of the approach against the image range used. To allow adirect comparison between the results obtained by the two former experiments, the same cross-validation procedure wasapplied.

4. Results and discussion

This section presents and discusses the results obtained for each experiment introduced in the previous section, usingvisible and mid-infrared ranges.




Table 3Success rates for DKMM transformation and SVM with 144 users.

Number of points Number of states Linear SVM RBF SVM Gamma

100 50 99.86% ± 0.14 99.86% ± 0.14 4 � 10�6

100 60 99.95% ± 0.11 100% ± 0 4 � 10�6

100 70 99.91% ± 0.08 99.91% ± 0.08 4 � 10�6

200 50 99.77% ± 0.08 99.77% ± 0.08 4 � 10�6

200 60 99.95% ± 0.08 99.95% ± 0.08 4 � 10�6

200 70 99.77% ± 0.08 99.77% ± 0.08 4 � 10�6

300 50 99.81% ± 0.08 99.81% ± 0.08 6 � 10�7

300 60 99.86% ± 0.01 99.86% ± 0.01 6 � 10�7

300 70 99.91% ± 0.08 99.91% ± 0.08 6 � 10�7

Table 4Success rates for SVM with 144 GPDS users for 60 DHMM states and 100 edges coding points, decreasing the training samples.

Number of points Number of samples training Linear SVM RBF SVM Gamma

100 5 100% ± 0 100% ± 0 4 � 10�6

100 4 99.92% ± 0.07 99.92% ± 0.07 4 � 10�6

100 3 99.87% ± 0.12 99.87% ± 0.12 4 � 10�6

100 2 99.71% ± 0.10 99.71% ± 0.10 4 � 10�6

100 1 99.42% ± 0.21 99.42% ± 0.21 4 � 10�6

Table 5Success rates for SVM with 287 UST users for 60 DHMM states and 100 edges coding points, decreasing the trainingsamples.


100 4 (left hand) 100% ± 0 100% ± 0 4 � 10�6

100 4 (right hand) 100% ± 0 100% ± 0 4 � 10�6

100 3 (left hand) 99.92% ± 0.17 99.92% ± 0.17 4 � 10�6

100 3 (right hand) 100% ± 0 100% ± 0 4 � 10�6

100 2 (left hand) 99.57% ± 0.44 99.67% ± 0.14 4 � 10�6

100 2 (right hand) 99.72% ± 0.07 99.72% ± 0.07 4 � 10�6

100 1 (left hand) 99.30% ± 0.12 99.34% ± 0.13 6 � 10�6

100 1 (right hand) 99.47% ± 0.07 99.59% ± 0.17 4 � 10�6


4.1. Visible range results

For the first experiment within the visible range, the GPDS database was used. A grid of values for the number of controlpoints, the number of DHMM states, the use of linear or RBF kernels for SVM and the gamma parameter of the latter weretested. The number of control points has been shifted between 25 and 350, and the number of DHMM states between 20 and140. Only the best results are shown in Table 3 (mean ± standard deviation). Note that these results have been obtained for a40% hold-out cross-validation procedure.

Table 4 shows the success rates for different number of training samples, between 5 and 1. These results were obtainedwith the best model obtained previously; 100 edges coding points and transformed by 60 HMM states.

For the second experiment the same criterion was applied over the UST database. The results can be observed in Table 5.Comparing Tables 4 and 5, it can be seen that the system keeps a good behavior with a configuration of 100 control points,

60 DHMM states and SVM with RBF kernel, when the number of users is increased by 130% for the second experiment. Thishighlights the robustness of the proposal in the visible range, when the number of users increases.

Finally, the system has also been applied on an authentication problem using both databases and following a similarexperimental protocol as in [26], obtaining the receiver operating characteristics (ROC) curves shown in Fig. 3.

The resolution of the extracted hand contour has a major impact on the system’s performance of many models. This im-pact is also affected by the nature of the database and the number of users. In this case, the proposed approach based onDHMMK has shown a high robustness to resolution changes, with the performance barely decaying from 99.71% to99.72%. This performance trend can be easily appreciated from ROC curves of Fig. 3.

4.2. Infrared range results

As explained in Section 3.3, the same system was applied to mid-infrared hand images of the mid-infrared GPDS database.Table 6 shows the results of these experiments.




10-4 10-3 10-2 10-1 100 101 1020

10

20

30

40

50

60

70

80

90

100

Gen

uine

Acc

epta

nce

Rat

e (%

)

False Accept Rate (%)

HMMK ROC for GPDS-ULPGC DatabaseHMMK ROC for UST Database

Fig. 3. Roc curve for GPDS and UST databases under our best model based on DHMMK using 2 training samples (better viewed in color). (For interpretationof the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 6Success rates for SVM using the mid-infrared images for 60 DHMM states and 100 edges coding points, decreasing thetraining samples.


100 5 100% ± 0 100% ± 0 4 � 10�6

100 4 100% ± 0 100% ± 0 4 � 10�6

100 3 100% ± 0 100% ± 0 4 � 10�6

100 2 100% ± 0 100% ± 0 4 � 10�6

100 1 99.76% ± 0.15 99.76% ± 0.15 4 � 10�6


Good results were achieved using the same configuration obtained on the visible range. In fact, because the database issmaller than the former two, the results are even better. Nevertheless, this demonstrates that the proposed method isindependent of the spectrum range and maintains high performance levels for different sensors and image resolution andquality.

One more experiment was executed in verification mode, reaching up to 0% of EER using a 20% hold-out cross-validationtechnique.

4.3. Discussion

Based on previous experiments, some authors have considered raw hand edge information as a bad classifying feature.Nowadays, many scientific references use other features such as hand geometry (width of fingers, distances, etc.), palmprint,texture of fingers, knuckle, and veins. However, only a few studies focused on hand-shape have been published. This ismainly because good results have proven very difficult to achieve. Thus, this work proposes the contour transformationby means of the DHMM kernel as a solution.

Each state on DHMM represents a variation of the contour, and the best discriminative system found had 60 states from100 points of contour description. On average, a set of 1, 2 or 3 points represent a state. As this has low success, the DHMMkernel has been applied instead as an enlarged representation, using the relation between bq(x), n(x,q) and n(q), according toEq. (8) of the HMM kernel.

Therefore, now the number of times that the model is localized in a state q is being represented, i.e. the data vector foreach state according to the probability of emission for the same data vector on each state. This is an enlarged representation.These new features have a large dataset and hence they are classified by an SVM, which has proven to have a good behaviorin such circumstances [5,42].

Success rates shown in Tables 3–5 prove that the DHMM kernel is indeed a very good and robust parameterization sys-tem. It has also been shown that working with 100 edge points and using 60 DHMM states drives the SVM to achieve the bestsuccess rates from the DHMM kernel. RBF and linear kernels can be used indistinctively within SVM, as the success rateshave barely shifted. Thus, the linear kernel might be a good option given that it is a slightly faster.

After fine tuning the architecture, the system obtained similar results with a larger data set (144 users; about 2.4 timesbigger) and a different representation range. Therefore, the validation of this method and the independency of the range have




Table 7Comparison with the state-of-the-art, for references which use hand-shape features with different datasets on recognition approach.

Reference Method Database Size (users) Success (%)

This proposal DHMMK + SVM 287 (UST database) 100This proposal DHMMK + SVM 144 (GPDS-ULPGC Database) 100[45] Modified Hausdorff distance 458 99.48[46] Lattice Similarity Degree 100 96.5[27] Hand-shape features + Naïve Bayes 100 96[13] Geometric features + HMM 26 90

Table 8Comparison with the state-of-the-art, for references which use hand-shape features with different datasets on identification approach.

Dataset Reference Method Accuracy(%)

UST database Thisproposal

DHMMK + SVM (2 samples for training) EER = 0.31

[38] Fusion of 20 finger widths (four from each finger), five finger lengths, five finger perimeters and fiveintra-palm distances and palmprint using LDA

EER = 0.43

[11] Width of fingers classified by Euclidean distance EER = 1.40[47] Ordinal feature codes based on Gabor on Hamming distance EER = 0.22[39] AdaBoost learning reducing with Local Discriminant Analysis EER = 0.35

GPDS-ULPGCdatabase

Thisproposal

DHMMK + SVM (2 samples for training) EER = 0.017

[38] Fusion of 20 finger widths (four from each finger), five finger lengths, five finger perimeters and fiveintra-palm distances and palmprint using LDA

EER = 0.047

[30] Textural information for Palmprint employing the Contourlet Transform EER = 0.70[36] Hand geometry by general regression neural network 93.33[1] Twenty-four features of four fingers for Euclidean Distance EER = 0.17[19] 80 widths for 4 fingers each finger using SVM-RBF 99.90

Mid-infrared GPDSdatabase

Thisproposal

DHMMK + SVM (3 samples for training) EER = 0

[32] 100 widths of each finger EER = 0.26[17] Finger widths, finger lengths and hand contour using LS-SVM EER = 0.13


been demonstrated. For 100 points of contour descriptors, 60 states of DHMM representation and gamma value of 4 � 10�6,similar success rates have been achieved, between 99.71% and 100% with linear as well as with RBF functions, using only 2training samples. Moreover, the decrease in the number of training samples from five to one had no effect on the system’sperformance. Therefore, the proposal shows encouraging scalability, stability and performance levels.

It is also interesting to note that the proposed approach is fast on testing. Using a high level programming language on acomputer with an Intel�Corel™ i5-460M Processor (3M Cache, 2.53GHz), and 4 GB RAM, the testing time is 327.51 ms persample. On the other hand, the training time is substantially longer, being slightly over 20 min. These time measurementswere reached training with 2 samples and using the remaining of the database to test (all used databases has 10 samples peruser).

Finally, a comparison between references of the state-of-the-art and the proposed approach is shown in Tables 7 and 8.While Table 7 offers a comparison between systems tested with different databases, Table 8 shows a comparative betweenmethods tested with the same databases as those used in this work.

It can be observed in Table 8 that the introduced approach performs better than the state-of-the-art on GPDS-ULPGC andmid-infrared GPDS databases. For the UST Database, this work’s architecture presents the second best accuracy. However, itis important to bear in mind that the experimental procedure used here used only 2 samples for training. Unfortunately, thisinformation (the number of training samples) is not included in [47].

Therefore, it can be concluded that the presented approach is a good and robust option for this biometric modality.

5. Conclusion

An original and robust approach has been built for automatic hand-shape recognition in different ranges, using thetransformation of hand edge using HMM kernel, and being classified with an SVM. The obtained success rates are over99.80% for all tested databases, them being 99.87% with GPDS 144-users database and using only 3 training samples,99.92% for UST database and 100% for mid-infrared GPDS database. The fact that these results were obtained with threedifferent databases, public and private, demonstrates the robustness of the proposed approach. In future works, hand





intra-modalities information will be used and data and score fusions will be applied to further increase the system’s perfor-mance. In addition, other public databases will be used to test the system.

Acknowledgments

This work is partially supported by funds from ‘‘Cátedra Telefónica 2009/10 – ULPGC’’ and by the Spanish Government,under Grant MCINN TEC2012-38630-C04-02.

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Hand shape identification on multirange images

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