Optimal Features Subset Selection and Classification for ... · PDF fileWe present a new iris...

Hindawi Publishing CorporationEURASIP Journal on Image and Video ProcessingVolume 2008 Article ID 743103 20 pagesdoi1011552008743103

Research ArticleOptimal Features Subset Selection and Classification forIris Recognition

Kaushik Roy and Prabir Bhattacharya

Concordia Institute for Information Systems Engineering Concordia University Montreal Quebec Canada H3G 1M8

Correspondence should be addressed to Kaushik Roy kaush roencsconcordiaca

Received 1 August 2007 Revised 19 November 2007 Accepted 11 March 2008

Recommended by Kenneth M Lam

The selection of the optimal features subset and the classification have become an important issue in the field of iris recognition Wepropose a feature selection scheme based on the multiobjectives genetic algorithm (MOGA) to improve the recognition accuracyand asymmetrical support vector machine for the classification of iris patterns We also suggest a segmentation scheme basedon the collarette area localization The deterministic feature sequence is extracted from the iris images using the 1D log-Gaborwavelet technique and the extracted feature sequence is used to train the support vector machine (SVM) The MOGA is appliedto optimize the features sequence and to increase the overall performance based on the matching accuracy of the SVM Theparameters of SVM are optimized to improve the overall generalization performance and the traditional SVM is modified toan asymmetrical SVM to treat the false accept and false reject cases differently and to handle the unbalanced data of a specificclass with respect to the other classes Our experimental results indicate that the performance of SVM as a classifier is better thanthe performance of the classifiers based on the feedforward neural network the k-nearest neighbor and the Hamming and theMahalanobis distances The proposed technique is computationally effective with recognition rates of 9981 and 9643 onCASIA and ICE datasets respectively

Copyright copy 2008 K Roy and P Bhattacharya This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

1 INTRODUCTION

There has been a rapid increase in the need of accurateand reliable personal identification infrastructure in recentyears and biometrics has become an important technologyfor the security Iris recognition has been considered as oneof the most reliable biometrics technologies in recent years[1 2] The human iris is the most important biometricfeature candidate which can be used for differentiating theindividuals For systems based on high quality imaging ahuman iris has an extraordinary amount of unique detailsas illustrated in Figure 1 Features extracted from the humaniris can be used to identify individuals even among geneti-cally identical twins [3] Iris-based recognition system can benoninvasive to the users since the iris is an internal organas well as externally visible which is of great importancefor the real-time applications [4] Based on the technologydeveloped by Daugman [3 5ndash7] iris scans have been used inseveral international airports for the rapid processing of pas-sengers through the immigration which have preregisteredtheir iris images Iris technology has also been widely used in

several countries for various security purposes and bythe United Nations High Commission for Refugees TheNational Institute of Standards and Technology (NIST) hasconducted a new technology development project for irisrecognition namely the iris challenge evaluation (ICE) [8]

11 Main contributions

We present a new iris segmentation approach based on thecollarette area localization along with the eyelids the eye-lashes and the noise detection techniques multiobjectivesgenetic algorithms (MOGA) is used to select the optimalfeatures and also to increase the recognition accuracy [9]The concept of asymmetrical SVM is used as iris patternclassifiers and in order to improve the classification accuracythe parameters of SVM are tuned carefully [10 11] Weperform a series of experiments to evaluate the performanceof the proposed approach In order to exhibit the efficiency ofour proposed approach we carry out extensive quantitativecomparisons with the other existing methods

2 EURASIP Journal on Image and Video Processing

(a) (b) (c)

(d) (e) (f)

Figure 1 Samples of iris images from CASIA [12] and ICE [8]datasets

The rest of this paper is organized as follows In Section 2we provide a brief description of our proposed approachIn Section 3 we describe the related work and some rele-vant background Descriptions of iris image preprocessingfeature extraction and encoding are given in Sections 4and 5 respectively Section 6 presents the feature selectionstrategy and Section 7 describes the classification process ofiris patterns Experimental results comparisons with othermethods and discussions are reported in Section 8 Section 9concludes the paper

2 PROPOSED APPROACH THE MAIN STEPS

Figure 2 illustrates the main steps of our proposed approachFirst the imagepreprocessing step performs the localizationof the pupil detects the iris boundary and isolates thecollarette region which is regarded as one of the mostimportant areas of the iris complex pattern The collaretteregion is less sensitive to the pupil dilation and usuallyunaffected by the eyelids and the eyelashes [13] We alsodetect the eyelids and the eyelashes which are the mainsources of the possible occlusion In order to achieve theinvariance to the translation and the scale the isolatedannular collarette area is transformed to a rectangular blockof fixed dimension and then the normalized image isenhanced The discriminating features are extracted fromthe transformed image and the extracted features are usedto train the SVM The optimal features subsetis selectedusing MOGA to increase the matching accuracy based onthe recognition performance of the SVM The parametersof the SVM are tuned to improve the overall generaliza-tion performance The traditional SVM is modified to anasymmetrical SVM and it is applied for the iris patternclassification to treat the cases of false accept or false rejectdifferently The classification accuracy of the proposed SVMis also compared with the feedforward neural network byusing the backpropagation (FFBP) the feedforward neuralnetwork by using the Levenberg-Marquardt rule (FFLM)the k-nearest neighbor (k-NN) and the Hamming and theMahalanobis distances

3 BACKGROUND

31 Related work

The usage of iris patterns for the personal identificationbegan in the late 19th century however the major investi-gations on iris recognition were started in the last decadeIn [15] the iris signals were projected into a bank of basisvectors derived by the independent component analysisand the resulting projection coefficients were quantized asfeatures A prototype was proposed in [16] to develop a1D representation of the gray-level profiles of the iris In[17] biometrics based on the concealment of the randomkernels and the iris images to synthesize a minimumaverage correlation energy filter for iris authentication wereformulated In [5ndash7] the multiscale Gabor filters were usedto demodulate the texture phase structure information ofthe iris In [13] an iris segmentation method was proposedbased on the crossed chord theorem and the collarette areaIn [18] iris recognition technology was applied in mobilephones In [19] correlation filters were utilized to measurethe consistency of the iris images from the same eye Aninteresting solution to defeat the fake iris attack based onthe Purkinje image was depicted in [20] An iris image wasdecomposed in [21] into four levels by using the 2D Haarwavelet transform the fourth-level high-frequency informa-tion was quantized to form an 87-bit code and a modifiedcompetitive learning neural network (LVQ) was adoptedfor classification In [22] a modification to the Houghtransform was made to improve the iris segmentation andan eyelid detection technique was used where each eyelidwas modeled as two straight lines A matching method wasimplemented in [23] and its performance was evaluated ona large dataset

In [24] a personal identification method based onthe iris texture analysis was described An algorithm wasproposed for iris recognition by characterizing the key localvariations in [25] A phase-based iris recognition algorithmwas proposed in [26] where the phase components wereused in 2D discrete Fourier transform of iris image with asimple matching strategy In [27] a system was proposedthat is capable of a detailed analysis of the eye region imagesin terms of the position of the iris degree of the eyelidopening and the shape the complexity and the textureof the eyelids A directional filter bank was used in [28]to decompose an iris image into eight directional subbandoutputs the normalized directional energy was extracted asfeatures and iris matching was performed by computingthe Euclidean distance between the input and the templatefeature vectors In [29] the basis of genetic algorithms wasapplied to develop a technique to improve the performanceof an iris recognition system In [30] the global textureinformation of iris images was used for ethnic classificationThe iris representation method of [16] was further developedin [31] to use the different similarity measures for matchingThe iris recognition algorithm described in [32] exploitedthe integrodifferential operators to detect the inner and outerboundaries of iris Gabor filters to extract the unique binaryvectors constituting the iris code and a statistical matcher

K Roy and P Bhattacharya 3

Iris image preprocessing

Iris imagePupillary

localizationLocalization

of irisCollarette area

isolation

Eyelids eyelashesand noisedetection

Normalization

Iris patternsclassification

Optimal sequenceof features Feature

selection

Featurevectors Feature

extraction

Normalizedimage

Figure 2 Flow diagram of the proposed iris recognition scheme

that analyzes the average Hamming distance between twocodes In [33] the performance of iris-based identificationsystem was analyzed at the matching score level A biometricsystem which achieves the offline verification of certified andcryptographically secured documents called ldquoEyeCertsrdquo wasreported in [34] for the identification of the people

An iris recognition method was used in [35] based onthe 2D wavelet transform for the feature extraction anddirect discriminant linear analysis for feature reduction withSVM techniques as iris pattern classifiers In [36] an irisrecognition method was proposed based on the histogram oflocal binary patterns to represent the iris texture and a graphmatching algorithm for structural classification An elasticiris blob matching algorithm was proposed to overcomethe limitations of local feature based classifiers (LFC) in[37] and in order to recognize the various iris imagesproperly a novel cascading scheme was used to combinethe LFC and an iris blob matcher In [38] the authorsdescribed the determination of eye blink states by trackingthe iris and the eyelids An intensity-based iris recognitionsystem was presented in [39] where the system exploitedthe local intensity changes of the visible iris textures In[40] the iris characteristics were analyzed by using theanalytic image constructed by the original image and itsHilbert transform The binary emergent frequency functionswere sampled to form a feature vector and the Hammingdistance was deployed for matching [41 42] In [43] theHough transform was applied for the iris localization aLaplacian pyramid was used to represent the distinctivespatial characteristics of the human iris and a modifiednormalized correlation was applied for the matching processIn [44] various techniques have been suggested to solve theocclusion problem that happens due to the eyelids and theeyelashes

In [45] we developed an iris recognition method basedon the SVM where we used the information of the wholeiris region for recognition and a traditional SVM wasused as iris pattern classifiers However in this paper wepropose a segmentation approach based on the collarettearea localization and the unique iris information betweenthe collarette boundary and pupil boundary is used insteadof using the complete information of the iris region for therecognition purpose The traditional SVM used in [45] ismodified in this paper to an asymmetrical SVM [11] andin order to reduce the computational cost the parametersof SVM are tuned carefully [46] We also propose a multi-objectives genetic algorithm (MOGA) to minimize the size

of features subset and the recognition error of the matchingprocess We provide a comparative analysis of some majorexisting works on iris recognition with our proposed schemein Table 1

From the above discussion we may divide the existing irisrecognition approaches roughly into four major categoriesbased on feature extraction scheme namely the phase-basedmethods [5ndash7 26] the zero-crossing representation methods[16 31] the texture analysis-based methods [21 24 28 3243 47ndash49] and the intensity variation analysis [15 25 50]methods Our proposed iris recognition scheme falls in thefourth category

Wavelets are used to decompose the data in the irisregion into components that appear at different resolutionsA number of wavelet filters also called a bank of waveletsare applied to the 2D iris region one for each resolution witheach wavelet a scaled version of some basis function Theoutput is then encoded in order to provide a compact anddiscriminating representation of the iris pattern A Gaborfilter is constructed by modulating a sinecosine wave witha Gaussian This allows providing the optimum conjointlocalization both in space and frequency since a sine waveis perfectly localized in frequency but not localized in spaceThe decomposition of a signal is accomplished by using aquadrature pair of Gabor filters with a real part specifiedby a cosine modulated by a Gaussian and an imaginary partspecified by a sine modulated by a Gaussian [14] The realand imaginary filters are also known as the even symmetricand odd symmetric components respectively The centerfrequency is specified by the frequency of the sinecosinewave and the bandwidth of the filter is specified by the widthof the Gaussian Daugman [6] used a 2D version of Gaborfilters in order to encode the iris pattern data A 2D Gaborfilter over the image domain (x y) is represented as

G(x y) = eminusπ[(xminusx0)2α2+(yminusy0)2β2]eminus2π[u0(xminusx0)+v0(yminusy0)] (1)

where (x0 y0) specifies the position in the image (αβ)denotes the effective width and length and (u0v0) indi-cates the modulation which has spatial frequency ω0 =(u2

0 + v20)

12 The odd symmetric and even symmetric 2D

Gabor filters are shown in Figure 3Daugman [5] used polar coordinates for the normaliza-

tion and in polar form the filters are given by

H(r θ) = eminusiω(θminusθ0)eminus(rminusr0)2α2eminusi(θminusθ0)2β2

(2)


Table 1 Comparison of existing iris recognition approaches

Iris recognition approaches Nature of feature Matching process Quality evaluation

Daugman [5] Binary features vector using2D Gabor filters

Hamming distancePerfect recognition rate andprovides a faster irispupildetection process

Wildes et al [43]Laplacian pyramid torepresent the spatialcharacteristics of iris image

Normalized correlation

Matching process is timeconsuming It may besuitable for identificationphase not for recognition

Boles and Boashash [16] 1D signatureTwo dissimilarityfunctions the learning andthe classification

Relatively low recognitionrate high EER fastermatching process simple1D feature vector

Ma et al [49]1D real-valued featurevector with the length of384

Nearest feature lineRelatively slow featureextraction process


Weighted Euclideandistance

Lower recognition rate andhigher EER

Ma et al [24]A feature vector of length1536 using a bank of spatialfilters

Nearest center classifier forclassification

Higher recognition rateand lower EER extra costfor feature reduction

Ma et al [25]1D integer-valued featurevector with the length of660

XOR operationVery good recognition rateand lower EER

Lim et al [21] 1D binary vector of length87

LVQ neural networkPoor recognition rate andhigher EER relativelycomplicated classifier

Sanchez-Reillo and Sanchez-Avila [32] 1D signatureEuclidean and Hammingdistances

Medium classification ratesimple 1D features

Liu et al [22] 2D Gabor wavelets Hamming distanceHigher recognition rate oncomplicated datasetmedium EER

Liu et al [23] 2D Gabor wavelets Hamming distance

Modified Hough transformis used for localizationrelatively lower recognitionrate

Proposed approach

Binary feature vector oflength 470 and 504 onCASIA and ICE datasetsrespectively using 1Dlog-Gabor filters

Asymmetrical SVM

Faster feature extractionprocess Relatively higherrecognition rate with lowerEER extra cost for featurereduction using MOGA butsuitable for dataset like ICE

where (αβ) is the same as in (1) and (r0 θ0) specify thecenter frequency of the filter The demodulation and phasequantization process can be represented as

hRe Im = sgnRe Im

intρ

intempty

I(ρ empty)eminusiω(θ0minusempty)eminus(r0minusρ)2α2eminus(θ0minusempty)β2

(3)

where hRe Im can be regarded as a complex-valued bit whosereal and imaginary components are dependent on the signof the 2D integral and I(ρ empty) is the raw iris image in adimensionless polar coordinate system

Gabor filters-based methods have been widely used asfeature extractor in computer vision especially for texture

analysis However one weakness of the Gabor filter inwhich the even symmetric filter will have a DC componentwhenever the bandwidth is larger than one octave Toovercome this disadvantage a type of Gabor filter knownas log-Gabor filter which is Gaussian on a logarithmicscale can be used to produce zero DC components forany bandwidth [14] The log-Gabor function more closelyreflects the frequency response for the task of analyzingnatural images and is consistent with measurement of themammalian visual system The log-Gabor filters are obtainedby multiplying the radial and the angular componentstogether where each even and odd symmetric pair of log-Gabor filters comprises a complex log-Gabor filter at one


x

z

y

(a)

x

z

y

(b)

Figure 3 A quadrature pair of 2D Gabor filters (a) Real component or even symmetric filter characterized by a cosine modulated by aGaussian (b) imaginary component or odd symmetric filter characterized by a sine modulated by a Gaussian [14]

scale The frequency response of a log-Gabor filters is givenas

G( f ) = exp

(minus(log

(f f0

))2

2(log(σ f0

))2

) (4)

where f0 is the center frequency and σ provides thebandwidth of the filter

32 Rubber sheet model for unwrapping

Taking the effect of several deformations and inconsistenciessuch as the variation of the size of the iris images capturedfrom different persons and even for irises from the sameeye the variation of iris and pupil centers due to the cameraposition the camera-to-eye distance the rotation of thecamera the head tilt and the rotation of the eye withinthe eye socket into account the annular collarette region isrequired to be transformed into a fixed dimension for furtherprocessing Daugmanrsquos rubber sheet model [6] is used inthis paper to unwrap the iris ring into a rectangular blockwith the texture and with a fixed size This process maps thedetected collarette area from Cartesian coordinates (x y) tothe normalized polar representation according to

I(x(r θ) y(r θ)) minusrarr I(r θ) (5)

with

x(r θ) = (1minus r)xp(θ) + rxz(θ)

y(r θ) = (1minus r)yp + r yz(θ)(6)

where I(x y) is the collarette area (x y) are the originalCartesian coordinates (xp yp) denote the center coordinatesof the pupil and (r θ) are the corresponding normalizedpolar coordinates The rubber sheet model considers thepupil dilation and the size inconsistencies to construct anormalized representation of the annular collarette area withthe constant dimensions In this way the collarette area ismodeled as a flexible rubber sheet anchored at the collaretteboundary with the pupil center as the reference point

33 Multiobjective optimization usinggenetic algorithms

Genetic algorithm (GA) is a class of optimization proceduresinspired by the mechanisms of evolution in nature [5152] GAs operate on a population of structures each ofwhich represents a candidate solution to the optimizationproblem encoded as a string of symbols ldquo(chromosome)rdquoand GA starts its search from the randomly generated initialpopulation In GA the individuals are typically representedby m-bit binary vectors and the resulting search spacecorresponds to anm-dimensional Boolean space The qualityof each candidate solution is evaluated by a fitness functionThe fitness-dependent probabilistic selection of individualsfrom the current population to produce the new individualsis used by GA [52] The two of the most commonlyused parameters of GA that represent individuals as binarystrings are mutation and crossover Mutation operates ona single string and changes a bit randomly and crossoveroperates on two parent strings to produce two offspringsGAs repeat the process of fitness-dependent selection andthe application of genetic operators to generate successivegenerations of individuals several times until an optimalsolution is obtained Feature subset selection algorithms canbe classified into two categories namely the filter and thewrapper approaches based on whether the feature selectionis performed independently of the learning algorithm ornot to construct the verifier In the filter approach thefeature selection is accomplished independently of learningalgorithms Otherwise the approach is called a wrapperapproach The filter approach is computationally moreefficient but its major drawback is that an optimal selectionof features may not be independent of the inductive andrepresentational biases of the learning algorithm that is usedto build the classifier On the other hand the wrappermethod involves the computational overhead of evaluatinga candidate feature subset by executing a selected learningalgorithm on the database using each feature subset underconsideration The performance of the GAs depends on


various factors such as the choice of genetic representationand operators the fitness function fitness-dependent selec-tion procedure and the several user-determined parameterslike population size probability of mutation and crossoverand so on

The feature subset selection presents a multicriterionoptimization function for example number of features andaccuracy of the classification in the context of practicalapplications such as iris recognition Genetic algorithmssuggest a particularly attractive approach to solve thiskind of problems since they are generally quite effectivein rapid global search of large nonlinear and poorlyunderstood spaces [52] The multiobjectives optimizationproblem consists of a number of objectives and is correlatedwith a number of inequality and equality constraintsThe solution to a multiobjective optimization problem isexpressed mathematically in terms of nondominated pointsthat is a solution is dominant over another only if it hassuperior performance in all criteria A solution is treatedto be the Pareto optimal if it cannot be dominated by anyother solution available in the search space [51] The conflictbetween the objectives is regarded as a common problemwith the multiobjective Therefore the most favorable Paretooptimum is the solution that offers the least objectiveconflict since in general none of the feasible solutions allowssimultaneous optimal solutions for all objectives [51 53]In order to find such solutions classical methods are usedto scalarize the objective vector into one objective andthe simplest of all classical techniques is the weighted summethod [52] In this method the objectives are aggregatedinto a single and parameterized objective through a linearcombination of the objectives However the scaling of eachobjective function is used to setup an appropriate weightvector It is likely that different objectives take different ordersof magnitude When the objectives are weighted to form acomposite objective function it is required to scale themappropriately so that each has more or less the same orderor magnitude Therefore the solution found through thisstrategy largely depends on the underlying weight vectorIn order to overcome such complexities the Pareto-basedevolutionary optimization has been used as an alternativeto the classical techniques such as weighted sum methodwhere the Pareto dominance has been used to determinethe reproduction probability of each individual Basically itconsists of assigning rank 1 to the nondominated individualsand removing them from contention then finding a newset of nondominated individuals ranked 2 and so forth[52] In this paper our problem consists of optimizing twoobjectives minimization of the number of features and theerror rate of the classifier Therefore we are concerned withthe multiobjectives genetic algorithms (MOGA)

4 IRIS IMAGE PREPROCESSING

First we outline our approach and then we describe furtherdetails in the following subsections The iris is surroundedby the various nonrelevant regions such as the pupil thesclera the eyelids and also noise caused by the eyelashes theeyebrows the reflections and the surrounding skin [15] We

need to remove this noise from the iris image to improve theiris recognition accuracy To do this we initially localize thepupil and iris region in the eye image Then the collarettearea is isolated using the parameters obtained from thelocalized pupil We also apply the eyelashes the eyelids andthe noise reduction methods to the localized collarette areaFinally the deformation of the pupil variation is reduced byunwrapping the collarette area to form a rectangular block offixed dimension [54]

41 Irispupil localization

The iris is an annular portion of the eye situated betweenthe pupil (inner boundary) and the sclera (outer boundary)Both the inner boundary and the outer boundary of atypical iris can be taken as approximate circles However thetwo circles are usually not concentric [24 25] We use thefollowing approach to isolate the iris and pupil boundariesfrom the digital eye image

(1) The iris image is projected in the vertical and hori-zontal directions to estimate approximately the centercoordinates of the pupil Generally the pupil is darkerthan its surroundings therefore the coordinatescorresponding to the minima of the two projectionprofiles are considered as the center coordinate valuesof the pupil (XpYp)

(2) In order to compute a more accurate estimate ofthe center coordinate of the pupil we use a simpleintensity thresholding technique to binarize the irisregion centered at (XpYp) The centroid of theresulting binary region is considered as a moreaccurate estimate of the pupil coordinates We canalso roughly compute the radius rp of the pupil fromthis binarized region

(3) Canny edge detection technique is applied to acircular region centered at (XpYp) and with rp +25 Then we deploy the circular Hough transform todetect the pupiliris boundary

(4) In order to detect the irissclera boundary we repeatstep 3 with the neighborhood region replaced by anannulus band of a width R outside the pupilirisboundary The edge detector is adjusted to thevertical direction to minimize the influence of theeyelids

(5) The specular highlight that typically appears in thepupillary region is one source of edge pixels Thesecan be generally eliminated by removing the Cannyedges at the pixels that have a high intensity value(For the ICE data-set it is 245) Figure 5 shows thelocalized pupils taken from the input iris images

42 Collarette boundary localization

Iris complex pattern provides many distinguishing charac-teristics such as arching ligaments furrows ridges cryptsrings freckles coronas stripes and collarette area [24] Thecollarette area is one of the most important parts of iris


Collaretteboundary

Collarette area

(a)

Collarette area isoccluded by the

eyelashes and theupper eyelid

(b)

Figure 4 (a) Circle around the pupil indicates the collarette region (b) Collarette area is occluded by the eyelashes and the upper eyelid

(a) (b) (c)

(d) (e) (f)

Figure 5 Collarette area localization (a) (b) and (c) from CASIAiris dataset and (d) (e) and (f) from ICE dataset

complex patterns see Figure 4 since it is usually less sensitiveto the pupil dilation and less affected by the eyelid and theeyelashes From the empirical study it is found that collaretteregion is generally concentric with the pupil and the radiusof this area is restricted in a certain range [13] The collarettearea is detected using the previously obtained center valueof the pupil as shown in Figure 5 Based on the extensiveexperimentation we prefer to increase the radius of the pupilup to a certain number of pixels (see Section 81 for theexperimental validation)

43 Eyelids eyelashes and noise detection

(i) Eyelids are isolated by first fitting a line to theupper and lower eyelids using the linear Houghtransform A second horizontal line is then drawnwhich intersects with the first line at the iris edge thatis closest to the pupil [14]

(ii) Separable eyelashes are detected using 1D Gaborfilters since a low output value is produced by theconvolution of a separable eyelash with the Gaussiansmoothing function Thus if a resultant point issmaller than a threshold it is noted that this pointbelongs to an eyelash

(iii) Multiple eyelashes are detected using the variance ofintensity and if the values in a small window arelower than a threshold the centre of the windowis considered as a point in an eyelash as shown inFigure 6

(I)

(a) (b) (c)

(d) (e) (f)

(II)

(a) (b) (c)

(d) (e) (f)

Figure 6 (I) CASIA iris images (a) (b) and (c) with the detectedcollarette area and the corresponding images (d) (e) and (f) afterdetection of noise eyelids and eyelashes (II) ICE iris images (a)(b) and (c) with the detected collarette area and the correspondingimages (d) (e) and (f) after detection of noise eyelids andeyelashes

44 Normalization and enhancement

We use the rubber sheet model [6] for the normalizationof the isolated collarette area The center value of the pupilis considered as the reference point and the radial vectorsare passed through the collarette region We select a numberof data points along each radial line that is defined asthe radial resolution and the number of radial lines goingaround the collarette region is considered as the angularresolution A constant number of points are chosen alongeach radial line in order to take a constant number ofradial data points irrespective of how narrow or wide the


(I)

θ

r

(a)

(b)

White region denotes noiseBlack portion represents region of interest

of the unwrapped iris image

(II)

(a)

(c)

(b)

(d)

Figure 7 (I) shows the normalization procedure on ICE dataset (II) (a) (b) show the normalized images of the isolated collarette regionsand (c) (d) indicate the enhanced images on the ICE dataset

radius is at a particular angle We build the normalizedpattern by backtracking to find the Cartesian coordinatesof data points from the radial and angular positions in thenormalized pattern [3 5 6] The normalization approachproduces a 2D array with horizontal dimensions of angularresolution and vertical dimensions of radial resolution formthe circular-shaped collarette area (See Figure 7I) In order toprevent non-iris region data from corrupting the normalizedrepresentation the data points which occur along the pupilborder or the iris border are discarded Figure 7II(a)(b)shows the normalized images after the isolation of thecollarette area Since the normalized iris image has relativelylow contrast and may have nonuniform intensity valuesdue to the position of the light sources a local intensity-based histogram equalization technique which helps toincrease the subsequent recognition accuracy is applied toenhance the normalized iris image quality Figure 7II(c)(d)also shows the effect of enhancement on the normalized irisimages

5 FEATURE EXTRACTION AND ENCODING

51 Gabor wavelets

In order to extract the discriminating features form thenormalized collarette region the normalized pattern isconvolved with 1D log-Gabor wavelets [14] First the 2D

normalized pattern is isolated into a number of 1D signalsand then these 1D signals are convolved with 1D Gaborwavelets The phasequantization approach proposed in [5]is applied to four levels on the outcome of filtering witheach filter producing two bits of data for each phasor Thedesirable feature of the phase code is selected to be a greycode where only a single bit changes while rotating formone phase quadrant to another unlike a binary code Theencoding process produces a bitwise template containing anumber of bits of information and a corresponding noisemask which corresponds to the corrupt areas within thecollarette pattern and marks bits in the template as corrupt

Since the phase information will be meaningless atregions where the amplitude is zero we mark these regionsin the noise mask The total number of bits in the templatewill be the double of the product of the angular resolutionthe radial resolution and the number of filters used Thefeature extraction process is shown in Figure 8

6 FEATURE SUBSET SELECTION USING MOGA

It is necessary to select the most representative featuresequence from a features set with relative high dimension[51] In this paper we propose MOGA to select the optimalset of features which provide the discriminating informationto classify the iris patterns In this subsection we presentthe choice of a representation for encoding the candidate


Original 2-Dunwrapped pattern

Original 1-D signal

Convolution of 1D signalwith 1D log-Gabor filter

Realresponse

Imaginaryresponse

(a)

Im

Re

[0 1] [1 1]

[0 0] [1 0]

(b)

1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0

(c)

Figure 8 Feature extraction and encoding process (a) feature extraction (b) phase quantization and (c) generated iris pattern

111 1 000 10 1010 1 0 0001 11 10 0

Feature 1st is selectedfor SVM classifier

Feature 15th is notselected for SVM

classifier

Length of chromosome l = feature dimension

Figure 9 Binary feature vector of l dimension

Selection of optimalfeatures using MOGA

Accuracy and numberof features

SVM classifier

Selected features

Figure 10 Feature selection process

solutions to be manipulated by the GAs and each individualin the population represents a candidate solution to thefeature subset selection problem If m be the total numberof features available to choose to represent from the patternsto be classified (m = 600 in our case for both data-sets) the individual is represented by a binary vector ofdimension m If a bit is a 1 it means that the correspondingfeature is selected otherwise the feature is not selected (SeeFigure 9) This is the simplest and most straightforwardrepresentation scheme [51] In this work we use the roulettewheel selection [51] which is one of the most commonand easy to implement selection mechanism Usually thereis a fitness value associated with each chromosome forexample in a minimization problem a lower fitness valuemeans that the chromosome or solution is more optimizedto the problem while a higher value of fitness indicates a lessoptimized chromosome Our problem consists of optimizing

two objectives

(i) minimization of the number of features

(ii) minimization of the recognition error rate of theclassifier (SVM in our case)

Therefore we deal with the multiobjectives optimizationproblem In order to generate the Pareto optimal setwe apply the weighting method proposed in [55] whichaggregates the objectives into a single and parameterizedobjective Such an aggregation is performed through a linearcombination of the objectives

Obj(y) = Obj1(y)timesw1 + Obj2(y)timesw2 (7)

where wi denotes the weights and it is normalized tosumwi = 1 without losing the generality Obj1(y) is the error

rate produced by the classifier for a given feature subset(represented by the chromosome y) and Obj2(y) denotes thenumber of features selected in the chromosome y Thereforethe fitness of a chromosome is represented by a singleand parameterized objective function Obj(y) The featuresubset selection using the MOGA involves the running of agenetic algorithm for several generations In this paper weprefer to use the wrapper approach based on the nature ofthe problem space Regarding a wrapper approach in eachgeneration evaluation of a chromosome (a feature subset)requires training the corresponding SVM and computing itsaccuracy This evaluation has to be performed for each ofthe chromosomes in the population Only the features in theparameter subset encoded by an individual are used to trainthe SVM classifier The performance of the SVM classifier isestimated using a validation dataset and is used to guide thegenetic algorithm as shown in Figure 10

7 MULTICLASS ASYMMETRICAL SUPPORT VECTORMACHINES AS IRIS PATTERN CLASSIFIERS

A support vector machine (SVM) is a well-accepted approachfor pattern classification due to its attractive features and


promising performance [10] Support vector classifiersdevise a computationally efficient way of learning goodseparating hyperplane in a high-dimensional feature spaceIn this work we apply SVM to classify the iris pattern dueto its outstanding generalization performance and promisingperformance as a multiclass classifier In an SVM a fewimportant data points called support vectors (SV) are selectedon which a decision boundary is exclusively dependent Oneproblem persists with the traditional approach of SVM isthat it does not separate the cases of false accept and falsereject [56] Therefore we prefer to apply the asymmetricalSVM in order to treat the cases of false accept and false rejectseparately and to control the unbalanced data of a specificclass with respect to the other classes We summarize thesesteps below

(1) Let us consider N sets of labeled inputoutput pairsxi yi i = 1 N isin X times +1minus1 where X is theset of input data in RD and yi represents the labels TheSVM approach aims to obtain the largest possible margin ofseparation The decision hyperplane can be expressed as

xmiddotw + b = 0 (8)

(2) If all the training data satisfy the constraints then

ximiddotw + b ge +1 for yi = +1 foralli = 1 N

ximiddotw + b le minus1 for yi = minus1 foralli = 1 N (9)

and the distance between the two hyperplanes is expressed as

2d = 2w (10)

where the distance d is considered as the safety margin of theclassifier

(3) Now by combining (9) into a single constraint weget

yi(

ximiddotw + b) ge 1 foralli = 1 N (11)

In the training phase the main goal is to find the SVthat maximizes the margin of separation d Alternatively asimilar objective can be achieved if we minimize w2 Thusthe goal is to minimize w2 subject to the constraint in (11)We can solve it by introducing Lagrange multipliers αi ge 0and a Lagrangian

L(w bα) = 12w2 minus

Nsumi=1

αi(yi(

ximiddotw + b)minus 1

) (12)

where L(w bα) is simultaneously minimized with respect tow and b and maximized with respect to αi

(4) Finally the decision boundary can be derived asfollows

f (x) = wmiddotx + b =Nsumi=1

yiαi(

xmiddotxi)

+ b = 0 (13)

(5) If the data points are not separable by a linearseparating hyperplane a set of slack or relaxation variables

ξ = ξ1 ξN is introduced with ξi ge 0 such that (11)becomes

yi(

ximiddotw + b) ge 1minus ξi forall i = 1 N (14)

The slack variables measure the deviation of the data pointsfrom the marginal hyperplane The new objective functionto be minimized becomes

12w2 + C

sumi

ξi subject to yi(

ximiddotw + b) ge 1minus ξi

(15)

where C is the user-defined penalty parameter that penalizesany violation of the safety margin for all the training data

(6) In order to obtain a nonlinear decision boundary wereplace the inner product (xmiddotxi) of (13) with a nonlinearkernel K(xmiddotxi) and get

f (x) =Nsumi=1

yiαiK(

xmiddotxi)

+ b (16)

(7) In order to change the traditional SVM into anasymmetrical SVM a constant g which is called an asym-metrical parameter is used It is used to adjust the decisionhyperplane Thus (8) becomes

xmiddotw + b + g = 0 (17)

(8) Therefore the decision function of (16) changes to

f (x) =Nsumi=1

yipropiK(

x xi)

+ b + g (18)

when g gt 0 it indicates that the classification hyperplane iscloser to positive samples By changing the value of g thevalue of false accept can be reduced We also compensatethe statistically under-presented data of a class with respectto other classes by controlling the value of the penaltyparameter C

The three basic kernels used in this paper are

Polynomial kernel K(x xi) = (1 + xmiddotxiσ2)p p gt 0

Radial Basis Function (RBF) kernel K(x xi) =expminusx minus xi22σ2 and

Sigmoidal Kernel K(x xi) = 1(1 + eminusxmiddotxi+bσ2)

71 SVM parameters tuning

It is important to improve the generalization performanceby adjusting the penalty parameter for error term C andby adjusting the kernel parameters A careful selection of atraining subset and of a validation set with a small number ofclasses is required to avoid training the SVM with all classesand to evaluate its performance on the validation set due toits high-computational cost when the number of classes ishigher In this paper the optimum parameters are selectedto tune the SVM A modified approach proposed in [46] isapplied here to reduce the cost of the selection procedure


as well as to adjust the parameters of the SVM We brieflydiscuss the steps below

After assigning the class label to the training data ofthe selected classes obtained by the parameter selectionalgorithm we divide 70 of the training data of each classdepending on the dataset used for training and the restof the training data is used for validation The Fisher leastsquare linear classifier is used with a low computation costfor each class [57] The performance of this linear classifieris evaluated on the validation set and the confusion matrixCM is defined as follows

CM =

⎛⎜⎜⎜⎜⎝

m11 m12 middot middot middot m1n


mn1 mn2 middot middot middot mnn

⎞⎟⎟⎟⎟⎠ (19)

Here each row i corresponds to the classwi and each columnj represents the number of classes classified to wj Thenumber of misclassified iris patterns is estimated for eachclass as follows

erri =nsum

j=1 j = imi j (20)

and then we sort the misclassified patterns erri i =1 2 n calculated from (20) in decreasing order andthe subscripts i1 i2 iI are assigned to the top I choicesassuming that I N Now we determine the numberof classes whose patterns can be classified to the class setwi1 wi2 wiI based on the following confusion matrix

V =I⋃

k=1

wj | mi j = 0

(21)

From the class set V we select the training and the crossvalidation set to tune C and the kernel parameters forthe SVM After a careful selection of C and the kernelparameters the whole training set with all classes is trained

8 RESULTS

We conduct the experimentation on two iris datasetsnamely the ICE (iris challenge evaluation) dataset createdby the University of Notre Dame USA [8] and the CASIA(Chinese Academy of SciencemdashInstitute of Automation)dataset [12] The ICE dataset is divided into two categoriesthe ldquogalleryrdquo images which are considered as good qualityimages and the ldquoproberdquo images which represent iris imagesof varying quality The iris images are intensity images witha resolution of 640 times 480 The average diameter of an irisis 228 pixels [8] The ICE database consists of left and rightiris images for experimentation We consider only the left irisimages in our experiments There are 1528 left iris imagescorresponding to the 120 subjects in our experiments Thenumber of iris images for each person ranges from 2ndash5in this database We have also used the CASIA iris imagedataset and each iris class is composed of seven samplestaken in two sessions three in the first session and four

in the second Sessions were taken with an interval of onemonth which is a real world application level simulationImages are 320 times 280 pixels gray scale taken by a digitaloptical sensor designed by NLPR [8] There are 108 classesof irises in a total of 756 iris images The experimentationis conducted in two stages performance evaluation of theproposed approach and comparative analysis of our methodwith the existing approaches in the field of iris recognitionIn the first stage of the experimentation we emphasize onthe performance evaluation of the current approach basedon the classification and the matching accuracy We evaluateour proposed method by comparing its recognition accuracywith the other classical classification methods and the match-ing strategies We show the performance of the proposedgenetic process for selecting the optimum features as wellas to increase the overall system accuracy The verificationperformance of the proposed approach is shown using areceiver operator characteristics (ROCs) curve We exhibit theeffect of false accept rate (FAR) and false reject rate (FRR)on different security requirements by changing the valuesof asymmetrical parameter for SVM The FAR measuresthe probability of accepting an imposter as an authorizedsubject and FRR is the probability of rejecting an authorizedsubject incorrectly We also measure the performance withequal error rate (EER) During the second stage we carryout a series of experimentation to provide a comparativeanalysis of our method with the existing methods in respectof recognition accuracy and computational complexity Wealso show the average time consumption of the different partsof the proposed iris recognition system

81 Performance evaluation of the proposed method

We evaluate the success rates for the proposed method onthe CASIA and ICE datasets by detecting the pupil boundaryand the collarette area The obtained success rate is 9986on CASIA where the proposed algorithm failed to identifythe pupil boundary in one case only The success rate ofthe correct pupil detection on the ICE dataset is 9770From the experimental results it is found that a reasonablerecognition accuracy is achieved when the collarette area isisolated by increasing the previously detected radius valueof the pupil up to a certain number of pixels A dropof matching error from 360 to 348 is observed inFigure 11(a) when the number of pixels is increased from 21to 22 Therefore we choose to increase the pupil radius upto 23 pixels because a stable matching accuracy of 9650is achieved in this case We would like to mention herethat in order to obtain an optimal value of collarette radiusSVM has been used to generate matching accuracy howeverMOGA is not applied in this case From Figure 11(b) it isfound that if we increase the pixel values up to 26 we obtainthe highest matching accuracy of 9972 since a relativelystable accuracy is achieved in the range of pixels 25ndash27 andafter this range the matching accuracy reduces drastically

In order to reduce the computational cost and speedup the classification a Fisher least square linear classifier isused as a low-cost preclassifier so that reasonable cumulativerecognition accuracy can be achieved to include the true


30252015105

Number of pixels increased

35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)

Figure 11 Selection of optimal number of pixels to be increased to obtain the collarette boundary for (a) ICE and (b) CASIA datasets

class label to a small number of selected candidates ForCASIA data set 10 candidates are chosen and the cumulativerecognition accuracy at rank 10 is 9990 In this work theselected cardinal number of set found from the experimen-tation by using the algorithm for SVM parameters tuningproposed in [46] is 24 As a result the sizes of trainingand validation sets for selecting the optimal parameter forC and γ are 118 (= 24lowast7lowast70) and 50 (= 24lowast7lowast30)respectively The parameter γ is set at 065 and C at 20 whenthe highest accuracy on validation set has been achieved withthe RBF kernel The SVM parameters are also tuned for theICE iris dataset For the ICE dataset we apply again theFisher least square linear classifier and 20 candidates arechosen [36] The cumulative recognition accuracy at rank20 is 9884 In this paper the selected cardinal numberof sets found from the experimentation is 32 by using thetuning algorithm for SVM parameter selection As a resultthe sizes of the training and validation sets for selecting theoptimal values of the C and σ2 are 112 (= 32lowast5lowast07) and48 (= 32lowast5lowast03) respectively The parameter σ2 is set at040 and the C set at 100 when the highest accuracy on thevalidation set is achieved with the RBF kernel for the ICEiris dataset In this paper we consider only those classes ofthe ICE database that have at least 5 probe images in orderto select the optimal parameter values Table 2 shows theperformance of different kernel functions Since the highestclassification accuracy is obtained by RBF kernel this kernelis used in our system for the iris pattern classification

In order to evaluate the matching accuracy only thecollarette area is used for recognition purpose instead ofusing the entire iris information For each iris pattern ofthe CASIA data set three irises taken in the first sessionare used to build the template and the remaining four irisesof the second session for testing For each person in theICE database one iris sample is used randomly from thegallery images to build the template The remaining irises

from the probe image set are used for testing In order toshow the effectiveness of SVM as a classifier we also providethe extracted features as input to the FFBP the FFLM andthe k-NN for classification and the accuracy of the classifiersfor various numbers of classes among the FFBP the FFLMthe SVM and the k-NN (k = 3) are shown in Figures 12(a)12(b) for the size of 600 features subset Several experimentsare conducted and the optimal values of the parameters forFFBP and FFLM are set as found in Table 3

Later the principal component analysis (PCA) [57] isused to reduce the dimension of the extracted feature vectorsand only the 50-bit feature sequence is used to measure theclassification performance of the SVM with the Mahalanobisdistance classifier (MDC) [57] along with the other classicmethods as shown in Figure 13 Dimension reduction isrequired due to the smaller available sample sizes which arenot suitable for the classification by using the Mahalanobisdistance From Figures 12 and 13 it is observed that that theperformance of the SVM as an iris classifier is better than theother classical methods though the classification accuracy isdecreased as number of classes is increased Figure 14 showsthe comparison of the feature dimension versus recognitionaccuracy among the hamming distance (HD) the FFBP theFFLM the k-NN and the SVM In this case only the RBFkernel is considered due its reasonable classification accuracyfor SVM as mentioned earlier From Figure 14 we can alsosee that with the increasing dimensionality of the featuresequence the recognition rate also increases rapidly for allsimilarity measures However when the dimensionality ofthe feature sequence is up to 600 or higher the recognitionrate starts to level off at encouraging rates of about 9962and 9621 on CASIA and ICE datasets respectively

For selecting the optimum subset of features to increasethe accuracy of the matching process MOGA involvesrunning the genetic process for several generations as shownin Figure 15 From this figure it is observed that the


1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)

Figure 12 Comparison of the classification accuracy among SVM FFBP FFLM and k-NN for 600-bit feature sequence (a) CASIA dataset(b) ICE dataset

108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)

Figure 13 Comparison of the classification accuracy of SVM with FFBP FFLM k-NN and MDC for 50-bit feature sequence (a) CASIAand (b) ICE

Table 2

Kernel type Classification accuracy () in ICE dataset Classification accuracy () in CASIA dataset

Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3

ParametersICE dataset CASIA dataset

FFBP FFLM FFBP FFLM

No of nodes in hidden layers 170 310 150 270

Iteration epoch 120 120 180 200


times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)

Figure 14 Comparison of recognition accuracy of SVM with FFBP FFLM k-NN and HD for different feature dimension (a) CASIA datasetand (b) ICE dataset

15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)

Figure 15 Variation of the recognition rates with generation (a) CASIA dataset and (b) ICE dataset

reasonable matching accuracy of 9970 is achieved at thegeneration 110 for the CASIA dataset and an accuracy of9642 is achieved at the generation of 150 for the case ofICE dataset The evolution of the MOGA can be observed inFigure 16 It is noticeable form this figure that the MOGArepresents a good convergence since average fitness of thepopulation approaches that of the minimum individualalong the generations We conduct several experimentationsand the arguments of the MOGA are set as follows when thereasonable accuracy is obtained

The recognition accuracy is compared between theproposed method using the information of collarette areaand the previous approach of [45] where the whole irisinformationbetween pupil and sclera boundary is considered

for recognition Figure 17 shows the efficiency of the currentapproach with MOGA and without MOGA in comparisonwith the previous method and it is found that the proposedmethod performs reasonably well for both of the data setsTherefore we see that performance of our approach isincreased when we use the MOGA for the feature subsetselection The proposed approach leads to a reasonablerecognition accuracy in the cases even when the eyelashesand the eyelids occlude the iris region badly so that thepupil is partly invisible The adjustment of the asymmetricalparameter g can be made to satisfy the several securityissues in iris recognition applications and to handle theunbalanced data of a specific class with respect to otherclasses The performance of a verification system is evaluated


150140120100806040205

Generation

Minimum fitnessAverage fitnessMaximum fitness

0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)

Figure 16 Variation of the fitness values with generation (a) CASIA dataset and (b) ICE dataset

times102964824126075

Feature dimension

Proposed approach without GAProposed approach with GAPrevious approach without GAPrevious approach with GA

95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)

Figure 17 Comparison of the recognition accuracies between the previous method and the proposed approach on (a) CASIA dataset (b)ICE dataset

Table 4

Parameters ICE dataset CASIA dataset

Population size 120 (the scale of iris sample) 108 (the scale of iris sample)

Length of chromosome code 600 (selected dimensionality of feature sequence) 600 (selected dimensionality of feature sequence)

Crossover probability 061 065

Mutation probability 0005 0002

Number of generation 150 110


10110010minus110minus2

False accept rate ()

Proposed approach (CASIA data set)Previous approach (CASIA data set)Proposed approach (ICE data set)Previous approach (ICE data set)

70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()

Figure 18 ROC curve shows the comparison between GAR andFAR for our previous approach and proposed approach

10010minus1

Value of asymmetrical parameter g

Proposed approach (ICE data set)Previous approach (ICE data set)Proposed approach (CASIA data set)Previous approach (CASIA data set)

100

101

Mat

chin

ger

ror

()

Figure 19 Comparison of recognition error between proposedmethod and our previous method [45] with different values ofasymmetrical parameter g

using ROC curve see Figure 18 which demonstrates howthe genuine acceptance rate (GAR) changes with the variationin FAR for our previous and proposed methods Fromthe experimentation we find that the proposed approachreduces the EER form 036 to 013 on CASIA and from072 to 039 on ICE datasets which represents a goodimprovement of our proposed method Figure 19 reveals thatthe proper selection of the asymmetrical parameter g leads toa lower recognition error both in the cases of the proposedand in the previous schemes

82 Comparison with existing methods

The methods proposed in (6 7 8) (53 4) (22 23) (3543) and (25 27 28) are the well-known existing approachesfor the iris recognition Furthermore these methods arebased on the phase the texture analysis and the zero-crossing representation of the iris Therefore we decide tocompare our algorithm with these methods We providethe recognition accuracies and time consumption of theproposed iris recognition scheme based on the ICE andCASIA datasets We would like to point out here that theexperimental results reported in Tables 5 and 6 have beenimplemented on the machines of different speed and onthe different datasets Therefore the results provided inTables 5 and 6 may not be interpreted as a real comparisonHowever we would also like to mention that the proposedscheme has been tested on the two data sets where ICEcontains complicated iris data of varying image qualityon a machine of higher speed From Table 5 we see thatmethods reported in [6 25] have better performance thanthe proposed approach on CASIA dataset followed by themethods in [16 22ndash24] From this table we can also seethat the proposed scheme provides a better accuracy on ICEdataset than the methods proposed in [16 23] We would liketo point out here that the experimentation of [23] is carriedout on ICE data set

Table 5 also demonstrates a comparison of the EERamong the different existing methods and from this tablewe find that our proposed method has less EER than themethods reported in [16 22 24 43] preceded by the methodproposed in [6 25] on the CASIA dataset The EER foundon ICE data set is 039 which is better than the EERsreported in [16 22 43] As no EER is reported in [23] weignore the EER from our consideration In order to achievehigh accuracy feature dimension should be small enoughIn our proposed method we input 600 features to MOGAand obtain a subset of 470 and 504 features after reductionwith slight improvement of recognition rates on CASIA andICE which are smaller than the number of features used in[6 24 25] where the number of feature components are2048 1536 and 660 respectively In our proposed methodwe use Gabor filters to capture the local variations of theisolated collarette region by comparing and quantizing thesimilarity between Gabor filters and local regions as themethods proposed in [6 25] One problem of the methoddepicted in [24] seems to be the usage of spatial filterswhich may fail to capture the fine spatial changes of theiris We overcome this possible drawback by capturing thelocal variation using Gabor filters and then we use MOGAto select the most discriminating feature sequence In [13]collarette area is used with the eyelash detection techniquefor the iris recognition However in our proposed schemewe successfully isolate the collarette region along with theeyelashes the eyelids and the noise detection method whichhelps to increase the recognition accuracy and consequentlyovercomes the problem when the pupil is occluded badlyby the eyelids and the eyelashes We conduct the aboveexperimentation on a 300 GHz Pentium IV PC with 1 GBRAM and we implemented our code in Matlab 72 Table 6


Table 5 Recognition rates and equal error rates

Methods Correct recognition rate () Equal error rate ()

Daugman [6] 100lowast 008lowast

Wildes et al [43] mdash 176lowast

Boles and Boashash [16] 9264lowast 813lowast

Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179

Liu et al [23] 8964 mdash

Roy and Bhattacharya [45] 9956 036

Proposed method (ICE dataset) 9643 039

Proposed method (CASIA dataset) 9981 013lowast

These results were published in [25] by using the bootstrap authors approximately predict the recognition rates of these methods

Table 6 Computational complexities

Methods Feature extraction (ms) Matching (ms) Feature extraction + Matching (ms) Others

Daugman [6] 6825lowast 43lowast 6868lowast mdash

Wildes et al [43] 2100lowast 4010lowast 6110lowast Registration

Boles and Boashash [16] 1703lowast 110lowast 1813lowast mdash

Ma et al [24] 2602 87 2689 Feature reduction

Ma et al [25] 2442 65 2507 mdash

Roy and Bhattacharya [45] 803 1672 2475 mdash

Proposed method (ICE dataset) 208 1507 1715 Feature reduction

Proposed method (CASIA dataset) 203 1304 1507 Feature reductionlowast

These results were published in [25] by using the bootstrap authors approximately predict the computational complexities

shows that our proposed approach significantly reduces thetime consumption than our previous method of [45] wherethe experimentation was performed on CASIA data set In[45] the Hough transform with Canny edge detection wasemployed for the segmentation In this proposed scheme weemploy the Hough transform in a certain range to restrict theexhaustive search thereby reducing the time consumption InTable 6 where the results of first five rows are taken from[25] we see that our current approach consumes less timethan the method in [6 16 24 25 43 45] if we take intoaccount the feature extraction phase only The reason is thatour method is based on 1D signal analysis and the othermethods mostly deploy the 2D mathematical calculationHowever our approach takes much time for recognitionas SVM is used for matching process We can see fromthe experimentation that the overall time consumption isless than the other methods reported in Table 6 Howeverthe experimental results reported in [25] for the methodsproposed in [6 16 24 43] were achieved in a machine of128 MB RAM running at 500 MHz speed

Our current approach requires an extra cost as incurredin [24] for the feature reduction The traditional featureselection schemes (like the principal component analysisindependent component analysis singular valued decomposi-tion etc) require sufficient number of samples per subjectsto select the salient features sequence However it is notalways realistic to accumulate a large number of samples due

to some security issues The MOGA suggests a particularlyattractive approach to solve this kind of problems sincethey are generally quite effective in rapid global search oflarge nonlinear and poorly understood spaces Thereforethe proposed technique of feature selection using MOGAperforms reasonably well even when the sample proportionbetween two classes is poorly balanced Moreover theproposed MOGA scheme shows an outstanding performancein the case when the iris dataset contains high-dimensionalfeatures set with relatively a lower sample size In [29] a basicgenetic algorithm was used to find a distribution of pointsover the iris region and this leads to a reasonable accuracyof 9970 on CASIA which is smaller in comparison withthe matching rate of the proposed approach on CASIAdataset However in this paper we propose MOGA wherethe main concerns are to minimize the recognition errorbased on the SVM performance on testing set and to reducethe number of features In [35] a traditional SVM is usedfor pattern matching which seems to fail to separate theFAR and the FRR with a matching accuracy of 9824The usage of asymmetrical SVM proposed in this paperdifferentiates the FAR and the FRR to meet the severalsecurity requirements depending on the various applicationareas with a reasonable recognition rates of 9981 and9643 on CASIA and ICE datasets respectively However afaster feature reduction approach was used in [35] based onthe direct discriminant analysis than the method proposed


Table 7 Time consumption of different parts of iris recognition system

Methods Iris segmentation (ms) Normalization (ms) Feature extraction (ms) Matching (ms) Total (ms)

Proposed approach (ICE dataset) 2145800 377 208 1507 2147892

Proposed approach (CASIA dataset) 2034710 163 203 1304 2036380

in this paper with MOGA Table 7 shows the overall timeconsumption of the proposed approach on the two datasets

83 Discussions

Based on the above experimentation we may depict thefollowing points

(i) The proposed method can be considered as a localvariation analysis method from the viewpoint offeature representation strategy as the phase infor-mation characterized by our representation schemereflects the local shape feature of the collarette regionIn general the methods based on local variationanalysis perform well than the other existing featurerepresentation scheme called texture analysis-basedmethod [24] The main drawback of the lattermethod is that it does not capture the local finechanges of the iris since the texture usually representsthe frequency information of a local region

(ii) Though the collarette area is insensitive to the pupildilation and less affected by the eyelids and theeyelashes there might be few cases where this regionis partially occluded since it is closed to pupil Ourproposed method of detecting the collarette areaalong with the eyelids the eyelashes (both in the casesof the separable and the multiple eyelashes) and thenoise removal techniques successfully overcome thisproblem and this also helps to increase the overallmatching accuracy

(iii) We find from the experimental results that the selec-tion of SVM parameters contributes in improving theclassification accuracy especially when the number ofclasses is higher

(iv) The tuned SVM with an additional asymmetricalparameter separates the FAR and the FRR accord-ing to different security demands and controls theunbalanced data with respect to other classes bychanging the penalty parameter C It is foundfrom the experimentation that the penalty for thecomputation of the asymmetrical SVM parameter isrelatively small

(v) From the experimentation it seems that the asym-metrical SVM can be used commercially due itsoutstanding performance as multiclass classifier andalso for those cases where the sample proportion ispoorly balanced between two classes Moreover theproposed SVM is well suited when the number ofsamples per individual is relatively small as the casefor ICE dataset

(vi) From the experimentation it is also observed thatthe feature selection method by using the MOGAincreases the recognition accuracy and contributesin reducing the feature dimension However MOGAincurs extra cost in order to find the optimalfeatures subset through several iterations Howeverthe proposed feature subset selection reduces thefeatures set relatively as compared to the other featurereduction strategies reported recently in the existingiris recognition schemes

(vii) The experimental results exhibit that the proposedalgorithm performs reasonably well if we consider theaccuracy

(viii) Although one might think that the proposed methodusing the collarette area has lesser information avail-able as compared to the other methods using thecomplete iris information the proposed method canbe used effectively for personal identification sincethe collarette area contains enough discriminatingfeatures

9 CONCLUSIONS

In this paper a new iris recognition method is proposedusing an efficient iris segmentation approach based on thecollarette area localization with the incorporation of theeyelashes and the eyelids detection techniques The 1D log-Gabor filters are used to extract the discriminating featuresand MOGA is applied for the feature subset selectionIn order to increase the feasibility of SVM in biometricsapplications it is modified to an asymmetrical SVM Theasymmetrical SVM with the collarette area localizationscheme can be applied in wide range of security-relatedapplication fields Experimental results exhibit an encour-aging performance as the accuracy is concerned especiallyon the ICE data set which contains relatively nonideal irisdata A comparative analysis among the existing schemes ofthe iris recognition has been conducted The performanceevaluation and comparisons with other methods indicatethat the proposed method is a viable and very efficientmethod for iris recognition In future the SVM boostingstrategy can be employed to reduce the computational timeof the overall iris recognition system

ACKNOWLEDGMENTS

The iris CASIA dataset is available on the web at httpwwwsinobiometricscomenglishIris20Databasesasp[12] TheICE dataset is obtained from NIST [8] A modified LIBSVM(Library for Support Vector Machines) tool has been used inthis paper for iris classification [58]


REFERENCES

[1] R P Wildes ldquoIris recognition an emerging biometrie tech-nologyrdquo Proceedings of the IEEE vol 85 no 9 pp 1348ndash13631997

[2] A Jain R Bolle and S Pankanti Biometrics Personal Identi-fication in a Networked Society Kluwer Academic PublishersNorwell Mass USA 1999

[3] J Daugman ldquoBiometric personal identification system basedon iris analysisrdquo 1994 US patent no 5291560

[4] T Mansfield G Kelly D Chandler and J Kane ldquoBiometricproduct testingrdquo Final Report National Physical LaboratoryMiddlesex UK 2001

[5] J G Daugman ldquoHigh confidence visual recognition of per-sons by a test of statistical independencerdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 15 no 11pp 1148ndash1161 1993

[6] J Daugman ldquoStatistical richness of visual phase informationupdate on recognizing persons by iris patternsrdquo InternationalJournal of Computer Vision vol 45 no 1 pp 25ndash38 2001

[7] J Daugman ldquoDemodulation by complex-valued waveletsfor stochastic pattern recognitionrdquo International Journal ofWavelets Multiresolution and Information Processing vol 1no 1 pp 1ndash17 2003

[8] httpirisnistgovICE[9] D E Goldberg Genetic Algorithms in Search Optimization

and Machine Learning Addison-Wesley Reading Mass USA1989

[10] V N Vapnik Statistical Learning Theory John Wiley amp SonsNew York NY USA 1998

[11] P Ding Z Chen Y Liu and B Xu ldquoAsymmetrical supportvector machines and applications in speech processingrdquo inProceedings of the IEEE International Conference on AcousticsSpeech and Signal Processing (ICASSP rsquo02) vol 1 pp 73ndash76Orlando Fla USA May 2002

[12] The CASIA dataset httpwwwsinobiometricscomenglishIris20Databasesasp

[13] X He and P Shi ldquoAn efficient iris segmentation method forrecognitionrdquo in Proceedings of the 3rd International Conferenceon Advances in Patten Recognition (ICAPR rsquo05) vol 3687 ofLecture Notes in Computer Science pp 120ndash126 SpringerBath UK August 2005

[14] L Masek Recognition of human iris patterns for biometricsidentification B Eng thesis University of Western AustraliaPerth Australia 2003

[15] K Bae S Noh and J Kim ldquoIris feature extraction usingindependent component analysisrdquo in Proceedings of the 4thInternational Conference on Audio- and Video-Based BiometricPerson Authentication (AVBPA rsquo03) vol 2688 pp 1059ndash1060Guildford UK June 2003

[16] W W Boles and B Boashash ldquoA human identificationtechnique using images of the iris and wavelet transformrdquoIEEE Transactions on Signal Processing vol 46 no 4 pp 1185ndash1188 1998

[17] S C Chong A B J Teoh and D C L Ngo ldquoIrisauthentication using privatized advanced correlation filterrdquoin Proceedings of the International Conference on Advances onBiometrics (ICB rsquo06) vol 3832 of Lecture Notes in ComputerScience pp 382ndash388 Springer Hong Kong January 2006

[18] D S Jeong H-A Park K R Park and J Kim ldquoIrisrecognition in mobile phone based on adaptive Gabor filterrdquoin Proceedings of the International Conference on Advances onBiometrics (ICB rsquo06) vol 3832 of Lecture Notes in ComputerScience pp 457ndash463 Springer Hong Kong January 2006

[19] B V K Vijaya Kumar C Xie and J Thornton ldquoIrisverification using correlation filtersrdquo in Proceedings of the 4thInternational Conference Audio- and Video-Based BiometricPerson Authentication (AVBPA rsquo03) vol 2688 of Lecture Notesin Computer Science pp 697ndash705 Guildford UK June 2003

[20] E C Lee K R Park and J Kim ldquoFake iris detection by usingpurkinje imagerdquo in Proceedings of the International Conferenceon Advances on Biometrics (ICB rsquo06) vol 3832 of LectureNotes in Computer Science pp 397ndash403 Springer Hong KongJanuary 2006

[21] S Lim K Lee O Byeon and T Kim ldquoEfficient iris recog-nition through improvement of feature vector and classifierrdquoElectronics and Telecommunications Research Institute Journalvol 23 no 2 pp 61ndash70 2001

[22] X Liu K W Bowyer and P J Flynn ldquoExperiments withan improved iris segmentation algorithmrdquo in Proceedings ofthe 4th IEEE Workshop on Automatic Identification AdvancedTechnologies (AUTO ID rsquo05) pp 118ndash123 Buffalo NY USAOctober 2005

[23] X Liu K W Bowyer and P J Flynn ldquoExperimental evalua-tion of iris recognitionrdquo in Proceedings of the IEEE ComputerSociety Conference on Computer Vision and Pattern Recognition(CVPR rsquo05) vol 3 pp 158ndash165 San Diego Calif USA June2005

[24] L Ma T Tan Y Wang and D Zhang ldquoPersonal identificationbased on iris texture analysisrdquo IEEE Transactions on PatternAnalysis and Machine Intelligence vol 25 no 12 pp 1519ndash1533 2003

[25] L Ma T Tan Y Wang and D Zhang ldquoEfficient iris recogni-tion by characterizing key local variationsrdquo IEEE Transactionson Image Processing vol 13 no 6 pp 739ndash750 2004

[26] K Miyazawa K Ito T Aoki K Kobayashi and H NakajimaldquoA phase-based iris recognition algorithmrdquo in Proceedings ofthe International Conference on Advances on Biometrics (ICBrsquo06) vol 3832 of Lecture Notes in Computer Science pp 356ndash365 Springer Hong Kong January 2006

[27] T Moriyama T Kanade J Xiao and J F Cohn ldquoMeticulouslydetailed eye region model and its application to analysisof facial imagesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 28 no 5 pp 738ndash752 2006

[28] C-H Park J-J Lee M J T Smith and K-H Park ldquoIris-basedpersonal authentication using a normalized directional energyfeaturerdquo in Proceedings of the 4th International Conferenceon Audio- and Video-Based Biometric Person Authentication(AVBPA rsquo03) vol 2688 pp 224ndash232 Guildford UK June2003

[29] M B Pereira and A C P Veiga ldquoApplication of geneticalgorithms to improve the reliability of an iris recognitionsystemrdquo in Proceedings of the IEEE Workshop on MachineLearning for Signal Processing (MLSP rsquo05) pp 159ndash164Mystic Conn USA September 2005

[30] X Qiu Z Sun and T Tan ldquoGlobal texture analysis ofiris images for ethnic classificationrdquo in Proceedings of theInternational Conference on Advances on Biometrics (ICB rsquo06)vol 3832 of Lecture Notes in Computer Science pp 411ndash418Springer Hong Kong January 2006

[31] C Sanchez-Avila R Sanchez-Reillo and D de Martin-Roche ldquoIris-based biometric recognition using dyadic wavelettransformrdquo IEEE Aerospace and Electronic Systems Magazinevol 17 no 10 pp 3ndash6 2002

[32] R Sanchez-Reillo and C Sanchez-Avila ldquoIris recognition withlow template sizerdquo in Proceedings of the 3rd International


Conference on Audio- and Video-Based Biometric PersonAuthentication (AVBPA rsquo01) pp 324ndash329 Halmstad SwedenJune 2001

[33] N A Schmid M V Ketkar H Singh and B CukicldquoPerformance analysis of iris-based identification system atthe matching score levelrdquo IEEE Transactions on InformationForensics and Security vol 1 no 2 pp 154ndash168 2006

[34] D Schonberg and D Kirovski ldquoEyeCertsrdquo IEEE Transactionson Information Forensics and Security vol 1 no 2 pp 144ndash153 2006

[35] B Son H Won G Kee and Y Lee ldquoDiscriminant irisfeature and support vector machines for iris recognitionrdquo inProceedings of the International Conference on Image Processing(ICIP rsquo04) vol 2 pp 865ndash868 Singapore October 2004

[36] Z Sun T Tan and X Qiu ldquoGraph matching iris image blockswith local binary patternrdquo in Proceedings of the InternationalConference on Advances on Biometrics (ICB rsquo06) vol 3832of Lecture Notes in Computer Science pp 366ndash372 SpringerHong Kong January 2006

[37] Z Sun Y Wang T Tan and J Cui ldquoImproving iris recog-nition accuracy via cascaded classifiersrdquo IEEE Transactions onSystems Man and Cybernetics C vol 35 no 3 pp 435ndash4412005

[38] H Tan and Y-J Zhang ldquoDetecting eye blink states by trackingiris and eyelidsrdquo Pattern Recognition Letters vol 27 no 6 pp667ndash675 2006

[39] Q M Tieng and W W Boles ldquoRecognition of 2D objectcontours using the wavelet transform zero-crossing represen-tationrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 19 no 8 pp 910ndash916 1997

[40] C Tisse L Martin L Torres and M Robert ldquoPersonidentification technique using human iris recognitionrdquo inProceedings of the 15th International Conference on VisionInterface (VI rsquo02) pp 294ndash299 Calgary Canada May 2002

[41] J P Havlicek D S Harding and A C Bovik ldquoThe mutli-component AM-FM image representationrdquo IEEE Transactionson Image Processing vol 5 no 6 pp 1094ndash1100 1996

[42] T Tangsukson and J P Havlicek ldquoAM-FM image segmenta-tionrdquo in Proceedings of the International Conference on ImageProcessing (ICIP rsquo00) vol 2 pp 104ndash107 Vancouver CanadaSeptember 2000

[43] R P Wildes J C Asmuth G L Green et al ldquoA machine-vision system for iris recognitionrdquo Machine Vision andApplications vol 9 no 1 pp 1ndash8 1996

[44] A Poursaberi and B N Araabi ldquoIris recognition for par-tially occluded images methodology and sensitivity analysisrdquoEURASIP Journal on Advances in Signal Processing vol 2007Article ID 36751 12 pages 2007

[45] K Roy and P Bhattacharya ldquoIris recognition with supportvector machinesrdquo in Proceedings of the International Confer-ence on Advances on Biometrics (ICB rsquo06) vol 3832 of LectureNotes in Computer Science pp 486ndash492 Springer Hong KongJanuary 2006

[46] J-X Dong A Krzyzak and C Y Suen ldquoAn improved hand-written Chinese character recognition system using supportvector machinerdquo Pattern Recognition Letters vol 26 no 12pp 1849ndash1856 2005

[47] Y Zhu T Tan and Y Wang ldquoBiometric personal identi-fication based on iris patternsrdquo in Proceedings of the 15thInternational Conference on Pattern Recognition (ICPR rsquo00)vol 2 pp 801ndash804 Barcelona Spain September 2000

[48] L Ma Y Wang and T Tan ldquoIris recognition based onmultichannel Gabor filteringrdquo in Proceedings of the 5th Asian

Conference on Computer Vision (ACCV rsquo02) vol 1 pp 279ndash283 Melbourne Australia January 2002

[49] L Ma Y Wang and T Tan ldquoIris recognition using circularsymmetric filtersrdquo in Proceedings of the 16th InternationalConference on Pattern Recognition (ICPR rsquo02) vol 2 pp 414ndash417 Quebec City Canada August 2002

[50] L Ma Personal identification based on iris recognition PhDdissertation Institute of Automation Chinese Academy ofSciences Beijing China 2003

[51] S Bandyopadhyay S K Pal and B Aruna ldquoMultiobjectiveGAs quantitative indices and pattern classificationrdquo IEEETransactions on Systems Man and Cybernetics B vol 34 no5 pp 2088ndash2099 2004

[52] L S Oliveira R Sabourin F Bortolozzi and C Y SuenldquoFeature selection using multiobjective genetic algorithmsfor handwritten digit recognitionrdquo in Proceedings of theInternational Conference on Pattern Recognition (ICPR rsquo02)vol 1 pp 568ndash571 Quebec City Canada August 2002

[53] K Deb Multiobjective Optimization Using Evolutionary Algo-rithms John Wiley amp Sons West Sussex UK 2004

[54] D H Ballard ldquoGeneralized Hough transform to detectarbitrary patternsrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 13 no 2 pp 111ndash122 1981

[55] P Hajela and C-Y Lin ldquoGenetic search strategies in multicri-terion optimal designrdquo Structural Optimization vol 4 no 2pp 99ndash107 1992

[56] H Gu Z Gao and F Wu ldquoSelection of optimal featuresfor iris recognitionrdquo in Proceedings of the 2nd InternationalSymposium on Neural Networks (ISNN rsquo05) vol 3497 ofLecture Notes in Computer Science pp 81ndash86 SpringerChongqing China May-June 2005

[57] R O Duda P E Hart and D G Stork Pattern RecognitionJohn Wiley amp Sons New York NY USA 2nd edition 2001

[58] httpwwwcsientuedutwsimcjlinlibsvm

INTRODUCTION

Main contributions

PROPOSED APPROACH THE MAIN STEPS

BACKGROUND

Related work

Rubber sheet model for unwrapping

Multiobjective optimization using genetic algorithms

IRIS IMAGE PREPROCESSING

Irispupil localization

Collarette boundary localization

Eyelids eyelashes and noise detection

Normalization and enhancement

FEATURE EXTRACTION AND ENCODING

Gabor wavelets

FEATURE SUBSET SELECTION USING MOGA

MULTICLASS ASYMMETRICAL SUPPORT VECTOR MACHINES AS IRIS PATTERN CLASSIFIERS

SVM parameters tuning

RESULTS

Performance evaluation of the proposed method

Comparison with existing methods

Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References


(a) (b) (c)

(d) (e) (f)

Figure 1 Samples of iris images from CASIA [12] and ICE [8]datasets

The rest of this paper is organized as follows In Section 2we provide a brief description of our proposed approachIn Section 3 we describe the related work and some rele-vant background Descriptions of iris image preprocessingfeature extraction and encoding are given in Sections 4and 5 respectively Section 6 presents the feature selectionstrategy and Section 7 describes the classification process ofiris patterns Experimental results comparisons with othermethods and discussions are reported in Section 8 Section 9concludes the paper

2 PROPOSED APPROACH THE MAIN STEPS

Figure 2 illustrates the main steps of our proposed approachFirst the imagepreprocessing step performs the localizationof the pupil detects the iris boundary and isolates thecollarette region which is regarded as one of the mostimportant areas of the iris complex pattern The collaretteregion is less sensitive to the pupil dilation and usuallyunaffected by the eyelids and the eyelashes [13] We alsodetect the eyelids and the eyelashes which are the mainsources of the possible occlusion In order to achieve theinvariance to the translation and the scale the isolatedannular collarette area is transformed to a rectangular blockof fixed dimension and then the normalized image isenhanced The discriminating features are extracted fromthe transformed image and the extracted features are usedto train the SVM The optimal features subsetis selectedusing MOGA to increase the matching accuracy based onthe recognition performance of the SVM The parametersof the SVM are tuned to improve the overall generaliza-tion performance The traditional SVM is modified to anasymmetrical SVM and it is applied for the iris patternclassification to treat the cases of false accept or false rejectdifferently The classification accuracy of the proposed SVMis also compared with the feedforward neural network byusing the backpropagation (FFBP) the feedforward neuralnetwork by using the Levenberg-Marquardt rule (FFLM)the k-nearest neighbor (k-NN) and the Hamming and theMahalanobis distances

3 BACKGROUND

31 Related work

The usage of iris patterns for the personal identificationbegan in the late 19th century however the major investi-gations on iris recognition were started in the last decadeIn [15] the iris signals were projected into a bank of basisvectors derived by the independent component analysisand the resulting projection coefficients were quantized asfeatures A prototype was proposed in [16] to develop a1D representation of the gray-level profiles of the iris In[17] biometrics based on the concealment of the randomkernels and the iris images to synthesize a minimumaverage correlation energy filter for iris authentication wereformulated In [5ndash7] the multiscale Gabor filters were usedto demodulate the texture phase structure information ofthe iris In [13] an iris segmentation method was proposedbased on the crossed chord theorem and the collarette areaIn [18] iris recognition technology was applied in mobilephones In [19] correlation filters were utilized to measurethe consistency of the iris images from the same eye Aninteresting solution to defeat the fake iris attack based onthe Purkinje image was depicted in [20] An iris image wasdecomposed in [21] into four levels by using the 2D Haarwavelet transform the fourth-level high-frequency informa-tion was quantized to form an 87-bit code and a modifiedcompetitive learning neural network (LVQ) was adoptedfor classification In [22] a modification to the Houghtransform was made to improve the iris segmentation andan eyelid detection technique was used where each eyelidwas modeled as two straight lines A matching method wasimplemented in [23] and its performance was evaluated ona large dataset

In [24] a personal identification method based onthe iris texture analysis was described An algorithm wasproposed for iris recognition by characterizing the key localvariations in [25] A phase-based iris recognition algorithmwas proposed in [26] where the phase components wereused in 2D discrete Fourier transform of iris image with asimple matching strategy In [27] a system was proposedthat is capable of a detailed analysis of the eye region imagesin terms of the position of the iris degree of the eyelidopening and the shape the complexity and the textureof the eyelids A directional filter bank was used in [28]to decompose an iris image into eight directional subbandoutputs the normalized directional energy was extracted asfeatures and iris matching was performed by computingthe Euclidean distance between the input and the templatefeature vectors In [29] the basis of genetic algorithms wasapplied to develop a technique to improve the performanceof an iris recognition system In [30] the global textureinformation of iris images was used for ethnic classificationThe iris representation method of [16] was further developedin [31] to use the different similarity measures for matchingThe iris recognition algorithm described in [32] exploitedthe integrodifferential operators to detect the inner and outerboundaries of iris Gabor filters to extract the unique binaryvectors constituting the iris code and a statistical matcher



Iris imagePupillary



isolation


Normalization



selection


extraction

Normalizedimage










0 + v20)





(2)




























Proposed approach


Asymmetrical SVM



hRe Im = sgnRe Im

intρ

intempty


(3)





x

z

y

(a)

x

z

y

(b)



G( f ) = exp

(minus(log

(f f0

))2

2(log(σ f0

))2

) (4)





with






















Collaretteboundary

Collarette area

(a)



(b)


(a) (b) (c)

(d) (e) (f)







(I)

(a) (b) (c)

(d) (e) (f)

(II)

(a) (b) (c)

(d) (e) (f)





(I)

θ

r

(a)

(b)



(II)

(a)

(c)

(b)

(d)




51 Gabor wavelets








Original 1-D signal


Realresponse

Imaginaryresponse

(a)

Im

Re

[0 1] [1 1]

[0 0] [1 0]

(b)

1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0

(c)


111 1 000 10 1010 1 0 0001 11 10 0



classifier





SVM classifier

Selected features



two objectives

















2d = 2w (10)



yi(




Nsumi=1

αi(yi(


) (12)




yiαi(

xmiddotxi)

+ b = 0 (13)



yi(



12w2 + C

sumi

ξi subject to yi(


(15)



f (x) =Nsumi=1

yiαiK(

xmiddotxi)

+ b (16)




f (x) =Nsumi=1

yipropiK(

x xi)

+ b + g (18)











CM =

⎛⎜⎜⎜⎜⎝




⎞⎟⎟⎟⎟⎠ (19)


erri =nsum

j=1 j = imi j (20)


V =I⋃

k=1

wj | mi j = 0

(21)


8 RESULTS







30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References



Iris imagePupillary



isolation


Normalization



selection


extraction

Normalizedimage










0 + v20)





(2)




























Proposed approach


Asymmetrical SVM



hRe Im = sgnRe Im

intρ

intempty


(3)





x

z

y

(a)

x

z

y

(b)



G( f ) = exp

(minus(log

(f f0

))2

2(log(σ f0

))2

) (4)





with






















Collaretteboundary

Collarette area

(a)



(b)


(a) (b) (c)

(d) (e) (f)







(I)

(a) (b) (c)

(d) (e) (f)

(II)

(a) (b) (c)

(d) (e) (f)





(I)

θ

r

(a)

(b)



(II)

(a)

(c)

(b)

(d)




51 Gabor wavelets








Original 1-D signal


Realresponse

Imaginaryresponse

(a)

Im

Re

[0 1] [1 1]

[0 0] [1 0]

(b)

1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0

(c)


111 1 000 10 1010 1 0 0001 11 10 0



classifier





SVM classifier

Selected features



two objectives

















2d = 2w (10)



yi(




Nsumi=1

αi(yi(


) (12)




yiαi(

xmiddotxi)

+ b = 0 (13)



yi(



12w2 + C

sumi

ξi subject to yi(


(15)



f (x) =Nsumi=1

yiαiK(

xmiddotxi)

+ b (16)




f (x) =Nsumi=1

yipropiK(

x xi)

+ b + g (18)











CM =

⎛⎜⎜⎜⎜⎝




⎞⎟⎟⎟⎟⎠ (19)


erri =nsum

j=1 j = imi j (20)


V =I⋃

k=1

wj | mi j = 0

(21)


8 RESULTS







30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References




























Proposed approach


Asymmetrical SVM



hRe Im = sgnRe Im

intρ

intempty


(3)





x

z

y

(a)

x

z

y

(b)



G( f ) = exp

(minus(log

(f f0

))2

2(log(σ f0

))2

) (4)





with






















Collaretteboundary

Collarette area

(a)



(b)


(a) (b) (c)

(d) (e) (f)







(I)

(a) (b) (c)

(d) (e) (f)

(II)

(a) (b) (c)

(d) (e) (f)





(I)

θ

r

(a)

(b)



(II)

(a)

(c)

(b)

(d)




51 Gabor wavelets








Original 1-D signal


Realresponse

Imaginaryresponse

(a)

Im

Re

[0 1] [1 1]

[0 0] [1 0]

(b)

1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0

(c)


111 1 000 10 1010 1 0 0001 11 10 0



classifier





SVM classifier

Selected features



two objectives

















2d = 2w (10)



yi(




Nsumi=1

αi(yi(


) (12)




yiαi(

xmiddotxi)

+ b = 0 (13)



yi(



12w2 + C

sumi

ξi subject to yi(


(15)



f (x) =Nsumi=1

yiαiK(

xmiddotxi)

+ b (16)




f (x) =Nsumi=1

yipropiK(

x xi)

+ b + g (18)











CM =

⎛⎜⎜⎜⎜⎝




⎞⎟⎟⎟⎟⎠ (19)


erri =nsum

j=1 j = imi j (20)


V =I⋃

k=1

wj | mi j = 0

(21)


8 RESULTS







30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References


x

z

y

(a)

x

z

y

(b)



G( f ) = exp

(minus(log

(f f0

))2

2(log(σ f0

))2

) (4)





with






















Collaretteboundary

Collarette area

(a)



(b)


(a) (b) (c)

(d) (e) (f)







(I)

(a) (b) (c)

(d) (e) (f)

(II)

(a) (b) (c)

(d) (e) (f)





(I)

θ

r

(a)

(b)



(II)

(a)

(c)

(b)

(d)




51 Gabor wavelets








Original 1-D signal


Realresponse

Imaginaryresponse

(a)

Im

Re

[0 1] [1 1]

[0 0] [1 0]

(b)

1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0

(c)


111 1 000 10 1010 1 0 0001 11 10 0



classifier





SVM classifier

Selected features



two objectives

















2d = 2w (10)



yi(




Nsumi=1

αi(yi(


) (12)




yiαi(

xmiddotxi)

+ b = 0 (13)



yi(



12w2 + C

sumi

ξi subject to yi(


(15)



f (x) =Nsumi=1

yiαiK(

xmiddotxi)

+ b (16)




f (x) =Nsumi=1

yipropiK(

x xi)

+ b + g (18)











CM =

⎛⎜⎜⎜⎜⎝




⎞⎟⎟⎟⎟⎠ (19)


erri =nsum

j=1 j = imi j (20)


V =I⋃

k=1

wj | mi j = 0

(21)


8 RESULTS







30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References

















Collaretteboundary

Collarette area

(a)



(b)


(a) (b) (c)

(d) (e) (f)







(I)

(a) (b) (c)

(d) (e) (f)

(II)

(a) (b) (c)

(d) (e) (f)





(I)

θ

r

(a)

(b)



(II)

(a)

(c)

(b)

(d)




51 Gabor wavelets








Original 1-D signal


Realresponse

Imaginaryresponse

(a)

Im

Re

[0 1] [1 1]

[0 0] [1 0]

(b)

1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0

(c)


111 1 000 10 1010 1 0 0001 11 10 0



classifier





SVM classifier

Selected features



two objectives

















2d = 2w (10)



yi(




Nsumi=1

αi(yi(


) (12)




yiαi(

xmiddotxi)

+ b = 0 (13)



yi(



12w2 + C

sumi

ξi subject to yi(


(15)



f (x) =Nsumi=1

yiαiK(

xmiddotxi)

+ b (16)




f (x) =Nsumi=1

yipropiK(

x xi)

+ b + g (18)











CM =

⎛⎜⎜⎜⎜⎝




⎞⎟⎟⎟⎟⎠ (19)


erri =nsum

j=1 j = imi j (20)


V =I⋃

k=1

wj | mi j = 0

(21)


8 RESULTS







30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References


(I)

θ

r

(a)

(b)



(II)

(a)

(c)

(b)

(d)




51 Gabor wavelets








Original 1-D signal


Realresponse

Imaginaryresponse

(a)

Im

Re

[0 1] [1 1]

[0 0] [1 0]

(b)

1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0

(c)


111 1 000 10 1010 1 0 0001 11 10 0



classifier





SVM classifier

Selected features



two objectives

















2d = 2w (10)



yi(




Nsumi=1

αi(yi(


) (12)




yiαi(

xmiddotxi)

+ b = 0 (13)



yi(



12w2 + C

sumi

ξi subject to yi(


(15)



f (x) =Nsumi=1

yiαiK(

xmiddotxi)

+ b (16)




f (x) =Nsumi=1

yipropiK(

x xi)

+ b + g (18)











CM =

⎛⎜⎜⎜⎜⎝




⎞⎟⎟⎟⎟⎠ (19)


erri =nsum

j=1 j = imi j (20)


V =I⋃

k=1

wj | mi j = 0

(21)


8 RESULTS







30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References



Original 1-D signal


Realresponse

Imaginaryresponse

(a)

Im

Re

[0 1] [1 1]

[0 0] [1 0]

(b)

1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0

(c)


111 1 000 10 1010 1 0 0001 11 10 0



classifier





SVM classifier

Selected features



two objectives

















2d = 2w (10)



yi(




Nsumi=1

αi(yi(


) (12)




yiαi(

xmiddotxi)

+ b = 0 (13)



yi(



12w2 + C

sumi

ξi subject to yi(


(15)



f (x) =Nsumi=1

yiαiK(

xmiddotxi)

+ b (16)




f (x) =Nsumi=1

yipropiK(

x xi)

+ b + g (18)











CM =

⎛⎜⎜⎜⎜⎝




⎞⎟⎟⎟⎟⎠ (19)


erri =nsum

j=1 j = imi j (20)


V =I⋃

k=1

wj | mi j = 0

(21)


8 RESULTS







30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References









2d = 2w (10)



yi(




Nsumi=1

αi(yi(


) (12)




yiαi(

xmiddotxi)

+ b = 0 (13)



yi(



12w2 + C

sumi

ξi subject to yi(


(15)



f (x) =Nsumi=1

yiαiK(

xmiddotxi)

+ b (16)




f (x) =Nsumi=1

yipropiK(

x xi)

+ b + g (18)











CM =

⎛⎜⎜⎜⎜⎝




⎞⎟⎟⎟⎟⎠ (19)


erri =nsum

j=1 j = imi j (20)


V =I⋃

k=1

wj | mi j = 0

(21)


8 RESULTS







30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References




CM =

⎛⎜⎜⎜⎜⎝




⎞⎟⎟⎟⎟⎠ (19)


erri =nsum

j=1 j = imi j (20)


V =I⋃

k=1

wj | mi j = 0

(21)


8 RESULTS







30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References


30252015105


35

4

45

5

55

6

65

7

Mat

chin

ger

ror

()

(a)

30252015105


0

05

1

15

2

25

3

35

4

45

5

Mat

chin

ger

ror

rate

()

(b)








1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References


1081009080706050403020105

Number of classes

SVMFFBP

FFLMk-NN

95

955

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(a)

1209070503010

Number of classes

SVMFFLM

FFBPk-NN

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


108100908070605040302010

Number of classes

SVMMDCFFBP

FFLMk-NN

55

60

65

70

75

80

85

Cla

ssifi

cati

onac

cura

cy(

)

(a)

120100806040200

Number of classes

SVMFFBPFFLM

MDCk-NN

96

965

97

975

98

985

99

995

100

Cla

ssifi

cati

onac

cura

cy(

)

(b)


Table 2


Polynomial 911 952

RBF 943 974

Sigmoid 912 956

Table 3


FFBP FFLM FFBP FFLM




times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References


times102964824126075

Feature dimension

SVMFFLMFFBP

HDk-NN

90

91

92

93

94

95

96

97

98

99

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension

SVMFFBPFFLM

HDk-NN

70

75

80

85

90

95

100

Rec

ogn

itio

nac

cura

cy(

)

(b)


15014012010080604020

Generation

995

9555

996

9965

997

9975

Acc

ura

cy(

)

(a)

22020018016014012010080604020

Generation

945

95

955

96

965

97

Acc

ura

cy(

)

(b)






150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References


150140120100806040205

Generation


0

2

4

6

8

10

12

14

16

Fitn

ess

valu

es(

)

(a)

220200180160140120100806040205

Generation


2

4

6

8

10

12

14

16

18

20

Fitn

ess

valu

es(

)

(b)


times102964824126075

Feature dimension


95

955

96

965

97

975

98

985

99

995

100

Rec

ogn

itio

nac

cura

cy(

)

(a)

times102964824126075

Feature dimension


90

91

92

93

94

95

96

97

Rec

ogn

itio

nac

cura

cy(

)

(b)


Table 4











70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References





70

75

80

85

90

95

100

Gen

uin

eac

cept

rate

()


10010minus1



100

101

Mat

chin

ger

ror

()












Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References







Ma et al [24] 9960 029

Ma et al [25] 100 007

Liu et al [22] 9708 179












Ma et al [25] 2442 65 2507 mdash














83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References







83 Discussions










9 CONCLUSIONS


ACKNOWLEDGMENTS



REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References


REFERENCES






























































INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References






























INTRODUCTION

Main contributions


BACKGROUND

Related work









Gabor wavelets




RESULTS



Discussions

CONCLUSIONS

ACKNOWLEDGMENTS

References

Optimal Features Subset Selection and Classification for ... · PDF fileWe present a new iris...

Documents

Transcript of Optimal Features Subset Selection and Classification for ... · PDF fileWe present a new iris...