AN EFFICIENT FACE RECOGNITION SYSTEM USING FACE ... · AN EFFICIENT FACE RECOGNITION SYSTEM USING...

AN EFFICIENT FACERECOGNITION SYSTEM USING

FACE RECOGNITION ALGORITHMSPCA, LDA AND ICA

Chatakunta Praveen Kumar1, S J Sowjanya2, R M Noorullah3

Assistant professor,Department of Computer Science and Engineering

Institute Of Aeronautical EngineeringHyderabad, India

[email protected]@gmail.com

[email protected]

July 12, 2018

Abstract

The variation in pose is one of the important param-eters to be considered to build a reliable face recognitionsystem. We have developed a face database named as FaceDatabase across Pose (FDP) simulating the variation in thepose. FDP has 500 people face samples recorded at five dif-ferent head aspects. Further, there are seven sample for eachhead aspect making 35 face samples of each person. For 125people there are additional three sample with varying ex-pression. All the images of a person are recorded in a singlesession. Uniform background is maintained and sunlight isused as a light source. We have evaluated Face RecognitionAlgorithms (FRAs) that uses PCA, LDA and ICA to repre-sent faces. The FRAs are evaluated on frontal faces and sidefaces. The FRAs are also evaluated on dataset with frontal

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International Journal of Pure and Applied MathematicsVolume 120 No. 6 2018, 2407-2433ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

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and side faces merged. We have proposed to apply ICA inthe space defined by LDA. From our experimental results,the recognition rate of FRAs is more on side faces than onfrontal faces. We have also compared the recognition rateof FRAs on using. Here we make use of cosine similarityand Euclidean distance as comparison matrices The PCAand LDA based FRAs give the better recognition rate forEuclidean distance than cosine similarity measure. We haveevaluated FRAs on dataset of 153 people with varying ex-pression. Using architecture-2, ICA in the space defined byLDA has outperformed all other FRAs.

Keywords: database across pose, PCA, LDA, FRA,ICA.

1 INTRODUCTION

Face recognition has numerous applications in areas such as au-thentication and law enforcement. Face recognition is a biometricwith an advantage that the person may not be required to do anyaction and also it is unobtrusive. We have implemented three vari-ants of Face Recognition Algorithms (FRAs), Principal ComponentAnalysis (PCA) [1], Linear Discriminant Analysis (LDA) [2] and In-dependent Component Analysis (ICA) [3]. We have evaluated thesethree algorithms on their rate of recognition by the varying head as-pect of persons. Towards this end, we have prepared a face databasecalled Face Database across Pose (FDP). FDP has 500 people facesrecorded in five varying head aspects, in that 125 people of themhave recorded in four varying expressions as well.A Face Recognition System

face recognition system is generally categorized into 4 parts asshown in figure 1:Face Detection, Face Normalization, Face Rep-resentation and Face Classification. Face Detection: In this stagethe face will be located and segmented out from the input image.Face Normalization: Based on the underlying approach for facerecognition, the segmented face part is rotated, scaled, aligned orprocessed as required.

Face Representation: In this stage the normalized face is repre-sented such that it is easy to classify the face to its respective class.The face representation is also known as face feature extraction.

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Figure 1: Face Recognition System

Face Classification: In this stage the input face feature is classifiedto its respective class with the help of a knowledge base and sim-ilarity measure. The knowledge base consists of knowledge (facefeatures) of each class based on ground truth information. Similar-ity measures are used to compare the input face feature with theknowledge base.Face Recognition Challenges

Face recognition problem can be further revised as the processof verifying or identifying the face residing in the digital imagecaptured from the real world. The conditions such as pose, illu-mination, expression and aging etc., impose random variation inthe pixel values that constitute face object. Such is the case; a

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method to derive a useful face representation given a face image isindeed a great challenge. Although face recognition Evaluation ofFace Recognition Algorithms by Varying Pose is a great challenge,the steps prior to face recognition are also not easy. The accuratedetection and segmentation of face part in the digital image is onemore challenge.

2 METHODS

We humans recognize known faces so quickly that we don’t evenrealize how we do it. Thus, this problem of face recognition hasattracted researchers from many fields namely computer graphics,psychology, computer vision and pattern recognition. Because ofthis literature on face recognition is ample and differing. A detailedsurvey on face recognition can be found in [4]. 2D face recognitionsystem is divided into 3 sections: Analytic, Holistic and HybridmethodsAnalytic Methods

In this method local features such as the nose, eyes and mouthand their location are extracted, distance and angles between theselocal feature are given as classifiers. Earlier works [5] have used theHidden Markov Model-(HMM) based methods that cover entireface features like forehead, eyes, nose, mouth and chin[7], in earliermethod width of head , the distance between eyes and distance fromeyes to the mouth etc are calculated. Lades et al proposed a graphstructure method called Dynamic Link Architecture, this methoduses the Gabor wavelets for recognition technique, this method ismost successful.Holistic Methods

In this many face recognition methods have been proposed basedon Principal Component Analysis, these methods uses appearancebased approaches where it takes whole image as the raw input forface recognition system. Kirby and Sirovich [10] proposed a methodfor successful reconstruction of faces using only few Eigen vectorscalled Principal Components (PCs). Later, Turk and Pentland [1]extended the work by Kirby and Sirovich to recognize human faces.LDA defines a projection which gives small within class scatter andlarge between class scatter. LDA requires a large training sample

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set for good generalization, which is usually not available for facerecognition applications. To address such small sample size prob-lems, Zhao et al [11] perform PCA to reduce feature dimensionbefore LDA projection. Meanwhile, Barlett et al [3] have adoptedIndependent Component Analysis (ICA) based projection of faceinto feature space, which uses higher order statistics of image pix-els. Nonlinear techniques for face recognition include, using neuralnetworks [12] [13] to classify global facial features and using SVMbinary classifier to classify inter-person and intra-person differenceclasses [14]. SVM binary classifier are sensitive to translation, ro-tation and pose changes, even this SVM binary classifier work wellfor frontal view face images[15].Hybrid Methods

Based on the observation that we humans use both local fea-tures and this whole appearance of the face to recognizing it severalhybrid methods have been proposed. The hybrid method combinesboth local and global approaches to recognize a face. One of theearly works is Pentlands modular Eigen faces [16], in which Eigenvectors were derived for facial local features such as eyes, nose, andmouth. Approaches proposed in [17] i e Active Appearance Modeland Active Shape Model are very well know, where ASM and AAMlearned from test images are used to generate shape and texture pa-rameters of the new face image, which are fed to a classifier.Previous Works and Proposed Work

The face recognition algorithms developed based on PCA [1]were evaluated mostly on face databases of frontal pose. TheLDA based algorithms [2] [11] were also evaluated on some lo-cal databases which consist of almost all of the frontal pose face.Bartlett et al [3] adopted ICA approach to 2D-face recognition andcomparative study of PCA and ICA has been made using FERETdatabase. Later in 2004 Kresimir Delac et al [18] made a compara-tive study of PCA, LDA and ICA based face recognition algorithmson FERET dataset. Performance evaluation of holistic methods onAverage Face database is conducted in [19], where the averagingprocess is done using pose-varied synthetic images generated froma 3D face database. Arathi Kothari et al [20] conducted perfor-mance evaluation of Eigenface and Fisherface approaches againsttwo constraints: pose and the size of training data. But the rota-tion of face is in 2D space. Pinar Santemiz et al [21] give a survey

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on evaluation of FRAs on side face, recognition and have mentionedsome of the databases containing side faces. In the literature thereis no clear documentation of evaluation of appearance based FRAsusing PCA, LDA and ICA across pose. The non-availability of theface database consisting sample at different head aspect is one moreconcern. Our goal is to evaluate the performance of PCA, LDAand ICA based approaches on the dataset containing face sampleat varying head aspect. Towards this end we have developed a facedatabase named as Face Database across Pose (FDP).

3 STATISTICAL APPROACHES TO

RECOGNIZE FACE

the three well know statistical approaches like Principal ComponentAnalysis (PCA), Linear Discriminant Analysis (LDA) and Indepen-dent Component Analysis (ICA) are used to better characterize theunderlying dynamics in the dataset of face images.Principal Component Analysis (PCA)

The PCA on a dataset X gives new m orthonormal basis suchthat Y the projection of dataset X on to this new space is uncorre-lated. In mathematical terms, let P be a matrix with orthonormalvectors as its columns. Then,

Y = PX (1)

The goal of PCA is to derive P such that

CV = Y Y T (2)

Cx is diagonal. One solution to this problem is Eigen vectordecomposition.Eigen values and Eigen vectors:

Eigen values and Eigen vectors can be calculated for all sym-metric matrices. Now let

CX = XXT (3)

is an outer covariance matrix of X and is symmetric. Eigenvector decomposition on Cx gives m orthonormal vectors in the

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columns of matrix E and corresponding Eigen values in the primarydiagonal of matrix V such that

CX = EV ET (4)

Let P = ET then

Y = ETX (5)

CY = ETX(ETX)T

CY = ETXXTE

CY = ETCXE

CY = ETEV ETE

CY = V (6)

thus, the projection of dataset X on ET will be uncorrelated.Eigen value and Eigen vector comes in a pair. That is, for a sym-metric matrix of size m x m there are m Eigen value and Eigenvector pairs. Eigen values are along primary diagonal of V and cor-responding Eigen vectors are the columns of E in the same order asEigen values. The variance of dataset X along different dimensionsis quantized in Eigen values and the direction of these variances inm-dimensional space is indicated by Eigen vectors. Based on the as-sumption that, the basis along which the dataset has larger varianceis of more significance, the Eigen vectors in the columns of E can beranked based on the diagonal values of V with higher values indi-cating higher rank for corresponding Eigen vectors. One can retainfirst few Eigen vectors as a basis there by retaining most of the vari-ance in original data distribution. This argument is strengthenedby the assumption that Signal to Noise Ratio (SNR) is quantized

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by variance and information along the basis with smaller varianceis considered as noise [22].Linear Discriminant Analysis (LDA)

The goal of LDA is to derive a new basis to represent data wereclass discrimination is maximized. The idea given by Fisher [23] isto derive a basis that increases the ratio between class scatter andwithin class scatter for a given dataset. The LDA on to a datasetX gives a new orthonormal basis such that class discrimination inY, the projection of X on to this new basis, is maximized.

Consider a set of N samples where each sample is a trial of anexperiment E.

X = [S1, S2, .SN ]

And assume each sample belongs to one of C classesX1, X2, ...XC .Let µ be the mean sample of samples in X. Then the measure ofbetween class scatter can be defined as

And the measure of within class scatter can be defined as

Where, is the mean sample of class Xi and Ni is the number ofsamples in class Xi. Let W be a matrix with orthonormal vectorsas its columns. Then Y=WX . The goal of LDA is to derive Wthat maximize criterion

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This criterion is known as ’fisher criterion’ and the optimum Wis given as

This can be brought down to a generalized Eigen value problemas

Where, W is the matrix containing vectors in its columns thatare orthogonal to each other and V is a diagonal matrix. W and Vcan be obtained by performing Eigen value decomposition on thematrix L = SB/SW . Since, there exists C classes the rank of SB

is C and there exist only C-1 significant Eigen vectors. The Eigenvector with maximum Eigen value has more discriminative power.Independent Component Analysis (ICA)

Independent Component Analysis is the abstrtaction of Prin-cipal Component Analysis. Let, X=[s1, s2.....sm] where si is ann-dimensional trial of a random experiment E and m is the numberof trials of experiment E. The projection of samples in X on to thespace defined by PCA will remove pair wise dependencies amongPCA coefficients. High order dependencies still exist in the jointdistribution of PCA coefficients. Barlow [24] has argued that suchdependencies provide knowledge and ICA try to find a linear trans-formation W where these dependencies are distant into individualcomponents (ICs).Comparison of PCA, LDA and ICA

The Figure 2. gives the inference about the orientation of fea-ture vectors derived by PCA, LDA and ICA. The orientation of themost significant vector obtained by PCA is along maximum over-all variation. The orientation of most significant vector is in thedirection where the ratio of scatter between classes to within classscatter is maximized. The independent components derived by ICAare directed towards statistical dependence between samples.

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PCA, LDA and ICA to Represent FacesThe three statistical approaches discussed in the previous sec-

tion can be used to represent the face. This section explains the ar-chitecture that use statistical methods to represent the face. Thatis, images are considered as vectors in a high dimensional space.The dimensionality is equal to the number of pixels in the image.Thus all the images used in these architecture should be resizedto the same dimensions. After resizing, images are organized ascolumn vectors by arranging image matrix columns one below theother. In other words , images are reshaped in to size (No rows *No columns)*1.

Figure 2: Two class problem to compare PCA, LDA and ICA

4 ALGORITHMS

Algorithm for ICA1step 1: Call load img function to load train images to columns ofmatrix C.step 2: calculate cov=CT *C.step 3: call built in function [E, V]=eig(cov).step 4: calculate R=ET *C. Retain most significant Eigen vectorsin the row of X.step 5: call[W , Wz] = runica(X).step 6: calculate F=R inv(W*Wz)

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step 7: call load img function to load train images to columns ofmatrix Ctest..step 8: calculate Rtest = ET ∗ Ctest.step 9: calculate Ftest = Rtest ∗ inv(W ∗WZ).step 10: call recog rate = eucdis(F, Ftest) function to find theRecognition rate.Algorithm for ICA2step 1: Call load img function to load train images to columns ofmatrix C.step 2: calculate cov=CT *C.step 3: call built in function [E, V]=eig(cov).step 4: calculate R=ET *C. Retain most significant Eigen vectorsin the row of R.step 5: call[W , Wz]=runica(R).step 6: calculate F=(R *W*Wz)step 7: call load img function to load train images to columns ofmatrix Ctest..step 8: calculate Rtest=E

T ∗ Ctest.step 9: calculate Ftest = (Rtest ∗W ∗WZ).step 10: call recog rate=euc dis(F , Ftest)fucntion to find the Recog-nition rate.Algorithm for LDAICA1step 1: Call load img function to load train images to columns ofmatrix C.step 2: Perform LDA on matrix to get LDs in the columns of E.step 3: calculate R=ET *C. Retain most significant LDs in the rowof X.step 4: call[W,Wz]=runica(R).step 5: calculate F=R *inv(W * Wz).step 6: call load img function to load train images to columns ofmatrix Ctest.step 7: calculate Rtest = ET ∗ Ctest.step 8: calculate Ftest = Rtest ∗ inv(W ∗WZ).step 9: call recog rate=euc dis(F , Ftest)function to find the Recog-nition rate.Algorithm for LDAICA2step 1: Call load img function to load train images to columns ofmatrix C.step 2: Perform LDA on matrix C to get L.Ds in the columns of E

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step 3: calculate E=RT *C, retain most significant LDs coefficientsin the row of R.step 4: call[W , Wz]=runica(R)step 5: calculate F=(R *W*Wz)step 6: call load img function to load train images to columns ofmatrix Ctest.step 7: calculate Rtest = ET ∗ Ctest.step 8: calculate Ftest = (Rtest ∗W ∗WZ).step 9: call recog rate=euc dis(F , Ftest)function to find the Recog-nition rate.Algorithm for runica functionstep 1: Function[w, wz]=runica(X)step 2: Call[Wz]=sphere(X)step 3: Initialize W to identity n x n matrixstep 4: Initialize I to identity n x n matrixstep 5: Initialize block-size B to 50 and learning ratestep 6: Initialize learning rate L to 0.005 for first 1000 iterationsand decrement by 0.001 for every 200 iterations thereafterstep 7: For i=1 to 1600 dostep 8: For each block XB of columns of X of size B dostep 9:

step 10: Endstep 11: Endstep 12: return W and Wz.step 13: EndAlgorithm for euc dis functionstep 1: Function Recograte = euc dis(F, Ftest)step 2: train=RT

step 3: test= RTr est

step 4: For each image coefficients testi in the columns of test dostep 5: For each image coefficients trainj in the columns of train dostep 6: dist(j,i)=dist(j,i)+(trainj − testi)

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step 7: Endstep 8:

step 9: Endstep 10: Initialise success=0step 11: For each test image i dostep 12: Find row position posj of the smallest value in the columni of diststep 13: Round trainlabel = posj/trainpop to ceilingstep 14: Round testlabel = i/testpop to ceilingstep 15: If testlabel == trainlabel dostep 16: sucess=sucess+1step 17: Endstep 18: Recograte = sucess/testpopstep 19: return Recogratestep 20: End.

5 RESULTS

The experimental design and gives the results obtained for varioustest cases. All the FRAs were executed on sub-database of FDPcontaining 469 subjects for not having enough samples for 31 sub-jects out of 500. This sub-database contains images with the onlyface part extracted and all the images are gray scale images resizedto dimension 46 56. The next section outlines the setup made toevaluate the FRAs.In set Front there are seven samples for eachperson taken at the frontal head aspect. In the set L1L2 samplesfrom head aspect left1 and left2 are combined together into onegroup. The same explanation applies for set R1R2, where headaspects are right1 and right2. In set LFR the samples from headaspect front, left1, left2, right1 and right2 are combined togetherinto a single group. All the FRAs wereexecuted independently onthese datasets.

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Evaluation of FRAs across DatasetsCase 1: Evaluation of PCA based FRA on different datasets

This test case gives the average recognition rate of PCA basedFRA on all the datasets given in the table 5.1. The Figure 3 plotsthe average recognition rate of this FRA with the varying numberof top PCs retainedCase 2: Evaluation of LDA based FRA on different datasets

This test case gives the average recognition rate of LDA basedFRA on all the datasets given in the table 1. The Figure 4 plotsthe average recognition rate of this FRA with varying number oftop LDs retained.Case 3: Evaluation of ICA1 on different datasets

This test case gives the average recognition rate of ICA1 on thefour datasets mentioned in Table 1. The Figure 5 plots the averagerecognition rate of ICA1 on different datasets.

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Figure 3: Average recognition rate of PCA based FRA on differentdatasets

Figure 4: Average recognition rate of LDA based FRA on differentdatasets

Figure 5: Average recognition rate of ICA1 on different datasets

Case 4: Evaluation of ICA2 on different datasetsThis test case gives the average recognition rate of ICA2 on the

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four datasets mentioned in Table 1. The Figure 6 plots the averagerecognition rate of ICA2 on different datasets.

Figure 6: Average recognition rate of ICA2 on different datasets

Case 5: Evaluation of LDA-ICA1 on different datasetsThis test case gives the average recognition rate of LDA-ICA1

on the four datasets mentioned in Table 1. The Figure 7 plots theaverage recognition rate of LDA-ICA1on different datasets.

Figure 7: Average recognition rate of LDA-ICA1 on differentdatasets

Case 6: Evaluation of LDA-ICA2 on different datasetsThis test case gives the average recognition rate of LDA-ICA2

on the four datasets mentioned in Table 1. The Figure 8, plots theaverage recognition rate of LDA-ICA2 on different datasets.Case 7: Comparison between FRAs on dataset Front

This test case compares the average recognition rate of FRAson dataset Front.

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Figure 8: Average recognition rate of LDA-ICA2 on differentdatasets

Figure 9: comparison between PCA and LDA based FRAs ondataset Front

Figure 10: Comparison of ICA based FRAs on dataset Front

The Figure 9 compares the recognition rate of PCA and LDAbased FRAs. The Figure 10 compares the recognition rate of ICA1,

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ICA2, LDAICA1 and LDAICA2.Case 8: Comparison between FRAs on dataset L1L2

This test case compares the average recognition rate of FRAs ondataset L1L2. The Figure 11 compares the recognition rate of PCAand LDA based FRAs. The Figure 12 compares the recognition rateof ICA1, ICA2, LDAICA1 and LDAICA2.

Figure 11: comparison between PCA and LDA based FRAs ondataset L1L2

Figure 12: Comparison of ICA based FRAs on dataset L1L2

Case 9: Comparison between FRAs on dataset R1R2This test case compares the average recognition rate of FRAs on

dataset R1R2. The Figure 13 compares the recognition rate of PCAand LDA based FRAs. The Figure 14 compares the recognition rateof ICA1, ICA2, LDAICA1 and LDAICA2.Case 10: Comparison between FRAs on dataset LFR

This test case compares the average recognition rate of FRAs ondataset LFR. The Figure 15 compares the recognition rate of PCA

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Figure 13: Comparison between PCA and LDA based FRAs ondataset R1R2

Figure 14: Comparison of ICA based FRAs on dataset R1R2

and LDA based FRAs. The Figure 16 compares the recognitionrate of ICA1, ICA2, LDAICA1 and LDAICA2.

Figure 15: Comparison between PCA and LDA based FRAs ondataset LFR

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Figure 16: Comparison of ICA based FRAs on dataset LFR

Comparison of FRAs with varying ExpressionThis section gives the recognition rate of FRAs in the condition

with varying expression. All the FRAs were trained on 4 neutralexpression samples each of 153 people and 3 samples with threedifferent expressions, each of 153 people were classified using Eu-clidean distance as the similarity measure.Case 11: Comparison between FRAs with varying expres-sion ion

This test case compares the average recognition rate of FRAsby varying expression. Figure 17 compares the recognition rate ofLDA and PCA. Figure 18 compares the recognition rate of ICAbased FRAs.

Figure 17: Comparison of PCA and LDA with varying expression

Evaluation of FRAs using different similarity measuresThis section gives the comparative results for the Euclidean dis-

tance and cosine similarity measure [3] used to classify testing face

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Figure 18: Comparison of ICA based FRAs with varying expression

images. The results given in this section are the average recognitionrate of FRAs on the dataset Front described in Table 1.Case 12: Evaluation of PCA based FRA using differentsimilarity measures

The Figure 18 shows the comparative results for Euclidean dis-tance and cosine similarity measure used to classify PCA repre-sented faces.

Figure 19: Comparative results of PCA based FRA using differentsimilarity measures

Case 13: Evaluation of LDA based FRA using differentsimilarity measures

The Figure 19 shows the comparative results for Euclidean dis-tance and cosine similarity measure used to classify LDA repre-sented faces.

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Figure 20: Comparative results of LDA based FRA using differentsimilarity measures

Case 14: Evaluation of ICA based FRAs using differentsimilarity measures

The Figure 20 gives the comparative results for Euclidean dis-tance and cosine similarity measure used to classify faces repre-sented using ICA1, ICA2, LDAICA1 and LDAICA2 face recogni-tion algorithms.

Figure 21: Comparative results of LDA based FRAs using differentsimilarity measures

We have evaluated different appearance based FRAs in differentconditions like frontal faces, side view faces. We have also evalu-ated the FRAs on dataset containing merged samples from frontand side views. From our experimental results, all the FRAs wehave evaluated perform better on side viewed faces than on frontalfaces. The performance of all the FRAs is more on left orientedfaces than on frontal or right oriented faces. The individual recog-

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nition rate of PCA, LDAICA1 and LDAICA2 is almost same onboth dataset Front and dataset LFR. The individual recognitionrate of LDA, ICA1 and ICA2 is less on the dataset Front thanon dataset LFR. The newly proposed LDAICA2 has outperformedthe other three FRAs based on ICA, on side view faces whereas ondataset LFR ICA1 gives the better recognition rate than other ICAbased FRAs. From the experimental results, it is evident that forfrontal faces the recognition rate of appearance based algorithmsis lesser than results given in previous research works. The reasonfor this may be more variation in the pose at frontal head aspect,larger dataset considered and especially including side faces in adataset. From Figure 5.17 and Figure 5.18 it is evident that thePCA and LDA based FRAs gives the better recognition rate forEuclidean distance as a similarity measure than cosine similaritymeasure. From Figure 5.19, it is evident that, when compared toPCA and LDA the ICA based FRAs gives a small difference in therecognition rate for Euclidean distance and cosine similarity mea-sure. ICA1 and LDAICA1 give better recognition rate for Euclideandistance whereas ICA2 and LDAICA2 give better recognition ratefor cosine similarity measure. The newly proposed LDAICA2 hasoutperformed all the other FRAs in varying expression.

6 CONCLUSION

The field face recognition gained lot of interest, where we extractthe face features and these are appearance based face recognitionalgorithms. The performance of these algorithms on face sampleswith varying pose is not clearly reported in the literature. Towardsthis, we have evaluated appearance based algorithms using PCA,LDA and ICA approaches. From the experimental results, it can beconcluded that the appearance based algorithms are not much ro-bust to pose changes. Also, these algorithms perform relatively wellon side faces than on frontal faces in our dataset. Further, we haveproposed a modification to both the ICA architecture to exploreits performance in the space defined by LDA. The ICA based onarchitecture-2 in the space defined by LDA outperforms the otherappearance based FRAs on face samples with varying expression.We have evaluated the FRAs to observe their recognition rate for

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Euclidean distance and cosine similarity measure. The PCA, LDA,ICA1 and LDAICA1 gives better recognition rate for Euclideandistance than for cosine similarity measure.

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