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This paper proposes an efficient face recognition system which is invariant to pose. It presents a transformation to generate features of the frontal face from a given posed image of a subject. The proposed system has been tested on three databases

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An Efﬁcient Pose Invariant Face RecognitionSystem
Jeet Kumar, Aditya Nigam, Surya Prakash and Phalguni Gupta
Abstract
This paper proposes an efﬁcient face recognition system which is invariantto pose. It presents a transformation to generate features of the frontal face froma given posed image of a subject. The proposed system has been tested on threedatabases
viz.
IITK, FERET and CMU-PIE. It has been observed that it performsbetter than the existing well known system.
Key words:
Face Recognition, Pose Invariant, Linear Object Class, Principal Com-ponent Analysis, Ridge Regression
1 Introduction
The use of biometrics has been increased substantially in personal security and ac-cess control applications. Fingerprint, face, iris and voice are commonly used bio-metric traits. Among these traits, face provides a more direct, friendly and conve-nient identiﬁcation method. It is more acceptable to users compared to other in-dividual biometric traits. There are many challenges in face recognition. Some of them are due to variation in face pose angle, illumination, expression and occlusion.Recognition of faces under change in poses has proved to be a difﬁcult problem.
Jeet KumarIndian Institute of Technology Kanpur, 208016, INDIA, e-mail: jeet@iitk.ac.inAditya NigamIndian Institute of Technology Kanpur, 208016, INDIA, e-mail: naditya@iitk.ac.inP SuryaIndian Institute of Technology Kanpur, 208016, INDIA, e-mail: psurya@iitk.ac.inPhalguni GuptaIndian Institute of Technology Kanpur, 208016, INDIA, e-mail: pg@iitk.ac.in1
2 Jeet Kumar, Aditya Nigam, Surya Prakash and Phalguni Gupta
This is because of the fact that face appearance changes drastically with changes infacial pose, due to misalignment as well as hiding of many facial features.Pose Invariant face recognition refers to recognizing face images of differentposes. Rotation of face image (rotation in tilt or yaw) induces very large changesin face appearance and recognition rates fall drastically when one tries to matchimages from two different poses of same person using any well known recognitiontechnique. There is a need of a pose tolerance technique because most of the time,for each test subject there exists only one gallery image for matching which is gener-ally a frontal face. Therefore, it is necessary to generate either the frontal face imageor the frontal face features from the non-frontal face image. Human beings can eas-ily recognize faces in varying poses. This is due to the fact that human learns somekind of transformation between different posed face images with the help of his dayto day experience. There is a need to obtain such a transform through learning andﬁnally transformation is used to generate front face features.If a face recognition system does not have a good pose tolerance, then for a testsubject, it would require him to be cooperative and look directly into the cameraand face recognition would be no longer passive and non-intrusive. In a securitysystem, face image data is obtained in any arbitrary situation without the notice of subject. So, it is needed to identify non-cooperative subjects in non-controlled andless restricted environment.Therefore, pose tolerance is required for face recogni-tion to achieve its advantage of being non-intrusive over other biometric traits likeﬁngerprint, iris.This paper deals with the problem of generating features of a frontal face fromthe features of a different pose image so that it can be matched with the galleryimage’s features. There exists a linear transformation which relates feature vectorof two different posed images using the assumptions of the Linear Object Class [1].Feature vectors are obtained for the images in frontal and a non-frontal poses byPrincipal Component Analysis [2]. Since the transformation between the features islinear, a regression technique can be used to obtain the transformation which is usedto obtain frontal face features of non-frontal probe images for matching.The rest of the paper is organized as follows: Section 2 presents the related work.The proposed system is explained in section 3. Performance of the system has beendiscussed in the next section. Conclusions are presented in the last section.
2 Existing Literature
The existing pose invariant face recognition approaches can mainly be classiﬁedinto three categories: (i)Model based approaches, (ii)Appearance based approachesand (iii)3D based approaches.Model based approaches try to extract geometrical parameters measuring the fa-cial parts while the appearance based approaches use the intensity or intensity de-rived parameters such as eigenfaces coefﬁcients to recognize faces. Model basedapproaches are based on Active Appearance model [7], Active Shape model [8],
An Efﬁcient Pose Invariant Face Recognition System 3
Elastic Bunch Graph Matching (EBGM) [17] which create and deform a genericface model to ﬁt with the input image. Control parameters of the face model areused as a feature vector fed to a classiﬁer. Appearance based approaches [4], [5], [6]are based on either feature extraction using Principle Component Analysis (PCA),Gabor ﬁlters or directly using the pixel intensity value. These approaches transformeither a non-frontal image directly or its feature vector to the same pose as stored inthe database and then use some matching strategy to recognize faces. 3D based ap-proaches [9] derive a morphable face model by transforming the shape and textureof the training images into a vector space representation. New faces and expressionscan be modeled by forming linear combination of the prototypes.Most of the existing approaches suffer from some problems. Model based ap-proaches are not automatic and need manual intervention for plotting landmark onfaces. Also, model generation is very computationally intensive. Using appearancebased approaches, one needs to ﬁnd the transformation more accurately, since theconventional least square technique does not perform well in presence of multi-collinearity and heteroscedasticity. Multicollinearity arises when two or more pre-dictor variables in a multiple regression model are highly correlated. Heteroscedas-ticity arises due to variance of regression estimation error not being constant for allvalues of independent variable, that is, error term could vary for each observation.Generating 3D models is extremely computationally intensive both in terms of timeand resources. Also, it requires more than one images of each subject in differentposes.
3 Proposed System
This paper has proposed an efﬁcient pose invariant face recognition system usingPrincipal Component Analysis (PCA) and regression model. It is based on assump-tion of the Linear Object Class(LOC) [1] and also uses the modular eigenspace [3]concept. The assumptions of the LOC are:1. The transformation relating feature vectors of the given and the desired poses islinear.2. A given feature vector of a face image can be represented as a linear combinationof corresponding training vectors of its pose.Face images also lie in the linear object class category. Once this linear transformis obtained, feature vectors of different poses can be obtained from one pose usingcorresponding transformation matrix between them. Modular eigen space conceptstates that corresponding to each ”view” set, that is, pose, there exist an eigenspace.So, every face image can be written as a linear combination of basis vectors of itsown vector space.Likeanyotherbiometricsystem,itconsistsofthreemajorsteps:(i)pre-processing,(ii)feature Extraction and (iii)matching and decision. In pre-processing step, it cropsthe face image and removes noise using a 2-level haar wavelet decomposition. PCA
4 Jeet Kumar, Aditya Nigam, Surya Prakash and Phalguni Gupta
has been used to extract features from the noise free facial image. Further, for aposed facial image, it uses a transformation, which has been learned through train-ing, to convert the features of posed image into estimated features of frontal image.To learn the transformation a more robust regression technique has been proposed.Finally euclidean distance metric is used to obtain the matching score between fea-tures of two facial image. This matching technique is more relevant to practicalpurposes. This system has been tested on IITK, FERET and CMU-PIE databases.Experimental results reveal that the proposed system performs better than all well-known systems on these databases.
3.1 Preprocessing
A two-level haar wavelet decomposition on face images has been used to removenoise and unnecessary details. The haar transform applied on any image yields fourtypes of features, namely approximation, horizontal, vertical and diagonal features.Only the approximation component which is the lower frequency component is pre-served at each level. Also, helps it reduces the size of the image.
3.2 Feature Extraction
Principal Component Analysis (PCA) [2] is applied on training data sets of eachpose. Dimensionality reduction using PCA is achieved by selecting only a few basisvectors among the set of basis vectors depending on their signiﬁcance. Signiﬁcanceis decided on the basis of eigen vectors preserving the most of energy, which isinterpreted from their corresponding eigen values. Total energy is the sum of eigenvalues of all the eigen vectors and preserved energy is the sum of eigen values of only the chosen eigen vectors. Once the signiﬁcant eigen vectors are selected, theimages are projected into the reduced vector space, that is, the vector space formedonly by the selected signiﬁcant eigen vectors. This projection coefﬁcients form thefeature vector and the reduced vector space forms the feature space. A feature vectoris either a column vector or row vector consisting of either the actual image pixelvalues or values obtained after applying a feature extraction technique like PrincipalComponent Analysis, Gabor ﬁlters, etc.Since there exist separate eigen spaces for each pose, frontal and non-frontal,eigenvectorsandeigenvaluescorrespondingtoeacheigenspaceareselected.Theseeigen vectors are linearly independent and hence they span the corresponding vec-tor space and form the set of basis vectors of that vector space. The eigen vectorscapture most of the variance, which is shown in Figure 1
An Efﬁcient Pose Invariant Face Recognition System 5
Fig. 1
First eigen face
3.3 Learning Transformation
Feature vectors of images in vector spaces of each pose are used to learn the lin-ear transformation between the feature vectors of frontal and non-frontal face im-age feature vectors. Let
A
P
and
A
F
be the matrix containing the feature vectors of non-frontal and frontal images of the training set respectively. Feature vectors of corresponding poses are present as column vector in the matrix
A
P
and
A
F
. Let
U
be the desired transformation matrix to be learn. Then we have
A
F
=
UA
P
(1)A possible solution of this equation is given by ordinary least squares solutionwhich is given by:
U
= ((
A
T P
A
P
)
−
1
A
T P
A
F
)
(2)The ordinary least square (OLS) solution is not found to be a good estimate. Abetter solution is given by the ridge regression which is:ˆ
β
= (
A
T P
A
P
+
λ
I
)
−
1
A
T P
A
F
(3)where
λ
is called the ridge parameter and is calculated iteratively such that thecovariance of the error converges and
error
=
A
F
−
A
P
ˆ
β
(4)The error term is reﬁned at each iteration till it reaches below a certain thresholdvalue. Ridge regression deliberately introduces bias into the estimation of
β
in orderto reduce the variability of the estimate. The resulting estimate has generally lowermean squared error than conventional approaches like the OLS estimate.Eq. 2 and Eq. 4 are used to get an OLS estimate and the estimation error matrixrespectively. Covariance of this error matrix is found by taking the sum of squaresof all elements in error matrix. This is the initial estimate of covariance of error. Aninitial guess for
λ
is done. Now, the estimation is done using Equation 3 and covari-ance of estimation error matrix is calculated, iteratively. Whenever the covarianceis lesser than its present estimate, the values of
λ
and covariance are updated. Finalestimate of
λ
is used to calculate the transformation matrix.

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