GRAM-SCHMIDT
ORTHOGONALIZATION BASED FACE
RECOGNITION USING DWT
Ramesha K
Department of Telecommunication Engineering, Vemana Institute of Technology, Koramangala,
Bangalore-560034, India
K B Raja
Department of Electronics and Communication Engineering, University Visvesvaraya College of Engineering, Bangalore University, K. R. Circle, Bangalore-560001, India
Abstract:
The personal identification based on face recognition is essential to create Unique Identification (UID) card, which can be used for voting in electoral systems, accessing secured areas, identification to avail government and nongovernment facilities. In this paper we propose the Gram-Schmidt Orthogonalization based Face Recognition using DWT (GSFRD). The Discrete Wavelet Transform is applied on face images of Libor Spacek database. The LL subband is considered and Fast Principal Component Analysis using Gram-Schmidt orthogonalization process is applied to generate feature coefficient vectors. The Euclidean Distance between test and database face image coefficient vectors are computed and compared with the predefined threshold value. It is observed that the face recognition rate is 100% and has better computational efficiency compared to existing algorithm with same Mean Square Error (MSE).
Key Words: Face Recognition, Discrete Wavelet Transforms, Fast Principal Component Analysis, Eigenvalue.
1. Introduction
Biometric pattern recognition systems are widely used in security areas. These systems use unique human characteristics such as fingerprints, iris, hand geometry, hand vein, voice, retina, face, enabling differentiation among human beings. Facial research in computer vision can be divided into several areas, such as face recognition, face detection, facial expressions analysis. Face recognition systems have a wide range of applications like human-computer interaction, image and film processing, and especially when dealing with security applications, like real-time subject identification and authentication, computer and physical access control, criminal screening and surveillance. It is also a research topic in several fields, like neural networks, computer graphics, image processing, computational vision and psychology. The biggest challenge in designing and implementing a robust face recognizer is that a human face can undergo several transformations such as i) the same person may use different face accessories like glasses, earrings, piercings and makeup, ii) many facial expressions like neutral, smile, anger, surprise, fear, disgust, and sadness or doing a grimace, iii) can have/wear mustache and beard, iv) he/she can change his/her hair into long/short/skin/fringe and even dye it and v) he/she can be at many different ages. These facial changes make the recognition task very difficult even minor mistakes made by human being from time to time.
In general the face recognition is carried out in four phases a) Image Acquisition, b) Preprocessing, c) Feature Extraction and d) Matching. The human face recognition techniques normally are applied to frontal faces and the recognition methods [1] are Eigenfaces, Artificial Neural Networks (ANN), Dynamic Link Architecture, Hidden Markov Models (HMM), Graph Matching, Geometrical Feature Matching, Template Matching, 3D Morphable Model, Line Edge Map (LEM), Support Vector Machine (SVM) and Multiple Classifier Systems (MCS).
a) Image acquisition: The face images can be considered from the publicly available databases such as Libor
images with a wide variety of poses, illumination angles, gestures, face occlusions, and illuminant colors. In order to compare the performance of face recognition algorithms there is need for a comprehensive, systematically annotated database with face images that have been captured (i) at variety of pose angles to permit testing of pose invariance, (ii) with a wide variety of illumination angles to permit testing of illumination invariance and (iii) under a variety of commonly encountered illumination color temperatures to permit testing of illumination color invariance.
b) Preprocessing: In this the size of the image may be changed by resizing the image. The illumination
compensation is performed using Discrete Cosine Transform (DCT) coefficients and homomorphic filtering technique, image enhancement like contrast stretching using histogram techniques, image restoration using noise models and averaging filters. Edge detection operators such as Sobel, Canny, and Robert etc. are used to detect face image edges. Pose and expression invariant techniques are also applied.
c) Feature Extraction: In this face features are based on i) edge features such as nose, eyes, mouth and lip
distances, ii) Principal Component Analysis (PCA), iii) Independent Component Analysis, iv) Fast Fourier Transform, v) Discrete Wavelet Transform (DWT), vi) LEM, vii) 3D Morphable model, viii) HMM, ix) Short Time Fourier Transform.
d) Matching: Normally face classification/matching is obtained using the techniques such as Euclidean Distance
(ED), Hamming Distance, Chi-square, ANN, SVM, MCS, Template Matching, Graph Matching, Random Forest and Mahanalobis Distance.
Contribution: In this paper we proposed GSFRD algorithm. The DWT is applied on face images and only LL
band is considered. The Fast PCA using Gram-Schmidt orthogonalization is used to create features of face images. The Euclidian Distance is used for matching of face images based on threshold values.
Organization: The research paper is organized into the following sections. Overview of the related work is given
in section 2. Necessary background for the proposed method is described in section 3. The GSFRD model is described in Section 4. Section 5 discusses the algorithm of GSFRD system. Performance analysis and results of the system is discussed in Section 6 and Conclusions are given in Section 7.
2. Related Work
M Bicego et al., [2] presented HMM and wavelet coding based face recognition system. For each face image a sequence of overlapping subimages is extracted and then wavelet coefficients are compared for each of the image. HMMs modeled the whole sequence. Virenndra P Vishwakarma et al., [3] proposed an approach for face recognition using DCT coefficients rescaling for illumination normalization, which uses the correlation of DCT low frequency coefficients to illumination variations. Input image contrast stretching is done using histogram equalization technique. To compensate illumination variations, the low frequency DCT coefficients are re-scaled to lower value. For further contrast enhancement the first coefficient is re-scaled to higher value. M A Anjum et al., [4] presented the double dimension reduction based face recognition. Dimension reduction to a certain resolution level for best recognition, image decimation algorithm is applied on face image and then DCT is applied. A subset of DCT coefficients from low to mid frequencies is extracted for recognition.
Byung-Joo Oh [5] proposed Radial Basis Function [RBF] network based on LDA for face recognition. Preprocessing on face input images is done by using PCA and LDA, and then LDA features are considered as the input of the RBF network for face recognition. A Abbas et al., [6] proposed a method to eliminate the expression and illumination invariant preprocessing techniques for face recognition. Smoothing the image to remove image details using wavelet transforms the expression variation effect is eliminated and combining this method with DCT method to eliminate illumination variations. M P Mahyabadi et al., [7] investigated face detection based on PCA and Adaptive Resonance Theory (ART) 2A neural network. Vector dimension is reduced by using PCA and neural network classifier ART-2A is used for face recognition. Gualberto Aguilar-Torres et al., [8] proposed a face recognition algorithm using Discrete Gabor Transform (DGT). The face image features vector is extracted using DGT and then feed into a multilayer perceptron to carry out the recognition task. The features vector, estimated using the DGT, presents a small intra-person variation while the inter-persons variation is considerably large. This fact provides robustness against changes in illumination, wardrobe, facial expressions, scale, and position inside the captured image, as well as inclination, noise contamination and filtering.
information of the extracted DCT features. The obtained local features are combined at the feature level and the decision level. Imran S Bajwa et al., [12] presented PCA classification system to classify the different types of single-layered and multi-layered clouds. PCA is the principal features of an image and these features discreetly represent an image. Qeethara Kadhim Al-Shayea et al., [13] concentrated on recognition rate of face recognition algorithms. The algorithms examined are: PCA, 2D-PCA column direction, 2D-PCA in row direction and Two Dimensional Two Directional PCA. The algorithm is implemented via DWT to minimize the images size and the complexity reduction is achieved by optimizing the number of operations needed.
Yuehui Chen et al., [14] proposed a face recognition approach by using DCT and hybrid Flexible Neural Tree (FNT) classification model. The DCT is used to extract the input features to build a face recognition system and the FNT is used to identify the faces. The FNT structure is developed using an evolutionary algorithm and the parameters are optimized by a particle swarm optimization algorithm. Sarawat Anam et al., [15] proposed a face recognition system using genetic algorithm and back-propagation neural network. Pre-processing is applied on the input image and face features are extracted using genetic algorithm. Classification is based on the back-propagation neural network. Zong X Lin et al., [16] proposed a practical preprocessing method to recover the vertical pose variation for the face recognition module of the intelligent robot guard. Fast semi-3D vertical pose recovery method evaluates the angle of the vertical pose variation by single 2D image view and thereby recovers the vertically rotated face to the nearly frontal view. The recovered face image is identified by the original face recognition module. The Gabor Wavelet Transform is used as the feature extraction core of the original face recognition module.
P Abouzar et al., [17] proposed a face recognition algorithm based on Wavelet Transform (WT) and DCT. Large reduction in the data size without loss of data is done by using WT and DCT. 2D WT is used to compress the data at various levels, to removes the high frequency noise from the input image. Features are extracted using PCA and then classification is done by using SVM. Ronny Tjahyadi et al., [18] discussed the face recognition problem via energy histogram of the DCT coefficients. Chengjun Liu [19] presented learning the Uncorrelated Color Space (UCS), the Independent Color Space (ICS), and the Discriminating Color Space (DCS) for face recognition. The new color spaces are derived from the RGB color space that defines the tristimuli R, G, and B component images. While the UCS decorrelates its three component images using PCA, the ICS derives three independent component images by means of blind source separation, such as independent component analysis. The DCS, which applies discriminant analysis, defines three new component images for face recognition. Color image representation is formed in these color spaces by concatenating their component images, and color image classification is achieved using the color image representation and an enhanced fisher model.
Yuchui Chen and Yaou Zhao [20] proposed face recognition using DCT and hierarchical RBF model. DCT is used to extract the input features to build a face recognition system and hierarchical RBF to identify the faces. Based on the predefined operator sets, a hierarchical RBF is created for input features. The hierarchical RBF structure is developed using extended compact genetic programming and the parameters are optimized by differential evolution. Anil Kumar Sao and B Yognannarayna [21] presented an algorithm on illumination variation in face recognition based on the phase of analytic image. Trigonometric functions of phase are used in the computation of analytic phase. Template matching is used to compare the functions of analytic phase for face recognition. The functions of the analytic phase are compressed using eigenanalysis. Fadi Dornaika and Bogdan Raducanu [22] proposed 3D head pose and facial actions real time tracker in monocular video sequences. Automatic 3D face pose initialization scheme for real time tracker employed 2D face detector and an eigenface system. Use the tracker in a human-robot interaction application in which the gaze of a robotic vision sensor is controlled through the estimated direction of the users gaze. Chao-Kuei Hsieh et al., [23] proposed the regularization based optical flow algorithm by using constraints on given point correspondences to compute precise pixel displacements and intensity variations. Optical flow computes for the input face expression variant face with respect to a reference neutral face image, remove the expression from the face image by elastic image warping to recognize the subject with facial expression. Wen-Hui Yang and Dao-Qing Dai [24] proposed two dimensional maximum margin feature extraction for face recognition. 2D two directional feature extractions based on maximal margin criterion and then LDA is performed in the 2D two directional maximal margin criterion subspaces.
Hongliang Li et al., [26] presented automatic face segmentation for real time video for face recognition. Learning based face detector is developed to find human faces. Face rejection cascade is used to remove negative samples and retaining face samples, speed up the detection process. Srinivas Nagamalla and Bibhas Chandra Dhara [27] presented face recognition algorithm using facial landmarks such as eyes, lips, mouth and lips. The probable landmarks are located from the gradient image and template matching is applied over a region around a probable position to detect exact location of the landmarks. Statistical and geometrical features are extracted from this region. PCA is used to reduce the dimension of the feature vector and mahalanobis distance is used to classify the images. Sidra Batool Kazmi et al., [28] presented automatic recognition of facial expressions from face images by using DWT features to a bank of five parallel neural networks. Each neural network is trained to recognize a particular facial expression, which is most sensitive to that expression. Multi-classification is achieved by combining multiple neural networks performing binary Multi-classification using one-against-all approach. The outputs of all neural networks are combined using a maximum function.
3. Background
3.1 . Principal component analysis
PCA identifies patterns in data and highlight the similarities and differences in data. Finding patterns in high dimensional data is difficult when graphical representation is not available. The advantage of PCA is that once identifies patterns in data, and compress the data by reducing the number of dimensions, without losing important information of an image. The set of images {xi} is represented by a matrix X image of size N*M,
where N is the number of pixels in an image and is given in Equation (1)
x
1,
x
2,
x
3,
...,
x
M
1
X
The Average face (mean) is computed in Equation (2)
21 1
M i i x M xThe average face is calculated and subtracted from each face in X, giving X1 as in Equation (3)
1 1 2
....
3
x
x
x
x
x
x
X
MThe principal components of this set are found by calculating the eigenvectors of the covariance matrix C is given in Equation (4)
1
4
1 1 T
X
X
C
M i
Since C is symmetric matrix and e1, e2,…, eN form a basis, (i.e., any vector X or X1 is written as a linear
combination of the eigenvectors) and b1, b2,…., bM is the coefficients given by Equation (5)
...
5
1 2 2 1 1
M i i i MM
e
b
e
b
e
b
e
b
X
Dimensionality reduction step take the ‘k’ eigenvectors corresponding to highest eigenvalues. These eigenvectors have the direction of the largest variance of the data. Now our face has only k-dimensions given in Equation (6)
)
6
(
1
k i i ie
b
X
Where k << M, then the facial image is projected into k less than M dimensions by using Equation (7).
7] , ... , , ,
[V1 V2 V3 Vk
where
V
i
e
iX
1 ande
i is the eigenvector of the eigenfaces. The calculated eigenvectors are used as an orthogonal basis to represent the training set faces. The training set faces are projected onto the k eigenvectors3.2. Gram–Schmidt orthogonalization process
The Gram–Schmidt procedure [29] is a method for orthonormalizing a set of vectors in an inner product space called as Euclidean space Rn. The Gram–Schmidt process takes a finite, linearly independent set S = {v1, v2, …,
vn} and generates an orthogonal set S′ = {u1, u2,….., uk} for k ≤ n that spans the same k-dimensional subspace of
Rn as S. The application of the Gram–Schmidt process to the column vectors of a full column rank matrix decomposes into an orthogonal and triangular matrix. A linearly independent vector set {v1, v2, . . . , vn } is
converted into a set of orthogonal vectors {u1, u2, . . . , un} by using Gram-Schmidt process. The vectors v1 and
v2 determine a plane. The vector u1 is the unit vector in the direction v1. The unit vector u2 lies in the plane of v1,
v2 and is normal to v1 on the same side as v2. The vector u3 is normal to the plane of v1, v2 on the same side as v3
etc. The projection is explained in the Figure 1.
Fig.1. Gram–Schmidt procedure.
The principal axes or leading/most dominant eigenvector is measured and the remaining basis vectors are measured one by one in a reducing order of dominance. The previously measured basis vectors are utilized for finding the present basis vector. The algorithm for the present vector will converge when the new and old values point in the same direction.
Gram-Schmidt algorithm
Step 1: The Gram Schmidt process takes finite, linearly independent set S = {v1, v2, v3, …., vn} and generate an
orthogonal set S = { u1, u2, u3, …., uk} that spans the same subspace as S. In general, set u1 = v1, and then each ui
is made orthogonal to the proceeding u1, u2,, …, ui-1. By subtraction of the projections of vi in the directions of
the u1, u2, …, ui-1. Gram-Schmidt orthogonalization process is given in Equation (8)
8
1 1 j i j j T j i T j i i
u
u
u
v
u
v
u
for i= 1, 2, 3, …., n. The vectors ui span the same subspace as the vi, the vectors ei orthonormal.
Step 2: Normalize ui, by dividing it by its norm as given in Equation (9)
9
i i
u
u
i
e
The Gram Schmidt process, defines the projection operator by using Equation (10)
10
,
,
)
(
u
u
u
u
v
v
proj
u
where u, and v denotes the dot product of the vectors u and v. The operator projects the vector v orthogonally
onto the vector u. The Gram Schmidt process then works as in Equation (11)
1 1
v
u
)
(
2 22
v
proj
1v
u
u) ( )
( 3 3
3
3 v proj 1 v proj 2 v
u u u
) ( )
( )
( 4 4 4
4
4 v proj1 v proj2 v proj3 v
u u u u …..
…….
(
)
(
11
)
1 1 k u k j k
k
v
proj
v
u
j
where the sequence {u1, u2, u3, ….,uk } is the required orthogonal vectors, and the normalized vectors {e1, e2, . . .
, ek} form an orthonormal set.
3.3. Fast PCA
PCA based system is affected by non-convergence state of the algorithm and high MSE. The major difference is for facial features such as eigenvalues and eigenvectors extraction using Gram–Schmidt Orthogonalization method instead of eigenvalue decomposition method in PCA. FPCA using Gram-Schmidt orthogonalization process to find leading eigenvectors converges in little iteration without any initial setting. Face recognition using FPCA decreases the decision time of a system, especially when high resolution images are used, hence FPCA is computationally more efficient, easy to implement and generates same MSE as that of PCA.
4. Face Recognition System Model In this section we discuss proposed model.
4.1. Block Diagram
The face recognition approach based on 2D-DWT and GSFRD is as shown in Figure 3.
4.1.1. Face image database
The face image samples are collected from website as well as captured from the mobile phones. Figure 2 shows few images of Libor Spacek face database. The data set used for training and testing purposes contains male, female and old person images of 180 * 200 pixels size. In this data set, twenty images of each person without background with very minor variation in head turn, tilt and slant are considered. The data set has images of small changes in face position because images have been acquired in speech mode with no variation in hair style and lighting, contains total twenty images of the same person is given in Figure 2 (a) to (f) of F1-F6.
Fig. 3. GSFRD Face Recognition System.
(a) Images of F1 (b)Images of F2
Database Face Images Test Face Images
2D-Discrete Wavelet Transform
Euclidian Distance Classifier LL Sub band
FPCA
Coefficient Vector
(c) Images of F3 (d) Images of F4
(e) Images of F5 (f) Images of F6
Fig. 2. Few images of Libor Spacek face database.
4.1.2.Two dimensional DWT
The decomposition can be applied at different levels repeatedly on low frequency channel (LL) to obtain next level decomposition. The image is decomposed into four subbands LL, LH, HL, and HH subbands by applying 2D-DWT on face image. The LL subband corresponds to low frequency components of an image and HL, LH and HH are high frequency components of an image corresponds to vertical, horizontal and diagonal subbands respectively. The LL subband we obtain is half the original image. Figure 4 shows the image decomposition based on wavelet scales. 2D-DWT gives dimensional reduction for less computational complexity, insensitive feature extraction, and multiresolution data approximation. This transform decomposes an image and hence different facial expressions can be attenuated by removing high frequency components.
Fig. 4. Image decomposition based on wavelet scales.
Wavelet coefficients are obtained by convolving a target function with wavelet kernels and mathematically DWT can be given as in Equation (12)
12
)
2
(
)
(
)
2
(
)
(
* ,
* ,
) (
q
n
g
n
x
a
q
n
h
n
x
d
DWT
p p q
p
p p q
p n x
The coefficients dp,q gives the component details to the wavelet function, where as ap,q gives approximation
components of the image. The h(n) and g(n) in the Equation (12) are functions gives the coefficients of high
pass and low pass filters respectively. The parameters p and q refers to wavelet scale and translation factors.
4.1.3. Fast principal component analysis
The PCA using Gram–Schmidt orthogonalization process is used to compute leading principal components by reducing feature dimension of database set and test faces.
The Euclidean distance between database set and test faces becomes error vector and the average error vector becomes the threshold value for face recognition. The minimum ED between database and test image are recorded which leads to Difference Error Vector (DEV). If the value of DEV is less than the value of threshold then the face image is concluded as match otherwise non-match.
5. Algorithm
Problem Definition: The Face recognition for the variation in the illumination and facial expression is carried
out using DWT and FPCA, with high recognition rate is given in Table 1.
Table.1. Algorithm of the GSFRD
6. Performance Analysis and Results
The Libor Spacek Face database consists of female and male images of size 180 * 200 each in speech mode is considered for performance analysis. The database considered has 20 images per person with no background, light variation, hair style change and with minor variations in head turn, tilt and slant. For testing purpose, 400 images of 20 persons are considered. First 10 images of each person are used to create a face database. The second set of 10 images of each person is used as test images to determine recognition rate. For non-matching, the test images are from different persons other than the persons used to create database.
From Table 2 it is observed that the average recognition rate is 100% in the case of proposed GSFRD algorithm compared to the average recognition rate of 80% in the case of existing algorithm.
Table 2. FPCA and GSFRD Face Recognition Rates
CPU time variation in the case of FPCA using Gram–Schmidt orthogonalization process is very low even for larger database compared to exponential increase in PCA method, and it is shown in Figure 5. The Figure 6 gives the face recognition rate using FPCA and GSFRD of eleven individuals F1-F11. It is seen that face recognition rate except F5 is 100% in the case of proposed GSFRD algorithm compared to 80% in FPCA.
The face recognition rate using Harr wavelet, scale-1 versus leading principal components is given in Figure 7. The GSFRD algorithm requires only few leading principal components to achieve 100% recognition accuracy with less computational time. Face match/non-match is based on the threshold value setting as given in Figure 8. The recognition rate is varying based on threshold selection. If the threshold value is increased beyond cutoff
Input: Face Images.
Output: Face Image match/non-match.
(1).Apply 2D-DWT on face database and consider only LL subband.
(2).FPCA is applied using Gram–Schmidt orthogonalization process to compute leading principal components to reduce feature dimension of database set.
(3).The steps 1 and 2 are repeated on test face image.
(4).The Euclidean distance between face database set and test face are recorded in EV. (5).Compute threshold value and DEV.
(6).If the threshold value is greater than DEV the face image is match else non-match.
Data base Recognition Rate
FPCA[30] GSFRD F1 90% 100% F2 100% 100% F3 100% 100% F4 50% 100% F5 90% 90% F6 90% 100% F7 100% 100% F8 100% 100% F9 90% 100%
F10 0% 100%
value the system will show all faces matching and if the threshold value is lesser than the cutoff value, then the system will show all faces non-matching.
Fig. 5. PCA and FPCA computation times Fig. 6. Recognition Rate of FPCA and GSFRD
Fig. 7. Recognition Rate Vs Principal components Fig. 8. Recognition Rate Vs Threshold
7. Conclusion
The face recognition is used to identify a person for all day to day transactions. The GSFRD algorithm is proposed in the paper. The face images from Libor Spacek database are considered for database and testing. The DWT is applied on face and considered only LL subband by leaving other subbands. The FPCA using Gram– Schmidt orthogonalization process is applied on LL subband to generate leading eigenvectors to compute face features. The Euclidean Distance is used to compare the features of database and test face images to declare face match/non-match. It is observed that the CPU time and recognition rate is improved in the proposed algorithm compared to the existing algorithm.
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Ramesha K awarded the B.E degree in E & C from Gulbarga University and M.Tech degree in Electronics from Visvesvaraya Technological University. He is pursuing his PhD. in Electronics and Communication Engineering at JNTU Hyderabad, under the guidance of Dr. K. B. Raja, Assistant Professor, Department of Electronics and Communication Engineering, University Visvesvaraya College of Engineering. He has over 6 Research publications in refereed International Journals and Conference Proceedings. He is currently an Assistant Professor, Dept. of Telecommunication Engineering, Vemana Institute of Technology, Bangalore. His research interests include Image processing, Computer Vision, Pattern Recognition, Biometrics, and Communication Engineering. He is a life member of Indian Society for Technical Education, New Delhi.
K B Raja is an Assistant Professor, Dept. of Electronics and Communication Engineering, University Visvesvaraya college of Engineering, Bangalore University, Bangalore. He obtained his BE and ME in Electronics and Communication Engineering from University Visvesvaraya College of Engineering, Bangalore. He was awarded Ph.D. in Computer Science and Engineering from Bangalore University. He has over 60 research publications in refereed International Journals and Conference Proceedings. His research interests include Image Processing, Biometrics, VLSI Signal Processing, computer networks.
