International Journal of Advanced Computer Engineering and Communication Technology (IJACECT)
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Multidirectional 2DPCA Based Face Recognition System
Shilpi Soni1, Raj Kumar Sahu2
1M.E. Scholar, Department of E&Tc Engg, CSIT, Durg
2Associate Professor, Department of E&Tc Engg, CSIT, Durg
Email:
1[email protected], 2 [email protected]Abstract— In this paper, Multidirectional 2DPCA is employed for face recognition of two different databases.
All face images are rotated and their two dimensional principal components are calculated as features as features of facial images. These features in various directions are fused to form features of an individual’s facial image. The results of this technique is compared over FERET database and an inhouse self made database. For FERET database, MDi2DPCA is giving 82.3% result and for self made database it is giving 91.67% result.
Keywords— PCA, 2DPCA, D2DPCA, MD2DPCA, Euclidean distance
I. INTRODUCTION
Face recognition technique deals with recognition of an individual personality on the basis geometric or statistical features of facial image. It includes face tracking n a video sequence, face detection, face verification, and finally face recognition. In all applications of FR technology, after extraction of facial images are converted into gray scale and normalized for testing. This paper is based on the work for improving recognition rate of various facial databases [1]. A face recognition system has to perform Face tracking, detection, verification and recognition. Face tracking expects proposition of faces based on their preceding trail and hence approximates the next position of those faces. Face detection collects information of the geometric replica of the face and non face images, and then accepts a two-class classification method to discriminate between them. Face verification deals with verification of a claimed person and face recognition concerns with distinguishing the identity of a person from a record of identified persons. In this work, principal component analysis is used for face recognition. PCA is also known as eigenvector method as it utilizes eigen values to represent linear variation in high-dimensional data. PCA is one dimensional method of data representation, but to increase recognition rate,
two dimensional representations is built-in in 2DPCA, which was proposed by Yang et al [2]. 2DPCA is more efficient than PCA. 2DPCA extract the feature from the matrix by projecting the image matrix along the projection axes that are the eigen vectors of the image scatter matrix. Recognition rate was further improved by Directional 2DPCA (Di2DPCA), which was proposed by Qi Zhu et al [3]. Di2DPCA can extract features from the matrices in any direction where as 2DPCA reflects the information in each row.
In this paper we are adopting face recognition technique by Di2DPCA technique. This paper is organized as follows: Section I was a brief introduction of this paper.
Section II is giving an overview of face recognition related works performed by before this work. Section III is describing Methodology. Section IV is the experimental results section where results obtained from Di2DPCA and finally Section V is the conclusion of this work.
II. RELATED WORK AND BACKGROUND
A Principal component analysis is the most popular dimensionality reduction technique used for image based feature collection. Turk et. al [4]. developed eigen face techniques for face recognition. Eigen vector and eigen values project the eigen faces which represent primary components of the faces. Weights derived from these eigen vectors are used to represent the facial features which are used for identification of individual faces from a database.
Binary PCA (B-PCA) [5]has been proposed to replace floating-point multiplications with integer additions, so the time complexity of the testing procedure can be significantly reduced. It was reported that B-PCA is 50 times faster than classical PCA.
Since PCA is an image-as-vector method, due to the vectorization effect of PCA, the spatial redundancy
within each image matrix is not taken into account, and some information on local spatial relationships is lost. In order to retain these information, 2DPCA is adopted which is an image-as-matrix method. For image-as- matrix methods, an image is treated as a matrix and thus does not destroy the spatial relationship of image pixels.
2DPCA takes a 2 dimensional-matrix-based representation model and image covariance matrix is constructed directly from the 2D image matrices.
2DPCA can evaluate the matrix accurately and computationally more efficiently than PCA [6,7].
Xu et al [8]. compared 2DPCA and PCA. A problem pertains with 2DPCA, that it needs more coefficients than PCA, so it needs more memory and more time in classification. To overcome these problems, Zhou et al [9,10]. proposed the bidirectional PCA (BDPCA) and Zhang et. al[11]. proposed the 2directional 2dimensional PCA ((2D)2PCA). BDPCA and (2D)2PCA reduces the dimension in both column and row directions, for feature extraction.
To maintain correlations between variations of rows and column diagonal principal component analysis (DiaPCA) is proposed by Zhang et al[11]. They performed this task by seeking the optimal projective vectors from the so called diagonal face images which are used to extract information in diagonal direction.
The features extracted from one or two directions are in sufficient for achieving high accuracy. Since vectors of the image matrix in different directions have different effects during correct classification. To extract features from the matrices in any direction, Qi Zhu et. al [12].
proposed directional 2DPCA (Di2DPCA). Their results are further improved by Xiao Hu et. al [13]. which proposed multi-oriented 2DPCA, where facial images are rotated by θ degrees using bilinear interpolation.
Facial features were extracted from origin face image and rotated images. Since the Di2DPCA can extract features from matrix in different directions, in this work, Multi-directional 2DPCA (MDi2DPCA) is incorporated to improve accuracy. Here matching score level fusion is used to integrate several Di2DPCA performed in different directions for face recognition.
III. METHODOLOGY
A In this paper, Multidirectional 2DPCA is used for feature extraction. Face image is taken as two dimensional matrixes and rotated in six different directions. Rotated images are appended to form array.
Recognition rate is compared for four different facial databases viz. FERET and an in house database. Feature Extraction process is described as below-
Training Phase- All training facial images which are under training database are cropped. These images are then rotated and appended as page wise arrays. Then mean of each array is calculated
(1)
This 2D matrix is the arithmetic average of the training images at each pixel point. Training images in each rotated image database are subtracted from their respective mean image to form variance.
Φ = Γ – Ψ (2)
All of these mean subtracted rotated images, i.e.
variance of each image, are appended to form an array.
Then covariance matrix is calculated from each variance matrix which is product of variance matrix with its transpose.
Χ = ΑT Α = (3)
Face Acquisition Face Database Formation
Training Dataset Testing Dataset
Rotate by xo Mean Image Calculation Variance Calculation Covariance Calculation Eigen Vector
Calculation Weight Matrix
Projection Matrix
Euclidean Calculation of xo rotated image Score Normalization
(Sigmoid Function)
Normalized Score Fusion (Weighted Summation)
Resultant Image (Minimum Fused Value)
Euclidean Calculation of yo rotated image
Histogram Equalization Histogram Equalization
Rotate by yo Mean Image Calculation Variance Calculation Covariance Calculation Eigen Vector
Calculation Weight Matrix
Projection Matrix
Rotate by xo Rotate by yo
Variance Calculation
Variance Calculation
Projection Matrix
Projection Matrix
Score Normalization (Sigmoid Function)
Fig. 1 Flow chart of Directional 2DPCA Algorithm Then covariance matrices of all facial images are added.
Eigen values & Eigen vectors are calculated as X ⋅νi = μi ⋅νi (4)
ΑT .Α. νi = μi ⋅νi (5) ΑT .Α ⋅ Α ⋅ νi = μi ⋅ Α ⋅ νi (6)
Χ ⋅ Α ⋅ νi = μi ⋅ Α ⋅ νi (7) Hence υi = Α ⋅ νi is one of the eigen vector of X.
Eigen vectors corresponding to highest eigen values are selected. Eigenface Matrix is calculated which is product of variance of each face image with d numbers of highest eigen vectors.
Φ = A. Υ (8)
Now projected train matrix calculation which is also termed as eigen face matrix and is calculated as
ωk= φT. Ai (9)
where i= 1, 2, 3……number of training images
Testing Phase- Facial images under test is then cropped and then rotated. The cropped and rotated test face imageis subtracted from mean image of database,
Φt = Γt – Ψ (10)
Projected Test image of each of rotated image is then calculated from their respective eigen face matrix.
ωt = φT . Φt (11)
Classification- Euclidean Distance is used to calculate the distance. It is given by
(12)
Normalization- By normalization, distance scores of each of left and right half face image are mapped between 0 and 1. Sigmoid function is used for normalization in this technique.
(13)
Where (14)
is normalized score, is raw distance score, µk is mean and σk is standard deviation of kth half face image Fusion- Fusion is combining of different feature vectors.
Here fusion is being performed by weighted summation method. It is given by
(15)
Fig. 2. In house Face image rotated by 0o, 10o, 20o, 30o, 40o, 50o
where values of weights are selected such that, w1 + w2
=1.
Recognition- At this stage, test image is recognized with training image. To carry out this task, simply minimum value of fused score s is found.
Output= min ( ) (16)
Its location reflects the facial image under test. Principal component
IV. EXPERIMENTAL RESULTS
In this paper, database used are In house & FERET face database base is used. Database used is In house self made Face database.This database contains images of 12 individuals with 9 image each. Rotated images and final output images by Directional 2DPCA are shown in fig 2
&fig. 3 . On the basis of results, Table I is drawn, comparing results face recognition by 1DPCA and Directional 2DPCA. And Table II is comparison of recognition rates by varying eigen values.
Face Image Under Test Resultant Facial Image
Fig .3.Test Image and Output Image
TABLEI
COMPARISON OF RECOGNITION RATE ON INHOUSE FACE DATABASE HAVING 12INDIVIDUALS S.
No.
Training images per class
Testing images per class
Recognition Rate (%) 1
6
8 1 91.67
2 7 2 75
3 6 3 69.44
4 4
8 1 91.67
5 7 2 75
6 6 3 69.44
On the basis of these results comparison plot is drawn
8 7 6
0 10 20 30 40 50 60 70 80 90 100
Number of Training Images per Class
Recognition Rate (%)
In FERET Database contains 1200 images, 300 persons with 4 images each. Rotated image and output image of FERET database are shown in fig. 4 and fig. 5
Fig.4. In FERET Face image rotated by 0o, 10o, 20o, 30o, 40°,50o
Face Image Under Test Resultant Facial Image
Fig.5. Test Image and Output Image
TABLEIII
COMPARISON OF RECOGNITION RATE ON FERETFACE DATABASE
S.
No.
No. of Rotations
No. of Eigen Features
Correct Outputs (out of
300 tests)
Recognition Rate (%)
1 6 20 245 81.67
2 30 242 80.67
3 4 20 247 82.33
4 30 242 80.67
6 4
0 10 20 30 40 50 60 70 80 90
Number of Rotating Directions
Recognition Rate (%)
20 Eigen Features 30 Eigen Features
V. CONCLUSIONS
The paper presents a face recognition approach using Multidirectional 2DPCA. In the first database which is FERET database, 4 training images are taken for 300 individuals and one image for testing. Recognition rate is calculated for varying direction of rotation. For 4 numbers of rotations and 20 numbers of eigen features recognition rate is maximum i.e 82.33%. In another database, which is In house database having 12 individuals, recognition rate is achieved maximum which is 91.67%, for both 6 and 4 directions of rotations in case of 8 images for training and one for testing image. Here also 20 numbers of eigen features are selected.
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