Robust Face Recognition using Voting by Bit-plane Images based on Sparse Representation

Plurality voting is widely employed as combination strategies in pattern recognition. As a technology proposed recently, sparse representation based classification codes the query image as a sparse linear combination of entire training images and classifies the query sample class by class exploiting the class representation error. In this paper, an improvement face recognition approach using sparse representation and plurality voting based on the binary bit-plane images is proposed. After being equalized, gray images are decomposed into eight bit-plane images, sparse representation based classification is exploited respectively on the five bit-plane images that have more discrimination information. Finally, the true identity of query image is voted by these five identities obtained. Experiment results shown that this proposed approach is preferable both in recognition accuracy and in recognition speed.


INTRODUCTION
Face recognition has been researched widely and an enormous amount of approaches have been proposed because of its broad applications in security, law enforcement, human-computer interaction, and entertainment.In which, Principal component analysis (PCA) [1] and Linear discriminant analysis (LDA) [2] have been the most popular subspace analysis techniques to learn the low-dimensional structure of high dimensional face data.Locality Preserving Projections (LPP) [3] preserves the local manifold structures of the face data.Wang [4] constructed the complex face image and recommended Bit-plane generalized PCA (BGPCA).Sparse representation classification has been paid more attention since Wright [5] regarded face recognition as a globally sparse representation problem and defined Randomfaces.Huang [6] proposed an improved method to produce sparse representation invariant to image-plane transformation by simultaneously recovering the transformation parameters and sparse representation vector when the test image was not aligned.Sparse representation classification (SRC) [7] introduced an orthogonal matrix, such as identity I, as an occlusion dictionary to code the outlier pixels.Yang [8] innovated Gabor features into SRC and proposed GSRC approach.Robust sparse coding (RSC) [9] casts the sparse coding as a sparsity-constrained robust regression problem.Though these approaches have the higher recognition accuracy, it is impossible to apply to real-time applications because they are time-consuming.As a combination strategy, voting strategy can achieve better performance and has been widely used in pattern recognition [10,11,12].Lin [13] demonstrated plurality voting is consisted with the Bayesian criterion and it outperforms majority voting in achieving a desirable trade-off between identification accuracy and rejection rate.Paul Watta [14] analyzed the performance of the plurality voting based ensemble classifier.This paper presents a novel face recognition approach using voting and sparse representation based on binary bit-plane images, having higher recognition rate and rapid speed.The rest of this paper is organized as follows: Image preprocessing and extraction of bit-plane image are introduced in section 2. The details of the sparse representation are given in Section 3. Proposed approach is presented in section 4. Experiment results and conclusion are given in section 5 and Section 6 respectively.

IMAGE PREPROCESS
By extracting each binary digit, the gray image with 256 gray levels can be decomposed into 8 bit-planes, from the least significant bit (bit-plane 1) to the most significant bit (bit-plane 8).The higher-order bit-plane embodies more visually significant data information [15].Fig. 1 shows an original face image and its 8 bitplanes, the higher-order bit-planes (1-4) carry the majority of the outline features; while the other bit-planes contain the more subtle details in the image.In order to enhance the global contrast and to make the subtle details much clearer, all the face images are first equalized using the cumulative distribution function in this proposed approach.The information distribution in the bit-plane images is changed after equalization.Fig. 2 provides the equalized image of the one shown in Fig. 1 (a) and its 8 bit-planes.There are also outline features in the bit-planes 1 and 2, and the top 3 bit-planes still contain abundance shape information. ( (3) (4)

SPARSE REPRESENTATION CLASSIFICATION
x is an m- dimensional vector corresponding to the th l sample of the th k individual.Over-complete dictionary expressed by is the concatenation of all training samples.y expresses the test sample.
Sparse representation based classification (SRC) proves that the test sample y of subject i can be sparse representation by the overcomplete dictionary X ideally as Utilizing regularized least square, we can obtain easily the unique coefficient vector , where  is regularization parameter, term of
Normalize the columns of the dictionary X to have unit l 2 -norm and denote by X ~,

FACE RECOGITION USING VOTING AND SPARSE REPRESENTATION
The proposed face recognition approach using plurality voting strategy and sparse representation based on bit-plane images (SRV_BP) includes image preprocessing, bit-plane selection and on-line recognition.

Image Preprocess
Eight training sets are obtained from the original training set after training images are preprocessed according to Section 1.

Let i l k
x denote the th i bit-plane image from the th l image of the denote the th i over- complete dictionary corresponding to the th i bit-plane (i=1, 2,…, 8).

Bit-plane Selection
Randomly select M (M<L) training images from each subject for training, and the rest for testing.

[ , , , ]
The right recognition rate corresponding to the i th bit-plane i  is computed by replacing y with each element i kt x and repeating the step (b)~(e) of the algorithm CRC_RLS.Integer i varies from 1 to 8, and the recognition rate vector is .Fig. 3 and Fig. 4 show the variation recognition rate of each bit-plane with the number of principal components retained, where BP1 to BP8 are abbreviations for the bit-plane 1 to bit-plane 8, respectively.The recognition rates of bit-plane 2 and of bit-plane 8 are equal no matter how many features are retained, so the two curves, BP2 and BP8, overlap together.It is clear that the 3 rd and the 4 th bit-planes contain more texture information which is unhelpful for classification, and experiment validated their recognition rates are always less than 0.25.So both bit-planes are discarded in the procedure of plurality voting.The 2 nd bit-plane has the same recognition rate to the 8 th bit-plane and they will bring the same identity for the test image, so the 2 nd bitplane is also discarded during the processing of voting.

On-line Recognition
The query image y is equalized and is decomposed into eight binary bit-plane images are assigned by Eq. ( 4): The total number of votes received by class m is presented by v presents a measure of the similarity between the input and class m.Let vector , the plurality voting fails.
In this case, the plurality voting is failure and the testing is rejected to recognition.

EXPERIMENTAL RESULTS
In this section, we test the performance of the proposed algorithm (SRV_BP) and compare it with PCA, RSC CRC_RLS on the AR database and ORL database.

ORL Face Database
ORL database contains 400 grayscale images from 40 individuals, each individual having 10 images.These images are normalized to 64×64.For each individual, 6 images are used for training and the rest are used for testing.For 160 testing images, there are 2 images could not be recognized by plurality voting when the feature dimension equals to 95.Table 1 gives the experiment results.

Comparison of recognition speed
We compare the recognition speed of the proposed method SRV_BP with the competing approaches SRC and CRC_RLS. 4 The results of ORL and AR are listed in table 3 and table 4 respectively.Optimal feature-dimension is the minimum featuredimension when the recognition rate reaches highest.The testing time is the average running time to accomplish one testing under the optimal feature-dimension.The proposed method SRV_BP includes image histogram equalization, bit-plane extraction, running CRC_RLS several times and plurality voting.Hence SRV_BP spends more time than CRC_RLS in recognizing, but its speed is faster than the SRC prominently.

CONCLUSION
A new face recognition approach with sparse representation and plurality voting based on the bit-plane images has been discussed in this article.According to the recognition rate and order of each bit-plane, five binary bit-plane images with more discrimination information are selected to vote the identity of testing image.In each bit-plane images, the testing image is represented sparsely by the training images under the l 2 -norm constraint, which solves the "lack of samples" problem in face recognition and avoids the expensive l 1 -minimization.Experimental results indicate that the proposed approach is superior both in the recognition rate and the speed.

ACKNOWLEDGMENT
This study was sponsored by Project of Shandong Province Higher Educational Science and Technology Program

Fig. 1
Fig.1 Original face image (a) and its eight bit-planes (b) Assume there are K classes and n k training samples included in the k th class, total number of training samples is size of w×h can be stacked as an m-dimension vector (m = w×h).Denote the training samples from the th

,
P can be regarded as the projection matrix.At the test stage, y is only simply projected onto P and is classified with ρ ˆ by evaluating which class leads to the minimum reconstruction error.The procedures of the CRC_RLS are summarized as follows.
vector associated with class k. c.Reconstruct K vectors

Fig. 3 Fig. 4
Fig.3 Variation in recognition rate of each bit-plane with the number of principal components retained on ORL database