人脸识别外文文献.doc

Method of Face Recognition Based on Red—Black
Wavelet Transform and PCA
Yuqing He， Huan He, and Hongying Yang
Department of Opto-Electronic Engineering,
Beijing Institute of Technology， Beijing, P。R。 China, 100081 20701170＠bit。edu。cn
Abstract。 With the development of the man—machine interface and the recogni-tion technology, face recognition has became one of the most important research aspects in the biological features recognition domain. Nowadays, PCA(Principal Components Analysis) has applied in recognition based on many face database and achieved good results。 However, PCA has its limitations： the large volume of computing and the low distinction ability. In view of these limitations， this paper puts forward a face recognition method based on red—black wavelet transform and PCA. The improved histogram equalization is used to realize image pre—processing in order to compensate the illumination。 Then， appling the red-black wavelet sub-band which contains the information of the original image to extract the feature and do matching。 Comparing with the traditional methods, this one has better recognition rate and can reduce the computational complexity.
Keywords： Red-black wavelet transform, PCA, Face recognition， Improved histogram equalization。
1 Introduction
Because the traditional status recognition (ID card， password, etc) has some defects， the recognition technology based on biological features has become the focus of the re—search。 Compared with the other biological features (such as fingerprints， DNA, palm prints, etc) recognition technology， people identify with the people around mostly using the biological characteristics of human face. Face is the most universal mode in human vision。 The visual information reflected by human face in the exchange and contact of people has an important role and significance. Therefore, face recognition is the easiest way to be accepted in the identification field and becomes one of most potential iden-tification authentication methods. Face recognition technology has the characteristics of convenient access， rich information. It has wide range of applications such as iden—tification, driver’s license and passport check， banking and customs control system, and other fields[1］。
The main methods of face recognition technology can be summed up to three kinds: based on geometric features， template and model separately。 The PCA face recognition method based on K—L transform has been concerned since the 1990s。 It is simple， fast. and easy to use。 It can reflect the person face’s characteristic on the whole. Therefore， applying PCA method in the face recognition is unceasingly improving.
D.-S。 Huang et al （Eds。): ICIC 2008， LNCS 5226， pp. 561–568， 2008. © Springer-Verlag Berlin Heidelberg 2008
This paper puts forward a method of face recognition based on Red—Black wavelet transform and PCA。 Firstly, using the improved image histogram equalization［2］ to do image preprocessing， eliminating the impact of the differences in light intensity。 Sec—ondly， using the Red-Black wavelet transform to withdraw the blue sub—band of the relative stable face image to obscure the impacts of expressions and postures. Then, using PCA to withdraw the feature component and do recognition。 Comparing with the traditional PCA methods, this one can obviously reduce computational complexity and increase the recognition rate and anti-noise performance. The experimental results show that this method mentioned in this paper is more accurate and effective.
2 Red—Black Wavelet Transform
Lifting wavelet transform is an effective wavelet transform which developed rapidly these years。 It discards the complex mathematical concepts and the telescopic and translation of the Fourier transform analysis in the classical wavelet transform。 It de-velops from the thought of the classical wavelet transform multi-resolution analysis. Red-black wavelet transform[3—4］ is a two—dimensional lifting wavelet transform［5—6］， it contains horizontal/vertical lifing and diagonal lifting. The specific principles are as bellow。
2.1 Horizontal /Vertical Lifting
As Fig。1 shows， horizontal /vertical lifting is divided into three steps:
1。 Decomposition: The original image by horizontal and vertical direction is divided into red and black block in a cross—block way。
2. Prediction： Carry on the prediction using horizontal and the
vertical direction four neighborhood’s red
blocks to obtain a black block predicted value。
Then， using the difference of the black block
actual value and the predicted value to
substitute the black block actual value. Its
result obtains the original image wavelet
coefficient。 As Fig。1（b) shows：
(1)
3。 Revision：
Using the horizontal and vertical direction four neighborhood’s black block's wavelet coefficient to revise the red block actual value to obtain the approximate signal. As Fig.1(c) shows：
（2）
In this way, the red block corresponds to the approximating information of the image, and the black block corresponds to the details of the image。
2.2 Diagonal Lifting
On the basis of horizontal /vertical lifting, we do the diagonal lifting。 As Fig.2 shows， it is also divided into three steps:
Fig.2。Diagonal lifting
1.Decomposition: After horizontal /vertical lifting, dividing the obtained red block into the blue block and the yellow block in the diagonal cross way。
2. Prediction： Using four opposite angle neighborhood’s blue block to predict a data in order to obtain the yellow block predicted value. Then the difference of the yellow block actual value and the predicted value substitutes the yellow block actual value. Its result obtains the original image wavelet coefficient of the diagonal direction。 As Fig.2(b） shows：
（3）
3。 Revision: Using four opposite angle neighborhood yellow block wavelet co—efficient to revise the blue block actual value in order to obtain the approximate signal。 As Fig。2（c) shows：
（4)
After the second lifting， the red—black wavelet transform is realized.
According to the Equations, it can analyze some corresponding relations between the red-black wavelet transform and the classical wavelet transform: namely, the blue block is equal to the sub—band LL of the classical tensor product wavelets， the yellow block is equal to sub-band HH and the black block is equal to sub-band HL and LH. Experimental results show that it discards the complex mathematical concepts and equations。 The relativity of image can mostly be eliminated and the sparser represen—tation of image can be obtained by the Red-Black wavelet transform。
The image after Red-Black wavelet transform is showed in the Fig.3（b）， on the left corner is the blue sub-band block image which is the approximate image of original image。
Fig.3.The result of red-black wavelet transform
3 Feature Extraction Based on PCA［7]
PCA is a method which analyses data in statistical way. This method discovers group of vectors in the data space。 Using these vectors to express the data variance as far as possible. Putting the data from the P-dimensional space down to M—dimensional space （ P>〉M)。 PCA use K—L transform to obtain the minimum—dimensional image recogni—tion space of the approximating image space. It views the face image as a high—dimensional vector. The high-dimensional vector is composed of each pixel. Then the high-dimensional information space maps the low-dimensional characteristic subspace by K-L transform。 It obtains a group of orthogonal bases through high-dimensional face image space K—L transform. The partial retention of orthogonal bases creates the low—dimensional subspace。 The orthogonal bases reserved is called “Principle component”。 Since the image corresponding to the orthogonal bases just like face, so this is also called “Eigenfaces” method。 The arithmetic of feature extraction are specified as follows:
For a face image of m × n， connecting its each row will constitute a row vector which has D= m × n dimensions。 The D is the face image dimensions. Supposing M is the number of training samples, is the face image vector which is derived from the jth picture， so the covariance matrix of the whole samples is:
（5）
And the μ is the average image vector of the training samples：
（6)
Orderingsoand its demision is DD.（7)
According to the principle of K—L transform， the coordinate we achieved is com—posed of eigenvector corresponding to nonzero eigenvalue of matrix Computing out the eigenvalue and Orthogonal normalized vector of matrix D×D directly is diffi-cult. So according to the SVD principle, it can figure out the eigenvalue and eigen-vector of matrix through getting the eigenvalue and eigenvector of matrix
is r nonzero eigenvalue of matrix：is the eigenvector corre-sponding to so the orthogonal normalized eigenvector of matrix is as bel—low：
This is the eigenvector ofArranging its eigenvalues according to the size: ,its corresponding eigenvector is . In this way, each face image can project on the sub—space composed of，…。 In order to reduce the dimension, it can select the former d eigenvectors as sub—space。 It can select d biggest eigenvectors according to the energy proportion which the eigenvalue occupies:
Usually ordering α=90％～99％。
As a result , the image corresponding to these eigenvectors are similar to the human face， it is also called “Eigenfaces".So the method which uses PCA transform is called“Eigenfaces"method。 Owing to the Drop—dimensional space composed of “Ei—genfaces”, each image can project on it and get a group of coordinate coefficients which shows the location of the sub-space of this image， so it can be used as the bases for face recognition。 Therefore, it can use the easiest Nearest Neighbor Classifier［8］ to classify the faces。
4 Experiments and Results
This part mainly verifies the feasibility and superiority of the algorithm through the comparison of the experimental data.
4.1 Experimental Conditions and Parameters
Selecting Images After Delamination。 After Red-Black wavelet transform， we only select the data of the blue block， because the part of the blue block represents the ap-proximating face image and it is not sensitive to the expression and illumination and even filtrates the image noise.
The Influence of The Blue Block Energy Caused By Decomposition Layers. In the experiment data[9］ of the Red—Black transform， we can find that it does not have the energy centralized characteristic under the situation of multi-layer decomposition。 As the Table 1 shows that different layer decompositions obtain different energies. Test image is the international standard image Lena512， its energy is 4.63431e+009 and entropy is 7。4455。
The original image energy wastage is due to the black and yellow block transform.
According to the former results and the size of the face image (112×92）, one layer decomposition can be done to achieve satisfactory results. The blue block sub-band not only has no incentive to expression and gestures， but also retains the difference of different faces. At the same time it reduces the image vector dimensions and the com—plexity of the algorithm。 If the size of the original image is bigger and the resolution is higher, the multi—layer decompositions can be considered。
Database Selection。 We choose the public ORL database to do some related ex-periments。 This database contains 40 different people’s images which are captured in different periods and situation. It has 10 pictures per person and 400 pictures in all. The background is black. Each picture has 256 grayscales and the size is 112×92. The face images in the database have the different facial expressions and the different facial detail changes。 The facial postures also have the changes. At present, this is the most extensive face database。
4。2 Experiment Processes and Results
The method of face recognition based on Red—Black wavelet transform and PCA shows as bellow: Firstly, using the improved image histogram equalization to do pretreatment，
eliminating the impact of the differences in light intensity。 Secondly, using the Red—black wavelet transform to withdraw the blue block sub-band of the relative stable person face image achieved the effects of obscuring impacts of expressions and pos-tures. Then， using PCA to withdraw the feature component and do recognition. We adopt 40 person and 5 pictures per person when training, so there are 200 pictures as the training samples all together. Then carrying on recognition to the other 200 pictures under the conditions of whether there are illumination and Red—Black wavelet trans—form or not。
Image Preprocessing。 First using the illumination compensation on the original face images (Fig。5) in the database， namely doing gray adjustment and normalization， the images （Fig。6） after transform are obviously clearer than the former ones and helpful for analysis and recognition。 Put the one layer Red—Black wavelet transform on the com—pensation images, then withdraw the images of the blue block sub-band which are the low-dimension approximating images of the original images （Fig。7)。 Appling Red-Black wavelet transform on the images plays an important role in obscuring the impacts of face expressions and postures and achieved good effects of reducing dimensions.
Feature Extraction and Matcing Results。 After the image preprocessing, we adopt PCA to extract features and recognize. This paper analyses the results of three models which separately are PCA combined with Red-Black wavelet transform, illumination compensation， Red-Black wavelet transform and illumination compensation。 The recognition rates， training and recognition time of different models are showed in the Table 2. We can see that withdrawing the blue block sub—band can obviously reduces the dimensions of the image vector and computation。 The reducing training time shows that the low resolution subgraph reduces the computational complexity of the PCA through the Red-Black wavelet transform。 Since illumination have great influence on feature extraction and recognition based on PCA， so the recognition effects can be enhanced by illumination compensation. Therefore， the combination of Red—Black wavelet transform, illumination compensation and PCA can achieve more satisfactory system performance。 Comparing with the traditional method using wavelet transform and PCA , the recognition rate is enhanced obviously。
5 Conclusion
The Red-Black wavelet transform divides the rectangular grid digital image into red and black blocks and uses the two—dimensional lifting form to construct sub-band。 It is an effective way to wipe off the image relativity and gets the more sparser image。 PCA extracts eigenvector on the basis of the whole face grayscale relativity。 The