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1、附 录一、英文原文An improved face recognition technique basedon modular PCA approachRajkiran Gottumukkal Vijayan K.AsariAbstractA face recognition algorithm based on modular PCA approach is presented in this paper. The proposed algorithm when compared with conventional PCA algorithm has an improved recognit
2、ion rate for face images with large variations in lighting direction and facial expression. In the proposed technique, the face images are divided into smaller sub-images and the PCA approach is applied to each of these sub-images. Since some of the local facial features of an individual do not vary
3、 even when the pose, lighting direction and facial expression vary, we expect the proposed method to be able to cope with these variations. The accuracy of the conventional PCA method and modular PCA method are evaluated under the conditions of varying expression, illumination and pose using standar
4、d face databases.Keywords: PCA; Face recognition; Modular PCA; Pose invariance; Illumination invariance1. IntroductionFace recognition is a difficult problem because of the generally similar shape of faces combined with the numerous variations between images of the same face. The image of a face cha
5、nges with facial expression, age, viewpoint, illumination conditions, noise etc. The task of a face recognition system is to recognize a face in a manner that is as independent as possible of these image variations.Automatic recognition of faces is considered as one of the fundamental problems in co
6、mputer vision and pattern analysis, and many scientists from different areas have addressed it. Chellappa et al. (1995) presented a survey on several statistical-based, neural network-based and feature-based methods for face recognition. Currently, one of the methods that yields promising results on
7、 frontal face recognition is the principal component analysis (PCA),which is a statistical approach where face images are expressed as a subset of their eigenvectors, and hence called eigenfaces (Sirovich and Kirby,1987; Turk and Pentland,1991;Moghaddam and Pentland,1997; Martinez, 2000; Graham and
8、Allinson,1998).PCA has also been used for handprint recognition (Murase et al.,1981), human-made object recognition (Murase and Nayar, 1995), industrial robotics (Nayar et al.,1996), and mobile robotics (Weng,1996).But results show that the recognition rate is not satisfactory for pose variations ex
9、ceeding 30 and extreme changes in illumination.The main objective of this research is to improve the accuracy of face recognition subjected to varying facial expression, illumination and head pose. As stated before, PCA method has been a popular technique in facial image recognition.But this techniq
10、ue is not highly accurate when the illumination and pose of the facial images vary considerably. In this research work an attempt is made to improve the accuracy of this technique under the conditions of varying facial expression, illumination and pose. We propose the modular PCA method, which is an
11、 extension of the conventional PCA method. In the modular PCA method the face images are divided into smaller images and the PCA method is applied on each of them. Whereas in the traditional PCA method the entire face image is considered, hence large variation in pose or illumination will affect the
12、 recognition rate profoundly. Since in the case of modular PCA method the original face image is divided into sub-images the variations in pose or illumination in the image will affect only some of the sub- images, hence we expect this method to have better recognition rate than the conventional PCA
13、 method. A similar method called modular eigenspaces was proposed by Pentland et al. (1994).In this method PCA is performed on the eyes and nose of the face image.This paper is organized as follows: Section 2 describes the conventional PCA method. Section 3 explains the modular PCA method. Section 4
14、 describes the face databases used for testing the face recognition methods. Section 5 presents simulation results obtained by applying the PCA method and the proposed modular PCA method to the face image sets with large light and pose variations. Finally, a conclusion is drawn in Section 6.2. Revie
15、w of the PCA methodThe PCA method has been extensively applied for the task of face recognition. Approximate reconstruction of faces in the ensemble was per- formed using a weighted combination of eigenvectors (eigenpictures), obtained from that ensemble (Sirovich and Kirby, 1987).The weights that c
16、haracterize the expansion of the given image in terms of eigenpictures are seen as global facial features. In an extension of that work, Kirby and Sirovich (1990) included the inherent symmetry of faces in the eigenpictures.All the face images in the face database are represented as very long vector
17、s, instead of the usual matrix representation. This makes up the entire image space where each image is a point Since the faces have a similar structure (eye, nose and mouth, position, etc.), the vectors representing them will be correlated. We will see that faces of the same class will group at a c
18、ertain location in the image space. Hence the face images are rep resented by a set of eigenvectors developed from a covariance matrix formed by the training of face images. The idea behind eigenimages (in our case eigenfaces) is to find a lower dimensional space in which shorter vectors will descri
19、be face images.Fig.1 illustrates this idea graphically.2.1. Computing eigenfacesConsider the face images in the face database to be of size L by L. These images can be represented as a vector of dimension L2 ,or a point in L2dimensional space. A set of images therefore corresponds to a set of points
20、 in this high dimensional space. Since facial images are similar in structure, these points will not be randomly distributed, and therefore can be described by a lower dimensional subspace.PCA gives the basis vectors for this subspace (which is called the face space).Each basis vector is of length L
21、2 , and is the eigenvector of the covariance matrix corresponding to the original face images.Let be the training set of face images. The average face is defined by （1）Each face differs from the average face by the vector.The covariance matrix C is obtained as （2）The eigenvectors of the covariance m
22、atrix are computed and the significant eigenvectors are chosen as those with the largest corresponding eigenvalus. From these eigenvectors, the weights for each image in the training set are computed as （3）Where s are the eigenvectors corresponding to thelargest eigenvalues of C and K varies from 1
23、to.2.2 ClassicationA test image Itest is projected into face space by the following operation: （4）pThe weights form a vector, which describes the contribution of each eigenface in representing the input face image. This vector can then be used to fit the test image to a predefined face class. A simp
24、le technique is to compute distance of from, where Tp is the mean weight vector of the pth class. The test image can be classified to be in class p when, where and is the threshold.3. Modular PCA methodThe PCA based face recognition method is not very effective under the conditions of varying pose a
25、nd illumination, since it considers the global information of each face image and represents them with a set of weights. Under these conditions the weight vectors will vary considerably from the weight vectors of the images with normal pose and illumination, hence it is difficult to identify them co
26、rrectly. On the other hand if the face images were divided into smaller regions and the weight vectors are computed for each of these regions, then the weights will be more representative of the local information of the face. When there is a variation in the pose or illumination, only some of the fa
27、ce regions will vary and rest of the regions will remain the same as the face regions of a normal image. Hence weights of the face regions not affected by varying pose and illumination will closely match with the weights of the same individuals face regions under normal conditions.Therefore it is ex
28、pected that improved recognition rates can be obtained by following the modular PCA approach. We expect that if the face images are divided into very small regions the global information of the face may be lost and the accuracy of this method may deteriorate.In this method, each image in the trainin
29、g set is divided into N smaller images. Hence the size of each sub-image will be L2 =N .These sub-images can be represented mathematically as （5）where i varies from 1 to M, M being the number of images in the training set, j varies from 1 to N , N being the number of sub-images and m and n vary from
30、 1 to .Fig2 shows the result of dividing a face image into four smaller images using Eq.(5) for N=4. The average image of all the training sub-images is computed as （6）The next step is to normalize each training sub-image by subtracting it from the mean as （7）From the normalized sub-images the covar
31、iance matrix is computed as （8）Next we find the eigenvectors of C that are associated with the largest eigenvalues. We represent the eigenvectors as .The weights are computed from the eigenvectors as shown below: （9）where K takes the values 1,2, n varies from 1 to,being the number of images per indi
32、vidual, and p varies from 1 to P ,P being the number of individuals in the training set. Weights are also computed for the test sub-images using the eigenvectors as shown in the next equation: （10）Mean weight set of each class in the training set is computed from the weight sets of the class as show
33、n below: （11）Next the minimum distance is computed as shown below: （12） （13）for a particular value of p, the corresponding face class in the training set is the closest one to the test image. Hence the test image is recognized as belonging to the pth face class.4. Image databasesThe performance of t
34、he conventional PCA based algorithm and the modular PCA based algorithm were evaluated with two image data- bases, UMIST and Yale. The UMIST database consists of images with varying pose and the Yale database consists of images with varying illumination and expressions. All the images in both the da
35、tabases were normalized and cropped to a size of 64 64 pixels.4.1. UMIST database-pose variantFor our tests we took a partial set of face images consisting of 10 images each of 20 different individuals from the UMIST face database. Each image of a person is taken at a different pose, with a normal e
36、xpression. Out of the ten images of a person, only eight were used for training and the remaining two were used to test the recognition rate.Fig.3a and b show the set of images of a person used for training and testing respectively. The choice of the training and testing images was made to test both
37、 the algorithms with head pose angles that lie outside the head pose angles they were trained with. The PCA and modular PCA methods may perform poorly with this selection of training and testing images, but our aim is to compare their performance for test images whose head pose angles lie outside th
38、e head pose angles of the training images.4.2. Yale database-expression and illumination variantThe Yale database has 165 images of 15 adults, 11 images per person. The face images vary with respect to facial expression and illumination. The images have normal, sad, happy, sleepy, surprised, and win
39、king expressions. There are also images where the position of the light source is at the center, left and right. In addition to these there are images with and without glasses. Out of the 11 images of a person, only eight were used for training and the remaining three were used to test the recogniti
40、on rates.Fig.4a and b show the set of images of a person used for training and testing respectively. The choice of the training and test images was made to facilitate comparison of performance of both the methods for test images with uneven illumination and partial occlusion.We also conducted experi
41、ments by leaving out one image from each individuals set of 11 images during training and testing the recognition rate with the images left out. This was repeated 11 times by leaving out a different image each time. This kind of testing is referred to as leave out one testing in the remainder of the
42、 paper.5. Test resultsWe tested the performance of PCA and modular PCA algorithms for varying number of eigenvectors. Considering more eigenvectors results in increased recognition rates, however the increase in computational cost is linear with the number of eigenvectors.Fig.5 shows the recognition
43、 rates of PCA and modular PCA for varying number of eigenvectors. The results shown in Fig.5 were obtained using the Yale face database by leaving out one testing. Threshold was not used for this testing; hence there are no rejections, only correct recognition or false recognition. It can also be ob
44、served from Fig.5 that the recognition rate is increasing in both PCA and modular PCA methods as we increase the value of, and there is not much improvement for .Similar results have been observed for values N = 4, 16, 64, 256 and 1024.The modular PCA results have also been compared with the results
45、 of modular eigenspaces described by Pentland et al.(1994).It has been observed that the modular PCA algorithm pro- vides better recognition rate with the added advantage that it does not require the detection of specific features like eye, nose and mouth.Tests in the remainder of this paper were co
46、nducted at =20, i.e. eigenvectors corresponding to the 20 maximum eigenvalues of the covariance matrix. The aim of our tests was to compare the two algorithms with varying pose and illumination face images and varying would have the same effect on both the algorithms as shown in Fig.5, hence only th
47、e first 20 eigenvectors were considered for the tests.When the size of the sub-images is less than or equal to4*4, the number of eigenvectors that can be obtained from the covariance matrix will be less than 20, since the size of the covariance matrix is less than or equal to 16 16. For the case whe
48、re eigenvectors are considered. For example when N =256,16 eigenvectors are considered. For the case where N =4096, the algorithm reduces to comparing the pixel values of test image and training images, pixel by pixel.We applied the PCA method and the modular PCA method to reconstruct the test images. In the case of the PCA method the image is reconstructed as