cvpr cvpr2013 cvpr2013-220 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Weihong Deng, Jiani Hu, Jun Guo
Abstract: The success of sparse representation based classification (SRC) has largely boosted the research of sparsity based face recognition in recent years. A prevailing view is that the sparsity based face recognition performs well only when the training images have been carefully controlled and the number of samples per class is sufficiently large. This paper challenges the prevailing view by proposing a “prototype plus variation ” representation model for sparsity based face recognition. Based on the new model, a Superposed SRC (SSRC), in which the dictionary is assembled by the class centroids and the sample-to-centroid differences, leads to a substantial improvement on SRC. The experiments results on AR, FERET and FRGC databases validate that, if the proposed prototype plus variation representation model is applied, sparse coding plays a crucial role in face recognition, and performs well even when the dictionary bases are collected under uncontrolled conditions and only a single sample per classes is available.
Reference: text
sentIndex sentText sentNum sentScore
1 cn Abstract The success of sparse representation based classification (SRC) has largely boosted the research of sparsity based face recognition in recent years. [sent-3, score-0.457]
2 A prevailing view is that the sparsity based face recognition performs well only when the training images have been carefully controlled and the number of samples per class is sufficiently large. [sent-4, score-0.569]
3 This paper challenges the prevailing view by proposing a “prototype plus variation ” representation model for sparsity based face recognition. [sent-5, score-0.51]
4 Based on the new model, a Superposed SRC (SSRC), in which the dictionary is assembled by the class centroids and the sample-to-centroid differences, leads to a substantial improvement on SRC. [sent-6, score-0.296]
5 Introduction The sparse representation-based classification (SRC) algorithm for face recognition was introduced by Wright et al. [sent-9, score-0.281]
6 The key idea of that paper is a judicious choice of dictionary: representing the test image as a sparse linear combination of the the training images themselves. [sent-11, score-0.171]
7 Motivated by the conditional equivalence of the sparsity measured by ? [sent-12, score-0.125]
8 Finally, the test sample is classified by checking which class yields minimum representation error. [sent-16, score-0.149]
9 The success of SRC has largely boosted the research of sparsity based face recognition. [sent-17, score-0.293]
10 combined SRC with markov random fields to recognize the disguise face with large contiguous occlusion [20]. [sent-21, score-0.24]
11 applied the sparse coding to jointly address blind image restoration and blurred face recognition [18]. [sent-25, score-0.308]
12 introduced a discriminative dictionary learning method to improve the accuracy and efficiency of face recognition [17]. [sent-27, score-0.402]
13 The sparse representation based face recognition assumes that the training images have been carefully controlled and that the number of samples per class is sufficiently large. [sent-29, score-0.504]
14 [14] It is the purpose of this paper to challenge the common view that the sparsity based face recognition is inadequate with the uncontrolled training samples. [sent-31, score-0.595]
15 The inferior performance of SRC can properly be traced to the training samples based dictionary that do not distinguish the classspecific prototype and the intra-class variation. [sent-32, score-0.472]
16 It is shown in this paper that a simple variant of SRC, which represents the test sample as a sparse linear combination of the class centroid and the differences to the class centroid, leads to an enormous improvement under the uncontrolled training conditions. [sent-33, score-0.615]
17 The Debates on SRC Denote the training samples of all k classes as the matrix A = [A1, A2 , . [sent-37, score-0.132]
18 , Ak] ∈ Rd×n, where the sub-matrix Ai ∈ Rd×ni stacks the training samples ofclass i. [sent-40, score-0.125]
19 Then, the 333999779 linear representation of a testing sample y can be rewritten as y = Ax0 + z (1) where x0 is a sparse vector whose entries are zeros except those associated with the ith class, and z ∈ Rd is a noise ttehormse w asitsho cb ioautendde wdi energy ? [sent-41, score-0.139]
20 2-regularized method, called collaborative representation based classification (CRC), had very competitive face recognition accuracy to the ? [sent-55, score-0.25]
21 Based on their results, the sparsity based face recognition seems to be useful, but not necessary. [sent-57, score-0.324]
22 It is possible that the sample size per class used in [19] is still not enough to directly ensemble a over-complete dictionary for the face recognition problem. [sent-61, score-0.521]
23 How to design an over-complete dictionary with limited sample size per class is an essential problem for sparsity based face recognition. [sent-64, score-0.594]
24 Prototype rithm plus Variation Model and Algo- The previous studies in [11] [13] [19] have revealed the limitations of sparsity based recognition when the training images are corrupted and the number of samples per class is insufficient. [sent-66, score-0.537]
25 This section introduces a prototype plus variation (P+V) model and a corresponding sparsity based classification algorithm to address these limitations of SRC. [sent-67, score-0.512]
26 We further assume that yp is sparsely generated using the model with a prototype dictionary (matrix) P = [P1, P2 , . [sent-73, score-0.4]
27 , Pk] ∈ Rd×m, where the sub-matrix Pi ∈ Rd×mi stacks the mi prototypical bases of class i. [sent-76, score-0.199]
28 If there are redundant and overcomplete facial variant bases in V , the combination coefficients in β0 are naturally sparse. [sent-81, score-0.189]
29 In general, P+V model has two advantages over the traditional sparse model in (3): • • P+V model improves the robustness against the contPa+mVina mtoivdee training samples. [sent-84, score-0.142]
30 By separating tth teh image contaminations to the variation matrix that is shared by all classes, the class-specific prototypes would become clean and natural, and thus the classification would not be deteriorated by the corrupted training sample. [sent-85, score-0.293]
31 P+V model requires less samples per class to construct an over-complete dictionary. [sent-86, score-0.135]
32 pAles sth pee rva crlaiasstio ton cmonatsrtirxu cist shared by all classes, the dictionary size of the class i is expanded from mi to mi + q. [sent-87, score-0.305]
33 Once q is sufficiently large, the overcomplete dictionary for each class can be readily constructed. [sent-88, score-0.291]
34 The illustrative examples of the prototype plus variation (P+V) model. [sent-90, score-0.344]
35 A Superposed SRC Algorithm To show the strength of the P+V model, we propose a very simple classification algorithm according to this model and demonstrate its effectiveness on face recognition un- der uncontrolled training conditions. [sent-95, score-0.491]
36 Given a data set with multiple images per subject, the ni samples of subject i, stacked as vectors, form a matrix Ai ∈ Rd×ni ,i = 1, . [sent-96, score-0.147]
37 As the prototypes are represented by class cen∈tr Roids, the variation matrix is naturally constructed by the sample based difference to the centroids as follows: V = [A1 − c1e1T, . [sent-112, score-0.284]
38 , Ak − ckekT] ∈ Rd×n (10) where ci is the class centroid of class i. [sent-115, score-0.17]
39 1 illustrates an typical examples of the prototype and variation matrices. [sent-117, score-0.249]
40 When number of samples per class is insufficient, and in particular when only a single sample per class is available, the intra-class variation matrix would become collapsed. [sent-118, score-0.366]
41 To address this difficult, one can acquire the variant bases from the generic subjects outside the gallery, as the P+V model has assumed that the intra-class variations of different subjects are sharable. [sent-119, score-0.219]
42 The nonzero coefficients are expected to concentrate on the centroid of the same class as the test sample and on the related intra-class differences. [sent-121, score-0.194]
43 Superposed Sparse Representation based Classification (SSRC) 1: Input: a matrix of training samples A = [A1, A2 , . [sent-123, score-0.132]
44 Compute the prototype matrix P according to (9), and the variation matrix V according to (10). [sent-127, score-0.309]
45 When the sample size per class is insufficient, the matrix V can be computed from a set of generic samples outside the gallery. [sent-128, score-0.244]
46 2: Derive the projection matrix Φ ∈ Rd×p by applying DPCerAiv on hthee p training samples A Φ, a ∈nd R project the prototype and variation matrices to the p-dimensional space. [sent-129, score-0.381]
47 new vector whose only nonzero entries are ∈the R entries in αˆ 1 that are associated with class i. [sent-177, score-0.125]
48 Related Works and Discussions There are several previous methods that aim to improve the robustness of SRC by appending additional bases to the conventional dictionary of training images. [sent-181, score-0.379]
49 addressed the disguise problem by adding a complete set of single-pixel based bases to the dictionary of SRC [15]. [sent-183, score-0.331]
50 Yang and Zhang [16] used the Gabor features for SRC with a learned Gabor occlusion dictionary to reduce the computational cost. [sent-184, score-0.239]
51 introduced Extended SRC (ESRC) method to address the undersampled problem of SRC by representing the typical facial variations in an additional dictionary [3]. [sent-186, score-0.296]
52 These methods are effective to improve the robustness against the corruption ofthe test images, but they are still sensitive to the corruption of the training images. [sent-187, score-0.316]
53 Comparative recognition rates of SSRC and other recognition methods. [sent-189, score-0.143]
54 504910% % The proposed P+V model and the corresponding SSRC algorithm, for the first time, design the dictionary by the decomposition of the training samples into the separated parts of prototypes and variations. [sent-200, score-0.356]
55 Therefore, the P+V model based classification is expected to be robust against the corruption of both the training and test images. [sent-201, score-0.212]
56 [2] also aimed to address the training corruption problem, but they only filtered out the corruption by low-rank and sparse decomposition, without any concern of the typical intra-class variations in the dictionary setting. [sent-203, score-0.548]
57 [13], SRC performs worse because the randomly selected training set contains corruption images occlusion that would break the sparsity assumption. [sent-232, score-0.342]
58 However, one should not deny the the usefulness of the sparsity based recognition according to the above results, as we find that the discrimination power of sparse representation relies heavily on the suitable choice of dictionary. [sent-233, score-0.268]
59 By simply re-designing the dictionary by the P+V model, the SSRC dramatically boost the sparsity based recognition accuracy to over 98%. [sent-236, score-0.38]
60 The ESRC method, which appends an intra-class dictionary to the training samples, also increases the accuracy to about 97%, but using a much larger dictionary of 2600 bases. [sent-237, score-0.464]
61 In total, there are 8 training images and 12 test images per person. [sent-241, score-0.162]
62 In total, there are 8 training images and 12 test images per person. [sent-243, score-0.162]
63 Sunglasses+Scarf: Seven neutral images and two corrupted images (aornfe: Sweivthe sunglasses aangde sth aen dot thwero w coitrhscarf) at session 1 are selected for training. [sent-244, score-0.404]
64 The comparative recognition rates between SRC and SSRC on the AR data set with different kinds of corrupted training images. [sent-246, score-0.262]
65 there are 9 training images and 17 test images (seven neutral images at session 2 plus the remaining ten occluded images) are available for this case. [sent-247, score-0.417]
66 We vary the dimension of the eigenspace from 20 to 500, and compare the recognition performance of between SRC and SSRC. [sent-248, score-0.142]
67 2 shows the comparative recognition rates between SRC and SSRC on the AR data set with different kinds of corrupted training im- ages, and one can see from the figure that SSRC outperforms SRC by a margin about 6% to 12%, depending on the percentage of occlusion. [sent-251, score-0.262]
68 Specifically, SRC performs better on the sunglasses scenario (about 84% accuracy with 20% occlusion) than the scarf scenario (about 80% accuracy with 40% occlusion), followed by the sunglasses+scarf scenario (about 78% accuracy). [sent-252, score-0.292]
69 The performance of SRC deteriorates when the percentage of occlusion involved in the training images increases, and this is an observation consistent with the common criticism on SRC with uncontrolled training images [14]. [sent-253, score-0.407]
70 Besides the boosted accuracy, SSRC displays the stability against various kinds of corruption in the training images. [sent-255, score-0.181]
71 The average accuracies of the first five methods are cited from [2], of which the best-performed method, denoted as LR+SI+SRC, applied low-rank matrix recovery with structural incoherence to filter out the corruption of the training images. [sent-257, score-0.26]
72 Comparative recognition rates of SSRC and other recognition methods. [sent-260, score-0.143]
73 (a) The cropped images of some gallery images and corresponding probe images in the FERET database. [sent-281, score-0.222]
74 (b) Example images of the differences to the class centroid computed from the FRGC version 2 database. [sent-282, score-0.131]
75 Recognition with Uncontrolled and Overcomplete Dictionary This experiment is designed to test the robustness of SSRC against complex facial variation in the real-world applications. [sent-286, score-0.172]
76 fb probe set contains 1,195 images taken with an alterfnba tpivroeb bfeac sieatl expression. [sent-288, score-0.128]
77 fc probe set contains 194 images taken under different lighting conditions. [sent-289, score-0.128]
78 dup1 probe set contains 722 images taken in a different tdimupe1. [sent-290, score-0.128]
79 dup2 probe set contains 234 images taken at least a year 2la pteror,b weh siecth c iosn a asiunbsse 23t o4f itmhea dup1 skeetn. [sent-291, score-0.128]
80 As there is only a single sample per gallery class, we construct the intra-class variation matrix from the standard training image set of the FRGC Version 2 database [9], which contains 12,766 frontal images of 222 people taken in the uncontrolled conditions. [sent-296, score-0.564]
81 Hence, in this experiment, the variation matrix is required to universally represent the complex facial variations under uncontrolled conditions. [sent-300, score-0.361]
82 For each feature, we test the recognition performance in the reduced PCA dimension of 125, 250, and 1000 respectively. [sent-302, score-0.124]
83 These results suggest that the P+V model is feasible for various feature representations, and thus it can be integrated with more informative features to address uncontrolled face recognition problem. [sent-319, score-0.434]
84 It should be mentioned that similar experimental results has been reported on ESRC method [3], but its intra-class variant dictionary are constructed from the generic training set of FERET database. [sent-321, score-0.318]
85 In contrast, our experiment, for the first time, justifies the effectiveness of the sparsity based face recognition when the dictionary bases are collectedfrom the uncontrolled conditions that are independent from the test condition. [sent-325, score-0.886]
86 2-norm regularization Over-complete Dictionary with Based on the results on the FERET database, we further investigate the role of sparsity in face recognition with an uncontrolled and over-complete dictionary. [sent-330, score-0.606]
87 1-norm indeed play a crucial role in face recognition given an uncontrolled and over-complete dictionary. [sent-386, score-0.432]
88 1-norm sparsity is different from that by Zhang et al. [sent-388, score-0.125]
89 Indeed, both observations are valid, but under different dictionary settings. [sent-390, score-0.203]
90 The dictionary of SSRC contains an over-complete set of intra-class variation bases, and most of which are irrelevant to the test sample. [sent-395, score-0.316]
91 Conclusions It has been shown in this paper that a simple separation between the prototype and variation components leads to an enormous improvement on sparsity based face recognition under uncontrolled training conditions. [sent-404, score-0.868]
92 1-norm regularization based sparse coding the algorithms accurately find out the intra-class variation bases from an over-complete dictionary that is constructed from uncontrolled generic images outside the gallery. [sent-408, score-0.801]
93 Our preliminary results suggest that the proposed prototype plus variation model provides a widely applicable framework to address uncontrolled face recognition problem. [sent-409, score-0.778]
94 Low-rank matrix recovery with structural incoherence for robust face recognition. [sent-428, score-0.205]
95 Extended src: Undersampled face recognition via intraclass variant dictionary. [sent-434, score-0.252]
96 Sparse representation for face recognition based on discriminative low-rank dictionary learning. [sent-453, score-0.432]
97 Towards a practical face recognition system: robust registration and illumination by sparse representation. [sent-502, score-0.26]
98 Gabor feature based sparse representation for face recognition with gabor occlusion dictionary. [sent-533, score-0.373]
99 Close the loop: Joint blind image restoration and recognition with sparse representation prior. [sent-548, score-0.143]
100 Sparse representation or collaborative representation: Which helps face recognition? [sent-554, score-0.177]
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