A Bottom-Up Dictionary Learning based

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A Bottom-Up Dictionary Learning based Classification for Face Recognition

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Paper ID 246

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Anonymous ACPR submission

Abstract

Eigenface [13], Fisherface [11] and Laplacianfaces [5]. In order to increase the robustness to facial variations, local feature based descriptors for facial image, such as local binary pattern (LBP) [2], Gabor feature [9] and their combinations have been proposed. For instance, Timo et al. [2] encoded the micro image pattern via LBP and then concatenated the histogram of LBP in each local region as the final descriptor. Recently general image representation has achieved significant progress due to the present of powerful image descriptors based on spatial pyramid matching (SPM) with sum pooling [8] and max pooling [14, 17]. This kind of descriptor consists of encoding local patch, pooling coding vectors in each region and concatenating the coefficients of all regions. In the step of local patch encoding, Kmeans and sparse coding are the popular dictionary learning approaches. SPM based descriptor has been widely used in general image classification, very few work has applied this kind of descriptor to face recognition except for some works, such as translation-invariant face recognition [18] and sparsely encoded local descriptor without pooling [3].

The design of image descriptor and classifier are two important issues in face recognition. Although many facial image descriptors (e.g., subspace learning, local binary pattern) and classifier (e.g., support vector machine, sparse representation based classifier) have been proposed, these two components seldomly belong to a same framework, which may prevent the discrimination being fully exploited. Inspired by the success of dictionary learning based descriptor and classifier, in this paper, we proposed a bottom-up dictionary learning based classification (BUDLC) for face recognition. In BUDLC, we generate the image descriptor via encoding local patches on a learned dictionary with a regularization of spatial and appearance consistence. Then with the generated image descriptor, a structured discriminative dictionary is learned for the image classifier by using the mixed-norm joint sparse representation. The BUDLC are extensively evaluated on several benchmark face databases, such as AR, Multi-PIE and LFW. Experimental results demonstrate that our algorithm outperforms many existing face recognition approaches.

Nearest neighbor (NN) and support vector machine (SVM) are two popular classifiers applied to face recognition. Very recently, sparse representation based classifier (SRC) [16] has shown very promising performance in face recognition. SRC encodes a query face image over all the training samples (i.e., dictionary) with sparse regularization over the coding coefficients,and classifies it by checking which class has the least reconstruction residual. Apart from the l1 /l0 -norm sparse regularization over the coding vector, Zhang et al. [20] proposed l2 -norm regularized collaborative representation based classifier (CRC), with competing accuracy but with much faster speed. Both SRC and CRC directly use the original training samples as the dictionary (representation basis). In order to fully exploit the discrimination of training samples, dictionary learning approaches have been developed by learning a shared dictionary [6, 21], class-specific dictionary [19], or the combination of them [7,22]. The shared dictionary is learned to represent the data of all classes, where a classifier over the coding coefficient is jointly learned. In class-specific dictionary learning, the dictionary atoms are predefined to have corre-

1. Introduction As one of the most challenging topics in computer vision and biometrics, face recognition has been attracting much attention for several decades. Various methods have been proposed to overcome the difficulties of face recognition, e.g., variations of illuminations, expression, pose and occlusion. Similar to the general image classification, face recognition also has two important components, i.e., image descriptor and classifier. A powerful face recognition system should has a discriminative image descriptor with preserving the identity but invariant to various variations described as above and a strong classifier to fully exploit the discrimination embedded in the feature space. Along these two directions, many face recognition approaches have been proposed [6, 7, 19]. A representative face image descriptor is the intensity feature and its subspace/manifold learning features, e.g., 1

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Notation λ, γ M X K

Description parameter number of clusters local patches number of classes

Notation P, D B Y A

Description patch/classification dictionary coefficients of X over P image descriptor coefficients of Y over D

Extract local patch feature

Patch dictionary learning

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Ø (·)

Figure 1. Image descriptor based on patch dictionary learning

Table 1. Notations and descriptions used in this paper

for classification, we use a class-shared dictionary, denoted by P , as the local patch dictionary. Meanwhile, we learn a set of class-specific dictionaries, denoted by Dj for class j, for the final image classification. Let Yi = [yi,1 , yi,2 , · · · , yi,ni ] be the final image descriptor of i-th class. The bottom-up dictionary learning model for classification could be written as

spondence to the class label so that each class has its own dictionary. Although the dictionary learning based representation classifier has shown very powerful classification ability in image classification, including face recognition, dictionary learning is not well exploited in the building of image descriptor. In this paper, we propose a bottom-up dictionary learning based classification for face recognition, where the dictionaries are well learned in the building of image descriptor and classifier. We build the image descriptor and classifier in a dictionary learning framework, where joint sparsity is used to regularize the coding vector to exploit the class and similarity information of training data. Based on the learned patch dictionary, discriminative descriptors of face images could be generated, while the final classification is conducted via collaborative representation based classifier using the learned classification dictionary. The proposed BUDLC is evaluated on several face databases, including AR, MultiPIE and LFW. Compared with the existing face recognition methods, BUDLC has shown significant improvements in various conditions. Frequently used notations and descriptions are summarized in Table 1. Section 2 presents the proposed BUDLC model. Section 3 describes the optimization of BUDLC. Section 4 conducts the experiments, and Section 5 concludes the paper.

min

D,A,P,B

K X {kYj − Dj Aj k2F + λkAj k2,1 j=1

+

M X

kXjm − P Bjm k2F + γkBjm k2,1 }

(2)

m=1

s.t. Yi,j = Φ(Bi,j ) P where k · k2,1 is defined as kAj k2,1 = k kaj,k k2 , aj,k is the k-th row vector of the matrix Aj , λ and γ are two scalar variables, Xjm is the m-th cluster in Xj and M is the total number of clusters in each class. Here the mixednorm k · k2,1 requires the between-row sparisity by using l1 -norm and regularizes variables in each row vector via l2 norm, making the coding coefficients of training samples in the same class/clusters similar. In Eq.(2) the optimization of P and B is the patch dictionary learning for image descriptor, while the optimization of D and A is the dictionary learning for classifier. Since the operator Φ(·) is a non-linear operation (e.g., max pooling), the involvement of Y in dictionary learning will make the optimization of Eq.(2) very complicated and easily drop to a local minimum. Therefore we simplified Eq.(2) by assuming yi,j = Φ(Bi,j ) to be independent from the learning of P , B, D and A. Then BUDLC could be divided into two sub-models: dictionary learning for image descriptor and dictionary learning for image classifier.

2. Bottom-up dictionary learning based classification In order to better take advantage of dictionary learning, we propose a bottom-up dictionary learning based classification method, in which both the image descriptor and classifier are based on dictionary learning. Let X = [X1 , X2 , · · · , XK ] be the set of local patches extracted from the training data, where Xi = [Xi,1 , Xi,2 , · · · , Xi,ni ] denotes the patches from i-th class data, Xi,j denotes the patches from j-th sample of i-th class, and K is the number of classes. Let Bi,j be coding matrix of Xi,j over the learned patch dictionary, the image descriptor of j-th training sample of i-th class, yi,j , could be represented as yi,j = Φ(Bi,j )

Cluster local patch

2.1. Patch dictionary learning for image descriptor Before giving the patch dictionary learning, we first show the flowchart of image descriptor based on patch dictionary learning in Fig. 1. Compared to the present approaches of bag of words (e.g., [14]), we proposed to cluster the local patch in each class and do dictionary learning and feature encoding based the clustering results.

(1)

where the operation of Φ(·) includes feature encoding on the patch dictionary and multi-scale spatial max pooling, similar to that of [14]. Since the local patch has very limited discrimination

2.1.1

Local patch clustering

Denote by Li = [Li,1 , Li,2 , · · · , Li,ni ] the spatial locations of patches from i-th class data, where Li,j is the 2

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3. Optimization of dictionary learning

locations of patches from j-th sample of i-th class. Although local patches have limited discrimination, there is much correlation between different local patches. In order to consider both the appearance and spatial consistence of the local patches, we define a new feature vector Zi = [(1 − w) ∗ Xi , w ∗ Li ], on which the clustering via K-mean is conducted Ind = Kmeans(Zi , M )

Both the dictionary learning models for image descriptor and classifier, Eq. (4) for each cluster and Eq. (6) for each class, have the same formulation min kG − EF k22 + λkF k2,1 E,F

which could be solved by an alternative optimizing the dictionary (e.g., E) and coding matrix (e.g., F ). When the coding matrix F is fixed, the dictionary E could be updated atom by atom via the method in [19]. When the dictionary E is fixed, Eq. (9) changes to a joint sparse coding problem

(3)

where w is a scalar variable to balance the contribution of spatial vector and appearance vector. 2.1.2

min kG − EF k22 + λkF k2,1

Patch dictionary learning

F

E (t+1) [k] = Λ[k]M ax(0, 1 − λ/(2σkΛ[k]k2 ))

j=1 m=1

Feature encoding on P

For the local patches extract from an image, we do feature coding as min kXj − P Bj k2F + γkBj k1 B

4. Experiment results

(5)

In this section, we verify the face recognition performance of BUDLC on AR [10], Multi-PIE [4] and LFWa [15] database. The parameter setting of BUDLC is discussed in section 4.1. Face recognition without occlusion are performed in section 4.2. The comparison on face recognition with challenging variations is presented in section 4.3.

Then the feature vector of this image could be generated by Eq. (1).

2.2. Dictionary learning for image classification When the training image descriptor Y has been generated, the dictionary learning for image classification from Eq. (2) could be written as K X min kYj − Dj Aj k2F + λkAj k2,1 (6) D,A

4.1. Parameter setting There are two regularization parameters, λ and γ , in BUDLC. λ and γ regularize the joint sparsity in classifier dictionary learning and patch dictionary learning respectively. In this paper, we set λ = γ = 0.001 if no specific instruction. In the patch dictionary learning, we set the number of clusters M in the training patches for each class as 10. The spatial block structure for the SPM is set as 1×1, 2 × 2 and 4 × 4 and the patch coding on the learned patch dictionary (i.e.,P ) is conducted via locality-constrained linear coding [14]. When w = 0, the clustering only considers the appearance of each local patch, when w = 1, the clustering only make the neighbored pixels in the same cluster. When 1 > w > 0, the clustering will make a balance between the similarity of appearance and spatial location. The number of atoms of j-th class classifier dictionary, Dj , is set as the number of training samples in j-th class.

j=1

where D = [D1 , D2 , · · · , DK ] is the dictionary to be learned and Dj is the class-specific dictionary associated to class j.

2.3. Classification model When a query face image comes, we could generate the its feature vector, y, via Eq.(1) based on the learned patch dictionary P . Then we conduct collaborative representation based classification [20] for z a0 = argmina ky − [D1 , D2 , · · · , DK ]ak22 + λkak22 (7) and the identity of the query sample is recognized via identity(z) = argmini ky − Di a0i k22

(11)

where σ is a scalar parameter in [12], M ax(·) is a maximal operator, E (t+1) [k] and Λ[k] are the k-th row vector of E t+1 and Λ, respectively. When the objective function values of Eq.(10) in adjacent iterations are close enough or the maximum number of iterations is reaches, the iterative optimization stops and output the learned dictionary P and D.

The local patches in the same cluster are similar to each other, so it is very reasonable to require that they should have similar sparse coding coefficients in Eq. (4). 2.1.3

(10)

which could be efficiently solved by the Iterative Projection Method [12]. Denote Λ = F (t) − (E T EF (t) − E T G)/σ, in the (t + 1)-th iteration, the solution could be written as

By assuming Y independent from dictionary learning, the patch dictionary learning could be represented as K X M X min kXjm − P Bjm k2F + γkBjm k2,1 (4) P,B

(9)

(8)

where the coding vector a0 = [a01 , a02 , · · · , a0K ] and a0i is the sub-vector associated with Di . 3

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Recognition rate (%)

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Dim 54 120 300 64×43

100 98 96 Random Kmeans KSVD BUDLC

94 92 200

400

600

800

NN 68.0 70.1 71.3 -

SVM 69.4 74.5 75.4 -

SRC 83.3 89.5 93.3 -

CRC 80.5 90.0 93.7 -

LBPCRC 95.3

SPM 97.4

BUDLC 98.9

Table 2. Face recognition rates (%) on the AR database without occlusion

1000

the number of patch dictionary atom

Figure 2. The recognition rates of different patch dictionary learning methods in different sizes of patch dictionary on the AR database

S2 S3 S4

The number of atoms of the patch dictionary P has a significant effect on the accuracy and efficiency of the BUDLC because the discrimination and feature length of image descriptor is closely related to the atom number of P . We compare BUDLC with different patch dictionary learning methods (e.g., random selection, K-means centers, and KSVD dictionary learning [1]) and different number of dictionary atoms on the AR database, which are followed by the classifier using SPM and linear SVM (SPMSVM). The comparison is shown in Fig. 2. It can be seen that as the increase of dictionary size, the accuracy of all methods improve. Consider the accuracy and efficiency, in the following experiments, we set the size of P as 600 in face recognition without occlusion and as 800 in face recognition with challenging variations. We can also observe that BUDLC has significant improvement over other methods. In patch dictionary learning, random selection, kmeans and KSVD have very close performance. So in the experiments SPMSVM, kmeans is used to generate the patch dictionary in default. The competing methods includes eigenface or intensitybased methods (e.g., NN, SVM, SRC and CRC), CRC with LBP feature (LBPCRC), SVM with SPM feature (SPM). The spatial block structure for the SPM is set as 1 × 1, 2 × 2 and 4×4. In order to make a fair comparison, the block division of LBP is 4 × 4.

NN 86.4 78.8 82.3

SVM 85.2 78.1 82.1

SRC 93.9 90.0 94.0

CRC 94.1 89.3 93.3

LBPCRC 96.6 93.7 94.6

SPM 96.9 96.2 97.6

BUDLC 96.9 96.9 98.6

Table 3. Face recognition rates (%) on the MultiPIE database without occlusion

SVM SRC Sunglass 53.5 87.0 Scarf 25.0 59.5

CRC LBPCRC SPM BUDLC 68.5 96.0 86.0 98.5 90.5 83.5 95.5 97.5

Table 4. Face recognition rates (%) on the AR database with disguise

2) Multi PIE database: The CMU Multi-PIE database [4] contains images of 337 subjects captured in four sessions with simultaneous variations in pose, expression, and illumination. Among these 337 subjects, all the 249 subjects in Session 1 were used. For the training set, we used the 14 frontal images with 14 illuminations1 with neutral expression. For the testing sets, 10 typical frontal images2 of illuminations taken with neutral expressions from Session 2 to Session 4 were used. The dimensionality of Eigenface is 300. Table 4.2 lists the recognition rates in three sessions by the competing methods. The results validate that BUDLC, LBPCRC and SPM are better than all the other methods. BUDLC still gets the best accuracy.

4.3. Face recognition with challenging variations 1) FR with real face disguise: As [16], in AR dataset 800 images (about 8 samples per subject) of non-occluded frontal views with various facial expressions were used for training, while the others with sunglasses and scarves were used for testing. The images were resized to 60×43. The results of competing methods are shown in Table 4.3. One can see that in this challenging case, BUDLC has shown a big improvement over all the other methods, with at least 2.5% and 2.0% improvements in sunglass and scarf disguise, respectively. 2) LFW: LFW is a large-scale database of face photographs designed for unconstrained FR with variations of pose, illumination, expression, misalignment and occlusion,

4.2. Face recognition without occlusion 1) AR database: As [16], we chose a subset (with only illumination and expression changes) that contains 50 male subjects and 50 female subjects from the AR dataset [1] in our experiments. For each subject, the 7 images from Session 1 were used for training, with other 7 images from Session 2 for testing. The size of image was cropped to 60 × 43. The comparison of competing methods is given in Table 4.2. We can see that the eigenface-based methods are significantly worse than BUDLC, SPM and LBPCRC. BUDLC has 1.5% improvement over the second best one, SPM. This shows the learned dictionary in BUDLC is more discriminative.

1 Illuminations 2 Illuminations

4

{0,1,3,4,6,7,8,11,13,14,16,17,18,19} {0,2,4,6,8,10,12,14,16,18}

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NN 12.1

SVM 48.7

SRC 50.3

CRC 52.7

LBPCRC SPM 50.9 64.2

BUDLC 74.1

[7] S. Kong and D. Wang. Learning inter-related visual dictionary for object recognition. In ECCV, 2012. 1 [8] S. Lazebnik, C. Schmid, and J. Ponce. Beyond bags of features: spatial pyramid matching for recognizing natural scene categories. In CVPR, 2006. 1 [9] C. Liu and H. Wechsler. Gabor feature based classification using the enhanced fisher linear discriminant model for face recognition. Image Processing, IEEE Transactions on, 11(4):328–340, 2002. 1 [10] A. Martinez and R. Benavente. The ar face database. Technical report, CVC Tech. Report, 1998. 3 [11] P. N.Belhumeur, J. P.Hespanha, and D. J.Kriegman. Eigenfaces vs. fisherfaces: Recognition using class specific linear projection. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 19(7):210–227, 1997. 1 [12] L. Rosasco, A. Verri, M. Santoro, S. Mosci, and S. Villa. Iterative projection methods for structured sparsely regularization. Technical report, MIT Technical Reports, 2009. 3 [13] M. Turk and A. Pentland. Eigenfaces for recognition. J. Cognitive Neuroscience, 3:71–86, 1991. 1 [14] J. Wang, J. Yang, K. Yu, F. Lv, T. Huang, , and Y. Gong. Locality-constrained linear coding for image classification. In CVPR, 2010. 1, 2, 3 [15] L. Wolf, T. Hassner, and Y. Taigman. Similarity scores based on background samples. In ACCV, 2009. 3, 5 [16] J. Wright, A. Y. Yang, A. Ganesh, and Y. Ma. Robust face recognition via sparse representation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 31(2):210– 227, 2009. 1, 4 [17] J. Yang, K. Yu, Y. Gong, and T. Huang. Linear spatial pyramid matching using sparse coding for image classification. In CVPR, 2009. 1 [18] J. Yang, K. Yu, and T. Huang. Supervised translationinvariant sparse coding. In CVPR, 2010. 1 [19] M. Yang, L. Zhang, X. Feng, and D. Zhang. Fisher discrimination dictionary learning for sparse representation. In ICCV, 2011. 1, 3 [20] L. Zhang, M. Yang, and X. Feng. Sparse representation or collaborative representation: Which helps face recognition? In ICCV, 2011. 1, 3 [21] Q. Zhang and B. Li. Discriminative k-svd for dictionary learning in face recognition. In CVPR, 2010. 1 [22] N. Zhou, Y. Shen, J. Peng, and J. Fan. Learning inter-related visual dictionary for object recognition. In CVPR, 2012. 1

Table 5. Face recognition rates (%) on the LFWa database

and so on. A subset of aligned LFW [15] is used in the experiments. In this subset which consists of 143 subjects with no less than eleven samples per subject, we use the first ten samples as training data and the remaining samples as testing data. Here the image is cropped and normalized to the size of 60 × 54 and γ = 0.01 for BUDLC. Table 4.3 lists the recognition rates of all the methods. Due to various variations, e.g., pose, occlusion, all the methods don’t get quite good performance (e.g., NN only gets 12.1% accuracy). However, compared to other methods, the advantage of BUDLC is significant, over 10% improvement, which clearly demonstrates that the proposed BUDLC could well exploit the discrimination in patch dictionary learning and classifier dictionary.

5. Conclusion We proposed a bottom-up dictionary learning based classification (BUDLC), which consists of dictionary learning for image descriptor and dictionary learning for image classifier. Instead of generating image descriptor and classifier using different kinds of approaches, the proposed BUDLC builds a framework of face recognition fully based on dictionary learning. Discriminative patch dictionary and classifier dictionary are learned by using the mixed-norm joint sparsity regularization. The extensive experiments demonstrated the effectiveness of BUDLC to other existing face recognition methods.

References [1] M. Aharon, M. Elad, and A. Bruchstein. K-svd:an algorithm for designing overcomplete dictionaries for sparse representation. Signal Processing, IEEE Transactions on, 54(11):4311–4322, 2006. 4 [2] T. Ahonen, A. Hadid, and M. Pietikainen. Face recognition with local binary patterns. In ECCV, 2004. 1 [3] Z. Cui, S. Shan, X. Chen, and L. Zhang. Sparsely encoded local descriptor for face recognition. In In Proc. FG, 2011. 1 [4] R. Gross, I. Matthews, J. Cohn, and T. Kanade. Multi-pie. Image and Vision Computing, 28(5):807–813, 2010. 3, 4 [5] X. He, S. Yan, Y. Hu, P. Niyogi, and H. jiang Zhang. Face recognition using laplacianfaces. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 27(3):328–340, 2005. 1 [6] Z. Jiang, Z. Lin, and L. S. Davis. Label consistent k-svd: Learning a discriminative dictionary for recognition. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 35(11):2651–2664, 2013. 1

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