cvpr cvpr2013 cvpr2013-178 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Amirreza Shaban, Hamid R. Rabiee, Mehrdad Farajtabar, Marjan Ghazvininejad
Abstract: Bag of words models for feature extraction have demonstrated top-notch performance in image classification. These representations are usually accompanied by a coding method. Recently, methods that code a descriptor giving regard to its nearby bases have proved efficacious. These methods take into account the nonlinear structure of descriptors, since local similarities are a good approximation of global similarities. However, they confine their usage of the global similarities to nearby bases. In this paper, we propose a coding scheme that brings into focus the manifold structure of descriptors, and devise a method to compute the global similarities of descriptors to the bases. Given a local similarity measure between bases, a global measure is computed. Exploiting the local similarity of a descriptor and its nearby bases, a global measure of association of a descriptor to all the bases is computed. Unlike the locality-based and sparse coding methods, the proposed coding varies smoothly with respect to the underlying manifold. Experiments on benchmark image classification datasets substantiate the superiority oftheproposed method over its locality and sparsity based rivals.
Reference: text
sentIndex sentText sentNum sentScore
1 These representations are usually accompanied by a coding method. [sent-11, score-0.484]
2 Recently, methods that code a descriptor giving regard to its nearby bases have proved efficacious. [sent-12, score-0.6]
3 These methods take into account the nonlinear structure of descriptors, since local similarities are a good approximation of global similarities. [sent-13, score-0.419]
4 However, they confine their usage of the global similarities to nearby bases. [sent-14, score-0.318]
5 In this paper, we propose a coding scheme that brings into focus the manifold structure of descriptors, and devise a method to compute the global similarities of descriptors to the bases. [sent-15, score-1.121]
6 Given a local similarity measure between bases, a global measure is computed. [sent-16, score-0.277]
7 Exploiting the local similarity of a descriptor and its nearby bases, a global measure of association of a descriptor to all the bases is computed. [sent-17, score-0.819]
8 Unlike the locality-based and sparse coding methods, the proposed coding varies smoothly with respect to the underlying manifold. [sent-18, score-1.075]
9 Experiments on benchmark image classification datasets substantiate the superiority oftheproposed method over its locality and sparsity based rivals. [sent-19, score-0.326]
10 Among these, BoW models, which are based on the representation of affine invariant descriptors of image patches, have proved to have great performance and are widely used in many applications such as image classification [15], image retrieval [20], and human pose estimation [1]. [sent-26, score-0.134]
11 Researchers have empirically found that, assigning each feature to nearby bases leads to remarkable improvement in accuracy. [sent-30, score-0.52]
12 Authors in [25] proved that under the manifold assumption, considering local bases in coding is essential for successful nonlinear feature learning. [sent-31, score-1.315]
13 [23] in their LLC method use k-nearest neighbor bases in the coding process and set the coding coefficient for other bases to zero. [sent-34, score-1.863]
14 Since the manifold is locally linear, a linear similarity measure is used for neighboring bases. [sent-35, score-0.367]
15 Although this coding scheme captures the local manifold structure, it’s not capable of binding this information to derive and utilize the global structure of the manifold. [sent-36, score-0.929]
16 To be more specific, two features that have different bases in their neighborhood generate completely different codings independent of their distance on the manifold. [sent-37, score-0.531]
17 To overcome this drawback, we propose a novel method called Local Similarity Global Coding (LSGC), that uses the local similarities between bases to obtain a nonlinear global similarity measure between local features and bases. [sent-38, score-1.005]
18 We first show that this coding scheme captures the global manifold structure and generates a smoother coding compared to LLC. [sent-39, score-1.387]
19 Next, we formulate the coding as a linear transformation of any local coding (which is obtained by an arbitrary local coding scheme such as LLC). [sent-40, score-1.595]
20 This formulation is of practical interest when the transformation from local to global coding is obtained by matrix-vector multiplication. [sent-41, score-0.6]
21 First, local points in the image are selected or densely sampled, and an affine invariant feature vector xi called the descriptor vector is extracted from each local point. [sent-51, score-0.209]
22 Each of these elements are called coding vectors ui. [sent-54, score-0.484]
23 Different algorithms use different codebook learning and coding schemes. [sent-56, score-0.571]
24 To aggregate the information of different local codings into one feature vector, local codings from image patches are merged together using a predefined pooling function: v = F(U) (1) where the ith column of U is the coding vector ui, F is the pooling function and v is the image feature vector. [sent-57, score-1.041]
25 Among them are max pooling [24], sum normalization [19], sum pooling and ? [sent-59, score-0.234]
26 × However, recent work empirically shows that the max pooling function leads to superior performance [24, 23]. [sent-61, score-0.131]
27 The max pooling function can be defined as: vj = max( |u1j |, |u2j | , . [sent-62, score-0.131]
28 , |ulj |) (2) where uij is the jth element of ui and l is the number of local points for each image. [sent-65, score-0.169]
29 Recent works mainly differ from each other in their dictionary learning and coding schemes. [sent-77, score-0.595]
30 In the rest of the paper consider base bi as the ith column of dictionary matrix B which has a total of c columns. [sent-79, score-0.294]
31 xi and ui are the local feature and corresponding coding for the ith local keypoint respectively. [sent-80, score-0.798]
32 Related Work In this section, we review commonly used methods in coding and dictionary learning for image classification. [sent-82, score-0.595]
33 , c where xi and ui are descriptor and coding vectors of the ith local point respectively. [sent-94, score-0.783]
34 n is the total number of local points and there are c bases in the dictionary B. [sent-95, score-0.568]
35 The first term represents the reconstruction error and the second term controls the sparsity of coding ui. [sent-96, score-0.51]
36 The sparsity prior plays a key role in coding, because it ensures that the coding captures outstanding patterns in local features. [sent-98, score-0.629]
37 Although ScSPM proves its performance it has one a major drawback: the coding does not change smoothly when xi varies on the manifold. [sent-102, score-0.618]
38 LScSPM [10] tries to overcome this problem by using manifold assumption. [sent-103, score-0.266]
39 ij where wij denotes the similarity between local features i and j. [sent-113, score-0.194]
40 This objective function differs from standard sparse coding in the regularization term, which guarantees that the sparse code varies smoothly on the data manifold. [sent-114, score-0.565]
41 The interpretation of smoothness term is that when wij for two local feature is high, their codings must be close in Euclidean space. [sent-115, score-0.2]
42 As suggested in [23], locality is more important than sparsity. [sent-172, score-0.125]
43 The fundamental assumption in their method is that the local features lie on a nonlinear m dimensional manifold where m is less that the dimension of the ambient space. [sent-173, score-0.428]
44 Mentioning locality, brings into consideration the nonlinear structure of the data manifold in the coding process. [sent-175, score-0.855]
45 In practice the second term is ignored and coding for each descriptor is obtained by optimizing only the first term using only k-nearest bases. [sent-189, score-0.526]
46 This leads to non-zero coefficients for the k-nearest bases and zero for the others. [sent-190, score-0.461]
47 σ Localized soft-assignment coding [17] expresses the coding coefficient as the probability that a local feature xi belongs to a basis bj and surpasses the performance of LLC. [sent-192, score-1.293]
48 Its local similarity measure is defined as: pij=? [sent-193, score-0.185]
49 Similar to LLC, coefficients for the k-nearest bases are computed and the others are set to zero. [sent-199, score-0.461]
50 Local coding methods like LLC and soft-assignment coding implicitly give regard to manifold structure, since local similarity a is valid approximation only for neighboring points. [sent-200, score-1.397]
51 However, these methods disregard global similarities between data, which could be captured using nonlinear similarity estimation methods. [sent-201, score-0.428]
52 Motivation Recent image classification methods that look at both reconstruction error and locality in dictionary learning prove to have top-notch performance [23]. [sent-203, score-0.285]
53 Looking at locality is a struggle to take the underlying nonlinear structure of local features into account. [sent-204, score-0.313]
54 Locality ensures that nearby bases are preferred in coding data points, and this implicitly dis- 222777999644 Figure 2: Kmeans dictionary learning. [sent-205, score-1.086]
55 The bases inherit the geometry of descriptors criminates in favor of the bases on the underlying manifold. [sent-207, score-0.985]
56 Since bases are usually samples of the manifold, the distance (or similarity) of data to these bases is an appropriate feature that embodies the geometry of the data. [sent-208, score-0.914]
57 Usual coding methods learn the bases by considering the manifold structure either explicitly or implicitly. [sent-209, score-1.182]
58 To elaborate, we refer to a closely related trend in large-scale and online manifold learning literature that tries to find only a few bases in order to best preserve the manifold structure. [sent-210, score-0.998]
59 Thus, the bases which are learned by k-means trace the manifold structure of local features. [sent-214, score-0.781]
60 Figure 2 illustrates how the bases learned by k-means cover the whole structure of data. [sent-215, score-0.459]
61 The fact that these bases trace the manifold is a motivation to take the natural similarity between bases into account when coding as well. [sent-217, score-1.704]
62 This leads to a better utilization of manifold structure in the coding process. [sent-218, score-0.752]
63 Exploiting the non-linear dependence of bases to each other a framework is proposed in order to find a global coding scheme for a descriptor. [sent-219, score-1.061]
64 Proposed Method Methods that take into account the manifold structure use only the k nearest bases in the coding process. [sent-221, score-1.182]
65 In this paper we present a novel algorithm extending the methods which rely only on local similarities between data and bases. [sent-223, score-0.255]
66 We claim that local similarities between bases are valuable in the sense that they can be used to estimate global similarities between local features and bases. [sent-224, score-1.028]
67 Considering bases learned by k-means, a local similarity between bases is proposed, which is then utilized to find a global similarity with regard to the manifold structure. [sent-225, score-1.443]
68 At last a coding scheme is presented to derive global similarities between descriptors and bases. [sent-226, score-0.826]
69 Local Similarity Choosing the similarity measure is arbitrary and the approach taken by any existing method (Gaussian kernel, LLC, Sparse Coding) can be adopted. [sent-229, score-0.128]
70 We take the Gaussian kernel approach which is commonly used as a local similarity measure in the manifold learning methods [2]: W(i,j) =? [sent-230, score-0.486]
71 0exp(−| bi−σbj| 2) oift hbjer∈wi kse-NN(bi) (8) While W captures only local similarities, in the next subsection we propose a probabilistic framework to find a global measure of the probability that a base belongs to other bases. [sent-231, score-0.246]
72 From Local to Global Similarity Given a matrix W that contains local similarities between bases, stochastic matrix P is defined by normalizing W: P = D−1W (9) where D is a diagonal? [sent-234, score-0.255]
73 p(bj |bi) can be interpreted as the probability that bj is a memb|ebr of a Gaussian distribution with mean bi and variance σ. [sent-243, score-0.272]
74 As matrix P measures the similarities between neighboring bases, the similarity between non-neighboring bases can be computed indirectly by random walks on the graph which has the adjacency matrix W [13]. [sent-244, score-0.723]
75 Suppose p(2) (bk |bi) represents indirect belonging of bi to bk which is not among bi’s neighbors. [sent-245, score-0.37]
76 Superscript 2 means an indirect dependence via 2 steps: p(2)(bk|bi) ? [sent-246, score-0.127]
77 1 222777999755 Therefore, elements of the matrix P2 are indirect similarities of order 2. [sent-256, score-0.266]
78 for the similarity of order t we use similarity of order t p(t)(bk|bi) − 1: ? [sent-259, score-0.19]
79 1 One can easily see that matrix Pt captures the similarities of order t. [sent-264, score-0.23]
80 Although for every t, Pt can be regarded as a measure of non-local similarity, a better measure of dependence of basis j on basis ican be defined as: S =1tmt? [sent-266, score-0.177]
81 −=10Pm, (12) which considers a multi-resolution non-local dependence from very local to more global ones. [sent-267, score-0.175]
82 (b) Global coding Figure 3: Comparing local and global coding scheme. [sent-367, score-1.084]
83 Hand-written Image Classification In this study we aim to compare the classification performance of a Linear SVM with different coding schemes. [sent-371, score-0.533]
84 We compare LSGC to LLC [23], soft assignment coding (SAC) [22], and localized soft assignment coding (LSAC) [17] on different benchmark image and hand-written letter datasets. [sent-372, score-1.172]
85 In SAC method for each data point x, despite localized soft assignment coding, all coding coefficients are computed. [sent-375, score-0.598]
86 In general, LSGC outperforms other coding methods with small numbers of labeled points. [sent-386, score-0.484]
87 Employing the max pooling method, we obtain the temporal features. [sent-394, score-0.131]
88 We consider five nearest neighbors in coding process and the bandwidth size parameter σ is set to the mean of standard deviation of the bases. [sent-397, score-0.484]
89 Note that for t = 1, our method is reduced to soft-assignment coding [17]. [sent-407, score-0.484]
90 the local similarity propagate sufficiently on the whole manifold. [sent-415, score-0.152]
91 We claim that the superiority of the results is due to considering global similarities in the coding process. [sent-495, score-0.813]
92 Conclusion and Future Work In this paper, we presented a method that uses the information about manifold structure of descriptors, to infer a global similarity measure between bases and descriptors. [sent-503, score-0.885]
93 We showed that by using a linear transformation that embodies the manifold information, we can obtain global similarities from the local ones. [sent-504, score-0.607]
94 In addition, by using global similarities between bases and descriptors in the coding process, a smoother coding is obtained compared to previous methods. [sent-505, score-1.742]
95 Our methods relies on the fact that the bases are sampling the data manifold which is done by k-means. [sent-506, score-0.669]
96 Incorporating dictionary learning methods which take the manifold struc- ture into account is remains as future work. [sent-507, score-0.35]
97 Man- [7] [8] [9] [10] [11] [12] [13] [14] ifold coarse graining for online semi-supervised learning. [sent-558, score-0.152]
98 Local features are not lonely–laplacian sparse coding for image classification. [sent-584, score-0.484]
99 Online manifold regularization: A new learning setting and empirical study. [sent-591, score-0.269]
100 Linear spatial pyramid matching using sparse coding for image classification. [sent-686, score-0.484]
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