nips nips2012 nips2012-106 knowledge-graph by maker-knowledge-mining

106 nips-2012-Dynamical And-Or Graph Learning for Object Shape Modeling and Detection

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Author: Xiaolong Wang, Liang Lin

Abstract: This paper studies a novel discriminative part-based model to represent and recognize object shapes with an “And-Or graph”. We deﬁne this model consisting of three layers: the leaf-nodes with collaborative edges for localizing local parts, the or-nodes specifying the switch of leaf-nodes, and the root-node encoding the global veriﬁcation. A discriminative learning algorithm, extended from the CCCP [23], is proposed to train the model in a dynamical manner: the model structure (e.g., the conﬁguration of the leaf-nodes associated with the or-nodes) is automatically determined with optimizing the multi-layer parameters during the iteration. The advantages of our method are two-fold. (i) The And-Or graph model enables us to handle well large intra-class variance and background clutters for object shape detection from images. (ii) The proposed learning algorithm is able to obtain the And-Or graph representation without requiring elaborate supervision and initialization. We validate the proposed method on several challenging databases (e.g., INRIA-Horse, ETHZ-Shape, and UIUC-People), and it outperforms the state-of-the-arts approaches. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 com Abstract This paper studies a novel discriminative part-based model to represent and recognize object shapes with an “And-Or graph”. [sent-7, score-0.266]

2 We deﬁne this model consisting of three layers: the leaf-nodes with collaborative edges for localizing local parts, the or-nodes specifying the switch of leaf-nodes, and the root-node encoding the global veriﬁcation. [sent-8, score-0.161]

3 (i) The And-Or graph model enables us to handle well large intra-class variance and background clutters for object shape detection from images. [sent-13, score-0.65]

4 1 Introduction Part-based and hierarchical representations have been widely studied in computer vision, and lead to some elegant frameworks for complex object detection and recognition. [sent-18, score-0.366]

5 structural switch) in hierarchy, which is the key to handle the large intra-class variance in object detection. [sent-21, score-0.277]

6 And-Or graph models are recently explored in [26, 27] to hierarchically model object categories via “and-nodes” and “or-nodes” that represent, respectively, compositions of parts and structural variation of parts. [sent-23, score-0.436]

7 The leaf-nodes in the bottom layer represent a batch of local classiﬁers of contour fragments. [sent-29, score-0.261]

8 1 the problem that the true contours of objects are often connected to background clutters due to unreliable edge extraction. [sent-36, score-0.399]

9 Each or-node is used to select one contour from the candidates detected via the associated leaf-nodes in the bottom layer. [sent-39, score-0.406]

10 The contours selected via the or-nodes are further veriﬁed as a whole, in order to make the detection robust against the background clutters. [sent-44, score-0.466]

11 Concretely, our model allows nearby contours to interact with each other. [sent-46, score-0.274]

12 , the layout of or-nodes and the activation of leaf-nodes) are implicitly inferred with the latent variables. [sent-52, score-0.161]

13 2 Related Work Remarkable progress has been made in shape-based object detection [6, 10, 9, 11, 19]. [sent-53, score-0.366]

14 By employing some shape descriptors and matching schemes, many works represent and recognize object shapes as a loose collection of local contours. [sent-54, score-0.331]

15 [6] used a codebook of PAS (pairwise adjacent segments) to localize object of interest; Maji et al. [sent-56, score-0.174]

16 Recently, the tree structure latent models [25, 5] have provided signiﬁcant improvements on object detection. [sent-58, score-0.223]

17 using conﬁgurable graph structures with And, Or nodes, has been applied in object and scene parsing [26, 18, 24] and action classiﬁcation [20]. [sent-67, score-0.346]

18 3(a) illustrates, the square on the top is the root-node representing the complete object instances. [sent-70, score-0.174]

19 The dashed circles derived from the root are z or-nodes arranged in a layout of b1 × b2 blocks, representing the object parts. [sent-71, score-0.246]

20 , collaborative edges) are deﬁned between the leaf-nodes that are associated with different or-nodes, in order to encode the compatibility of object parts. [sent-85, score-0.25]

21 Suppose a contour fragment c on the edge map X is captured by the block located at pi = (px , py ), as the input of classiﬁer. [sent-91, score-0.55]

22 The response of classiﬁer Lj at location pi of the edge map X is deﬁned as: l RLj (X, pi ) = max ωj · ϕl (pi , c), (1) c∈X l where ωj is a parameter vector, which is set to zero if the corresponding leaf-node Lj is nonexistent. [sent-94, score-0.479]

23 l Then we can detect the contour from edge map X via the classiﬁer, cj = argmaxc∈X ωj · ϕl (pi , c). [sent-95, score-0.381]

24 , z is proposed to specify a proper contour from a set of candidates detected via its children leaf-nodes. [sent-99, score-0.406]

25 For each or-node Ui , we deﬁne the deformation feature as ϕs (p0 , pi ) = (dx, dy, dx2 , dy 2 ), where (dx, dy) is the displacement of the or-node position pi to the expected position p0 determined by the root-node. [sent-102, score-0.475]

26 Then the cost of locating Ui at pi is: s Costi (p0 , pi ) = −ωi · ϕs (p0 , pi ), (2) s ωi s where is a 4-dimensional parameter vector corresponding to ϕ (p0 , pi ). [sent-103, score-0.704]

27 For each leaf-node Lj associated with Ui , we introduce an indicator variable vj ∈ {0, 1} representing whether it is activated or not. [sent-105, score-0.186]

28 Thus, the response of the or-node Ui is deﬁned as, ∑ RUi (X, p0 , pi , vi ) = RLj (X, pi ) · vj + Costi (p0 , pi ). [sent-110, score-0.728]

29 (3) j∈ch(i) Collaborative Edge: For any pair of leaf-nodes (Lj , Lj ′ ) respectively associated with two different or-nodes, we deﬁne the collaborative edge between them according to their contextual cooccurrence. [sent-111, score-0.155]

30 That is, how likely it is that the object contains contours detected via the two leaf-nodes. [sent-112, score-0.549]

31 Root-node: The root-node represents a global classiﬁer to verify the ensemble of contour fragments C r = {c1 , . [sent-121, score-0.392]

32 For better understanding, we refer H = (P, V ) as the latent variables during inference, where P implies the deformation of parts represented by the or-nodes and V implies the discrete distribution of leaf-nodes (i. [sent-130, score-0.149]

33 4 Inference The inference task is to localize the optimal contour fragments within the detection window, which is slidden at all scales and positions of the edge map X. [sent-156, score-0.663]

34 Assuming the root-node is located at p0 , the object shape is localized by maximizing RG (X, H) deﬁned in (6): S(p0 , X) = max RG (X, H). [sent-157, score-0.297]

35 the local classiﬁers) are utilized to detect contour fragments within the edge map X. [sent-160, score-0.471]

36 Assume that leaf-node Lj , j ∈ ch(i) associated with Ui is activated, vj = 1, and the optimal contour fragment cj is localized by maximizing the response in Eq. [sent-161, score-0.477]

37 Then we generate i,j a set of candidates for each or-node, {cj , p∗ }, each of which is one detected contour fragments via i,j the leaf-nodes. [sent-163, score-0.537]

38 These sets of candidates will be passed to the top-down step where the leaf-node activation vi for Ui can be further validated. [sent-164, score-0.143]

39 We calculate the response for the bottom-up step, as, z ∑ Rbot (V ) = (11) RUi (X, p0 , p∗ , vi ), i i=1 where V = {vi } denotes a hypothesis of leaf-node activation for all or-nodes. [sent-165, score-0.147]

40 In practice, we can further prune the candidate contours by setting a threshold on Rbot (V ). [sent-166, score-0.274]

41 Thus, given the V = {vi }, we can select an ensemble of contours C r = {c1 , . [sent-167, score-0.274]

42 , cz }, each of which is detected by an activated leaf-node, Lj , vj = 1. [sent-170, score-0.337]

43 Top-down veriﬁcation: Given the ensemble of contours C r , we then apply the global classiﬁer at the root-node to verify C r by Eq. [sent-171, score-0.274]

44 By incorporating the bottom-up and top-down steps, we obtain the response of And-Or graph model by Eq. [sent-174, score-0.163]

45 The ﬁnal detection is acquired by selecting the maximum score in Eq. [sent-176, score-0.192]

46 This algorithm iterates to determine the And-Or graph structure in a dynamical manner: given the inferred latent variables H = (P, V ) in each step, the leaf-nodes can be automatically created or removed to generate a new structural conﬁguration. [sent-179, score-0.415]

47 To be speciﬁc, a new leaf-node is encouraged to be created as the local detector for contours that cannot be handled by the current model(Fig. [sent-180, score-0.359]

48 (13) The optimization of this function can be solved by using structural SVM with latent variables, ∑ 1 min ∥ω∥2 + D [max(ω · ϕ(Xk , y, H) + L(yk , y, H)) − max(ω · ϕ(Xk , yk , H))], ω 2 y,H H N (14) k=1 where D is a penalty parameter(set as 0. [sent-192, score-0.4]

49 We deﬁne that L(yk , y, H) = 0 if yk = y, “1” if yk ̸= y in our method. [sent-194, score-0.496]

50 (14) into a convex and concave form as, ∑ ∑ 1 min[ ∥ω∥2 + D max(ω · ϕ(Xk , y, H) + L(yk , y, H))] − [D max(ω · ϕ(Xk , yk , H))] ω y,H H 2 N N k=1 k=1 = min[f (ω) − g(ω)], (15) (16) ω where f (ω) represents the ﬁrst two terms, and g(ω) represents the last term in (15). [sent-203, score-0.248]

51 The original CCCP includes two iterative steps: (I) ﬁxing the model parameters, estimate the latent variables H ∗ for each positive samples; (II) compute the model parameters by the traditional structural SVM method. [sent-204, score-0.152]

52 (I) For optimization, we ﬁrst ﬁnd a hyperplane qt to upper bound the concave part −g(ω) in Eq. [sent-210, score-0.187]

53 We construct qt by ∗ calculating the optimal latent variables Hk = argmaxH (ωt ·ϕ(Xk , yk , H)). [sent-213, score-0.417]

54 Since ϕ(Xk , yk , H) = 0 when yk = −1, we only take the positive training samples into account during computation. [sent-214, score-0.496]

55 Then ∑N ∗ the hyperplane is constructed as qt = −D k=1 ϕ(Xk , yk , Hk ). [sent-215, score-0.435]

56 Accordingly, the hyperplane qt would change with ϕ(X, y, H ∗ ), and would lead to non-convergence of learning. [sent-219, score-0.187]

57 Given ϕ(Xk , yk , Hk ) of all positive samples, we apply PCA on them, K ∑ ∗ ϕ(Xk , yk , Hk ) ≈ u + βk,i ei , (18) i=1 where K is the number of the eigenvectors, ei the eigenvector with its parameter βk,i . [sent-225, score-0.578]

58 We set K a ∑K ∗ large number so that ||ϕ(Xk , yk , Hk ) − (u + i=1 βk,i ei )||2 < σ, ∀k. [sent-226, score-0.289]

59 For the jth bin of the feature 5 ( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) (a) (b) (c) Figure 2: A toy example for structural clustering. [sent-227, score-0.206]

60 (a) shows the feature vectors ϕ of the samples associated with Ui , and the intensity of the feature bin indicates the feature value. [sent-232, score-0.271]

61 The red and green bounding boxes on the vectors indicate the non-principal features representing the detected contour fragments via two different leaf-nodes. [sent-233, score-0.527]

62 For each or-node Ui , a set of detected contour fragments, {c1 , c2 , . [sent-242, score-0.362]

63 The feature vectors for these contours that are generated by the leaf-nodes, {ϕl (p1 , c1 ), . [sent-246, score-0.375]

64 More speciﬁcally, once we select the jth bin for the l all feature vectors ϕ , it can be either principal or not in different vectors ϕ. [sent-253, score-0.171]

65 We thus refactor the feature vectors of these contours as {ϕ′ (p1 , c1 ), . [sent-255, score-0.375]

66 To trigger the structural reconﬁguration, for each ornode Ui , we perform the clustering for detected contour fragments represented by the newly formed feature vectors. [sent-260, score-0.709]

67 We ﬁrst group the contours detected by the same leaf-node into the same cluster as a temporary partition. [sent-261, score-0.375]

68 And the close contours are grouped into the same cluster. [sent-263, score-0.315]

69 represent the similar contour with the same bins in the complete feature vector ϕ. [sent-266, score-0.328]

70 Please recall that the vector of one contour is part of ϕ. [sent-267, score-0.261]

71 Their parameters can be learned based on the feature vectors of contours within the clusters. [sent-274, score-0.375]

72 • One leaf-node is removed when the feature bins related to it are zero, which implies the contours detected by the leaf-node are grouped to another cluster. [sent-275, score-0.528]

73 After the structural reconﬁguration, we denote ∗ ∗ all the feature vectors ϕ(Xk , yk , Hk ) are adjusted to ϕd (Xk , yk , Hk ). [sent-279, score-0.7]

74 Then the new hyperplane is ∑N d ∗ generated as qt = −D k=1 ϕd (Xk , yk , Hk ). [sent-280, score-0.435]

75 ∗ (III) Given the newly generated model structures represented by the feature vectors ϕd (Xk , yk , Hk ), d we can learn the model parameters by solving ωt+1 = argminω [f (ω) + ω · qt ]. [sent-281, score-0.469]

76 By substituting d −g(ω) with the upper bound hyperplane qt , the optimization task in Eq. [sent-282, score-0.187]

77 (15) can be rewritten as, ∑ 1 ∗ min ∥ω∥2 + D [max(ω · ϕ(Xk , y, H) + L(yk , y, H)) − ω · ϕd (Xk , yk , Hk )]. [sent-283, score-0.248]

78 , U8 ; a practical detection with the activated leafnodes are highlighted by red. [sent-296, score-0.285]

79 ω∗ = D ∑ ∗ αk,y,H ∆ϕ(Xk , y, H), (20) k,y,H ∗ where ∆ϕ(Xk , y, H) = ϕd (Xk , yk , Hk ) − ϕ(Xk , y, H). [sent-298, score-0.248]

80 For each training sample (whose contours have been extracted), we partition it into a regular layout of several blocks, each of which corresponds to one or-node. [sent-305, score-0.346]

81 The contours fallen into the block are treated as the input for learning. [sent-306, score-0.32]

82 Once there are more than two contours in one block, we select the one with largest length. [sent-307, score-0.274]

83 Then the leaf-nodes are generated by clustering the selected contours without any constraints, and we can thus obtain the initial feature vector ϕd for each sample. [sent-308, score-0.341]

84 6 Experiments We evaluate our method for object shape detection, using three benchmark datasets: the UIUCPeople [17], the ETHZ-Shape [7] and the INRIA-Horse [7]. [sent-309, score-0.297]

85 For positive samples, we extract their clutter-free object contours; for negative samples, we compute their edge maps by using the Pb edge detector [12] with an edge link method. [sent-316, score-0.445]

86 During detection, the edge maps of test images are extracted as for negative training samples, within which the object is searched at 6 different scales, 2 per octave. [sent-318, score-0.307]

87 For each contour as the input to the leaf-node, we sample 20 points and compute the Shape Context descriptor for each point; the descriptor is quantized with 6 polar angles and 2 radial bins. [sent-319, score-0.329]

88 We adopt the testing criterion deﬁned in the PASCAL VOC challenge: a detection is counted as correct if the intersection over union with the groundtruth is at least 50%. [sent-320, score-0.192]

89 To evaluate the beneﬁt from the collaborative edges, we degenerate our model to the And-Or Tree (AOT) by removing the collaborative edges. [sent-326, score-0.152]

90 3(c) illustrates, the average precisions (AP) of detection by applying AOG and AOT are 56. [sent-328, score-0.192]

91 709 (b) Table 1: (a) Comparisons of detection accuracies on the UIUC-People dataset. [sent-383, score-0.192]

92 metric mentioned in [18], to calculate the detection accuracy, we only consider the detection with the highest score on an image for all the methods. [sent-385, score-0.384]

93 (b),(c) and (d) shows a few object shape detections by applying our method on the three datasets, and the false positives are annotated by blue frames. [sent-402, score-0.297]

94 It is shown that our system substantially outperforms the recent methods: the AOG and AOT models achieve detection rates of 89. [sent-409, score-0.192]

95 We test our method with more object categories on the ETHZ-Shape dataset: Applelogos, Bottles, Giraffes, Mugs and Swans. [sent-418, score-0.174]

96 7 Conclusion This paper proposes a discriminative contour-based object model with the And-Or graph representation. [sent-425, score-0.347]

97 Our method achieves the state-of-art of object shape detection on challenging datasets. [sent-427, score-0.489]

98 Schiele, Pictorial structures revisited: People detection and articulated pose estimation, In CVPR, 2009. [sent-435, score-0.192]

99 Schiele, Discriminative structure learning of hierarchical representations for object detection, In CVPR, 2009. [sent-493, score-0.174]

100 Joachims, Learning structural svms with latent variables, In ICML, 2009. [sent-527, score-0.152]

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