iccv iccv2013 iccv2013-21 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Chang Ma, Zhongqian Dong, Tingting Jiang, Yizhou Wang, Wen Gao
Abstract: In thispaper, wepropose a novelperception-based shape decomposition method which aims to decompose a shape into semantically meaningful parts. In addition to three popular perception rules (the Minima rule, the Short-cut rule and the Convexity rule) in shape decomposition, we propose a new rule named part-similarity rule to encourage consistent partition of similar parts. The problem is formulated as a quadratically constrained quadratic program (QCQP) problem and is solved by a trust-region method. Experiment results on MPEG-7 dataset show that we can get a more consistent shape decomposition with human perception compared with other state-of-the-art methods both qualitatively and quantitatively. Finally, we show the advantage of semantic parts over non-meaningful parts in object detection on the ETHZ dataset.
Reference: text
sentIndex sentText sentNum sentScore
1 In addition to three popular perception rules (the Minima rule, the Short-cut rule and the Convexity rule) in shape decomposition, we propose a new rule named part-similarity rule to encourage consistent partition of similar parts. [sent-2, score-1.183]
2 Experiment results on MPEG-7 dataset show that we can get a more consistent shape decomposition with human perception compared with other state-of-the-art methods both qualitatively and quantitatively. [sent-4, score-0.721]
3 Finally, we show the advantage of semantic parts over non-meaningful parts in object detection on the ETHZ dataset. [sent-5, score-0.528]
4 Introduction Many psychological studies have shown the important role of parts that plays in object perception and recognition , (e. [sent-7, score-0.353]
5 We argue that perceptual meaningful parts have the advantage in many vision tasks, such as object detection, because such parts are usually more stable in different environments. [sent-17, score-0.431]
6 In addition, the semantic parts are useful injudging the affordance ofobjects and they are the key to transferring the knowledge between different objects via the shared parts [1]. [sent-22, score-0.494]
7 In order to obtain semantic parts, perception-rule-based methods are often adopted to decompose a shape into a number of parts (e. [sent-23, score-0.583]
8 , the Minima rule [8], the Short-cut rule [20] and the Convexity rule [11, 21]. [sent-29, score-0.717]
9 The Minima rule suggests the shape should be divided at loci of negative minima of curvature along the contour. [sent-30, score-0.487]
10 The Short-cut rule suggests to decompose shapes into parts using the shortest possible cuts. [sent-32, score-0.582]
11 [7] proposed methods for approximate shape decomposition based on the Convexity rule. [sent-34, score-0.442]
12 [14] formulated the convex shape decomposition as a linear programming problem and considers the Short-cut rule. [sent-36, score-0.478]
13 [9] proposed methods for perception-based shape decomposition which add the Minima rule in their works. [sent-39, score-0.681]
14 In this paper, we propose a new method to acquire semantic parts via perception-based shape decomposition. [sent-40, score-0.451]
15 Therefore, besides the existing rules adopted by [9, 14, 17], we add a new rule to encourage the consistent decomposition of similar parts. [sent-46, score-0.741]
16 In addition, most of the works based on the Convexity rule tend to generate redundant parts in order to satisfy the convexity constraint. [sent-47, score-0.71]
17 To prove the advantage of semantic parts in the vision tasks, we conduct the object detection experiment on the ETHZ dataset [6]. [sent-57, score-0.395]
18 We use the semantic parts obtained by the proposed decomposition method to detect objects in natural scenes and compare the detection rate with the same detection method using a set of non-semantic random parts. [sent-58, score-0.649]
19 The result shows that the detection rate of using the semantic parts is much better than the random parts, especially in the cases of objects with articulation. [sent-59, score-0.329]
20 Perception Rules The three perception rules usually adopted by humans to decompose a shape include the Minima rule [8], the Short- cut rule [20] and the Convexity rule [11, 21]. [sent-67, score-1.455]
21 The Minima rule suggests that the endpoints of a cut usually locate at the places where the curvature is local minimum. [sent-68, score-0.475]
22 The Shortcut rule prefers to minimize the total cut length, and the Convexity rule requires parts to be convex. [sent-69, score-0.867]
23 Formulation Perceptual-based shape decomposition is to decompose a shape into non-overlapping parts consistently with human perception. [sent-78, score-0.945]
24 In our problem, parts are generated by a set of cuts on a shape. [sent-79, score-0.483]
25 So the problem can be formulated as selecting an optimal subset of candidate cuts which can derive perceptual-based parts and do not intersect with each other. [sent-81, score-0.592]
26 We define Cp as a set of candidate cuts and C∗ as the selected optimal cuts. [sent-82, score-0.366]
27 According to the Short-cut rule [20], L is the cut length vector s. [sent-88, score-0.429]
28 I() nist a sfeucntc,ti Hon(i t,hja)t measures tthheimprovement of shape convexity by a cut. [sent-94, score-0.369]
29 Convexity Constraint As strict convex shape decomposition can generate many spurious parts due to the noise (e. [sent-101, score-0.677]
30 , given a threshold ε, we want to ensure the concavity of a decomposed part is less than ε. [sent-107, score-0.377]
31 In the following, we first introduce the concavity measurement of two points and a part as proposed in [14], then present the method of generating cuts to ensure the convexity of parts, followed by the formulation of the convexity constraint in Eq. [sent-109, score-1.111]
32 1), the concavity of two points within a shape w. [sent-116, score-0.486]
33 Any pair of points whose concavity is− more than ε is defined as a mutex pair [14]. [sent-129, score-0.886]
34 (a) Vertices p2 and p3 is a mutex pair while p1 and p2 is not under the threshold ε. [sent-140, score-0.483]
35 (b) Red lines SS1 and SS2 are two candidate cuts generated by S, the orange lines are the skeleton of the shape. [sent-143, score-0.494]
36 If we consider all the directions, then the concavity of a pair of points is defined as Concavity(p1,p2) = mfaxConcavityf(p1,p2), (3) For a shape part P, its concavity is defined as Concavity(P) =p1∈mPa,p2x∈PConcavity(p1,p2), (4) where p1 and p2 are two arbitrary points in P. [sent-144, score-0.928]
37 If the concavity of every pair of points in a part is less than ε, then the concavity of the part is less than ε. [sent-145, score-0.775]
38 To ensure all the decomposed parts are we shall separate all the mutex pairs of a shape by cuts, although some of these cuts are spurious. [sent-147, score-1.151]
39 Our goal is to find the optimal set of cuts for shape decomposition. [sent-148, score-0.44]
40 In order to extend the concept of mutex pair from point to point set, two concavity measures of two point sets R1 and R2 are defined as ε-convex, w(R1,R2) =p1∈Rm1,ipn2∈R2Concavity(p1,p2), (5) W(R1,R2) =p1∈Rm1a,px2∈R2Concavity(p1,p2). [sent-149, score-0.777]
41 (6) If w(R1 , R2) ≥ ε, every pair of points from R1 and R2 forms a mutex pair. [sent-150, score-0.519]
42 We use the method in [4, 14] to find mutex pairs of regions in our implementation and select a subset of candidate cuts to satisfy them in order to get ε-convex decomposition. [sent-156, score-0.801]
43 2 Generating candidate cuts to separate the mutex pairs By considering the Minima rule introduced above, we propose candidate cuts using all the saddle points of a shape. [sent-159, score-1.534]
44 The two points are the contacting points × between the shape contour and its maximal disk centered at the skeleton point [18]. [sent-167, score-0.406]
45 Hence, to get a candidate cut, we first compute the skeleton of a shape using method in [18], then find the symmetric points of the saddle point S based on its skeletons, i. [sent-171, score-0.486]
46 Then the cuts SS1 and SS2 are two candidate cuts generated by S. [sent-174, score-0.65]
47 3 Formulating the convexity constraint The candidate cuts generated by the above method are usually surplus. [sent-177, score-0.611]
48 We shall select an “optimal” set of cuts that is able to separate all the mutex pairs, and hence generates near-convex parts. [sent-178, score-0.752]
49 ) To achieve this, a binary matrix A is defined, which signifies the separation relationship between the mutex pairs (MP = {mp1 , mp2 , . [sent-181, score-0.41]
50 nIfu a mbeurte oxf pair mpi can be separated by a cut Cj, then A(i, j) = 1; otherwise 0. [sent-187, score-0.379]
51 So if we constrain A(i, :)x ≥ 1, then mutex pair riw i ss separated a wt ele casotn once by tih,e:) optimal stheet no fm cuts, which is also u? [sent-188, score-0.531]
52 × mutex pair R1 and R2 can be separated by the combination of cuts C1 and C2, so there is no need for C3. [sent-190, score-0.815]
53 Pruning redundant cuts Although we can satisfy all the mutex pairs using the above constraint, it can produce redundant cuts. [sent-191, score-0.812]
54 This is due to the double counting of mutex pairs. [sent-192, score-0.41]
55 However, the combination of two lower level cuts C1 and C2 is also able to separate R1 and R2; in addition, they can separate the two rear legs of the camel as well. [sent-199, score-0.453]
56 We design a series of matrices of which Ai2 is a binary matrix signifying the separation of mutex pair A{21,2,···,m} 887755 by all candidate cut pairs. [sent-201, score-0.755]
57 If the mutex pair mpi can be separated by the comibsi nna ×tio nn. [sent-203, score-0.575]
58 We extend the above convexity constraint to A(i, :)x + 12xTAi2x ≥ 1to enforce that the ith mutex pair must be separated exith ≥er 1 by a single c thuta or teh iet hco mmubteixna ptiaoirn mofu stwt boe. [sent-205, score-0.776]
59 Hsim() – the part-similarity term We aim to encourage a consistent decomposition of similar parts. [sent-209, score-0.371]
60 3, each candidate cut can separate the shape into two portions and we choose the smaller one as its corresponding part. [sent-211, score-0.461]
61 1, we define Hsim (i, j) = φ(Ti, Tj) to account for the similarity of a pair of contours derived from cut Ci and cut Cj . [sent-225, score-0.508]
62 I() – the cut income term In order to improve the convexity of the decomposed parts, we employ the cut income term as proposed in [9]. [sent-229, score-0.891]
63 The income of a cut is defined as the concavity of the separated mutex pair of regions by the cut. [sent-230, score-1.142]
64 1 (b), the concavity of mutex pair (blue regions) is fS − fp based on Eq. [sent-232, score-0.777]
65 We sample the corresponding contour of each cut and compute the similarity between every two contours to get part-similarity matrix Hsim. [sent-263, score-0.345]
66 In the first experiment, we compare our results with human decomposition on the MPEG-7 dataset. [sent-275, score-0.333]
67 Both the quantitative and qualitative evaluations show the improved consistency to human performance compared with other shape decomposition methods. [sent-276, score-0.53]
68 To justify the motivation of this work, we show that object detection on the ETHZ dataset using semantically meaningful parts greatly improve the detection rate than using non-meaningful parts, especially in the case of object articulation. [sent-277, score-0.329]
69 These parts greatly affect the convexity of the object shape. [sent-286, score-0.412]
70 In order to entertain the convexity constraint, curved parts will be cut into pieces as shown in Fig. [sent-287, score-0.679]
71 4 (c)) and map the cuts back to the original shape (Fig. [sent-292, score-0.44]
72 In the straightening process, the skeleton is straightened firstly, then shift the points on the contour accordingly. [sent-294, score-0.349]
73 (a) The decomposition result on the original shape without straightening. [sent-298, score-0.442]
74 2 Experiment method To verify the consistency of the decomposition by the proposed method with the human decomposition, we choose 20 representative categories which are suitable for decomposition from the MPEG-7 shape dataset as shown in Fig. [sent-303, score-0.846]
75 In each shape category, for each instance i, we define G(i, 1) to measure the decomposition similarity between the proposed method and the humans; we define G(i, 2) to measure the decomposition consistency among humans. [sent-310, score-0.769]
76 gi (j, k) is the matching score function between the jth decomposition with the k-th decomposition on the i-th shape instance. [sent-316, score-0.728]
77 ), (15) where Aijq is the area of part Pijq which denotes the q-th part of the j-th decomposition for shape i. [sent-321, score-0.544]
78 If two parts have little intersection, the F1 is close to 0 and we define F1 = 0 if two parts do not overlap. [sent-331, score-0.398]
79 To further show that the proposed method is more statistically consistent with human decomposition than the other methods, we conduct the pairwise t-test experiment. [sent-340, score-0.441]
80 If the decomposition consistency between the proposed method and human is less than the consistency among human beings, the testing result is 1; otherwise 0. [sent-342, score-0.486]
81 From Table 2 we can see that on 17 object classes the decomposition consistency by the proposed method is not significantly less than human, whereas the other methods only get 7, 9, 11 and 14 classes. [sent-343, score-0.352]
82 4 Qualitatively visual comparison Some visual comparisons between the proposed method and MNCD [17], PSD [9] and human decomposition are shown in Fig. [sent-347, score-0.333]
83 The results by our method are consistent with human decomposition statistically in 17 categories out of 20. [sent-376, score-0.439]
84 This makes the decomposed parts more consistent with human perception. [sent-378, score-0.334]
85 So when ε increases, the decomposition will ignore smaller concave parts due to local distortions and get a relatively robust result. [sent-410, score-0.51]
86 A larger b encourages more cuts with similar parts, hence, can get more semantic decomposition. [sent-413, score-0.405]
87 We decompose the shapes to generate semantic parts (Fig. [sent-419, score-0.439]
88 In comparison, we simply replace the semantic parts with a set of random parts (not semantically meaningful as shown in Fig. [sent-422, score-0.556]
89 We can see that the semantic parts can boost the performance on all categories, which demonstrates the representative power of the proposed semantic parts. [sent-436, score-0.391]
90 The semantic parts capture the anatomy structure and keep rigid in articulation; however, the random parts may change drastically. [sent-439, score-0.494]
91 9 shows some decomposition results of shapes with holes. [sent-444, score-0.329]
92 Because the cup handle is a curved branch and cannot be straightened by the preprocessing method, redundant cuts are generated. [sent-445, score-0.518]
93 10 shows a failure example of the proposed method although our method generates shorter cut length than human and more similar parts, the decomposition is not consistent with human perception. [sent-447, score-0.614]
94 It shows the limitation of shape decomposition only based on generic perception rules. [sent-449, score-0.567]
95 Conclusion In this paper, we propose a method to decompose a shape into semantic parts. [sent-456, score-0.353]
96 Apart from three existing perception rules, we propose a part-similarity rule to encourage consistent cuts for similar parts. [sent-457, score-0.733]
97 By jointly considering these perception rules, we formulate the shape decomposition problem as a quadratically constrained quadratic program problem and solve it by a trust-region method. [sent-458, score-0.641]
98 An object detection experiment is also conducted on the ETHZ dataset to demonstrate the advantage of the semantic parts over the non-meaningful parts for shape representation. [sent-460, score-0.718]
99 Convexity rule for shape decomposition based on discrete contour evolution. [sent-550, score-0.756]
100 From partial shape matching through local deformation to robust global shape similarity for object detection. [sent-580, score-0.346]
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