cvpr cvpr2013 cvpr2013-468 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Yansheng Ming, Hongdong Li, Xuming He
Abstract: This paper aims to extract salient closed contours from an image. For this vision task, both region segmentation cues (e.g. color/texture homogeneity) and boundary detection cues (e.g. local contrast, edge continuity and contour closure) play important and complementary roles. In this paper we show how to combine both cues in a unified framework. The main focus is given to how to maintain the consistency (compatibility) between the region cues and the boundary cues. To this ends, we introduce the use of winding number–a well-known concept in topology–as a powerful mathematical device. By this device, the region-boundary consistency is represented as a set of simple linear relationships. Our method is applied to the figure-ground segmentation problem. The experiments show clearly improved results.
Reference: text
sentIndex sentText sentNum sentScore
1 local contrast, edge continuity and contour closure) play important and complementary roles. [sent-16, score-0.507]
2 The main focus is given to how to maintain the consistency (compatibility) between the region cues and the boundary cues. [sent-18, score-0.31]
3 To this ends, we introduce the use of winding number–a well-known concept in topology–as a powerful mathematical device. [sent-19, score-0.814]
4 However, salient contour extraction is a challenging task as it involves both region and boundary information, requiring integration ofbottom-up image cues and top-down semantic priors. [sent-27, score-0.739]
5 Contour extraction has been approached through two complementary directions: one is to treat the problem as a (2D) region segmentation task [18, 23, 7], and the other focuses on the intrinsic 1D contour detection aspect of the problem (such as snake/level-set methods). [sent-30, score-0.594]
6 There has been a trend of jointly using, or combining both contour cues and region cues. [sent-31, score-0.569]
7 In the continuous domain, active contour model was adapted to use both region and contour cues [20] [25]. [sent-32, score-0.973]
8 In the discrete domain, contour cues (such as curvature) have been introduced to region-segmentation methods (e. [sent-33, score-0.427]
9 This paper aims to develop a more consistent approach to salient contour extraction that tightly integrates both region cues and boundary cues. [sent-37, score-0.739]
10 Our insight is that, to achieve jointly utilizing both aspects of image cues, using a simple linear combination of a region objective function and a contour objective function is not sufficient. [sent-38, score-0.567]
11 A key issue, that must be taken into account, is the conditions under which the consistency (or compatibility) between the region variables and the edge variables is satisfied. [sent-39, score-0.329]
12 Our key intuition that motivates this model is a well-known fact: contour and region form certain kind of “duality” relationship. [sent-45, score-0.511]
13 The above observation motivates our winding number approach of this paper. [sent-52, score-0.781]
14 By definition, winding number, which involves a set of closed ( but not necessarily simple) planar curves and a point in the plane, refers to the number 222888111 686 of times the curves revolves around this point. [sent-53, score-0.825]
15 The key idea of this paper is that if the region labels are restricted to be the winding numbers of the curves, then the region-contour consistency condition can be effectively captured by a very small set of linear constraints. [sent-54, score-1.063]
16 Using the winding number concept, we present a new salient contour detection model, integrating the region segmentation cue into the ratio-based contour detection framework [22][19]. [sent-55, score-1.889]
17 In particular, we focus on the foreground segmentation task, in which the winding number can be transformed to region label exactly. [sent-56, score-1.033]
18 Our objective function includes constraints from contour saliency, region similarity and contour smoothness, and can be efficiently solve by linear programming approximately. [sent-57, score-0.946]
19 Our method is evaluated on the Weizmann horse images and Berkeley segmentation dataset, showing advantages over pure contour or region based approaches. [sent-58, score-0.611]
20 Although this paper focuses on middle-level perceptual grouping, we believe that our method is applicable too for higher level tasks such as object detection where contour cues and region cues are both helpful. [sent-59, score-0.627]
21 Section 3 presents the winding number method in detail. [sent-62, score-0.781]
22 In Section 4, our method is used for integrating region cue and contour cues to achieve salient contour extraction. [sent-63, score-1.108]
23 Related work Our work is closely related to contour grouping and image segmentation. [sent-66, score-0.406]
24 Most of the contour grouping methods start with local edge detection e. [sent-67, score-0.486]
25 For example, contour smoothness prior is popularly employed as a prominent contour cue [12] [24]. [sent-71, score-0.816]
26 We will demonstrate our winding number method under the graph partition framework. [sent-73, score-0.781]
27 There are several previous works which attempted to incorporate both region cues and contour cues. [sent-79, score-0.569]
28 Interveningcontour [10] is one of the early efforts to use local contour strength for region segmentation. [sent-80, score-0.533]
29 GPAC method [20] has shown the flexibility to accommodate both region and contour cues in one energy function. [sent-85, score-0.589]
30 Stahl and Wang [19] modified the ratio contour method [22] by replacing the total length with total area as the denominator which resulted in segmentation of more regular shape. [sent-87, score-0.485]
31 In contrast, the winding number constraints used by our method is a set of global constraints. [sent-90, score-0.819]
32 The winding number concept not only leads to smaller number of constraints, but also makes the framework potentially applicable to multiple-label segmentation, although not demonstrated in this paper. [sent-91, score-0.814]
33 Finally, the concept of winding number (rotation index) has been used for ensuring contour topology in [8]. [sent-92, score-1.207]
34 Winding number representation This section first presents our salient contour extraction problem setting, which is based on superpixel oversegmentation. [sent-95, score-0.54]
35 3 presents the main idea of our winding number-based method. [sent-99, score-0.781]
36 Basic edge and region hypotheses We formulate the salient contour extraction problem as an energy minimization problem defined on both region and edge hypotheses. [sent-102, score-0.95]
37 It is important to note that our winding number formulation is not restricted to the superpixel setup, but applies to general boundary-region graph as well. [sent-107, score-0.835]
38 ΦW (x, y) = 0 ΦC (x, y) = 0 x ∈ X, y ∈ Y (2) (3) (4) where the energy function E captures various region priors and contour priors. [sent-126, score-0.531]
39 Our main contribution of this paper is the introduction and construction of a compact set of “winding number constraints”, Eq (2) in the above formulation, which captures the consistency relationship between edge variables and region variables. [sent-128, score-0.304]
40 The edge continuity constraints Eq (3) is necessary for ensuring the edges forms cycles in the graph. [sent-129, score-0.297]
41 This condition guarantees that every edge must be a part of a closed region boundary, and every region is enclosed by a boundary (or contour). [sent-134, score-0.495]
42 Conversely, violating this condition will lead to the break of contour connectedness/closure condition, as shown in work [2]. [sent-135, score-0.403]
43 Next section will show that this condition is guaranteed by our constraint sets based on the winding number concept. [sent-136, score-0.815]
44 Winding number and its fast computation We realize that the winding number concept, from topological study, provides an elegant and effective means to parameterize the region-contour consistency constraint in image segmentation. [sent-139, score-0.838]
45 The winding number ofa point induced by a closed curve is defined as the number of times this curve travels around the point counterclockwise [15]. [sent-140, score-0.892]
46 For a set of contour, the induced winding number can be defined as the sum of winding numbers induced by every contour. [sent-141, score-1.651]
47 Provable by the celebrate Residue Theorem [15], the winding number of all the image points inside an atom region must be all equal. [sent-142, score-0.994]
48 Based on this remarkable result, we reach our winding number constraint, viz. [sent-143, score-0.781]
49 The label of a region can be identified by its winding number induced by contour. [sent-144, score-0.978]
50 Figure-2 illustrates how different contour labels result in different segmentations. [sent-147, score-0.397]
51 The rest of the figure shows different segmentations induced by different contour orientation. [sent-152, score-0.403]
52 Regions with the same winding number are considered as in the same region. [sent-154, score-0.781]
53 number constraints, unique or not, guarantee the consistency between region labels and the corresponding contour labels. [sent-155, score-0.596]
54 First of all, the winding numbers of adjacent regions will be different if one of the conjugate edges between them is active. [sent-156, score-0.95]
55 1 Secondly, the Residue Theorem also suggests that two regions which are not separated by any edges must have the same winding number. [sent-157, score-0.869]
56 In conclusion, this winding number scheme does encode the regioncontour consistency condition compactly and efficiently. [sent-159, score-0.872]
57 The benefit of such winding number scheme also lies in that: it leads to a set of linear constraints. [sent-160, score-0.781]
58 This can be made evident by examining the fast computation procedure of winding number computation (c. [sent-161, score-0.781]
59 Then we draw an arbitrary path starting from inside a region to outside of the image frame, then the winding number of the region equals to the number of edges crossing the path from the right side minus the number ofedges crossing from the left side. [sent-166, score-1.315]
60 222888112088 path to outside of the image frame, the winding number of a point equals the number of edges crossing from right (red dot) minus the number of edges crossing from the left (green dot). [sent-168, score-1.099]
61 Formally, the winding number of the region i is computed as: xi = ? [sent-170, score-0.923]
62 Eq (5) for all atom regions together can be represented as the following winding number constraint, denoted as ΦW in Eq (2): x = My, (6) where M is a matrix whose entries are 0, 1, or −1. [sent-175, score-0.872]
63 For a network without source and sink, it can be shown that all the flows can be decomposed into a set of cycles and the winding number can be computed. [sent-184, score-0.81]
64 2 For a general K-way cut problem, the winding number constraint may restrict the feasible set of region labels. [sent-185, score-0.923]
65 However, for the figure-ground segmentation problem, which is of interest to this paper, the following proposition shows that the winding number constraints do not restrict the solution of segmentation at all. [sent-186, score-0.935]
66 For any segmentation in which the regional labels can only be zero and one, there always exists a set of oriented boundaries such that the regional labels equal the winding numbers induced by the set of boundaries. [sent-188, score-1.01]
67 However, they do not affect correctness of the winding number computation. [sent-190, score-0.781]
68 Then, for an atom region whose label is one, we set a cycle of its adjacent edges in counterclockwise direction to be active. [sent-194, score-0.389]
69 This cycle of edges will induce a winding number one to this region, and a winding number zero to other regions. [sent-195, score-1.661]
70 Consequently, every atom region in the foreground has a winding number one. [sent-197, score-1.025]
71 Last, the conjugate edges which are both active can be removed without affecting the winding number of any region. [sent-198, score-0.921]
72 Therefore, the resulted contour is the one consistent with the given segmentation. [sent-199, score-0.369]
73 Ratio-based contour detection and segmentation methods have been studied in [22] [19] [11] [17]. [sent-202, score-0.427]
74 Using the contour cue, the objective function can be the ratio of contour gap over total contour length or figural areas. [sent-203, score-1.232]
75 Here, we use ratio-based method as an example to demonstrate the effectiveness of our winding number scheme. [sent-204, score-0.781]
76 1, we will show how the contour gap information is integrated with the region similarity cue. [sent-206, score-0.552]
77 Incorporation of region similarity cue The contour-based energy function our method adopts is a ratio between the contour gap and the areas of foreground, defined as ([19]): EAB((xy)) (8) The boundary term measures the gap in the contour: EB(y) = αb? [sent-211, score-0.82]
78 The first two sets of constraints are the continuity constraints Eq (3) and winding number constraints Eq (2). [sent-229, score-0.953]
79 For the figure-ground segmentation problem, it is necessary to limit any region and edge label to be zero and one. [sent-231, score-0.301]
80 Although Eq f(i1n3ed) i sa good enough for ensuring t0h,e1 region-contour consistency, the formulation can be further simplified by replacing region labels with edge labels using Eq (6). [sent-235, score-0.302]
81 Incorporation of curvature cue Recognized as the Gestalt law of good continuity, human vision systems have the preference for grouping the smooth contours together. [sent-241, score-0.335]
82 The smoothness of contour is traditionally measured by integral of squared curvature of all the contour points. [sent-243, score-0.886]
83 The binary junction variable zij is associated with the junction formed by edge yi and Figure4. [sent-245, score-0.317]
84 The curvature weight uij is the sum of squared curvature along both edges. [sent-255, score-0.296]
85 (9) equals to the number of edge pixels in the segment minus the sum of the probability of each edge pixel being a true contour point. [sent-303, score-0.583]
86 Experiments To demonstrate the effectiveness of combining region and contour information, our method is compared with the superpixel closure method (SC for short) [11] and the normalized cuts [18] (Ncuts) on the Weizmann horse dataset [5]. [sent-339, score-0.721]
87 These results show that our method achieves better results than methods only using region or contour cue. [sent-341, score-0.511]
88 Similar region cue is 222888222311 used in our region term. [sent-345, score-0.362]
89 Paper [19] proposes a cost function which is the ratio of contour gap over areas. [sent-346, score-0.433]
90 In this experiment, the curvature term is not used and the weight between the region term and boundary term is fixed by a validation set. [sent-349, score-0.433]
91 However, obtaining a complete contour of horses is still challenging due to several reasons. [sent-351, score-0.399]
92 However, the region similarity cue used in our model helps distinguish background region from the foreground horse region. [sent-361, score-0.435]
93 This results show that region homogeneity cue alone is not enough for segmenting salient foreground region. [sent-366, score-0.364]
94 Note that our results in Figure 6 appear to be a single contour due to the property of the objective function. [sent-367, score-0.397]
95 The winding number constraints, however, do not require the solution to be a Jordan curve. [sent-368, score-0.781]
96 The second column is the output contour overlaid on the input images. [sent-383, score-0.369]
97 The first column shows the original image, the second column shows the results of contour overlaid on the image. [sent-388, score-0.369]
98 Conclusion and future work A winding number based method, is introduced in this paper for enforcing the region-contour consistency constraints. [sent-392, score-0.838]
99 Our experiments show that evident improvements can be made for the task of salient contour extraction when both region cue and contour cue are employed. [sent-394, score-1.153]
100 Connected contours: A new contour completion model that respects the closure effect. [sent-502, score-0.443]
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