nips nips2008 nips2008-95 knowledge-graph by maker-knowledge-mining

95 nips-2008-Grouping Contours Via a Related Image

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Author: Praveen Srinivasan, Liming Wang, Jianbo Shi

Abstract: Contours have been established in the biological and computer vision literature as a compact yet descriptive representation of object shape. While individual contours provide structure, they lack the large spatial support of region segments (which lack internal structure). We present a method for further grouping of contours in an image using their relationship to the contours of a second, related image. Stereo, motion, and similarity all provide cues that can aid this task; contours that have similar transformations relating them to their matching contours in the second image likely belong to a single group. To ﬁnd matches for contours, we rely only on shape, which applies directly to all three modalities without modiﬁcation, in contrast to the specialized approaches developed for each independently. Visually salient contours are extracted in each image, along with a set of candidate transformations for aligning subsets of them. For each transformation, groups of contours with matching shape across the two images are identiﬁed to provide a context for evaluating matches of individual contour points across the images. The resulting contexts of contours are used to perform a ﬁnal grouping on contours in the original image while simultaneously ﬁnding matches in the related image, again by shape matching. We demonstrate grouping results on image pairs consisting of stereo, motion, and similar images. Our method also produces qualitatively better results against a baseline method that does not use the inferred contexts. 1

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 While individual contours provide structure, they lack the large spatial support of region segments (which lack internal structure). [sent-8, score-0.852]

2 We present a method for further grouping of contours in an image using their relationship to the contours of a second, related image. [sent-9, score-1.834]

3 Stereo, motion, and similarity all provide cues that can aid this task; contours that have similar transformations relating them to their matching contours in the second image likely belong to a single group. [sent-10, score-1.945]

4 Visually salient contours are extracted in each image, along with a set of candidate transformations for aligning subsets of them. [sent-12, score-0.849]

5 For each transformation, groups of contours with matching shape across the two images are identiﬁed to provide a context for evaluating matches of individual contour points across the images. [sent-13, score-1.715]

6 The resulting contexts of contours are used to perform a ﬁnal grouping on contours in the original image while simultaneously ﬁnding matches in the related image, again by shape matching. [sent-14, score-2.214]

7 We demonstrate grouping results on image pairs consisting of stereo, motion, and similar images. [sent-15, score-0.322]

8 1 Introduction Researchers in biological vision have long hypothesized that image contours (ordered sets of edge pixels, or contour points) are a compact yet descriptive representation of object shape. [sent-17, score-1.224]

9 In computer vision, there has been substantial interest in extracting contours from images as well as using object models based on contours for object recognition ([15, 5]), and 3D image interpretation [11]. [sent-18, score-1.917]

10 We examine the problem of grouping contours in a single image aided by a related image, such as stereo pair, a frame from the same motion sequence, or a similar image. [sent-19, score-1.426]

11 Relative motion of contours in one image to their matching contours in the other provides a cue for grouping. [sent-20, score-1.959]

12 The contours themselves are detected bottom-up without a model, and are provided as input to our method. [sent-21, score-0.756]

13 While contours already represent groupings of edges, they typically lack large spatial support. [sent-22, score-0.847]

14 Region segments, on the other hand, have large spatial support, but lack the structure that contours provide. [sent-23, score-0.796]

15 Therefore, additional grouping of contours can give us both qualities. [sent-24, score-0.895]

16 This has important applications for object recognition and scene understanding, since these larger groups of contours are often large pieces of objects. [sent-25, score-0.877]

17 Figure 1 shows a single image in the 1st column, with contours; in the other columns, top row, are different images related by stereo, motion and similarity to the ﬁrst, shown with their contours. [sent-26, score-0.438]

18 Below each of these images are idealized groupings of contours in the original image. [sent-27, score-0.933]

19 Note that internal contours on cars and buildings are grouped, providing rich, structured shape information over a larger image region. [sent-28, score-1.169]

20 1 Stereo Motion Similarity Image 2 Image 1 Grouping in image 1 using related images Figure 1: Contours (white) in the image on the left can be further grouped using the contours of a second, related image (top row). [sent-29, score-1.442]

21 2 Related Work Stereo, motion, and similar image matching have been studied largely in isolation, and often with different purposes in mind than perceptual grouping. [sent-31, score-0.324]

22 Much of the stereo literature focuses on perpixel depth recovery; however, as [7] noted, stereo can be used for perceptual grouping without requiring precise depth estimation. [sent-32, score-0.639]

23 These approaches to motion and stereo are largely region-based, and therefore do not provide the same internal structure that groups of contours provide. [sent-34, score-1.172]

24 Similar image matching has been used for object recognition [1], but is rarely applied to image segmentation. [sent-35, score-0.577]

25 In work on contours, [12] matched contour points in the context of aerial imagery, but use constraints such as ordering of matches along scanlines that are not appropriate for motion or similar images, and do not provide grouping information. [sent-36, score-0.72]

26 [9] grouped image pixels into contours according to similar motion using optical ﬂow as a local cue. [sent-37, score-1.124]

27 [8] grouped and matched image regions across different images and unstable segmentations (as we do with contours), but the regions lack internal structure. [sent-39, score-0.394]

28 [2, 6] used stereo pairs of images to detect depth discontinuities as potential object boundaries. [sent-40, score-0.441]

29 However, these methods will not detect and group group contours in the interior of fronto-parallel surfaces. [sent-41, score-0.82]

30 A set of contours Ii , where the jth contour Ci Ii is an ordered subset of points in Ii : j C pkn ] Ii . [sent-48, score-1.027]

31 A transformation Ti that aligns a subset of contours (e. [sent-50, score-0.788]

32 A subset of contours Coni in each image, known as a context, such that the two subsets C C 0 1 I1 , Con2 0 1 I2 . [sent-55, score-0.756]

33 Coni = Con1 Con2 ; Con1 i i i i j Each Coni is vector that indicates which contours are in the context for image Ij . [sent-57, score-1.044]

34 j We further deﬁne the following variables on contours C1 = [pk1 pkn ]: j 1. [sent-59, score-0.789]

35 Good continuation - for contours that overlap signiﬁcantly, we prefer that they are present in the same group, if they are grouped at all. [sent-69, score-0.794]

36 Common fate by shape: contours with similar transformations mapping them to their matches should be grouped. [sent-71, score-0.93]

37 We also require that each contour point in a grouped contour and its matching point in the second image have similar local shape. [sent-72, score-0.794]

38 Shape in each image is deﬁned with respect to a subset of image contours known as a context; we will explain the importance of choosing the correct context for shape comparison, as ﬁrst noted in [16]. [sent-73, score-1.418]

39 Maximality/simplicity: We would like to group as many of the contours as possible into as few groups as possible, while still maintaining the similarity of local shape described above. [sent-75, score-1.063]

40 This combination of the MRF standard graph matching technique with an LP for inferring context for accurate matching by shape is our main contribution. [sent-81, score-0.604]

41 4 Matching and Context Selection We can evaluate the hypothesis of a particular contour point match by comparing the local shape around the point and around its match. [sent-84, score-0.492]

42 Although local features such as curvature and simple proximity (in the case of roughly aligned contours) have been used for matching ([12]), inconsistencies in the input contours across two images make these them prone to error. [sent-85, score-1.049]

43 In a), the contours do not match, while in e), a “7” shape is common to both. [sent-89, score-0.947]

44 As an example, we use the shape context, an image feature that has been widely used for shape matching ([1]). [sent-98, score-0.706]

45 Brieﬂy, a shape context provides a log-polar spatial histogram that records the number of points that fall into a particular bin. [sent-99, score-0.336]

46 In Figure 2 c,g), shape contexts (darker bins mean larger bin count) with large spatial support placed according to the rough alignment exhibit high dissimilarity in both cases, failing to ﬁnd a match in a). [sent-100, score-0.519]

47 The large feature failed because contours in each image that had no match in the other image were used in computing the shape context. [sent-101, score-1.398]

48 Inferring which contours to include and which to omit would give better features, as in Figure 2 d),h). [sent-102, score-0.756]

49 This ﬁxes the completeness problem, while retaining soundness: no combination of contours in the two images in a) can produce matching shapes. [sent-103, score-1.012]

50 Therefore, with rough alignment we can cast the ﬁrst step of shape matching as context selection: which subset of contours, or context, to use for feature computation. [sent-104, score-0.478]

51 Given the correct context, matching individual contour points is much easier. [sent-105, score-0.379]

52 1 Selection Problem We can neatly summarize the effect of a particular context selection on a shape context as seen in Figure 3. [sent-107, score-0.45]

53 The bin counts for a shape context can be encoded as a vector, represented by the shape contexts and their vector representations alongside. [sent-110, score-0.676]

54 SC has dimensions nBins by nContours, where nBins is the number of bins in the shape context (and the length of the associated vector). [sent-112, score-0.321]

55 The entry SC(i j) is the bin count for bin i and contour j. [sent-113, score-0.352]

56 For each j 0 1 , which indicates contour Ci in an image Ii , we associate an selection indicator variable selj i whether or not the contour is selected; the vector of these indicator variables is seli . [sent-114, score-0.727]

57 Then the shape context bin counts realized by a particular selection of contours is SCseli , simply the multiplication of the matrix SC and the vector seli . [sent-115, score-1.254]

58 d) shows the effect on the shape context histogram of various context selections. [sent-116, score-0.401]

59 2 Shape context matching cost The effectiveness of selection depends signiﬁcantly on the shape context matching cost. [sent-118, score-0.755]

60 Traditional matching costs (Chi-square, L1 , L2 ) only measure similarity, but selecting no contours in either image gives a perfect matching cost, since in both shape contexts, all bins will be 0. [sent-119, score-1.437]

61 While similarity is important, so is including more contours rather than fewer (maximality). [sent-120, score-0.789]

62 The selection process is run for each transformation to infer a context suitable for evaluating contour point matches via shape. [sent-122, score-0.5]

63 The intersection term encourages higher bin counts in each shape context and therefore the inclusion of more contours. [sent-124, score-0.394]

64 We begin with two C input images, where the contours are in rough alignment (by applying known Ti to I1 ). [sent-130, score-0.797]

65 Multiple shape contexts are placed in each image on a uniform grid (an approximation of Matchj l(j)=i , since we initially have no matches). [sent-131, score-0.465]

66 Our goal is to select contours in each image to minimize the sum of SCMatchCost for each pair of shape contexts. [sent-133, score-1.13]

67 For each shape context j in each image i, we compute the corresponding j j shape context matrix SCi . [sent-134, score-0.775]

68 SCi j for each image has been color coded to show the SCi matrix corresponding to each shape context. [sent-136, score-0.374]

69 SCi selci is then the realized bin counts for i all the shape contexts in image Ii under selection selci . [sent-139, score-0.692]

70 We seek to choose selc1 and selc2 such that SC1 selc1 SC2 selc2 in a shape sense; entries of SC1 selc1 and SC2 selc2 , or realized bin counts, are in correspondence, so we can score these pairs of bin counts using BinMatchCost. [sent-140, score-0.405]

71 Figure 5 depicts an idealized selection process for two images (only the contours are shown). [sent-156, score-0.931]

72 For groups of SIFT matches that describe similar transformations, a transformation Ti is extracted and warps the contours in image 1 to line up with those of image 2, in c). [sent-157, score-1.32]

73 The selection problem is formulated separately for each set of aligned contours d). [sent-158, score-0.84]

74 Two correct transforms align the car and person, and the selection result includes the respective contours (rows 1,2 of e). [sent-160, score-0.825]

75 We can view the context selection procedure for minimizing Fi as choosing the context of contours so as to best reduce the matching cost of the hypothesized inter-image matches for contours with label i, under the transformation Ti . [sent-162, score-2.081]

76 5 Graph Cuts for Group Assignment and Matching We previously computed context selections (as solutions to the SelectionCost LP), which found groups of contours in each image that have similar shape, Con = {Con1 , . [sent-165, score-1.115]

77 Note that a j contour C1 need not be selected as context in a particular group a in order to have lj = a. [sent-174, score-0.472]

78 j k The binary potentials φ(lj , lk ) encode the preference that overlapping contours C1 , C1 have the same label: 1 a=b φ(lj = a, lk = b) = (1) 1−τ a=b where 0 ≤ τ ≤ 1 controls the penalty of having different labels. [sent-177, score-0.808]

79 Two contours overlap if they contain at least one point in common. [sent-179, score-0.756]

80 , pkn ] can be matched in the second image with respect to the context {Con1 , Con2 }. [sent-183, score-0.338]

81 Instead of using all contours image 1 as nodes in the MN, we only allow contours were selected in at least one of the context Con1 ; likewise, we only permit i matches to points in image 2 that appear in a contour selected in at least one Con2 . [sent-186, score-2.319]

82 This better j allows us to deal with contours that appear only in one image and thus cannot be reliably grouped based on relative motion. [sent-187, score-0.977]

83 Columns 3,4: grouping results for our method and baseline; groups of contours are a single color. [sent-190, score-0.946]

84 If more than half the points in the ﬁnal assignment ∗ lj for a contour were occluded, we marked the entire contour as occluded, and it was not displayed. [sent-200, score-0.573]

85 Since we omitted all selection information, all contours in the 1st image were included in the MN P as nodes, and their contour points were allowed to match to any contour point in I2 . [sent-201, score-1.527]

86 6 Experiments We tested our method and the baseline over stereo, motion and similar image pairs. [sent-204, score-0.35]

87 Input contours in each image were extracted automatically using the method of [15]. [sent-205, score-0.956]

88 SIFT matches were extracted from images, keeping only conﬁdent matches as described in [10]; matches proposing similar transformations were pruned to a small set, typically 10-20. [sent-206, score-0.403]

89 Because of the high quality of the inferred contexts, we used large shape contexts (radius 90 pixels, in images of size 400 by 500), which 7 made matching very robust. [sent-207, score-0.522]

90 Shape contexts were placed on a uniform grid atop the registered contours (via Ti ) with a spacing 50 pixels in the x and y dimensions. [sent-209, score-0.871]

91 Image pairs were taken from the Caltech 101 dataset [4] and from a stereo rig with 1m baseline mounted on a car from our lab (providing stereo and motion images). [sent-210, score-0.637]

92 Groups for stereo image pairs are colored according to disparity. [sent-214, score-0.408]

93 Due to the lack of large context, the baseline method is able to ﬁnd a good match for a given contour point under almost any group hypothesis lj = a, since in cluttered regions, there are always nearby matches. [sent-215, score-0.518]

94 7 Conclusion We introduced the problem of grouping of contours in an image using a related image, such as stereo, motion or similar, as an important step for object recognition and scene understanding. [sent-219, score-1.271]

95 Grouping depends on the ability to match contours across images to determine their relative motion. [sent-220, score-0.958]

96 Selecting a good context for shape evaluation was key to robust simultaneous and grouping of contours across images. [sent-221, score-1.209]

97 Future work will include trying to learn 3D object models from stereo and motion images, and a probabilistic formulation of the matching framework. [sent-223, score-0.542]

98 Introducing learning to improve the grouping result is also an area of signiﬁcant interest; some shape conﬁgurations are more reliable for matching than others. [sent-224, score-0.471]

99 Recognition of object contours from stereo images: an edge combination approach. [sent-258, score-1.034]

100 Contour context selection for object detection: A set-to-set contour matching approach. [sent-317, score-0.564]

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