cvpr cvpr2013 cvpr2013-71 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Kevin Karsch, Zicheng Liao, Jason Rock, Jonathan T. Barron, Derek Hoiem
Abstract: Early work in computer vision considered a host of geometric cues for both shape reconstruction [11] and recognition [14]. However, since then, the vision community has focused heavily on shading cues for reconstruction [1], and moved towards data-driven approaches for recognition [6]. In this paper, we reconsider these perhaps overlooked “boundary” cues (such as self occlusions and folds in a surface), as well as many other established constraints for shape reconstruction. In a variety of user studies and quantitative tasks, we evaluate how well these cues inform shape reconstruction (relative to each other) in terms of both shape quality and shape recognition. Our findings suggest many new directions for future research in shape reconstruction, such as automatic boundary cue detection and relaxing assumptions in shape from shading (e.g. orthographic projection, Lambertian surfaces).
Reference: text
sentIndex sentText sentNum sentScore
1 edu Abstract Early work in computer vision considered a host of geometric cues for both shape reconstruction [11] and recognition [14]. [sent-2, score-0.446]
2 However, since then, the vision community has focused heavily on shading cues for reconstruction [1], and moved towards data-driven approaches for recognition [6]. [sent-3, score-0.649]
3 In this paper, we reconsider these perhaps overlooked “boundary” cues (such as self occlusions and folds in a surface), as well as many other established constraints for shape reconstruction. [sent-4, score-0.929]
4 In a variety of user studies and quantitative tasks, we evaluate how well these cues inform shape reconstruction (relative to each other) in terms of both shape quality and shape recognition. [sent-5, score-0.701]
5 Our findings suggest many new directions for future research in shape reconstruction, such as automatic boundary cue detection and relaxing assumptions in shape from shading (e. [sent-6, score-0.684]
6 Early approaches to object recognition [14] considered shape reconstruction as the first step. [sent-11, score-0.203]
7 As data-driven approaches to recognition became popular, researchers began to represent shape implicitly through weighted image gradient features, rather than explicitly through reconstruction [13]. [sent-12, score-0.203]
8 In this paper, we focus on improving our understanding of the importance of boundary shape cues for 3D shape reconstruction and recognition. [sent-34, score-0.59]
9 In particular, we consider boundaries due to object silhouette, self-occlusion (depth discontinuity) and folds (surface normal discontinuity). [sent-35, score-0.483]
10 We also consider cues for whether boundaries are soft (extrema of curved surface) or sharp. [sent-36, score-0.275]
11 On the standard dataset, reconstructions using various cues are compared via metrics of surface normal and depth accuracy. [sent-38, score-0.542]
12 Our main contribution is to evaluate the importance of various boundary and shading cues for shape reconstruction and shape-based recognition. [sent-41, score-0.824]
13 We extend Barron and Malik’s shape from shading and silhouette method [1] to include interior occlusions with figure/ground labels, folds, and sharp/soft boundary labels. [sent-42, score-0.789]
14 The standard evaluation is based on depth error, surface normal, shading, or reflectance on the MIT Intrinsic Image dataset. [sent-43, score-0.254]
15 We also introduce perceptual and recognition-based measures of reconstruction quality for the PASCAL VOC dataset (Fig 1 shows one example of the types of reconstructions we evaluate, and the annotation required by our algorithm). [sent-44, score-0.193]
16 Furthermore, much work has gone into shape-based representations for recognition, focusing on the cues provided by the silhouette 222111666311 Input image/labels silh +selfocc +folds Figure1. [sent-46, score-0.592]
17 Foragiveni putimage,wehand-labelgeometric uesincluding: +occ+folds +shading +shading+occ+folds smooth silhouette contour (red), sharp silhouette contour (cyan), self occlusions (green), and folds (orange). [sent-47, score-1.322]
18 We then use various combinations of these cues (as well as appearance-based cues) to obtain different shape reconstructions (see Sec 3). [sent-48, score-0.44]
19 We evaluate these reconstructions in a variety of tasks in order to find which set(s) of cues may be most beneficial for reconstructing shapes. [sent-49, score-0.363]
20 Our findings suggest a 3D representation that incorporates interior occlusions and folds might benefit such existing systems. [sent-54, score-0.443]
21 Our study is a good step towards understanding shape reconstruction in the context of recognition, but we must leave several aspects of this complex problem unexplored. [sent-56, score-0.238]
22 Eventually, we will want automatic recovery of shape cues and reconstruction algorithms that handle uncertainty. [sent-58, score-0.415]
23 Second, cues such as ground contact points and object-level shape priors are useful but not investigated. [sent-59, score-0.373]
24 Cues for object reconstruction We focus on reconstructing shape from geometric cues, revisiting early work on reconstructing shape from line drawings [11, 12]. [sent-64, score-0.49]
25 Through human labeling, we collect information about an object’s silhouette, self-occlusions, and folds in the surface. [sent-65, score-0.405]
26 Since appearance can be a helpful factor in determining shape, we also investigate the benefit of shading cues using the shape-from-shading priors of Barron and Malik [1]. [sent-66, score-0.607]
27 Following Barron and Malik’s notation, we write Z for the surface (represented by a height field viewed orthographically), and N : R → R3 aas h tehieg hfutn fiectlidon v itehwate dtak oertsh oag hreapighhitc afil eyld), t aon dsur Nfac :e R Rno →rma Rls (component-wise; N = (Nx, Ny, Nz)). [sent-69, score-0.189]
28 The silhouette is rich with shape information, both perceptually and geometrically [10]. [sent-74, score-0.342]
29 At the occluding contour of an object, the surface is tangent to all rays from the vantage point, unless however there is a discontinuity in surface normals across the visible and non-visible regions of the object (e. [sent-75, score-0.592]
30 We treat these two cases separately, labeling parts of the silhouette as smooth if the surface normal should lie perpendicular to both the viewing direction and image silhouette, and sharp otherwise1 . [sent-78, score-0.536]
31 In the case of a smooth silhouette contour, the z-component of the normal is 0, and the x and y components are normal to the silhouette (i. [sent-79, score-0.572]
32 Denoting (nx , ny) as normals of the silhouette contour, and Csmooth as the set of pixels labelled as the smooth part of the silhouette, we write the silhouette constraint as: fsfc(Z) =i∈C? [sent-82, score-0.64]
33 (2) This is the most typical constraint used in shape-fromcontour algorithms (hence the notation fsfc), and is identical to that used by Barron and Malik, with the notable exception that we only enforce the constraint when the silhouette is not sharp. [sent-85, score-0.285]
34 If the silhouette is labelled sharp, there is no added constraint. [sent-86, score-0.223]
35 The boundary of a selfocclusion implies a discontinuity in depth, and thus the surface along the foreground boundary should be constrained to be tangent to the viewing direction. [sent-89, score-0.405]
36 Besides knowing a self occlusion boundary, it is also mandatory to know which side of the contour is in front of the other (figure and ground labels). [sent-90, score-0.272]
37 With this information, we impose additional surface normal constraints along self occlusion boundaries (Cselfocc): fselfocc(Z) =i∈? [sent-91, score-0.356]
38 (3) Notice that there is no explicit constraint to force the height of the foreground to be greater than that of the background; however, by constraining the foreground normals to be pointing outward and perpendicular to the viewing direction, the correct effect is achieved. [sent-94, score-0.269]
39 A fold in the surface denotes a discontinuity in surface normals across a contour along the object, e. [sent-97, score-0.731]
40 folds on a cube are at 90◦, but this is not always the case), and can be convex (surface normals pointing away from × each other) or concave (surface normals pointing towards each other). [sent-102, score-0.708]
41 Our labels consist of fold contours and also a flag denoting whether the given fold is convex or concave. [sent-103, score-0.488]
42 We did not annotate exact fold orientation as this task is susceptible to human error and tedious. [sent-104, score-0.218]
43 We incorporate fold labels by adding another term to our objective function, developed using intuition from Malik and Maydan [12]. [sent-105, score-0.218]
44 The idea is to constrain normals at pixels that lie across a fold to have convex or concave orientation (depending on the label), and to be oriented consistently in the direction of the fold. [sent-106, score-0.335]
45 , Nir as two corresponding normals across pixel iin the fold contour C. [sent-108, score-0.426]
46 We use the albedo and illumination priors of Barron and Malik to incorporate shading cues into our reconstructions. [sent-126, score-0.679]
47 For brevity, we denote priors on reflectance as g(R), and priors on illumination as h(L), where R is log-diffuse reflectance (logalbedo) and L is the 27-dimensional RGB spherical harmonic coefficient vector. [sent-129, score-0.296]
48 Jointly estimating shape along with albedo and illumination requires an additional constraint that forces a rendering of the surface to match the input image. [sent-131, score-0.346]
49 Assuming Lambertian reflectance and disregarding occlusions, our render- ing function is simply reflectance multiplied by shading (or in log space, log-reflectance plus log-shading). [sent-132, score-0.511]
50 Denoting I as the log-input image, R as log-diffuse reflectance (logalbedo), and S(Z, L) as the log-shaded surface Z under light L, we write the shape-from-shading constraint as: csfs (Z, R, L) = R + S(Z, L) − I. [sent-133, score-0.332]
51 Notice that shading cues are only incorporated if δsfs > 0; otherwise, our reconstructions rely purely on geometric information. [sent-139, score-0.705]
52 com/sibl 222111666533 Input + annotations +occ+folds View 1 View 2 +shading View 1 +shading+occ+folds View 2 View 1 View 2 contour (red), sharp silhouette contour (cyan), self occlusions (green), and folds (orange). [sent-145, score-1.065]
53 This paper is the first that we know of to provide a rigorous analysis of shape reconstruction on typical objects in consumer photographs (e. [sent-150, score-0.203]
54 Evaluation of shape and appearance cues In this section, we examine each of the cues used in our shape reconstruction method, and hope to find a cue or set of cues that lead to better shape estimates (qualitatively, and in terms of recognition ability). [sent-160, score-1.114]
55 Our objective function (Eq 1) allows us to easily produce shape reconstructions for various combinations of cues by turning “on” and “off” different cues; equivalently, setting the corresponding weights to 1 (on) or 0 (off). [sent-161, score-0.477]
56 We use six different cue combinations to see which cue or set of cues contribute most to a better reconstruction. [sent-162, score-0.319]
57 These six combinations are: • • • • • • silh: Priors on silhouette shape and surface smoothness; iP. [sent-163, score-0.499]
58 and fold constraints (δsfc = +occ+folds: Silhouette, self occlusion and fold cons+torcaicn+tsfo o(lδdsfsc: = Si δlhsoeulfoecttce =, s δeflfold osc =clu 1si). [sent-168, score-0.59]
59 Note that silh cues are present in each algorithm (hence the ‘+’ prefix). [sent-176, score-0.369]
60 To find which cues are most critical for recovering shape, we evaluate each algorithm on a variety of tasks that measure shape quality and shape recognition. [sent-177, score-0.45]
61 Since we do not have ground truth shape for VOC objects, we conduct two user studies to evaluate qualitative performance: qualitative rating and shape-based recognition. [sent-181, score-0.352]
62 Finally, we ran a quantitative comparison of depth and surface normals using the MIT depth dataset. [sent-183, score-0.316]
63 The remainder of this section details our results for each of these tasks, split under headings concerning shape quality and shape recognition. [sent-184, score-0.238]
64 The goal of these experiments is to find a common set of cues, or shape reconstruction algorithm(s), that consistently report the best shape. [sent-188, score-0.203]
65 The qualitative rating portion of the user study collected subjects’ ratings for each of the six shape reconstruction algorithms. [sent-190, score-0.501]
66 3) that displays the visualization of the six shape estimation results side by side on the screen and allows parQuality rating from user study certain rating was assigned to it during the qualitative rating user study. [sent-192, score-0.683]
67 For example, for the left most column, +shading was rated above silh approximately 60% of the time, below silh about 10% of the time, and rated the same otherwise. [sent-197, score-0.488]
68 Shading seems to help when accompanied by with a silhouette cues, but when additional boundary cues are present, shading tends to produce more artifacts than improvements. [sent-198, score-0.844]
69 We also see a strong improvement from combining fold and occlusion contours. [sent-199, score-0.249]
70 Figure 4 shows the aver- aged rating score grouped by algorithm; where a higher average rating indicates a better shape. [sent-206, score-0.246]
71 In every case, as intuition suggests, adding more geometric cues leads to a more preferable shape. [sent-207, score-0.243]
72 Here, we see geomet222111666755 ric cues (other than silh) were consistently preferred over shading cues; in one example, +occ+folds was rated higher than +shading+occ+folds about 40% of the time. [sent-209, score-0.652]
73 Using ground truth shapes available from the MIT Intrinsic Image dataset [8], we analyze our shape reconstructions using established errors metrics. [sent-211, score-0.283]
74 46739A0 48E273† We observe that adding geometric cues generally increase quantitative performance. [sent-219, score-0.243]
75 We also consider that object silhouette could be a dominating factor for recognition; to reduce this factor, we show a silhouette-masked view of each result first (Fig. [sent-234, score-0.264]
76 For each algorithm, the left bar shows the result from the masked view; the right bar shows that result from the unmasked view. [sent-246, score-0.205]
77 In the masked view, +occ+folds yields the lowest recognition error, consistent with qualitative rating portion of our user study. [sent-247, score-0.258]
78 on each reconstruction as well as rgb, rgb+occ+folds, and rgb+shading+occ+folds for the kernel matching method to determine if shape and shading cues add information compared to RGB alone. [sent-258, score-0.768]
79 The shape reconstructions increase the accuracy of the result, but this could be partially due to the mask provided by the height which is not available in the RGB only method. [sent-267, score-0.254]
80 Conclusion We demonstrate a simple and extensible technique for reconstructing shape from images, resurrecting highly informative cues from early vision work. [sent-269, score-0.397]
81 Our method itself is an extension of Barron and Malik’s [1] reconstruction framework, and we show how additional cues can be incorporated in this framework to create improved reconstructions. [sent-270, score-0.296]
82 Through our experiments, we have shown the necessity of considering cues that go beyond typical shape-fromshading constraints. [sent-271, score-0.212]
83 In almost every task we assessed, using more geometric cues gives better results. [sent-272, score-0.243]
84 For humanbased tasks, shading cues seem to help when applied with to silhouette cues (+shading consistently outperforms silh), but adds little information once additional boundary cues are incorporated (+occ+folds performs similarly to +shad- ing+occ+folds); see Figs 4 and 7. [sent-273, score-1.268]
85 As one might expect, adding geometric features to the existing rgb information improves recognition accuracy, and shape tends to be more revealing than appearance alone. [sent-276, score-0.221]
86 better than +shading+occ+folds (Fig 7; masked errors), and shading cues seem to have an adverse effect on automatic recognition algorithms (Table 1). [sent-278, score-0.621]
87 One interesting observation from our experiments is that our shading cues tend to confound boundary cues; e. [sent-282, score-0.621]
88 It seems counterintuitive that incorporating shading information would degrade reconstructions, and we offer several possible causes. [sent-286, score-0.353]
89 Foremost is the fact that we weight all terms equally, whereas learning these weights from ground truth will lead to better shading reconstructions (evidenced especially by our quantitative results on the MIT Intrinsic dataset in Sec 3. [sent-287, score-0.499]
90 Our evaluations show that self occlusion and fold cues are undoubtedly helpful, and most importantly, point in many directions for improving existing shape reconstruction algorithms. [sent-295, score-0.787]
91 Extracting boundary cues, such as folds and self occlusions, automatically from photographs is a logical next step. [sent-296, score-0.584]
92 Appendix: Fold constraint implementation Consider the (i)th point on the contour C, parametrized by position p = [px , py] and tangent vector u = [ux , uy], both on the image plane. [sent-421, score-0.228]
93 By default, this fold is convex g—en ftol vdeecdto irn: tvhe = =di [r−euction of negative Z. [sent-424, score-0.218]
94 = [round (px vx) , round (py vy)] = [round (px − vx) , round (py − vy)] pr (9) (10) Given a normal field N we compute the normal of the surface at these “left” and “right” points: N? [sent-427, score-0.286]
95 Nzr) (13) If c = 1, then the cross product of the surface normals on both sides of the contour is exactly equal to the tangent vector, and the surface is therefore convexly folded in the direction of the contour. [sent-439, score-0.579]
96 Intuitively, to force the surface to satisfy the fold constraint imposed by the contour, we should force c to be as close to 1 as possible. [sent-442, score-0.421]
97 But constraining c = 1is not appropriate for our purposes, as it ignores the fact that u and therefore v lie in an image plane, while the true tangent vector of the contour may not be parallel to the image plane. [sent-444, score-0.197]
98 -insensitive hinge loss which allows for fold contours to be oriented as much as 45◦ out of the image plane. [sent-452, score-0.246]
99 = 1 is only satisfied by a perfect fold whose crease is parallel with the image plane. [sent-456, score-0.218]
100 = √12 produces folds that are roughly 90◦, and which look reasonable upon inspection. [sent-458, score-0.405]
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