iccv iccv2013 iccv2013-330 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Claudia Nieuwenhuis, Evgeny Strekalovskiy, Daniel Cremers
Abstract: We propose a convex multilabel framework for image sequence segmentation which allows to impose proportion priors on object parts in order to preserve their size ratios across multiple images. The key idea is that for strongly deformable objects such as a gymnast the size ratio of respective regions (head versus torso, legs versus full body, etc.) is typically preserved. We propose different ways to impose such priors in a Bayesian framework for image segmentation. We show that near-optimal solutions can be computed using convex relaxation techniques. Extensive qualitative and quantitative evaluations demonstrate that the proportion priors allow for highly accurate segmentations, avoiding seeping-out of regions and preserving semantically relevant small-scale structures such as hands or feet. They naturally apply to multiple object instances such as players in sports scenes, and they can relate different objects instead of object parts, e.g. organs in medical imaging. The algorithm is efficient and easily parallelized leading to proportion-consistent segmentations at runtimes around one second.
Reference: text
sentIndex sentText sentNum sentScore
1 The key idea is that for strongly deformable objects such as a gymnast the size ratio of respective regions (head versus torso, legs versus full body, etc. [sent-2, score-0.186]
2 We propose different ways to impose such priors in a Bayesian framework for image segmentation. [sent-4, score-0.313]
3 We show that near-optimal solutions can be computed using convex relaxation techniques. [sent-5, score-0.334]
4 Extensive qualitative and quantitative evaluations demonstrate that the proportion priors allow for highly accurate segmentations, avoiding seeping-out of regions and preserving semantically relevant small-scale structures such as hands or feet. [sent-6, score-0.664]
5 They naturally apply to multiple object instances such as players in sports scenes, and they can relate different objects instead of object parts, e. [sent-7, score-0.11]
6 The algorithm is efficient and easily parallelized leading to proportion-consistent segmentations at runtimes around one second. [sent-10, score-0.297]
7 Image Sequence Segmentation Automatic image sequence segmentation denotes the task of jointly segmenting one or several objects from a series of images taken under different view points, lighting conditions and background scenes. [sent-14, score-0.299]
8 The difficulty lies in the fact that none of the objects’ properties is guaranteed to be preserved over time. [sent-15, score-0.089]
9 Both the geometry and the photometry of the objects of interest may change from one image to the next. [sent-16, score-0.038]
10 Changing illumination affects the observed color model, different viewpoints lead to different object scales and possibly self-occlusions, whole parts of the object can even vanish from the image, and objects may occlude each other in the case of multiple foreground objects. [sent-17, score-0.271]
11 Moreover, articulations and non-rigid deformations give rise to substantial shape changes. [sent-18, score-0.211]
12 Multi-label segmentation with length regularity Multi-label segmentation with proportion priors Figure 1. [sent-20, score-0.705]
13 Proportion priors allow to constrain the relative size between different object parts (e. [sent-21, score-0.397]
14 They enable stable segmentations over long image sequences, preventing the seeping out of regions into the background (e. [sent-24, score-0.236]
15 the green hair region) or the removal of semantically important small parts (e. [sent-26, score-0.146]
16 and exploiting information which is shared among the images is a challenging task. [sent-29, score-0.037]
17 In general, the co-segmentation problem deals with the situation that we have no knowledge on the object ofinterest besides that it appears in all images. [sent-30, score-0.095]
18 To make the problem tractable many approaches introduced at least some kind of prior knowledge based on training data or user scribbles [1, 12, 7, 21]. [sent-31, score-0.112]
19 The resulting optimization problems are often iterative and hard to optimize [12, 19, 11, 20] leading to runtimes of several seconds or even minutes. [sent-32, score-0.115]
20 For complex real-world image sequences the task of leveraging relevant shared information for co-segmentation remains an open challenge. [sent-33, score-0.037]
21 In this paper, we propose a Bayesian framework for multi-region co-segmentation which allows to impose learned proportion priors — see Figure 1. [sent-34, score-0.574]
22 We show that near-optimal solutions can be efficiently computed by means of convex relaxation techniques. [sent-35, score-0.334]
23 Unfortunately, this limits the applicability to rigid objects observed from similar viewpoints. [sent-39, score-0.061]
24 Upon strong viewpoint changes, articulations or non-rigid deformations, the arising segmentations are too different in their shape to be accounted for. [sent-40, score-0.198]
25 — — Color similarity: On the other extreme are methods which make no assumptions on shape similarity, but which strongly rely on similarity of color or feature distributions [19, 11, 6, 1, 21, 5]. [sent-42, score-0.156]
26 Recent approaches relax these assumptions, requiring less color similarity [7] and instead derive high level knowledge on object properties such as object subspaces [12] or region correspondences [20]. [sent-44, score-0.201]
27 To increase the stability of segmentation results, it was suggested [8] to impose shape moment constraints into variational segmentation methods. [sent-46, score-0.391]
28 Since these constraints are absolute, they are not invariant to changes in scale, viewpoint, occlusions or multiple object instances and are thus not applicable to the general co-segmentation problem. [sent-47, score-0.133]
29 The central idea is to tackle the problem in a multilabel framework where an object, say an athlete, is made up of multiple components (the various limbs of the body). [sent-51, score-0.106]
30 While the object may undergo substantial changes — rigid body motion, articulation, non-rigid deformation — what is typ- ically preserved is the relative size of object parts (e. [sent-52, score-0.648]
31 the head to the entire body), the object part proportions. [sent-54, score-0.12]
32 We formulate image sequence segmentation as a problem of Bayesian inference and introduce proportion priors to restrict the relative size of object parts. [sent-55, score-0.801]
33 This approach comes with the following advantages: • It can handle overlapping color distributions, moderately Ivtar ciaanb hlea lighting lcaopnpdinitgion cos,l vra driisoturisb object mscoadleesr taenldy multiple foreground objects. [sent-56, score-0.239]
34 The proposed ratio constraints preserve small or elongated object parts. [sent-57, score-0.19]
35 • It extends recent convex relaxation techniques [9, 2, 23] Ifrto emxt emnudlsti rleabceeln segmentation taot imonult teilcahbneilq sequence segmentation. [sent-58, score-0.579]
36 We present an efficient optimization scheme which can be parallelized with runtimes of around one second to compute pixel-accurate segmentations. [sent-59, score-0.168]
37 • The approach yields state-of-the-art results on the ICoseg bTehnec ahpmparorka cfohr y iseulbddsi svitsaitbe-loe object sequences. [sent-60, score-0.055]
38 Multilabel Image Sequence Segmentation Let I Ω → R3 denote an input image of the sequence : defiLneetd I on tΩhe → →do Rmain Ω ⊆ R2. [sent-62, score-0.078]
39 The task of segmentation is dtoe partition thhee d image? [sent-63, score-0.121]
40 plane Rinto a set of n pairwise disjoint regions Ωi s. [sent-64, score-0.048]
41 tpheu n regions ienagch l pixel belongs nto}: Ωi = {x ? [sent-75, score-0.048]
42 can compute nsu tchhe a segmentation by maximizing the condi? [sent-79, score-0.161]
43 l (1) lm It combines the observation likelihood P(I | l) (typically favoring a ceosl tohre-b oabsesedr region aiksesloihcoiaotidon P)( Iw |itlh) prior kanlloyw fal-edge P(l) regarding what kinds of partitionings are more or leedsgse likely. [sent-82, score-0.15]
44 In the case of image sequence segmentation, commonly used color and boundary length priors are often insufficient to obtain good results. [sent-83, score-0.332]
45 Secondly, the color distributions of object and background may have substantial overlap and may exhibit strong variations across images. [sent-85, score-0.312]
46 In order to stabilize the segmentation process against color and lighting variations, pose changes and substantial non-rigid deformations, and in order to leverage it to a parsing of objects into their semantic components, we propose to introduce proportion priors into the optimization problem. [sent-86, score-0.801]
47 Framework for Proportion Preserving Priors In the following, we will introduce proportion priors as a means to impose information on the relative size of respective object parts. [sent-89, score-0.713]
48 Whereas the absolute size of parts will vary with viewing angle and distance from the camera, their relative size is typically well preserved – i. [sent-90, score-0.27]
49 the size of the head is typically 10% of the size of the entire body. [sent-92, score-0.147]
50 Let us assume that the object we want to segment can be divided into n−1 sub-regions (e. [sent-93, score-0.055]
51 head, feet, body and bhaen ddisv)i dwedith i ntthoe nn−-th1 region denoting t. [sent-95, score-0.12]
52 Then in the Bayesian framework, the prior P(l) = iPm(aΩg1e , . [sent-97, score-0.072]
53 constraint relates the size Ωi of the i-th region to the size ? [sent-110, score-0.121]
54 tation we want to impose regions of short boundary length Per(Ωi), whose ratios additionally follow a learned (or specified) ratio probability distribution Pp P(Ωi|Ωn) =C1exp? [sent-114, score-0.546]
55 Finally, we assume each background Ωn to be equally likely a priori, so that P(Ωn) = const. [sent-117, score-0.059]
56 uInalsltyea lidk of maximizing tPh(aItP| l)(PΩ(l) in (1) we minimize its negative logarithm manizdin ogb Ptai(nI |tlh)eP energy E(Ω1 , . [sent-118, score-0.04]
57 Contribution: Proportion Preserving Priors In this section we propose two different proportion preserving priors: the uniform distribution prior and the Laplace distribution prior. [sent-133, score-0.541]
58 Both assume that the ratios of the object parts follow a specific distribution Pp(ri) whose parameters are se fsotlimloawte ad sfpreomcif sample bdauttaio, ni. [sent-134, score-0.401]
59 sample segmentations from which ratio samples can be obtained. [sent-136, score-0.226]
60 To convert the energy in (5) to a convex optimization problem in Section 2. [sent-137, score-0.252]
61 3, the key challenge is to express the terms −log Pp(ri) in (5) as a convex function of the varitaebrlmess ai := P|Ωi |/|Ω|, which denote the fraction of the size of region =Ωi | Ωwi|/th| respect tho dtheneo image fsraizceti. [sent-138, score-0.617]
62 Uniform Distribution Prior (6) As a first case, we assume a uniform distribution of the ratios ri over a specific interval [li , hi] . [sent-145, score-0.671]
63 The left and right boundaries li and hi are computed from training data by means of maximum likelihood estimation, which assigns li and hi the minimum and maximum values of the sample ratios, respectively. [sent-146, score-0.226]
64 ≤ hi, (7) Since −log Pp is either constant or infinity, this prior corresponds tloo 2g(nP −1) constraints in the optimization problem: li(1 − an) ≤ ai ≤ hi(1 − an) ∀1 ≤ i < n. [sent-149, score-0.389]
65 (8) These relative ratio constraints are linear and thus convex in terms of the ai. [sent-150, score-0.39]
66 The advantage of this prior is the simple computation and the convexity of the constraints. [sent-151, score-0.072]
67 Yet, in the case of large variations of the ratios ri in the sample data (i. [sent-152, score-0.579]
68 2 Laplace Distribution Prior The Laplace distribution prior penalizes deviations of the ratios ri from their median r¯i . [sent-158, score-0.705]
69 In this way, the influence of ratio sample outliers on the constraints is limited. [sent-159, score-0.135]
70 We assume the following Laplace distribution Pp(ri) =2σ1iexp? [sent-160, score-0.054]
71 g the prior with respect to the other terms, we get the energy of the ? [sent-170, score-0.112]
72 (10) Unfortunately, after replacing ri by (6), this function is not convex in ai and an. [sent-172, score-0.834]
73 For example, for ri < r¯i we obtain Ep(ri) = σμi ( r¯i −1−aain ), which is not convex in an for fixed ai. [sent-173, score-0.555]
74 To make globa1l− oaptimization possible, in the following we propose two methods to convexify this prior. [sent-174, score-0.046]
75 First, we consider the convex relaxation of Ep as a function Ep(ai , an), i. [sent-176, score-0.334]
76 The definition domain of Ep is naturally given by ai , an ≥ 0 and ai + an 1, where the latter inequality follows fr≥om 0 ? [sent-179, score-0.607]
77 ≤ ≤ W 1e, wobhtaeirne tthhee convex relaxation ≤ E1 := σμi? [sent-181, score-0.334]
78 22333300 In contrast to the Laplace prior (10) this approximation is convex. [sent-189, score-0.072]
79 However, E1 is minimal not only for ai = r¯i (1 − an) but also for an = 1, ai = 0, i. [sent-190, score-0.558]
80 Thus, this prior is biased towards smaller foreground object areas. [sent-193, score-0.18]
81 This can be understood as an additional compactness prior which removes cluttered background regions, but sometimes also parts of the objects. [sent-194, score-0.187]
82 As shown in the last paragraph, even the greatest convex lower bound E1 is too small. [sent-196, score-0.251]
83 As a second convexification method we propose a convex upper bound on Ep. [sent-198, score-0.297]
84 Note that Ep does not have a lowest upper bound, in contrast to the convex relaxation case. [sent-199, score-0.334]
85 To arrive at one possible solution, the idea is to write Ep in (10) by replacing the ratios ri by the ai in (6) Ep=σμi? [sent-200, score-0.858]
86 ·√1 −1 an and apply Young’s inequality pq ≤ 41εp2 + εq2, valid for aanlld p, q ∈ly R Y oaunndg arbitrary ε >y p0q ( w≤e choose ε = 10 in the experiments). [sent-204, score-0.092]
87 nIdt i asr equivalent >to 0 0( ( 2√1εp −oo√seεεq )2 = ≥ 1 00. [sent-205, score-0.038]
88 (12) This energy is convex: the first addend is a linear transformation of the convex function (x,y) → ∈ R,y > 0, and the second one is obviously convex in an ∈ [0, 1). [sent-209, score-0.503]
89 ation ai ≈ r¯i (1 − an) regardless of the size of the object. [sent-211, score-0.32]
90 It also avo≈ids¯ r large background regions as E2 → ∞ for an → 1, which can be alleviated by using a small→ ε. [sent-212, score-0.107]
91 Since (12) is used for all 1 ≤ i < n, for optimization it willS i bnec eco (1n2v)e nisie unste tdo decouple th ie < ais f froorm o an using nth iet dual representation 1 = supβ≥ ? [sent-213, score-0.092]
92 froer txh e= l 0ft a hnadnβ yd =siαd 0e, asn dde fains ezder aos f ∞or xx r=y y y∈ <= R 0 , 0? [sent-217, score-0.086]
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