iccv iccv2013 iccv2013-297 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Ali Elqursh, Ahmed Elgammal
Abstract: The vast majority of work on motion segmentation adopts the affine camera model due to its simplicity. Under the affine model, the motion segmentation problem becomes that of subspace separation. Due to this assumption, such methods are mainly offline and exhibit poor performance when the assumption is not satisfied. This is made evident in state-of-the-art methods that relax this assumption by using piecewise affine spaces and spectral clustering techniques to achieve better results. In this paper, we formulate the problem of motion segmentation as that of manifold separation. We then show how label propagation can be used in an online framework to achieve manifold separation. The performance of our framework is evaluated on a benchmark dataset and achieves competitive performance while being online.
Reference: text
sentIndex sentText sentNum sentScore
1 Online Motion Segmentation using Dynamic Label Propagation Ali Elqursh Ahmed Elgammal Rutgers University Abstract The vast majority of work on motion segmentation adopts the affine camera model due to its simplicity. [sent-1, score-0.677]
2 Under the affine model, the motion segmentation problem becomes that of subspace separation. [sent-2, score-0.694]
3 Due to this assumption, such methods are mainly offline and exhibit poor performance when the assumption is not satisfied. [sent-3, score-0.109]
4 This is made evident in state-of-the-art methods that relax this assumption by using piecewise affine spaces and spectral clustering techniques to achieve better results. [sent-4, score-0.558]
5 In this paper, we formulate the problem of motion segmentation as that of manifold separation. [sent-5, score-0.701]
6 We then show how label propagation can be used in an online framework to achieve manifold separation. [sent-6, score-0.639]
7 Introduction Since the early 20th century, gestalt psychologist have identified common fate as one of the most important cues for dynamic scene understanding. [sent-9, score-0.152]
8 In the field of Computer Vision, this is reflected by the vast amount of literature on motion segmentation, video segmentation, and tracking. [sent-10, score-0.269]
9 Specifically, motion segmentation deals with the problem of segmenting feature trajectories according to different motions in the scene, and is an essential step to achieve object segmentation and scene understanding. [sent-11, score-1.344]
10 Recent years have witnessed a large increase in the proportion of videos coming from streaming sources such as TV Broadcast, internet video streaming, and streaming from mobile devices. [sent-12, score-0.337]
11 Unfortunately, most motion segmentation techniques are mainly offline and with a high computational complexity. [sent-13, score-0.503]
12 Thus rendering them ineffective for processing videos from streaming sources. [sent-14, score-0.181]
13 This highlights the need for novel online motion segmentation techniques. [sent-15, score-0.578]
14 There exist a plethora of applications that would benefit from online motion segmentation. [sent-16, score-0.391]
15 For example, currently activity recognition is either restricted to videos captured from stationary cameras (where existing background subtraction techniques can be used to segment the differ- Figure1. [sent-17, score-0.097]
16 ent actors [18]), or restricted to process videos offline using motion segmentation techniques. [sent-19, score-0.568]
17 Another domain that would benefit from online motion segmentation is in that of 3D TV processing. [sent-21, score-0.578]
18 A real-time motion segmentation would enable performing 2D-to-3D conversion and video re-targeting on the fly on viewers devices. [sent-22, score-0.479]
19 Other applications include online detection and segmentation of moving targets, and visual surveillance from mobile platforms to name a few. [sent-23, score-0.428]
20 Many approaches for motion segmentation are based on the fact that trajectories generated from rigid motion and under affine projection spans a 4-dimensional subspace. [sent-24, score-1.519]
21 Most notably in [4], the problem is reduced to sorting of a matrix called shape interaction matrix with entries that represent the likelihood of a pair of trajectories belonging to 2008 the same object. [sent-26, score-0.685]
22 In [11] the problem is reformulated as an instance of subspace separation, making the connection explicit. [sent-27, score-0.114]
23 First, formulating the problem as that of factorizing a trajectory matrix has led many approaches to assume that trajectories span the entire frame sequence. [sent-29, score-0.896]
24 To handle the case where parts of trajectories are missing, such approaches borrow ideas from matrix completion. [sent-30, score-0.583]
25 However, this is only successful up to a limit, since it assumes that at least there exist some trajectories that span the entire frame sequences. [sent-31, score-0.675]
26 Second, the affine camera assumption restricts the applicability of motion segmentation to those videos where the assumption is satisfied. [sent-32, score-0.799]
27 To overcome the later problem, we assume a general perspective camera instead of an affine camera. [sent-34, score-0.187]
28 On the other hand, to overcome the former problem, we mea- sure the similarity between trajectories using a metric that depends only on the overlapping frames. [sent-35, score-0.622]
29 We propose an approach that achieves online motion segmentation by segmenting a set of manifolds through dynamic label propagation and cluster splitting. [sent-36, score-1.033]
30 Starting from an initialization computed over a fixed number of frames, we maintain a graph of pairwise similarity between trajectories in an online fashion. [sent-37, score-0.785]
31 To move to the next frame we propagate the label information from one frame to the next using label propagation. [sent-38, score-0.262]
32 The label propagation respects the computed graph structure while taking into account the previous labeling. [sent-39, score-0.218]
33 To handle cases where new evidence suggests that one cluster comes from two differently moving objects, we evaluate each cluster and measure a normalized cut cost of splitting the cluster. [sent-40, score-0.134]
34 Figure 1 shows frames 40 and 150 of the sequence marple7 and the segmentation by our approach. [sent-42, score-0.255]
35 First we show how trajectories belonging to a rigid object with smooth depth variation form a manifold of dimension 3. [sent-46, score-0.939]
36 This generalizes the problem of affine motion segmentation from subspace separation (linear manifold segmentation) to that of (gen- eral) manifold segmentation. [sent-47, score-1.333]
37 It also explains why previous approaches using spectral clustering methods produced superior results while using simpler models. [sent-48, score-0.34]
38 Second, we show that the problem of online manifold segmentation can be cast in a label propagation framework using Markov Random walks. [sent-49, score-0.884]
39 Related Work Approaches to motion segmentation (and similarly subspace separation) can be roughly divided into four categories: statistical, factorization-based, algebraic, and spectral clustering. [sent-51, score-0.768]
40 For example, in [9] the Expectation-Maximization (EM) algorithm was used to tackle the clustering problem. [sent-53, score-0.131]
41 Robust statistical methods, such as RANSAC [6], repeatedly fits an affine subspace to randomly sampled trajectories and measures the consensus with the remaining trajectories. [sent-54, score-0.794]
42 The trajectories belonging to the subspace with the largest number of inliers are then removed and the procedure is repeated. [sent-55, score-0.723]
43 However, it is frequently the case that multiple rigid motions are dependent, such as in articulated motion. [sent-58, score-0.14]
44 Algebraic methods, such as GPCA [19] are generic subspace separation algorithms. [sent-60, score-0.241]
45 They do not put assump- tions on the relative orientation and dimensionality of motion subspaces. [sent-61, score-0.303]
46 However, their complexity grows exponentially with the number of motions and the dimensionality of the ambient space. [sent-62, score-0.104]
47 Spectral clustering-based methods [21, 2, 12], use local information around the trajectories to compute a similarity matrix. [sent-63, score-0.58]
48 It then use spectral clustering to cluster the trajectories into different subspaces. [sent-64, score-0.952]
49 One such example is the approach by Yan et al [21], where neighbors around each trajectory are used to fit a subspace. [sent-65, score-0.15]
50 An affinity matrix is then built by measuring the angles between subspaces. [sent-66, score-0.164]
51 Spectral clustering is then used to cluster the trajectories. [sent-67, score-0.198]
52 Similarly, sparse subspace clustering [5] builds an affinity matrix by representing each trajectory as a sparse combination of all other trajectories and then applies spectral clustering on the resulting affinity matrix. [sent-68, score-1.57]
53 Spectral clustering methods represent the state-of-the-art in motion segmentation. [sent-69, score-0.355]
54 We believe this can be explained because the trajectories do not exactly form a linear subspace. [sent-70, score-0.545]
55 With the realization of accurate trackers for dense long term trajectories such as [13, 15] there have been great interest in exploiting dense long term trajectories in motion segmentation. [sent-72, score-1.348]
56 [2] achieves motion segmentation by creating an affinity matrix capturing similarity in translational motion across all pairs of trajectories. [sent-74, score-0.868]
57 Spectral clustering is then used to over-segment the set of trajectories. [sent-75, score-0.131]
58 [7] pro- poses a two step process that first uses trajectory saliency to segment foreground trajectories. [sent-78, score-0.182]
59 This is followed by a two-stage spectral clustering of an affinity matrix computed 2009 over figure trajectories. [sent-79, score-0.504]
60 The success of such approaches can be attributed in part to the large number of trajectories available. [sent-80, score-0.545]
61 Such trajectories help capture the manifold structure empirically in the spectral clustering framework. [sent-81, score-1.141]
62 Our approach is also based on building an affinity matrix between all pairs of trajectories, however we process frames online and do not rely on spectral clustering. [sent-82, score-0.54]
63 Deviating from the spectral clustering, is the idea ofusing nonlinear dimensionality reduction (NLDR) techniques followed by clustering to achieve motion segmentation [8]. [sent-83, score-0.888]
64 To our knowledge our approach is the first to achieve online motion segmentation, while spending a constant computation time per frame. [sent-85, score-0.433]
65 We explicitly model trajectories as lying on a manifold, and thus are able to handle videos where the affine camera assumption is not satisfied. [sent-86, score-0.848]
66 Our method also takes into account the entire history of the trajectory in computing the similarity matrix. [sent-87, score-0.219]
67 Basic Formulation of Motion Segmentation In this section we show how the problem of motion segmentation can be cast as a manifold segmentation problem. [sent-89, score-0.978]
68 First, we show how trajectories in the three-dimensional space form a threedimensional manifold. [sent-91, score-0.578]
69 Next, we show how the projection of these trajectories to 2D image coordinates also form a three-dimensional manifold. [sent-92, score-0.621]
70 Let X be an open set of points in 3D comprising a single rigid object. [sent-93, score-0.074]
71 of trajectories can be therefore defined by the set Γ(f) = {(x1, . [sent-106, score-0.545]
72 , xF) ∈ R3F : xi = fi(x1) i = 1}, with subspace topology. [sent-109, score-0.114]
73 , Γf(Ff are co Xnti bneuo tuhse maps tainodn fi sπ a restriction of a continuous map, is also continuous. [sent-119, score-0.083]
74 It is also a homeomorphism because it has a continuous inverse. [sent-120, score-0.093]
75 This implies that the space of trajectories is a manifold of dimension three. [sent-121, score-0.801]
76 Furthermore, we can show that projecting the 3D trajectories into the image coordinates also induces a mani- φ φo φ fz[xy]Tbe the camera projection func- fold. [sent-122, score-0.673]
77 Let g(x) = tion that projects a point in the camera coordinate system to image coordinates, where f is the camera focal length. [sent-123, score-0.104]
78 It is therefore easy to show that G(Ω) is also a manifold of dimension three. [sent-139, score-0.256]
79 Note that even though we know that trajectories in image space form a manifold, we do not have an analytical manifold. [sent-140, score-0.545]
80 However, under the assumption that the manifold is densely sampled, empirical methods can be used to model the manifold. [sent-141, score-0.307]
81 In addition, note that each distinct motion in the scene will generate one manifold. [sent-142, score-0.224]
82 In this paper we rely on label propagation and dense trajectory tracking to solve the manifold separation problem. [sent-143, score-0.751]
83 To see why label propagation is well suited for the manifold separation problem, consider the simple two moons example shown at the top Figure 2. [sent-144, score-0.701]
84 Separating the two moons can be cast as a manifold separation problem. [sent-145, score-0.539]
85 However, when applying spectral clustering on this example, due to the proximity, one cluster leaks over the other cluster. [sent-146, score-0.407]
86 On the other hand, with proper initialization, label propagation is able to successfully segment the two moons. [sent-147, score-0.25]
87 Approach Starting from dense trajectories that are continuously extended and introduced, our approach continuously updates a segmentation of the trajectories corresponding to different motions. [sent-150, score-1.403]
88 To achieve this, we start by explaining how the similarities (affinities) between trajectories can be updated in an online framework (Subsection 5. [sent-151, score-0.71]
89 Next we introduce the necessary background on label propagation and show how it can be used to maintain a segmentation over dynamically changing manifolds (Subsection 5. [sent-153, score-0.571]
90 Online Affinity Computation As identified by the previous section, trajectories belonging to a single object lie on a three-dimensional manifold. [sent-159, score-0.642]
91 However, such manifolds are not static as they are a function of the motion of the object, which changes over time. [sent-160, score-0.319]
92 To model such dynamic manifolds without resorting to resolving for each frame, we design a distance metric that can be computed incrementally. [sent-161, score-0.21]
93 In addition, the metric must capture the similarity in spatial location and motion. [sent-163, score-0.077]
94 The intuition is that if two trajectories are relatively close to each other and move similarly, then they are likely to belong to the same object. [sent-164, score-0.545]
95 In this subsection we show how one such metric can be computed incrementally. [sent-165, score-0.13]
96 A trajectory Ta = {pia = (xia, yai) : i∈ A} is represented as a sequence of points pia that spans ifr ∈am Ae}s iins rtehper esseet nAte. [sent-167, score-0.371]
97 F aosr a simplicity we reserve superscripts for frame references and subscripts for trajectory identification. [sent-168, score-0.32]
98 The motion of a trajectory between frames iand j in the x and y direction is denoted by uia:j = xja − xia and vai:j = yaj − yai. [sent-169, score-0.509]
99 Given tw−o x trajectories Ta an−d yTb we define two distance metrics d1M:t (Ta, Tb) and dS1:t (Ta, Tb) representing the difference in motion and spatial location up to time t respec- × tively. [sent-170, score-0.769]
100 The max function helps “remember” large differences in motion and spatial location. [sent-172, score-0.224]
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