iccv iccv2013 iccv2013-441 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Susanna Ricco, Carlo Tomasi
Abstract: Dense motion of image points over many video frames can provide important information about the world. However, occlusions and drift make it impossible to compute long motionpaths by merely concatenating opticalflow vectors between consecutive frames. Instead, we solve for entire paths directly, and flag the frames in which each is visible. As in previous work, we anchor each path to a unique pixel which guarantees an even spatial distribution of paths. Unlike earlier methods, we allow paths to be anchored in any frame. By explicitly requiring that at least one visible path passes within a small neighborhood of every pixel, we guarantee complete coverage of all visible points in all frames. We achieve state-of-the-art results on real sequences including both rigid and non-rigid motions with significant occlusions.
Reference: text
sentIndex sentText sentNum sentScore
1 Instead, we solve for entire paths directly, and flag the frames in which each is visible. [sent-4, score-0.731]
2 As in previous work, we anchor each path to a unique pixel which guarantees an even spatial distribution of paths. [sent-5, score-0.646]
3 Unlike earlier methods, we allow paths to be anchored in any frame. [sent-6, score-0.611]
4 By explicitly requiring that at least one visible path passes within a small neighborhood of every pixel, we guarantee complete coverage of all visible points in all frames. [sent-7, score-0.806]
5 Introduction The goal of long-range, high-density motion estimation in video analysis is to compute the life of every point in a dense sampling of the visible surfaces in the scene. [sent-10, score-0.317]
6 The image projection of a scene point moves along a path in the image plane. [sent-11, score-0.425]
7 In a dense motion estimate, at least one path passes through every pixel of the sequence. [sent-13, score-0.578]
8 The computed paths can propagate to multiple frames any annotations or edits made in a single frame, thereby easing video labeling and editing. [sent-15, score-0.614]
9 If visible paths can be extrapolated into regions where they are occluded, the occluding object can be removed from the video by painting the pixels it occupies with the extrapolated colors. [sent-16, score-0.801]
10 Videos can be segmented into separate objects by clustering paths into coherent groups. [sent-17, score-0.568]
11 We find motion in all regions visible in any frame. [sent-26, score-0.248]
12 Lagrangian motion (b) only computes paths for points visible in the first or last frame. [sent-27, score-0.827]
13 To this end, we assume that (i) image paths live in a low-dimensional space, (ii) appearance remains approximately constant along the visible portion of a path, and (iii) exactly one world point is visible at every image point. [sent-33, score-0.95]
14 Like them—and several others—we assume that paths belong to a low-dimensional subspace. [sent-37, score-0.568]
15 We also anchor each path to a single pixel in the sequence, so as to keep paths from bunching up. [sent-38, score-1.214]
16 Similarly to LME, we also describe path visibility with a binary, per-frame flag, and cast motion estimation as energy minimization. [sent-39, score-0.748]
17 First, we do not have fixed “reference frames” to anchor paths into. [sent-41, score-0.802]
18 By default, LME selects the first and last frame as reference frames and estimates paths for only those scene points that are visible in one of those frames. [sent-42, score-0.969]
19 Figure 1 illustrates this limitation; LME misses large regions in an intermediate frame because the surfaces are not visible in either reference frame. [sent-43, score-0.325]
20 To guarantee that all visible surfaces are associated with paths, LME would have to select every frame as a reference frame, an approach that quickly becomes computationally infeasible for long videos. [sent-44, score-0.349]
21 The greater flexibility of our method allows for both anchors in any frame and more realistic regularization functionals leading to more accurate paths. [sent-47, score-0.238]
22 For example, in LME, the regularization terms only enforce consistency between paths anchored in the same reference frame; our method encourages consistency across all frames. [sent-48, score-0.712]
23 Third, we formulate the computation of the visibility flag as a Maximum a Posteriori (MAP) Markov Random Field (MRF) estimation problem, for which an efficient solution method is available. [sent-50, score-0.383]
24 This formulation allows for the explicit enforcement of the constraint that there must be some visible path at every pixel. [sent-51, score-0.566]
25 Their paths start in regions with sufficient texture, but cover more image regions than feature trackers like KLT [14] do. [sent-58, score-0.641]
26 Highcost paths end at suspected occlusions, and new ones are started to fill gaps. [sent-61, score-0.568]
27 Structure-from-motion methods regularize more globally by assuming rigid motion—a restrictive assumption—for which image paths can be proven [20] to lie in a space of low and known dimension. [sent-63, score-0.601]
28 These techniques precompute paths with frame-to-frame trackers, and de-noise them post facto by projection into a low-dimensional subspace. [sent-65, score-0.632]
29 More recent methods apply subspace constraints during path estimation to track points that are hard for a frame-toframe tracker to follow. [sent-66, score-0.505]
30 Early approaches applied subspace constraints during optical flow estimation to improve estimates in untextured regions of rigid scenes [12] or sampled from a path subspace to improve motion estimates along intensity edges affected by the aperture problem [21]. [sent-67, score-0.841]
31 They compute full-length paths for every point in a selected reference frame. [sent-70, score-0.678]
32 LME finds paths by optimizing a global energy function over the entire video. [sent-73, score-0.594]
33 It models visibility explicitly, and reconnects paths across brief occlusions. [sent-74, score-0.834]
34 As explained earlier, we improve upon LME by removing its reliance on reference frames, handling visibility combinatorially rather than by approximate relaxation, and minimizing energy by direct optimization rather than variational methods. [sent-75, score-0.329]
35 Model Let p be an index into a set of paths xp(t) : T → R2, where T is the (discrete) time domain of( t)he : Tvid →eo sequence. [sent-78, score-0.568]
36 A is path disi vcirseitbel)e iamt etim deo mt iifnf oitfs visibility flag νp(t) : T → {0, 1} is equal to 1 at time t. [sent-79, score-0.798]
37 te Bdo ftohr f ualnl paths in a given video sequence. [sent-81, score-0.568]
38 To ensure at least one visible path per pixel in every frame, we anchor xp(t) to point up in some frame τp by letting xp(τp) = up and νp(τp) = 1. [sent-82, score-0.959]
39 22446655 We require (and automatically select) enough anchor points to have some path pass through every pixel in the video. [sent-83, score-0.733]
40 Paths are assumed to be in the space spanned by a sequence-specific basis of paths {ϕ1 , . [sent-85, score-0.613]
41 1 The motion relative to the anchor point xp(τp) = up is determined by the unknown coefficients cp = (cp1 , . [sent-93, score-0.464]
42 Since paths in a video with F frames have F points, the standard basis over R2F can represent any path exactly. [sent-97, score-1.034]
43 Given basis paths and anchor points, we find paths and visibility flags by interleaving computing optimal paths given visibility with computing optimal visibility given paths. [sent-100, score-3.007]
44 Section 4 shows how to find the path basis and initial anchors, and Section 5 shows how to adjust the anchors and compute optimal paths and visibility. [sent-102, score-1.127]
45 Optimal paths Given a basis of paths and a set of anchors, we find the best motion coefficients for each path by minimizing an objective function that penalizes changes in appearance along a path (temporal smoothness) and differences between nearby paths (spatial smoothness): ? [sent-105, score-2.72]
46 (2c to measure the difference between the image intensity I(cp, t) = I(xp(t)) of the path in frame t and that at the anchor up in frame τp. [sent-114, score-0.848]
47 The multiplier αpq couples nearby paths that have similar appearance, and is equal to αpq= exp? [sent-121, score-0.621]
48 A small patch (red dashed squares) around each path in every frame is transported along the current path estimates and monitored for consistent appearance. [sent-126, score-1.025]
49 The arm patch (top right) is most consistent, and makes this the controlling path at that point and frame. [sent-127, score-0.502]
50 Points along paths that either coincide with or are substantially parallel to a nearby controlling path have their observed visibility flag ˆν p(t) set to 1. [sent-128, score-1.444]
51 Observed flags affect the estimated visibility flags at the nodes of a MRF that enforces spatial and temporal consistency of the flags and ensures that at least one path is visible at every pixel. [sent-130, score-1.572]
52 if the path p is visible in the anchor frame of path q (that is, if νp(τq) = 1) and passes close enough to the anchor of q (that is, if | |xp(τq) − uq | | < Δ). [sent-131, score-1.493]
53 Optimal visibility The binary visibility flag νp(t) for each path and frame is modeled as a MRF whose structure depends on the current estimates xp(t) of the paths p ∈ P. [sent-135, score-1.732]
54 he ≤ tw Δo points vp(t −all1) f axendd vp(t + 1) that are temporally adjacent to vp(t) along path p (temporal neighborhood). [sent-144, score-0.439]
55 Each node in the MRF is associated with a binary observed visibility flag ˆν p(t) computed from the data as follows. [sent-145, score-0.405]
56 Path points in each frame are scored by their patch consistency, which measures how little a patch around vp(t) changes as it is transported by the current estimates of paths near vp(t) to (i) a few frames before and after time t, and (ii) the anchor frame τp for path p. [sent-146, score-1.601]
57 We use equation (11) from LME [16] to compute patch consistency and declare = Δ the controlling path at vp(t) to be the most consistent path through the spatial neighborhood of vp(t). [sent-147, score-0.892]
58 =F1||xp(t) − xq(t)| (6) be the average distance between two paths, and let p∗ be 22446666 the controlling path at vp(t). [sent-149, score-0.435]
59 Then, the observed visibility νˆp(t) is defined as follows (see also Figure 2): ˆνp(t) =? [sent-150, score-0.266]
60 (7) In words, a path p is observed to be visible at vp(t) when it either coincides with (p = p∗ so that d¯pp∗ = 0) or is nearly parallel (d¯pp∗ 4) to the controlling path p∗ at vp(t). [sent-152, score-0.951]
61 Because we require 4t)h atot paths mntursolt lbineg gv pisaitbhle p in their anchor frames, we also always set νˆp(τp) = 1. [sent-153, score-0.822]
62 The observed visibility flags ˆν p(t) influence the (hidden) visibility flags νp(t) through a data term in the MRF. [sent-154, score-0.984]
63 We define the following average measure of intensity change along the visible portion of path p: ≤ Δp=? [sent-155, score-0.584]
64 − νˆp(t) (9) The terms with multiplier λL bias estimated visibility values νp(t) toward observed values νˆp(t). [sent-162, score-0.288]
65 Setting a point to be visible incurs the additional charge ΔIp(t), equal to the change in intensity between anchor and current point. [sent-163, score-0.51]
66 The weights on edges between the random variables of the MRF encourage both temporal and spatial consistency among visibility values. [sent-165, score-0.328]
67 = λT|νp(t) − νp(t + 1)| (10) is added between temporally adjacent neighbors to discourage changes of visibility along a path. [sent-168, score-0.314]
68 (13) In words, ΔIpq (t) measures difference in appearance between paths in a single frame, and ΔIpq measures a similar difference between anchor points. [sent-177, score-0.802]
69 The combined effect of these two terms is to push discontinuities in visibility closer to intensity boundaries, and the division by d¯pq reduces the spatial discontinuity penalty between unrelated paths. [sent-178, score-0.355]
70 To enforce the physical constraint that there must be some visible point at every pixel, we clamp some visibility values to 1 and remove the corresponding nodes from the MRF. [sent-179, score-0.5]
71 Specifically, we require that νp(τp) = 1 and νp∗ (t) = 1with p∗ a controlling path in frame t. [sent-180, score-0.534]
72 Preliminaries Before we solve for motion and visibility, we select basis paths and an initial set of anchors, paths, and visibility flags. [sent-183, score-0.96]
73 Finding the basis paths Basis paths are obtained by first tracking a sparse set of feature points with a frame-to-frame tracker [14]. [sent-186, score-1.218]
74 This yields several tracks, that is, paths that do not necessarily extend through the entire sequence. [sent-187, score-0.568]
75 We scale path coordinates so that the mean per-path motion between frames is one pixel. [sent-197, score-0.502]
76 Initialization To cover every pixel in a video sequence with paths, we need to create a number of paths of the same order of the number of visible points in the sequence. [sent-200, score-0.861]
77 Placing anchor points at every pixel in the first and last frame at worst overestimates the true number of anchors needed by a factor of two. [sent-201, score-0.596]
78 We place additional anchors to cover visible regions that happen to be occluded in these two particular frames by following a procedure inspired by Sundaram et al. [sent-202, score-0.379]
79 We first concatenate optical flow vectors into multiframe tracks, which we break when the optical flow field fails a forwardbackward consistency check or when the point is too close 22446677 to a motion boundary (equations (5) and (6) from [19], respectively). [sent-204, score-0.383]
80 Track fragments that start in the first frame are converted into paths with anchor points in the first frame. [sent-207, score-1.038]
81 If the fragments are long enough, the initial coefficients for the path are computed by projecting the track onto the path basis. [sent-208, score-0.954]
82 Otherwise, we select coefficients by copying from nearby track fragments, picking the coefficients that create the path with the best brightness constancy measured over a few frames. [sent-209, score-0.62]
83 Track fragments that reach the last frame are converted into paths anchored at points in the last frame using the same procedure. [sent-210, score-0.946]
84 The temporal extent of the track fragments provides an initial conservative estimate for the path visibility flags. [sent-211, score-0.814]
85 For all other track fragments, we place a (possible) anchor point in the frame in which they are initialized and convert to a path as before. [sent-212, score-0.795]
86 We iterate through these poten- tial paths and only include the anchor points for those that differ from already included paths by more than an average of 2 pixels per frame. [sent-213, score-1.428]
87 Figure 3a shows the anchor points selected in this way for the marple7 sequence. [sent-214, score-0.271]
88 Colors other than gray are anchors, and similar colors correspond to similar sets of path coefficients. [sent-215, score-0.375]
89 Figure 3b shows the color-coded anchor points after convergence. [sent-218, score-0.271]
90 Optimization Starting with the paths and visibility flags constructed as described in Section 4. [sent-220, score-1.06]
91 2, we interleave two steps during optimization: a combinatorial optimization step finds visibility flags νp(t) for the current path estimates, and a continuous optimization step updates path coefficients cp given the current visibility estimates. [sent-221, score-1.715]
92 In the process, we add anchor points until every pixel in the sequence has at least one path through it, and remove anchors of invisible paths. [sent-222, score-0.895]
93 We stop when the maximum change in every path falls below one pixel in every frame. [sent-223, score-0.512]
94 The initial path estimates are often poor along occlusion boundaries, because visibility is not yet accounted for. [sent-224, score-0.709]
95 Because of this, we heuristically regroup paths between each combinatorial and continuous step to let foreground and background vie for paths between them. [sent-225, score-1.197]
96 We now describe the continuous step, path regrouping, combinatorial step, anchor management, and termination. [sent-226, score-0.67]
97 We update path coefficients by minimizing the energy function (2) via trust-region Newton conjugate gradients optimization [15]. [sent-228, score-0.484]
98 The sparsity pattern of H changes over time because the coupling coefficients αpq in equation (5) depend in turn on the path coefficients. [sent-230, score-0.457]
99 When computing successive conjugate gradients, we treat the terms αpq as constants—a good approximation for small path perturbations—and recompute them between full descent steps. [sent-231, score-0.397]
100 After 40 descent steps, we allow paths to copy their coefficients and visibility flags from one of their neighbors if doing so improves the path’s fit to data. [sent-233, score-1.15]
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