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A database and evaluation methodology for optical flow
 In Proceedings of the IEEE International Conference on Computer Vision
, 2007
"... The quantitative evaluation of optical flow algorithms by Barron et al. (1994) led to significant advances in performance. The challenges for optical flow algorithms today go beyond the datasets and evaluation methods proposed in that paper. Instead, they center on problems associated with complex n ..."
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Cited by 407 (22 self)
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The quantitative evaluation of optical flow algorithms by Barron et al. (1994) led to significant advances in performance. The challenges for optical flow algorithms today go beyond the datasets and evaluation methods proposed in that paper. Instead, they center on problems associated with complex natural scenes, including nonrigid motion, real sensor noise, and motion discontinuities. We propose a new set of benchmarks and evaluation methods for the next generation of optical flow algorithms. To that end, we contribute four types of data to test different aspects of optical flow algorithms: (1) sequences with nonrigid motion where the groundtruth flow is determined by tracking hidden fluorescent texture, (2) realistic synthetic sequences, (3) high framerate video used to study interpolation error, and (4) modified stereo sequences of static scenes. In addition to the average angular error used by Barron et al., we compute the absolute flow endpoint error, measures for frame interpolation error, improved statistics, and results at motion discontinuities and in textureless regions. In October 2007, we published the performance of several wellknown methods on a preliminary version of our data to establish the current state of the art. We also made the data freely available on the web at
Secrets of Optical Flow Estimation and Their Principles
, 2010
"... The accuracy of optical flow estimation algorithms has been improving steadily as evidenced by results on the Middlebury optical flow benchmark. The typical formulation, however, has changed little since the work of Horn and Schunck. We attempt to uncover what has made recent advances possible throu ..."
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Cited by 195 (10 self)
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The accuracy of optical flow estimation algorithms has been improving steadily as evidenced by results on the Middlebury optical flow benchmark. The typical formulation, however, has changed little since the work of Horn and Schunck. We attempt to uncover what has made recent advances possible through a thorough analysis of how the objective function, the optimization method, and modern implementation practices influence accuracy. We discover that “classical” flow formulations perform surprisingly well when combined with modern optimization and implementation techniques. Moreover, we find that while median filtering of intermediate flow fields during optimization is a key to recent performance gains, it leads to higher energy solutions. To understand the principles behind this phenomenon, we derive a new objective that formalizes the median filtering heuristic. This objective includes a nonlocal term that robustly integrates flow estimates over large spatial neighborhoods. By modifying this new term to include information about flow and image boundaries we develop a method that ranks at the top of the Middlebury benchmark.
Global Stereo Reconstruction under Second Order Smoothness Priors
"... Secondorder priors on the smoothness of 3D surfaces are a better model of typical scenes than firstorder priors. However, stereo reconstruction using global inference algorithms, such as graphcuts, has not been able to incorporate secondorder priors because the triple cliques needed to express t ..."
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Cited by 127 (8 self)
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Secondorder priors on the smoothness of 3D surfaces are a better model of typical scenes than firstorder priors. However, stereo reconstruction using global inference algorithms, such as graphcuts, has not been able to incorporate secondorder priors because the triple cliques needed to express them yield intractable (nonsubmodular) optimization problems. This paper shows that inference with triple cliques can be effectively optimized. Our optimization strategy is a development of recent extensions to αexpansion, based on the “QPBO ” algorithm [5, 14, 26]. The strategy is to repeatedly merge proposal depth maps using a novel extension of QPBO. Proposal depth maps can come from any source, for example frontoparallel planes as in αexpansion, or indeed any existing stereo algorithm, with arbitrary parameter settings. Experimental results demonstrate the usefulness of the secondorder prior and the efficacy of our optimization framework. An implementation of our stereo framework is available online [34].
Motion Detail Preserving Optical Flow Estimation
"... We discuss the cause of a severe optical flow estimation problem that fine motion structures cannot always be correctly reconstructed in the commonly employed multiscale variational framework. Our major finding is that significant and abrupt displacement transition wrecks smallscale motion structur ..."
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Cited by 72 (1 self)
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We discuss the cause of a severe optical flow estimation problem that fine motion structures cannot always be correctly reconstructed in the commonly employed multiscale variational framework. Our major finding is that significant and abrupt displacement transition wrecks smallscale motion structures in the coarsetofine refinement. A novel optical flow estimation method is proposed in this paper to address this issue, which reduces the reliance of the flow estimates on their initial values propagated from the coarser level and enables recovering many motion details in each scale. The contribution of this paper also includes adaption of the objective function and development of a new optimization procedure. The effectiveness of our method is borne out by experiments for both large and smalldisplacement optical flow estimation.
Fusion Moves for Markov Random Field Optimization
"... The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combi ..."
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Cited by 68 (5 self)
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The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combination process the fusion move. By employing recently developed graph cut based algorithms (socalled QPBOgraph cut), the fusion move can efficiently combine two proposal labelings in a theoretically sound way, which is in practice often globally optimal. We demonstrate that fusion moves generalize many previous graph cut approaches, which allows them to be used as building block within a broader variety of optimization schemes than were considered before. In particular, we propose new optimization schemes for computer vision MRFs with applications to image restoration, stereo, and optical flow, among others. Within these schemes the fusion moves are used 1) for the parallelization of MRF optimization into several threads; 2) for fast MRF optimization by combining cheaptocompute solutions; and 3) for the optimization of highly nonconvex continuouslabeled MRFs with 2D labels. Our final example is a nonvision MRF concerned with cartographic label placement, where fusion moves can be used to improve the performance of a standard inference method (loopy belief propagation).
Learning optical flow
 In Proc. ECCV
, 2008
"... Abstract. Assumptions of brightness constancy and spatial smoothness underlie most optical flow estimation methods. In contrast to standard heuristic formulations, we learn a statistical model of both brightness constancy error and the spatial properties of optical flow using image sequences with as ..."
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Cited by 46 (7 self)
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Abstract. Assumptions of brightness constancy and spatial smoothness underlie most optical flow estimation methods. In contrast to standard heuristic formulations, we learn a statistical model of both brightness constancy error and the spatial properties of optical flow using image sequences with associated ground truth flow fields. The result is a complete probabilistic model of optical flow. Specifically, the ground truth enables us to model how the assumption of brightness constancy is violated in naturalistic sequences, resulting in a probabilistic model of “brightness inconstancy”. We also generalize previous highorder constancy assumptions, such as gradient constancy, by modeling the constancy of responses to various linear filters in a highorder random field framework. These filters are free variables that can be learned from training data. Additionally we study the spatial structure of the optical flow and how motion boundaries are related to image intensity boundaries. Spatial smoothness is modeled using a Steerable Random Field, where spatial derivatives of the optical flow are steered by the image brightness structure. These models provide a statistical motivation for previous methods and enable the learning of all parameters from training data. All proposed models are quantitatively compared on the Middlebury flow dataset. 1
Power Watershed: A Unifying GraphBased Optimization Framework
, 2011
"... In this work, we extend a common framework for graphbased image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of ..."
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Cited by 42 (8 self)
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In this work, we extend a common framework for graphbased image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes. Introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework. We then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm, which we term power watershed. In particular when q = 2, the power watershed leads to a multilabel, scale and contrast invariant, unique global optimum obtained in practice in quasilinear time. Placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation.
Power watersheds: A new image segmentation framework extending graph cuts, random walker and optimal spanning forest
"... In this work, we extend a common framework for seeded image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of a pa ..."
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Cited by 40 (11 self)
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In this work, we extend a common framework for seeded image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes. Introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watersheds in this same framework. We then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm, which we term power watersheds. Placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watersheds to optimize more general models of use in application beyond image segmentation. 1.
Surface Stereo with Soft Segmentation
"... This paper proposes a new stereo model which encodes the simple assumption that the scene is composed of a few, smooth surfaces. A key feature of our model is the surfacebased representation, where each pixel is assigned to a 3D surface (planes or Bsplines). This representation enables several impo ..."
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Cited by 30 (2 self)
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This paper proposes a new stereo model which encodes the simple assumption that the scene is composed of a few, smooth surfaces. A key feature of our model is the surfacebased representation, where each pixel is assigned to a 3D surface (planes or Bsplines). This representation enables several important contributions: Firstly, we formulate a higherorder prior which states that pixels of similar appearance are likely to belong to the same 3D surface. This enables to incorporate the very popular color segmentation constraint in a soft and principled way. Secondly, we use a global MDL prior to penalize the number of surfaces. Thirdly, we are able to incorporate, in a simple way, a prior which favors low curvature surfaces. Fourthly, we improve the asymmetric occlusion model by disallowing pixels of the same surface to occlude each other. Finally, we use the known fusion move approach which enables a powerful optimization of our model, despite the infinite number of possible labelings (surfaces). 1.