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179
Fast approximate energy minimization with label costs
, 2010
"... The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simult ..."
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Cited by 110 (9 self)
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The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simultaneously optimize “label costs ” as well. An energy with label costs can penalize a solution based on the set of labels that appear in it. The simplest special case is to penalize the number of labels in the solution. Our energy is quite general, and we prove optimality bounds for our algorithm. A natural application of label costs is multimodel fitting, and we demonstrate several such applications in vision: homography detection, motion segmentation, and unsupervised image segmentation. Our C++/MATLAB implementation is publicly available.
Learning CRFs using Graph Cuts
"... Abstract. Many computer vision problems are naturally formulated as random fields, specifically MRFs or CRFs. The introduction of graph cuts has enabled efficient and optimal inference in associative random fields, greatly advancing applications such as segmentation, stereo reconstruction and many o ..."
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Cited by 104 (8 self)
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Abstract. Many computer vision problems are naturally formulated as random fields, specifically MRFs or CRFs. The introduction of graph cuts has enabled efficient and optimal inference in associative random fields, greatly advancing applications such as segmentation, stereo reconstruction and many others. However, while fast inference is now widespread, parameter learning in random fields has remained an intractable problem. This paper shows how to apply fast inference algorithms, in particular graph cuts, to learn parameters of random fields with similar efficiency. We find optimal parameter values under standard regularized objective functions that ensure good generalization. Our algorithm enables learning of many parameters in reasonable time, and we explore further speedup techniques. We also discuss extensions to nonassociative and multiclass problems. We evaluate the method on image segmentation and geometry recognition. 1
P³ & beyond: Solving energies with higher order cliques
 IN COMPUTER VISION AND PATTERN RECOGNITION
, 2007
"... In this paper we extend the class of energy functions for which the optimal αexpansion and αβswap moves can be computed in polynomial time. Specifically, we introduce a class of higher order clique potentials and show that the expansion and swap moves for any energy function composed of these pote ..."
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Cited by 102 (17 self)
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In this paper we extend the class of energy functions for which the optimal αexpansion and αβswap moves can be computed in polynomial time. Specifically, we introduce a class of higher order clique potentials and show that the expansion and swap moves for any energy function composed of these potentials can be found by minimizing a submodular function. We also show that for a subset of these potentials, the optimal move can be found by solving an stmincut problem. We refer to this subset as the P n Potts model. Our results enable the use of powerful move making algorithms i.e. αexpansion and αβswap for minimization of energy functions involving higher order cliques. Such functions have the capability of modelling the rich statistics of natural scenes and can be used for many applications in computer vision. We demonstrate their use on one such application i.e. the texture based video segmentation problem.
Dynamic Graph Cuts for Efficient Inference in Markov Random Fields
"... In this paper we present a fast new fully dynamic algorithm for the stmincut/maxflow problem. We show how this algorithm can be used to efficiently compute MAP solutions for certain dynamically changing MRF models in computer vision such as image segmentation. Specifically, given the solution of ..."
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Cited by 77 (3 self)
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In this paper we present a fast new fully dynamic algorithm for the stmincut/maxflow problem. We show how this algorithm can be used to efficiently compute MAP solutions for certain dynamically changing MRF models in computer vision such as image segmentation. Specifically, given the solution of the maxflow problem on a graph, the dynamic algorithm efficiently computes the maximum flow in a modified version of the graph. The time taken by it is roughly proportional to the total amount of change in the edge weights of the graph. Our experiments show that, when the number of changes in the graph is small, the dynamic algorithm is significantly faster than the best known static graph cut algorithm. We test the performance of our algorithm on one particular problem: the objectbackground segmentation problem for video. It should be noted that the application of our algorithm is not limited to the above problem, the algorithm is generic and can be used to yield similar improvements in many other cases that involve dynamic change.
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).
What metrics can be approximated by geocuts, or global optimization of length/area and flux
 In ICCV
, 2005
"... In [3] we showed that graph cuts can find hypersurfaces of globally minimal length (or area) under any Riemannian metric. Here we show that graph cuts on directed regular grids can approximate a significantly more general class of continuous nonsymmetric metrics. Using submodularity condition [1, 1 ..."
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Cited by 67 (11 self)
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In [3] we showed that graph cuts can find hypersurfaces of globally minimal length (or area) under any Riemannian metric. Here we show that graph cuts on directed regular grids can approximate a significantly more general class of continuous nonsymmetric metrics. Using submodularity condition [1, 11], we obtain a tight characterization of graphrepresentable metrics. Such “submodular” metrics have an elegant geometric interpretation via hypersurface functionals combining length/area and flux. Practically speaking, we extend “geocuts ” algorithm [3] to a wider class of geometrically motivated hypersurface functionals and show how to globally optimize any combination of length/area and flux of a given vector field. The concept of flux was recently introduced into computer vision by [13] but it was mainly studied within variational framework so far. We are first to show that flux can be integrated into graph cuts as well. Combining geometric concepts of flux and length/area within the global optimization framework of graph cuts allows principled discrete segmentation models and advances the state of the art for the graph cuts methods in vision. In particular, we address the “shrinking ” problem of graph cuts, improve segmentation of long thin objects, and introduce useful shape constraints. 1.
Coupled Object Detection and Tracking from Static Cameras and Moving Vehicles
, 2008
"... We present a novel approach for multiobject tracking which considers object detection and spacetime trajectory estimation as a coupled optimization problem. Our approach is formulated in a Minimum Description Length hypothesis selection framework, which allows our system to recover from mismatches ..."
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Cited by 66 (10 self)
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We present a novel approach for multiobject tracking which considers object detection and spacetime trajectory estimation as a coupled optimization problem. Our approach is formulated in a Minimum Description Length hypothesis selection framework, which allows our system to recover from mismatches and temporarily lost tracks. Building upon a stateoftheart object detector, it performs multiview/multicategory object recognition to detect cars and pedestrians in the input images. The 2D object detections are checked for their consistency with (automatically estimated) scene geometry and are converted to 3D observations which are accumulated in a world coordinate frame. A subsequent trajectory estimation module analyzes the resulting 3D observations to find physically plausible spacetime trajectories. Tracking is achieved by performing model selection after every frame. At each time instant, our approach searches for the globally optimal set of spacetime trajectories which provides the best explanation for the current image and for all evidence collected so far while satisfying the constraints that no two objects may occupy the same physical space nor explain the same image pixels at any point in time. Successful trajectory hypotheses are then fed back to guide object detection in future frames. The optimization procedure is kept efficient through incremental computation and conservative hypothesis pruning. We evaluate our approach on several challenging video sequences and demonstrate its performance on both a surveillancetype scenario and a scenario where the input videos are taken from inside a moving vehicle passing through crowded city areas.
On the optimality of treereweighted maxproduct message passing
 In UAI
, 2005
"... Treereweighted maxproduct (TRW) message passing [9] is a modified form of the ordinary maxproduct algorithm for attempting to find minimal energy configurations in Markov random field with cycles. For a TRW fixed point satisfying the strong tree agreement condition, the algorithm outputs a config ..."
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Cited by 66 (5 self)
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Treereweighted maxproduct (TRW) message passing [9] is a modified form of the ordinary maxproduct algorithm for attempting to find minimal energy configurations in Markov random field with cycles. For a TRW fixed point satisfying the strong tree agreement condition, the algorithm outputs a configuration that is provably optimal. In this paper, we focus on the case of binary variables with pairwise couplings, and establish stronger properties of TRW fixed points that satisfy only the milder condition of weak tree agreement (WTA). First, we demonstrate how it is possible to identify part of the optimal solution—i.e., a provably optimal solution for a subset of nodes — without knowing a complete solution. Second, we show that for submodular functions, a WTA fixed point always yields a globally optimal solution. We establish that for binary variables, any WTA fixed point always achieves the global maximum of the linear programming relaxation underlying the TRW method. 1
Transforming an arbitrary minsum problem into a binary one
, 2006
"... In this report we show, that an arbitrary MinSum problem (i.e. a MinSum problem with an arbitrary finite set of states) can be adequately transformed into a binary one (i.e. into a MinSum problem with only two states). Consequently all known results for binary MinSum problems can be easily extended ..."
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Cited by 61 (2 self)
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In this report we show, that an arbitrary MinSum problem (i.e. a MinSum problem with an arbitrary finite set of states) can be adequately transformed into a binary one (i.e. into a MinSum problem with only two states). Consequently all known results for binary MinSum problems can be easily extended to the general case. For instance it gives the possibility to solve exactly submodular MinSum problems with more than two states by using MinCutMaxFlow based technics.