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A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problem
"... Seven years ago, Szeliski et al. published an influential study on energy minimization methods for Markov random fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the ph ..."
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Cited by 48 (13 self)
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Seven years ago, Szeliski et al. published an influential study on energy minimization methods for Markov random fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenominal success of random field models means that the kinds of inference problems we solve have changed significantly. Specifically, the models today often include higher order interactions, flexible connectivity structures, large labelspaces of different cardinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of 24 stateofart techniques on a corpus of 2,300 energy minimization instances from 20 diverse computer vision applications. To ensure reproducibility, we evaluate all methods in the OpenGM2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types.
Higherorder segmentation via multicuts
 CORR ABS/1305.6387
"... Multicuts enable to conveniently represent discrete graphical models for unsupervised and supervised image segmentation, based on local energy functions that exhibit symmetries. The basic Potts model and natural extensions thereof to higherorder models provide a prominent class of representatives, ..."
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Cited by 7 (1 self)
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Multicuts enable to conveniently represent discrete graphical models for unsupervised and supervised image segmentation, based on local energy functions that exhibit symmetries. The basic Potts model and natural extensions thereof to higherorder models provide a prominent class of representatives, that cover a broad range of segmentation problems relevant to image analysis and computer vision. We show how to take into account such higherorder terms systematically in view of computational inference, and present results of a comprehensive and competitive numerical evaluation of a variety of dedicated cuttingplane algorithms. Our results reveal ways to evaluate a significant subset of models globally optimal, without compromising runtime. Polynomially solvable relaxations are studied as well, along with advanced rounding schemes for postprocessing.
Partial optimality by pruning for MAPinference with general graphical models
 In CVPR
, 2014
"... We consider the energy minimization problem for undirected graphical models, also known as MAPinference problem for Markov random fields which is NPhard in general. We propose a novel polynomial time algorithm to obtain a part of its optimal nonrelaxed integral solution. Our algorithm is initiali ..."
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Cited by 4 (1 self)
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We consider the energy minimization problem for undirected graphical models, also known as MAPinference problem for Markov random fields which is NPhard in general. We propose a novel polynomial time algorithm to obtain a part of its optimal nonrelaxed integral solution. Our algorithm is initialized with variables taking integral values in the solution of a convex relaxation of the MAPinference problem and iteratively prunes those, which do not satisfy our criterion for partial optimality. We show that our pruning strategy is in a certain sense theoretically optimal. Also empirically our method outperforms previous approaches in terms of the number of persistently labelled variables. The method is very general, as it is applicable to models with arbitrary factors of an arbitrary order and can employ any solver for the considered relaxed problem. Our method’s runtime is determined by the runtime of the convex relaxation solver for the MAPinference problem. 1.
C.: Global MAPoptimality by shrinking the combinatorial search area with convex relaxation
, 2013
"... We consider energy minimization for undirected graphical models, also known as the MAPinference problem for Markov random fields. Although combinatorial methods, which return a provably optimal integral solution of the problem, made a significant progress in the past decade, they are still typicall ..."
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Cited by 4 (2 self)
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We consider energy minimization for undirected graphical models, also known as the MAPinference problem for Markov random fields. Although combinatorial methods, which return a provably optimal integral solution of the problem, made a significant progress in the past decade, they are still typically unable to cope with largescale datasets. On the other hand, large scale datasets are often defined on sparse graphs and convex relaxation methods, such as linear programming relaxations then provide good approximations to integral solutions. We propose a novel method of combining combinatorial and convex programming techniques to obtain a global solution of the initial combinatorial problem. Based on the information obtained from the solution of the convex relaxation, our method confines application of the combinatorial solver to a small fraction of the initial graphical model, which allows to optimally solve much larger problems. We demonstrate the efficacy of our approach on a computer vision energy minimization benchmark. 1
Joint Semantic Segmentation and 3D Reconstruction from Monocular Video
"... Abstract. We present an approach for joint inference of 3D scene structure and semantic labeling for monocular video. Starting with monocular image stream, our framework produces a 3D volumetric semantic + occupancy map, which is much more useful than a series of 2D semantic label images or a spar ..."
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Cited by 3 (0 self)
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Abstract. We present an approach for joint inference of 3D scene structure and semantic labeling for monocular video. Starting with monocular image stream, our framework produces a 3D volumetric semantic + occupancy map, which is much more useful than a series of 2D semantic label images or a sparse point cloud produced by traditional semantic segmentation and Structure from Motion(SfM) pipelines respectively. We derive a Conditional Random Field (CRF) model defined in the 3D space, that jointly infers the semantic category and occupancy for each voxel. Such a joint inference in the 3D CRF paves the way for more informed priors and constraints, which is otherwise not possible if solved separately in their traditional frameworks. We make use of class specific semantic cues that constrain the 3D structure in areas, where multiview constraints are weak. Our model comprises of higher order factors, which helps when the depth is unobservable. We also make use of class specific semantic cues to reduce either the degree of such higher order factors, or to approximately model them with unaries if possible. We demonstrate improved 3D structure and temporally consistent semantic segmentation for difficult, large scale, forward moving monocular image sequences. Fig. 1. Overview of our system. From monocular image sequence, we first obtain 2D semantic segmentation, sparse 3D reconstruction and camera poses. We then build a volumetric 3D map which depicts both 3D structure and semantic labels. 1
MAPInference on Large Scale HigherOrder Discrete Graphical Models by Fusion Moves
"... Many computer vision problems can be cast into optimization problems over discrete graphical models also known as Markov or conditional random fields. Standard methods are able to solve those problems quite efficiently. However, problems with huge label spaces and or higherorder structure remain c ..."
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Cited by 2 (1 self)
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Many computer vision problems can be cast into optimization problems over discrete graphical models also known as Markov or conditional random fields. Standard methods are able to solve those problems quite efficiently. However, problems with huge label spaces and or higherorder structure remain challenging or intractable even for approximate methods. We reconsider the work of Lempitsky et al. 2010 on fusion moves and apply it to general discrete graphical models. We propose two alternatives for calculating fusion moves that outperform the standard in several applications. Our generic software framework allows us to easily use different proposal generators which spans a large class of inference algorithms and thus makes exhaustive evaluation feasible. Because these fusion algorithms can be applied to models with huge label spaces and higherorder terms, they might stimulate and support research of such models which may have not been possible so far due to the lack of adequate inference methods. 1
Scalable Semidefinite Relaxation for Maximum A Posterior Estimation
"... Maximum a posteriori (MAP) inference over discrete Markov random fields is a fundamental task spanning a wide spectrum of realworld applications, which is known to be NPhard for general graphs. In this paper, we propose a novel semidefinite relaxation formulation (referred to as SDR) to estimat ..."
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Cited by 2 (1 self)
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Maximum a posteriori (MAP) inference over discrete Markov random fields is a fundamental task spanning a wide spectrum of realworld applications, which is known to be NPhard for general graphs. In this paper, we propose a novel semidefinite relaxation formulation (referred to as SDR) to estimate the MAP assignment. Algorithmically, we develop an accelerated variant of the alternating direction method of multipliers (referred to as SDPADLR) that can effectively exploit the special structure of the new relaxation. Encouragingly, the proposed procedure allows solving SDR for largescale problems, e.g., problems on a grid graph comprising hundreds of thousands of variables with multiple states per node. Compared with prior SDP solvers, SDPADLR is capable of attaining comparable accuracy while exhibiting remarkably improved scalability, in contrast to the commonly held belief that semidefinite relaxation can only been applied on smallscale MRF problems. We have evaluated the performance of SDR on various benchmark datasets including OPENGM2 and PIC in terms of boththe quality of the solutions and computation time. Experimental results demonstrate that for a broad class of problems, SDPADLR outperforms stateoftheart algorithms in producing better MAP assignments in an efficient manner. 1.
Learning to Search in BranchandBound Algorithms∗
"... Branchandbound is a widely used method in combinatorial optimization, including mixed integer programming, structured prediction and MAP inference. While most work has been focused on developing problemspecific techniques, little is known about how to systematically design the node searching str ..."
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Branchandbound is a widely used method in combinatorial optimization, including mixed integer programming, structured prediction and MAP inference. While most work has been focused on developing problemspecific techniques, little is known about how to systematically design the node searching strategy on a branchandbound tree. We address the key challenge of learning an adaptive node searching order for any class of problem solvable by branchandbound. Our strategies are learned by imitation learning. We apply our algorithm to linear programming based branchandbound for solving mixed integer programs (MIP). We compare our method with one of the fastest opensource solvers, SCIP; and a very efficient commercial solver, Gurobi. We demonstrate that our approach achieves better solutions faster on four MIP libraries. 1
HierarchicallyConstrained Optical Flow
"... This paper presents a novel approach to solving optical flow problems using a discrete, treestructured MRF derived from a hierarchical segmentation of the image. Our method can be used to find globallyoptimal matching solutions even for problems involving very large motions. Experiments demons ..."
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This paper presents a novel approach to solving optical flow problems using a discrete, treestructured MRF derived from a hierarchical segmentation of the image. Our method can be used to find globallyoptimal matching solutions even for problems involving very large motions. Experiments demonstrate that our approach is competitive on the MPISintel dataset and that it can significantly outperform existing methods on problems involving large motions. 1.