High-arity interactions, polyhedral relaxations, and cutting plane algorithm for soft constraint optimisation (MAP-MRF)

Werner, Tomáš

doi:10.1109/cvpr.2008.4587355

Cited by 58 publications

(73 citation statements)

References 12 publications

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“…Label costs are an important special case of 'higharity' potentials recently studied in computer vision (e.g. Werner, 2008;Woodford et al, 2009). From an energy standpoint there are a number of works that combine data costs D with V and/or H. Table 1 lists a small selection of such works in computer vision.…”

Section: Review Of Related Workmentioning

confidence: 99%

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Minimizing Energies with Hierarchical Costs

et al. 2012

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Computer vision is full of problems elegantly expressed in terms of energy minimization. We characterize a class of energies with hierarchical costs and propose a novel hierarchical fusion algorithm. Hierarchical costs are natural for modeling an array of difficult problems. For example, in semantic segmentation one could rule out unlikely object combinations via hierarchical context. In geometric model estimation, one could penalize the number of unique model families in a solution, not just the number of models-a kind of hierarchical MDL criterion. Hierarchical fusion uses the well-known α-expansion algorithm as a subroutine, and offers a much better approximation bound in important cases.

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Section: Review Of Related Workmentioning

confidence: 99%

“…Ours is therefore a graph cut approach that does not rely on QPBO, message passing (Kolmogorov, 2006), or other LP relaxations (Werner, 2008). Furthermore we, -handle energies with label costs (…”

Section: Hierarchical Fusion Algorithm (H-fusion)mentioning

confidence: 99%

Minimizing Energies with Hierarchical Costs

et al. 2012

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“…The MRF can be associated a "standard" integer linear program, growing exponentially with the order of the maximal clique. Problems of this form were considered in [30].…”

Section: Linear Programming and Higher Order Mrfsmentioning

confidence: 99%

“…The first technique is called min-sum diffusion and applicable only to the linear program derived from the higher order MRF. It was used for the higher order terms in [30], where it is described in detail. Here we only mention that the method is doing a reparameterization of the cost function, i.e.…”

Section: Do We Need Standard Solvers?mentioning

confidence: 99%

“…Starting from [10] we derive a linear program that corresponds to a higher order MRF of a form considered in [30]. We then compare the two formulations and try suboptimal solving strategies such as min-sum diffusion (see [30]) and a (prematurely terminated) convex augmented Lagrangian solver. Previously, customized interior point methods have been investigated [4] for inequality constrained linear programs.…”

Section: Introductionmentioning

confidence: 99%

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Curvature Regularity for Multi-label Problems - Standard and Customized Linear Programming

Schoenemann

Kuang

Kahl

2011

Lecture Notes in Computer Science

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Abstract. We follow recent work by Schoenemann et al. [25] for expressing curvature regularity as a linear program. While the original formulation focused on binary segmentation, we address several multi-label problems, including segmentation, denoising and inpainting, all cast as a single linear program. Our multi-label segmentation introduces a "curvature Potts model" and combines a well-known Potts model relaxation [14] with the above work. For inpainting, we improve on [25] by grouping intensities into bins. Finally, we address the problem of denoising with absolute differences in the data term. Furthermore, we explore alternative solving strategies, including higher order Markov Random Fields, min-sum diffusion and a combination of augmented Lagrangians and an accelerated first order scheme to solve the linear programs.

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Graphical Models and Belief Propagation Hierarchy for Physics-Constrained Network Flows

Chertkov

Misra

Vuffray

et al. 2018

Energy Markets and Responsive Grids

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In this manuscript we review new ideas and first results on application of the Graphical Models approach, originated from Statistical Physics, Information Theory, Computer Science and Machine Learning, to optimization problems of network flow type with additional constraints related to the physics of the flow. We illustrate the general concepts on a number of enabling examples from power system and natural gas transmission (continental scale) and distribution (district scale) systems.

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High-arity interactions, polyhedral relaxations, and cutting plane algorithm for soft constraint optimisation (MAP-MRF)

Cited by 58 publications

References 12 publications

Minimizing Energies with Hierarchical Costs

Minimizing Energies with Hierarchical Costs

Curvature Regularity for Multi-label Problems - Standard and Customized Linear Programming

Graphical Models and Belief Propagation Hierarchy for Physics-Constrained Network Flows

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