A Linear Programming Approach to Max-Sum Problem: A Review

Werner, Tomáš

doi:10.1109/tpami.2007.1036

Cited by 276 publications

(371 citation statements)

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“…A number of techniques solve a Linear Programming (LP) relaxation of this problem [36], which is given by relaxing the boolean constraints (2d) to the unit interval, i.e. µ i (s), µ ij (s, t) ≥ 0.…”

Section: Preliminaries: Map Inference In Mrfsmentioning

confidence: 99%

Diverse M-Best Solutions in Markov Random Fields

Batra

Yadollahpour

Guzman-Rivera³

et al. 2012

Computer Vision – ECCV 2012

110

155

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Abstract. Much effort has been directed at algorithms for obtaining the highest probability (MAP) configuration in probabilistic (random field) models. In many situations, one could benefit from additional highprobability solutions. Current methods for computing the M most probable configurations produce solutions that tend to be very similar to the MAP solution and each other. This is often an undesirable property. In this paper we propose an algorithm for the Diverse M-Best problem, which involves finding a diverse set of highly probable solutions under a discrete probabilistic model. Given a dissimilarity function measuring closeness of two solutions, our formulation involves maximizing a linear combination of the probability and dissimilarity to previous solutions. Our formulation generalizes the M-Best MAP problem and we show that for certain families of dissimilarity functions we can guarantee that these solutions can be found as easily as the MAP solution.

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Section: Preliminaries: Map Inference In Mrfsmentioning

confidence: 99%

Diverse M-Best Solutions in Markov Random Fields

Batra

Yadollahpour

Guzman-Rivera³

et al. 2012

Computer Vision – ECCV 2012

110

155

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show abstract

“…The scalars λ s and δ weigh the importance of the terms (set to 1 and 0.2 in our experiments). We perform the inference in the MRF by efficient and fast publicly available max-sum solver [29] based on linear programming relaxation and its Lagrangian dual. Figure 6 shows some examples of the proposed change detection algorithm.…”

Section: Pairwise Termmentioning

confidence: 99%

Detecting Changes in Images of Street Scenes

Košecká

2013

Computer Vision – ACCV 2012

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Abstract. In this paper we propose an novel algorithm for detecting changes in street scenes when the vehicle revisits sections of the street at different times. The proposed algorithm detects structural geometric changes, changes due to dynamically moving objects and as well as changes in the street appearance (e.g. posters put up) between two traversal times. We exploit geometric, appearance and semantic information to determine which areas have changed and formulate the problem as an optimal image labeling problem in the Markov Random Field framework. The approach is evaluated on street sequences from 3 different locations which were visited multiple times by the vehicle. The proposed method is applicable to monitoring and updating models and images of urban environments.

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“…It is a variational optimization algorithm designed to solve the LP-relaxation of a discrete energy minimization problem. This LP-relaxation was studied in, e.g., original paper [10], review [14]). The TRW-S algorithm has the same asymptotic behavior as algorithms in [6,14].…”

Section: Contribution and Outlinementioning

confidence: 99%

“…This LP-relaxation was studied in, e.g., original paper [10], review [14]). The TRW-S algorithm has the same asymptotic behavior as algorithms in [6,14]. It may not solve the LP-relaxation problem, since its stationary points satisfy only a necessary optimality condition (studied in [10,14,5]).…”

Section: Contribution and Outlinementioning

confidence: 99%

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Efficient MRF deformation model for non-rigid image matching

Shekhovtsov

Kovtun

Hlaváč

2008

Computer Vision and Image Understanding

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We propose a novel MRF-based model for deformable image matching. Given two images, the task is to estimate a mapping from one image to the other maximizing the quality of the match. We consider mappings defined by a discrete deformation field constrained to preserve 2D continuity. We pose the task as finding MAP configurations of a pairwise MRF. We propose a more compact MRF representation of the problem which leads to a weaker, though computationally more tractable, linear programming relaxation -the approximation technique we choose to apply. The number of dual LP variables grows linearly with the search window side, rather than quadratically as in previous approaches. To solve the relaxed problem (suboptimally), we apply TRW-S (Sequential Tree-Reweighted Message passing) algorithm [13,5]. Using our representation and the chosen optimization scheme, we are able to match much wider deformations than was considered previously in global optimization framework. We further elaborate on continuity and data terms to achieve more appropriate description of smooth deformations. The performance of our technique is demonstrated on both synthetic and real-world experiments.

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A Linear Programming Approach to Max-Sum Problem: A Review

Cited by 276 publications

References 50 publications

Diverse M-Best Solutions in Markov Random Fields

Diverse M-Best Solutions in Markov Random Fields

Detecting Changes in Images of Street Scenes

Efficient MRF deformation model for non-rigid image matching

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