Optimizing Binary MRFs via Extended Roof Duality

Rother, Carsten; Kolmogorov, Vladimir; Lempitsky, Victor; Szummer, Martin

doi:10.1109/cvpr.2007.383203

Cited by 371 publications

(375 citation statements)

References 16 publications

Supporting

Mentioning

373

Contrasting

Unclassified

Order By: Relevance

“…The 1990s turned Loopy Belief Propagation (LBP) [15] and Graph Cuts [11] into mainstream methods. A lot of recent efforts are going into optimization methods such as quadratic pseudo-boolean optimization [18], linear programming primal-dual, or other dual methods [29]. In this work we focus mainly on LBP methods, and more particular on the max-product approach [30], which we adapt based on the FCT.…”

Section: Map Inference -Discrete Mrfmentioning

confidence: 99%

Efficient Loopy Belief Propagation Using the Four Color Theorem

Timofte

Gool

2013

Advanced Topics in Computer Vision

View full text Add to dashboard Cite

Summary. Recent work on early vision such as image segmentation, image denoising, stereo matching, and optical flow uses Markov Random Fields. Although this formulation yields an NP-hard energy minimization problem, good heuristics have been developed based on graph cuts and belief propagation. Nevertheless both approaches still require tens of seconds to solve stereo problems on recent PCs. Such running times are impractical for optical flow and many image segmentation and denoising problems and we review recent techniques for speeding them up. Moreover, we show how to reduce the computational complexity of belief propagation by applying the Four Color Theorem to limit the maximum number of labels in the underlying image segmentation to at most four. We show that this provides substantial speed improvements for large inputs, and this for a variety of vision problems, while maintaining competitive result quality.

show abstract

Section: Map Inference -Discrete Mrfmentioning

confidence: 99%

Efficient Loopy Belief Propagation Using the Four Color Theorem

Timofte

Gool

2013

Advanced Topics in Computer Vision

View full text Add to dashboard Cite

show abstract

“…4. Our model was also optimized with roof duality (RD) [15]. Our method was constantly faster than RD and at the same time giving a very small relative duality gap.…”

Section: Methodsmentioning

confidence: 99%

“…We also identify submodular relationships; however, we go beyond submodularity to enable other geometric relationships and priors to be incorporated into the model. The standard technique for solving non-submodular energies of this type is roof duality (RD) [15]. However, the method is quite memory intensive and may fail in giving a complete segmentation without time-consuming probing.…”

Section: Introductionmentioning

confidence: 99%

Optimization for Multi-Region Segmentation of Cardiac MRI

Ulén

Strandmark

Kahl

2012

Statistical Atlases and Computational Models of the Heart. Imaging and Modelling Challenges

View full text Add to dashboard Cite

Abstract. We introduce a new multi-region model for simultaneous segmentation of the left and right ventricles, myocardium and the left ventricular papillary muscles in MRI. The model enforces geometric constraints such as inclusion and exclusion between the regions, which makes it possible to correctly segment different regions even though the intensity distributions are identical. We efficiently optimize the model using Lagrangian duality which is faster and more memory efficient than current state of the art. As the optimization is based on global techniques, the resulting segmentations are independent of initialization. We evaluate our approach on two benchmarks with competitive results.

show abstract

“…In the recent years, a number of extremely efficient optimization methods were re-introduced (e.g. Tree-reweighted Message Passing [9], the Fast Primal-Dual Method [10] or the Extended Roof Duality [11]) resulting on a great variety of optimization algorithms addressing the expectations of the field both in terms of optimality properties of the attained solution as well as in terms of computational complexity for low-rank (pair-wise) graphical models.…”

Section: Inference On Graphical Modelsmentioning

confidence: 99%

(Hyper)-graphical models in biomedical image analysis

Paragios

Ferrante

Glocker

et al. 2016

Medical Image Analysis

View full text Add to dashboard Cite

Computational vision, visual computing and biomedical image analysis have made tremendous progress over the past two decades. This is mostly due the development of efficient learning and inference algorithms which allow better and richer modeling of image and visual understanding tasks. Hyper-Graph representations are among the most prominent tools to address such perception through the casting of perception as a graph optimization problem. In this paper, we briefly introduce the importance of such representations, discuss their strength and limitations, provide appropriate strategies for their inference and present their application to address a variety of problems in biomedical image analysis.

show abstract

Optimizing Binary MRFs via Extended Roof Duality

Cited by 371 publications

References 16 publications

Efficient Loopy Belief Propagation Using the Four Color Theorem

Efficient Loopy Belief Propagation Using the Four Color Theorem

Optimization for Multi-Region Segmentation of Cardiac MRI

(Hyper)-graphical models in biomedical image analysis

Contact Info

Product

Resources

About