Introducing Curvature into Globally Optimal Image Segmentation: Minimum Ratio Cycles on Product Graphs

Schoenemann, Thomas; Cremers, Daniel

doi:10.1109/iccv.2007.4408973

Cited by 38 publications

(39 citation statements)

References 18 publications

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“…For contouror edge-based segmentation methods researchers have successfully developed algorithms to optimally impose curvature regularity using shortest path approaches [1] or ratio cycle formulations [19] on a graph representing the product space of image pixels and tangent angles [18]. In the regionbased settings considered, curvature is usually handled by local evolution methods [7,9,17,22].…”

Section: Damaged Imagementioning

confidence: 99%

Curvature regularity for region-based image segmentation and inpainting: A linear programming relaxation

Schoenemann¹,

Kahl

Cremers³

2009

2009 IEEE 12th International Conference on Computer Vision

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107

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We consider a class of region-based energies for image segmentation and inpainting which combine region integrals with curvature regularity of the region boundary. To minimize such energies, we formulate an integer linear program which jointly estimates regions and their boundaries. Curvature regularity is imposed by respective costs on pairs of adjacent boundary segments.By solving the associated linear programming relaxation and thresholding the solution one obtains an approximate solution to the original integer problem. To our knowledge this is the first approach to impose curvature regularity in region-based formulations in a manner that is independent of initialization and allows to compute a bound on the optimal energy.In a variety of experiments on segmentation and inpainting, we demonstrate the advantages of higher-order regularity. Moreover, we demonstrate that for most experiments the optimality gap is smaller than 2% of the global optimum. For many instances we are even able to compute the global optimum.

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Section: Damaged Imagementioning

confidence: 99%

Curvature regularity for region-based image segmentation and inpainting: A linear programming relaxation

Schoenemann¹,

Kahl

Cremers³

2009

2009 IEEE 12th International Conference on Computer Vision

Self Cite

107

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“…Additionally, there have been some studies on formulating image segmentation as an optimization problem (Levachkine and Sossa, 2000;Schoenemann and Cremers, 2007). Intuitively, the case of the parameter-fitting for image segmentation also inherently lends itself as an optimization problem.…”

Section: Optimizing Parametersmentioning

confidence: 99%

Time-Weighted Evaluation of Image Segmentation With a Genetic Algorithm

Hassan

Fleury

Clark

2010

Proceedings of the International Conference on Computer Vision Theory and Applications

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Abstract:Quantitative evaluation of segmentation algorithms implies rigorous testing against ground truth segmentations. Though under-reported in the literature, the performance of a segmentation algorithm depends on the choice of input parameters. When testing extends over an algorithms parameter space, then the search for satisfactory settings has a considerable cost in time. This paper considers the use of a genetic algorithm (GA) to avoid an exhaustive search. As application of the GA drastically reduces search times, the paper investigates how best to apply the GA in terms of initial candidate population, convergence speed, and application of a final polishing round. To further reduce evaluation time and subsequent image batch-processing times, this paper introduces a time factor into the GA cost function. It is found that this procedure while preserving the GA solution also improves interpretation and parameter selection.

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“…More recently, this has been generalized to ratio functionals [24], which in practice is even more efficient. Curvature has also been explored for the problem of trace inference [20].…”

Section: Introductionmentioning

confidence: 99%

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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Introducing Curvature into Globally Optimal Image Segmentation: Minimum Ratio Cycles on Product Graphs

Cited by 38 publications

References 18 publications

Curvature regularity for region-based image segmentation and inpainting: A linear programming relaxation

Curvature regularity for region-based image segmentation and inpainting: A linear programming relaxation

Time-Weighted Evaluation of Image Segmentation With a Genetic Algorithm

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

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