An Experimental Comparison of Discrete and Continuous Shape Optimization Methods

Klodt, Maria; Schoenemann, Thomas; Kolev, Kalin; Schikora, Marek; Cremers, Daniel

doi:10.1007/978-3-540-88682-2_26

Cited by 52 publications

(56 citation statements)

References 35 publications

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“…The introduction of higher-order regularizers in respective energy minimization approaches is known to give rise to substantial computational challenges. Some of the most powerful approaches to image segmentation are based on region integrals with regularity terms defined on the region boundaries [3,15,17,5,8,9,13]. While many such methods make use of length as a regularity term, only few use curvature regularity.…”

Section: Introductionmentioning

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: Introductionmentioning

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

View full text Add to dashboard Cite

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“…Furthermore, the primal dual algorithm [4] used for solving the continuous saddle-point problem is defined point-wise and can thus be parallelized in a straight-forward manner and run in parallel using modern GPU's or other parallel architectures. For a detailed discussion see [19,11].…”

Section: Input Imagementioning

confidence: 99%

A Co-occurrence Prior for Continuous Multi-label Optimization

Souiai

Strekalovskiy

Nieuwenhuis

et al. 2013

Lecture Notes in Computer Science

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Abstract. To obtain high-quality segmentation results the integration of semantic information is indispensable. In contrast to existing segmentation methods which use a spatial regularizer, i.e. a local interaction between image points, the co-occurrence prior [15] imposes penalties on the co-existence of different labels in a segmentation. We propose a continuous domain formulation of this prior, using a convex relaxation multi-labeling approach. While the discrete approach [15] is employs minimization by sequential alpha expansions, our continuous convex formulation is solved by efficient primal-dual algorithms, which are highly parallelizable on the GPU. Also, our framework allows isotropic regularizers which do not exhibit grid bias. Experimental results on the MSRC benchmark confirm that the use of co-occurrence priors leads to drastic improvements in segmentation compared to the classical Potts model formulation when applied .

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“…Nevertheless, over recent years people have developed efficient algorithms for approximate minimization including the graph cut based alpha expansions [7] or various forms of convex relaxation [8][9][10]. In this work, we will make use of convex relaxation techniques because they do not exhibit any grid bias and are easily parallelized [11].…”

Section: Related Workmentioning

confidence: 99%

Wehrli 2.0: An Algorithm for “Tidying up Art”

Ufer

Souiai

Cremers

2012

Computer Vision – ECCV 2012. Workshops and Demonstrations

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Abstract. We propose an algorithm for automatizing the task of "Tidying up Art" introduced by the comedian Wehrli [1]. Driven by a strong sense of order and tidyness, Wehrli systematically dissects famous artworks into their constituents and rearranges them according to certain ordering principles. The proposed algorithmic solution to this problem builds up on a number of recent advances in image segmentation and grouping. It has two important advantages: Firstly, the computerized tidying up of art is substantially faster than manual labor requiring only a few seconds on state-of-the-art GPUs compared to many hours of manual labor. Secondly, the computed part decomposition and reordering is fully reproducible. In particular, the arrangement of parts is determined based on mathematically transparent criteria rather than the invariably subjective and irreproducible human sense of order.

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An Experimental Comparison of Discrete and Continuous Shape Optimization Methods

Cited by 52 publications

References 35 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

A Co-occurrence Prior for Continuous Multi-label Optimization

Wehrli 2.0: An Algorithm for “Tidying up Art”

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