A finite algorithm for finding the projection of a point onto the canonical simplex of ? n

Michelot, Christian

doi:10.1007/bf00938486

Cited by 192 publications

(151 citation statements)

References 6 publications

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“…4. Estimation of the variance ρ bg (x) of the spatial kernel in (14) for the background region from the red scribbles. The spatial variance is proportional to the distance of each pixel to the closest background scribble point.…”

Section: A Space Variant Texture and Color Distributionmentioning

confidence: 99%

“…After the spatially varying color distribution we will now formulate the spatially varying texture distribution P(s x |l(x) = i,x) -see (12). Using a Parzen density estimator in a similar way as in (14) to obtain a texture distribution is only possible for very small patches due to the high dimensionality of the distribution, which would require a prohibitively large amount of samples not provided by the user scribbles. For this reason we will formulate a spatially varying texture distribution based on the co-support in equation (1).…”

Section: A Space Variant Texture and Color Distributionmentioning

confidence: 99%

“…Based on the segment probabilities P I(x), s x l(x) = i, x given in (12), (14) and (17) we now define an energy optimization problem for the task of segmentation. We specify the prior P(l) in (10) to favor regions of shorter boundary…”

Section: Variational Formulationmentioning

confidence: 99%

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Co-Sparse Textural Similarity for Interactive Segmentation

Nieuwenhuis

Hawe

Kleinsteuber

et al. 2014

Computer Vision – ECCV 2014

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Abstract. We propose an algorithm for segmenting natural images based on texture and color information, which leverages the co-sparse analysis model for image segmentation. As a key ingredient of this method, we introduce a novel textural similarity measure, which builds upon the cosparse representation of image patches. We propose a statistical MAP inference approach to merge textural similarity with information about color and location. Combined with recently developed convex multilabel optimization methods this leads to an efficient algorithm for interactive segmentation, which is easily parallelized on graphics hardware. The provided approach outperforms state-of-the-art interactive segmentation methods on the Graz Benchmark.

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Section: A Space Variant Texture and Color Distributionmentioning

confidence: 99%

Section: A Space Variant Texture and Color Distributionmentioning

confidence: 99%

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Co-Sparse Textural Similarity for Interactive Segmentation

Nieuwenhuis

Hawe

Kleinsteuber

et al. 2014

Computer Vision – ECCV 2014

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“…In the case of multi-region segmentation some constraints can be included directly into this projection [16]. This scheme is parallelizable, so we consider a GPU-implementation.…”

Section: Do We Need Standard Solvers?mentioning

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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“…The ROF type problems with the vectorial total variation as a regularizer, which are at the core of the resulting FISTA scheme, can be minimized with algorithms in [20]. For the also required backprojections onto simplices we recommend the method in [21]. Thus, we can turn our attention towards computing a minimizer in practice.…”

Section: Regularizationmentioning

confidence: 99%

Convex Relaxation for Multilabel Problems with Product Label Spaces

Goldluecke

2010

Computer Vision – ECCV 2010

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Abstract. Convex relaxations for continuous multilabel problems have attracted a lot of interest recently [1][2][3][4][5]. Unfortunately, in previous methods, the runtime and memory requirements scale linearly in the total number of labels, making them very inefficient and often unapplicable for problems with higher dimensional label spaces. In this paper, we propose a reduction technique for the case that the label space is a product space, and introduce proper regularizers. The resulting convex relaxation requires orders of magnitude less memory and computation time than previously, which enables us to apply it to large-scale problems like optic flow, stereo with occlusion detection, and segmentation into a very large number of regions. Despite the drastic gain in performance, we do not arrive at less accurate solutions than the original relaxation. Using the novel method, we can for the first time efficiently compute solutions to the optic flow functional which are within provable bounds of typically 5% of the global optimum.

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A finite algorithm for finding the projection of a point onto the canonical simplex of ? n

Cited by 192 publications

References 6 publications

Co-Sparse Textural Similarity for Interactive Segmentation

Co-Sparse Textural Similarity for Interactive Segmentation

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

Convex Relaxation for Multilabel Problems with Product Label Spaces

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