A Survey and Comparison of Discrete and Continuous Multi-label Optimization Approaches for the Potts Model

Nieuwenhuis, Claudia; Töppe, Eno; Cremers, Daniel

doi:10.1007/s11263-013-0619-y

Cited by 53 publications

(52 citation statements)

References 49 publications

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“…Typically the projected solution deviates less than 1% from the optimal energy, i.e. the results are very close to global optimality [20].…”

Section: Methodsmentioning

confidence: 70%

“…However, a computationally tractable convex relaxation of this functional has been proposed in [3,4,12,22,34]. For more information and implementation details see [20]. Due to the convexity of the problem the resulting solutions have the following properties: Firstly, the segmentation is independent of the initialization.…”

Section: Minimization Via Convex Relaxationmentioning

confidence: 99%

“…To rewrite energy (20) in terms of the indicator functions u i , we have to rewrite the boundary length prior in (19). The boundary of the set indicated by u i can be written by means of the total variation.…”

Section: Conversion To a Convex Differentiable Problemmentioning

confidence: 99%

“…∀x ∈ Ω , see [34,20]. D u i denotes the distributional derivative of u i (which is D u i = ∇u i dx for differentiable u i ).…”

Section: Conversion To a Convex Differentiable Problemmentioning

confidence: 99%

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Co-Sparse Textural Similarity for Interactive Segmentation

Nieuwenhuis

Hawe

Kleinsteuber

et al. 2014

Computer Vision – ECCV 2014

Self Cite

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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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“…Typically the projected solution deviates less than 1% from the optimal energy, i.e. the results are very close to global optimality [20].…”

Section: Methodsmentioning

confidence: 70%

Section: Minimization Via Convex Relaxationmentioning

confidence: 99%

Section: Conversion To a Convex Differentiable Problemmentioning

confidence: 99%

“…∀x ∈ Ω , see [34,20]. D u i denotes the distributional derivative of u i (which is D u i = ∇u i dx for differentiable u i ).…”

Section: Conversion To a Convex Differentiable Problemmentioning

confidence: 99%

See 2 more Smart Citations

Co-Sparse Textural Similarity for Interactive Segmentation

Nieuwenhuis

Hawe

Kleinsteuber

et al. 2014

Computer Vision – ECCV 2014

Self Cite

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show abstract

“…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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Interactive volumetric segmentation for textile micro‐tomography data using wavelets and nonlocal means

MacNeil

Ushizima

Panerai

et al. 2019

Statistical Analysis

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This work addresses segmentation of volumetric images of woven carbon fiber textiles from micro‐tomography data. We propose a semi‐supervised algorithm to classify carbon fibers that requires sparse input as opposed to completely labeled images. The main contributions are: (a) design of effective discriminative classifiers, for three‐dimensional textile samples, trained on wavelet features for segmentation; (b) coupling of previous step with nonlocal means as simple, efficient alternative to the Potts model; and (c) demonstration of reuse of classifier to diverse samples containing similar content. We evaluate our work by curating test sets of voxels in the absence of a complete ground truth mask. The algorithm obtains an average 0.95 F1 score on test sets and average F1 score of 0.93 on new samples. We conclude with discussion of failure cases and propose future directions toward analysis of spatiotemporal high‐resolution micro‐tomography images.

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A Survey and Comparison of Discrete and Continuous Multi-label Optimization Approaches for the Potts Model

Cited by 53 publications

References 49 publications

Co-Sparse Textural Similarity for Interactive Segmentation

Co-Sparse Textural Similarity for Interactive Segmentation

A Co-occurrence Prior for Continuous Multi-label Optimization

Interactive volumetric segmentation for textile micro‐tomography data using wavelets and nonlocal means

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