Variational segmentation algorithms with label frequency constraints

Kropotov, Dmitry; Laptev, Dmitry; Osokin, Anton; Vetrov, Dmitry

doi:10.1134/s1054661810030089

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…There have been a number of works that separately consider constraints on total number of nodes that take a specific label (e.g. [31]). The SMR approach can easily handle general linear constraints such as i∈V p∈P…”

Section: Linear Global Constraintsmentioning

confidence: 99%

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Submodular Relaxation for Inference in Markov Random Fields

Osokin

Vetrov

2015

IEEE Trans. Pattern Anal. Mach. Intell.

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In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approach (SMR) based on a Lagrangian relaxation of the initial problem. Unlike the dual decomposition approach of Komodakis et al. [29] SMR does not decompose the graph structure of the initial problem but constructs a submodular energy that is minimized within the Lagrangian relaxation. Our approach is applicable to both pairwise and high-order MRFs and allows to take into account global potentials of certain types. We study theoretical properties of the proposed approach and evaluate it experimentally.

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Section: Linear Global Constraintsmentioning

confidence: 99%

“…There have been a number of works that separately consider constraints on total number of nodes that take a specific label (e.g. [31]).…”

Section: Linear Global Constraintsmentioning

confidence: 99%

Submodular Relaxation for Inference in Markov Random Fields

Osokin

Vetrov

2015

IEEE Trans. Pattern Anal. Mach. Intell.

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“…or use various forms of relaxations of the original problem to facilitate computations: e.g., spectral relaxations (Olsson et al (2008)), semidefinite programming (Keuchel et al (2003); Lisser and Rendl (2003); Hager et al (2009)), or variational inference approximations (Kropotov et al (2010)). …”

Section: Introductionmentioning

confidence: 99%

Segmentation with area constraints

Niethammer

Zach

2013

Medical Image Analysis

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Image segmentation approaches typically incorporate weak regularity conditions such as boundary length or curvature terms, or use shape information. High-level information such as a desired area or volume, or a particular topology are only implicitly specified. In this paper we develop a segmentation method with explicit bounds on the segmented area. Area constraints allow for the soft selection of meaningful solutions, and can counteract the shrinking bias of length-based regularization. We analyze the intrinsic problems of convex relaxations proposed in the literature for segmentation with size constraints. Hence, we formulate the area-constrained segmentation task as a mixed integer program, propose a branch and bound method for exact minimization, and use convex relaxations to obtain the required lower energy bounds on candidate solutions. We also provide a numerical scheme to solve the convex subproblems. We demonstrate the method for segmentations of vesicles from electron tomography images.

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A Framework for Detecting Polarity Inversion Lines from Longitudinal Magnetograms

Cai

Aydin

et al. 2020

2020 IEEE International Conference on Big Data (Big Data)

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Variational segmentation algorithms with label frequency constraints

Cited by 3 publications

References 11 publications

Submodular Relaxation for Inference in Markov Random Fields

Submodular Relaxation for Inference in Markov Random Fields

Segmentation with area constraints

A Framework for Detecting Polarity Inversion Lines from Longitudinal Magnetograms

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