Exact optimization for Markov Random Fields with convex priors

Hiroshi Ishikawa

doi:10.1109/TPAMI.2003.1233908

Exact optimization for Markov Random Fields with convex priors

Hiroshi Ishikawa^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

403 Citations (Scopus)

Abstract

We introduce a method to solve exactly a first order Markov Random Field optimization problem in more generality than was previously possible. The MRF shall have a prior term that is convex in terms of a linearly ordered label set. The method maps the problem into a minimum-cut problem for a directed graph, for which a globally optimal solution can be found in polynomial time. The convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method.

Original language	English
Pages (from-to)	1333-1336
Number of pages	4
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	25
Issue number	10
DOIs	https://doi.org/10.1109/TPAMI.2003.1233908
Publication status	Published - 2003 Oct
Externally published	Yes

Keywords

Global optimization
Markov random field
Maximum flow
Minimum cut

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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10.1109/TPAMI.2003.1233908

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title = "Exact optimization for Markov Random Fields with convex priors",

abstract = "We introduce a method to solve exactly a first order Markov Random Field optimization problem in more generality than was previously possible. The MRF shall have a prior term that is convex in terms of a linearly ordered label set. The method maps the problem into a minimum-cut problem for a directed graph, for which a globally optimal solution can be found in polynomial time. The convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method.",

keywords = "Global optimization, Markov random field, Maximum flow, Minimum cut",

author = "Hiroshi Ishikawa",

note = "Funding Information: The author would like to thank Professor Davi Geiger for his advice and encouragement. This work was supported in part by US National Science Foundation grant no. IIS-9733913. This paper is in memory of Dr. Henning Biermann (16 October 1972-1 July 2002).",

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N1 - Funding Information: The author would like to thank Professor Davi Geiger for his advice and encouragement. This work was supported in part by US National Science Foundation grant no. IIS-9733913. This paper is in memory of Dr. Henning Biermann (16 October 1972-1 July 2002).

PY - 2003/10

Y1 - 2003/10

N2 - We introduce a method to solve exactly a first order Markov Random Field optimization problem in more generality than was previously possible. The MRF shall have a prior term that is convex in terms of a linearly ordered label set. The method maps the problem into a minimum-cut problem for a directed graph, for which a globally optimal solution can be found in polynomial time. The convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method.

AB - We introduce a method to solve exactly a first order Markov Random Field optimization problem in more generality than was previously possible. The MRF shall have a prior term that is convex in terms of a linearly ordered label set. The method maps the problem into a minimum-cut problem for a directed graph, for which a globally optimal solution can be found in polynomial time. The convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method.

KW - Global optimization

KW - Markov random field

KW - Maximum flow

KW - Minimum cut

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JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

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ER -

Exact optimization for Markov Random Fields with convex priors

Abstract

Keywords

ASJC Scopus subject areas

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