A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-Norm Fidelity

Fang Li; Stanley Osher; Jing Qin; Ming Yan

doi:10.1007/s10915-016-0183-z

A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-Norm Fidelity

Fang Li, Stanley Osher, Jing Qin, Ming Yan

Mathematics

Producción científica: Article › revisión exhaustiva

24 Citas (Scopus)

Resumen

In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the convergence of the algorithm.

Idioma original	English
Páginas (desde-hasta)	82-106
Número de páginas	25
Publicación	Journal of Scientific Computing
Volumen	69
N.º	1
DOI	https://doi.org/10.1007/s10915-016-0183-z
Estado	Published - oct 1 2016

Nota bibliográfica

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Financiación

The research of F. Li was supported by the 973 Program 2011CB707104 and the Science and Technology Commission of Shanghai Municipality (STCSM) 13dz2260400, the research of S. Osher and J. Qin was supported by ONR Grants N00014120838 and N00014140444, NSF Grants DMS-1118971 and CCF-0926127, and the Keck Foundation, the research of M. Yan was supported by NSF Grants DMS-1317602. The work was done when the first author was visiting UCLA Department of Mathematics.

Financiadores	Número del financiador
National Science Foundation (NSF)	0926127, 1317602, CCF-0926127, 1118971, 1440415, DMS-1118971
Office of Naval Research	N00014140444, N00014120838
W. M. Keck Foundation	DMS-1317602
Science and Technology Commission of Shanghai Municipality	13dz2260400

ASJC Scopus subject areas

Software
General Engineering
Computational Mathematics
Theoretical Computer Science
Applied Mathematics
Numerical Analysis
Computational Theory and Mathematics

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abstract = "In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the convergence of the algorithm.",

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AB - In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the convergence of the algorithm.

KW - ADMM

KW - Fuzzy membership function

KW - Image segmentation

KW - L1-norm

KW - Segmentation accuracy

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A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-Norm Fidelity

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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