A modified Chan-Vese model and its theoretical proof

Ling Pi; Yaxin Peng; Chunli Shen; Fang Li

doi:10.1016/j.jmaa.2008.10.050

A modified Chan-Vese model and its theoretical proof

Ling Pi^*
, Yaxin Peng
, Chunli Shen
, Fang Li

^*Corresponding author for this work

School of Mathematical Sciences

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

6 Scopus citations

Abstract

We present a modified Chan-Vese functional and give its theoretical proof. By using the geometric heat flow method to all the Euler-Lagrange equations, a system of evolution equations in level set formulation is derived. We study the existence of solution to this system by Schauder fixed point theorem and the implicit function theorem in Banach space. This variational formulation can detect interior and exterior boundaries of desired object(s) in color images.

Original language	English
Pages (from-to)	627-634
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	351
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2008.10.050
State	Published - 15 Mar 2009

Keywords

Desired object(s)
Discrimination function
Implicit function theorem in Banach space
Schauder fixed point theorem
Viscosity solution

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10.1016/j.jmaa.2008.10.050

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AU - Shen, Chunli

AU - Li, Fang

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N2 - We present a modified Chan-Vese functional and give its theoretical proof. By using the geometric heat flow method to all the Euler-Lagrange equations, a system of evolution equations in level set formulation is derived. We study the existence of solution to this system by Schauder fixed point theorem and the implicit function theorem in Banach space. This variational formulation can detect interior and exterior boundaries of desired object(s) in color images.

AB - We present a modified Chan-Vese functional and give its theoretical proof. By using the geometric heat flow method to all the Euler-Lagrange equations, a system of evolution equations in level set formulation is derived. We study the existence of solution to this system by Schauder fixed point theorem and the implicit function theorem in Banach space. This variational formulation can detect interior and exterior boundaries of desired object(s) in color images.

KW - Desired object(s)

KW - Discrimination function

KW - Implicit function theorem in Banach space

KW - Schauder fixed point theorem

KW - Viscosity solution

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DO - 10.1016/j.jmaa.2008.10.050

M3 - 文章

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

A modified Chan-Vese model and its theoretical proof

Abstract

Keywords

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