A modified Chan–Vese model and its theoretical proof

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 theor...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 351; no. 2; pp. 627 - 634
Main Authors: Pi, Ling, Peng, Yaxin, Shen, Chunli, Li, Fang
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.03.2009
Elsevier
Subjects:
Desired object(s)
Discrimination function
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Implicit function theorem in Banach space
Mathematical analysis
Mathematics
Partial differential equations
Real functions
Schauder fixed point theorem
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Viscosity solution
Discrimination function
Schauder fixed point theorem
Implicit function theorem in Banach space
Desired object(s)
Viscosity solution
Viscosity
Euler equation
Euler Lagrange equation
Level set
Existence of solution
Evolution equation
Heat flow
Banach space
Lagrange equation
Equation system
Functional
Fix point
Fixed point theorem
Mathematical analysis
Implicit function theorem
Application
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.10.050