A Note on the Discrete Binary Mumford-Shah Model

Authors

Jérôme Darbon

Where

Proceedings of the international Computer Vision / Computer Graphics Collaboration Techniques and Applications (MIRAGE 2007)

Place

Paris, France

Type

inproceedings

Projects

Olena

Keywords

Image

Date

2006-12-29

Abstract

This paper is concerned itself with the analysis of the two-phase Mumford-Shah model also known as the active contour without edges model introduced by Chan and Vese. It consists of approximating an observed image by a piecewise constant image which can take only two values. First we show that this model with the $L^{1}$-norm as data fidelity yields a contrast invariant filter which is a well known property of morphological filters. Then we consider a discrete version of the original problem. We show that an inclusion property holds for the minimizers. The latter is used to design an efficient graph-cut based algorithm which computes an exact minimizer. Some preliminary results are presented.

Bibtex (lrde.bib)

@InProceedings{	  darbon.07.mirage,
  author	= {J\'er\^ome Darbon},
  title		= {A Note on the Discrete Binary {Mumford-Shah} Model},
  booktitle	= {Proceedings of the international Computer Vision /
		  Computer Graphics Collaboration Techniques and Applications
		  (MIRAGE 2007)},
  year		= 2007,
  address	= {Paris, France},
  month		= mar,
  abstract	= {This paper is concerned itself with the analysis of the
		  two-phase Mumford-Shah model also known as the active
		  contour without edges model introduced by Chan and Vese. It
		  consists of approximating an observed image by a piecewise
		  constant image which can take only two values. First we
		  show that this model with the $L^1$-norm as data fidelity
		  yields a contrast invariant filter which is a well known
		  property of morphological filters. Then we consider a
		  discrete version of the original problem. We show that an
		  inclusion property holds for the minimizers. The latter is
		  used to design an efficient graph-cut based algorithm which
		  computes an exact minimizer. Some preliminary results are
		  presented.}
}