A Note on the Discrete Binary Mumford-Shah Model

From LRDE

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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.}
}