# A Note on the Discrete Binary Mumford-Shah Model

### From LRDE

- 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 **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.} }