A Note on the Discrete Binary Mumford-Shah Model

Abstract. This paper is concerned itself with the analysis of the twophase 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 L1 -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.

• Type: Conference
• Year: 2007
• Where: MIRAGE
• Authors: Jérôme Darbon
• Keywords: Computer Vision, Contrast Invariant filter, MIRAGE 2007, Piecewise Constant Image, Twophase Mumford-shah Model