Mathematical Analysis of An Extended Mumford-Shah Model for Image Segmentation

Authors:
Trevor Chi-Yuen Tao;David James Crisp;John Hoek
Affiliations:
Aff1 Aff2;Aff3 Aff4;Discipline of Applied Mathematics, University of Adelaide, Adelaide, Australia 5005
Venue:
Journal of Mathematical Imaging and Vision
Year:
2006

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Abstract

Morel and Solimini have established proofs of important properties of segmentations which can be seen as locally optimal for the simplest Mumford-Shah model in the continuous domain. A weakness of the latter is that it is not suitable for handling noisy images. We propose a Bayesian model to overcome these problems. We demonstrate that this Bayesian model indeed generalizes the original Mumford-Shah model, and we prove it has the same desirable properties as shown by Morel and Solimini.