Mathematical analysis of an extended mumford-shah model for image segmentation

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.