In region-based image segmentation, two models dominate the field: the Mumford-Shah functional and statistical approaches based on Bayesian inference. Whereas the latter allow for numerous ways to describe the statistics of intensities in regions, the first includes spatially smooth approximations. In this paper, we show that the piecewise smooth Mumford-Shah functional is a first order approxi...

The Mumford-Shah model has been one of the most powerful models in image segmentation and denoising. The optimization of the multiphase Mumford-Shah energy functional has been performed using level sets methods that optimize the Mumford-Shah energy by evolving the level sets via the gradient descent. These methods are very slow and prone to getting stuck in local optima due to the use of the gr...

A diverse body of research has demonstrated that people update their beliefs to a greater extent when receiving good news compared to bad news. Recently, a paper by Shah et al. claimed that this asymmetry does not exist. Here we carefully examine the experiments and simulations described in Shah et al. and follow their analytic approach on our data sets. After correcting for confounds we identi...

In this paper we investigate the image of the l-adic representation attached to the Tate module of an abelian variety over a number field with endomorphism algebra of type I or II in the Albert classification. We compute the image explicitly and verify the classical conjectures of Mumford-Tate, Hodge, Lang and Tate, for a large family of abelian varieties of type I and II. In addition, for this...

In this paper it is shown that any regular critical point of the Mumford-Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the L1 -topology.

Shah-Waardenburg syndrome (SWS) is a neurocristopathy and is characterized by Hirschsprung's disease (HD), deafness, and depigmentation of hairs, skin, and iris. Is a very rare congenital disorder with variable clinical expression. This report describes a 4-day-old male newborn with Waardenburg's syndrome associated with aganglionosis of the colon and terminal ileum, and review the relevant lit...

The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on Γ-convergence and bounded variation functions theories. Some new regularization results, make possible to imagine a finite element resolution method. In a first time, the Mu...