We propose a novel image segmentation model, called the Semi-Supervised Subspace Mumford-Shah model, which incorporates subspace clustering techniques into a Mumford-Shah model to solve texture segmentation problems. While the natural unsupervised approach to learn a feature subspace can easily be trapped in a local solution, we propose a novel semi-supervised optimization algorithm that makes ...

We present an estimation-theoretic approach to curve evolution for the Mumford-Shah problem. By viewing an active contour as the set of discontinuities in the Mumford-Shah problem, we may use the corresponding functional to determine gradient descent evolution equations to deform the active contour. In each gradient descent step, we solve a corresponding optimal estimation problem, connecting t...

The aim of this paper is to provide a formal link between an oscillatory neural model, whose phase is represented by a difference equation, and the Mumford and Shah functional. A Riemannian metric is induced by the pattern of neural connections, and in this setting the difference equation is studied. Its Euler–Lagrange operator Γ-converges as the dimension of the grid tends to 0 to the Mumford ...

In a recent paper, Soni and Shah [Soni, H., Shah, N. H., 2008. Optimal ordering policy for stock-dependent demand under progressive payment scheme. European Journal of Operational Research 184, 91-100] developed a model to find the optimal ordering policy for a retailer with stock-dependent demand and a supplier that offers a progressive payment scheme to the retailer. This note corrects some e...

This paper is the first part of an ongoing project aimed at providing a local minimality criterion, based on a second variation approach, for the triple point configurations of the Mumford-Shah functional.

We prove an ε-regularity theorem at the endpoint of connected arcs for 2-dimensional Mumford-Shah minimizers. In particular we show that, if in a given ball Br(x) the jump set of a given MumfordShah minimizer is sufficiently close, in the Hausdorff distance, to a radius of Br(x), then in a smaller ball the jump set is a connected arc which terminates at some interior point y0 and it is C 1,α up...

We prove higher integrability for the gradient of local minimizers of the Mumford-Shah energy functional, providing a positive answer to a conjecture of De Giorgi [5].