The calibration method is used to identify some minimizers of the Mumford-Shah functional. The method is then extended to more general free discontinuity problems.

We propose a novel variational approach based on a level set formulation of the Mumford-Shah functional and shape priors. We extend the functional by a labeling function which indicates image regions in which the shape prior is enforced. By minimizing the proposed functional with respect to both the level set function and the labeling function, the algorithm selects image regions where it is fa...

In this paper, we present a method for the numerical minimization of the Mumford–Shah functional that is based on the idea of topological asymptotic expansions. The basic idea is to cover the expected edge set with balls of radius ε > 0 and use the number of balls, multiplied with 2ε, as an estimate for the length of the edge set. We introduce a functional based on this idea and prove that it c...

We show that if (u,K) is a global minimizer for the Mumford-Shah functional in R , and if K is a smooth enough cone, then (modulo constants) u is a homogenous function of degree 1 2 . We deduce some applications in R as for instance that an angular sector cannot be the singular set of a global minimizer, that if K is a half-plane then u is the corresponding cracktip function of two variables, o...

Image segmentation is a complex task, since it involves the manipulation of different kind of objects such as functions, domains in R and curves. In this work we propose a two-dimensional image segmentation method, using the Mumford and Shah’s one dimensional technique, performing vertical and horizontal sweeps. This is in contrast to the technique that involves the generalization of the Mumfor...

Riemann surfaces with nodes can be described by introducing simple composite operators in matrix models. In the case of the Kontsevich model, it is sufficient to add the quadratic, but “non-propagating”, term (tr[X]) to the Lagrangian. The corresponding JenkinsStrebel differentials have pairwise identified simple poles. The result is in agreement with a conjecture formulated by Kontsevich and r...

A study on the contamination of ground water by industrial effluent in different areas Kala Shah Kaku has been conducted. is one Punjab. The major causes drinking such areas. Grounwater samples have analyzed for their characteristics. Standard laboratory techniques employed to determine various parameters from samples. mean values pH, Na+ , and SO4 2- are within permissible limits WHO standards...