Khyati Patel Brijesh Shah

s. m. shah

We prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on ∂U . The proof is obtained by using...

The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of F-convergence by a séquence of intégral functionals defined on piecewise affine functions. Résumé. La fonctionnelle de Mumford et Shah, proposée pour l'étude du problème de la segmentation d'images, est approchée au sens de la F-convergence par une suite de fonctionnelles intégrales déf...

This paper presents a novel adaptive vision system for accurate segmentation of tissue structures in echographic medical images. The proposed vision system incorporates a level-set deformable model based on a modified Mumford-Shah functional, which is estimated over sparse foreground and background regions in the image. This functional is designed so that it copes with the intensity inhomogenei...

Formulae for the number of branch points of one-dimensional orbifolds defined over a non-archimedean local field and uniformisable by discrete projective linear groups are given. They depend only on the uniformising group. The method of equivariant pasting reveals the possible relative position of the branch points.

The problem of testing equality of several binomial proportions to a speci)ed standard is considered. An exact method of testing based on the test statistic considered in Kulkarni and Shah (Statist. Probab. Lett. 25 (1995) 213) is proposed. Exact properties of the exact method and the approximate method due to Kulkarni and Shah are evaluated numerically for the two-sample case. Numerical studie...

Using a calibration method we prove that, if Γ ⊂ Ω is a closed regular hypersurface and if the function g is discontinuous along Γ and regular outside, then the function uβ which solves { ∆uβ = β(uβ − g) in Ω \ Γ ∂νuβ = 0 on ∂Ω ∪ Γ is in turn discontinuous along Γ and it is the unique absolute minimizer of the nonhomogeneous Mumford-Shah functional