A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on H1 0 (Γ) , Γ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact ...

with its favorable geographical location, qazvin has long been a center of civilization in the iranian plateau. due to its strategic importance and being situated on the way to routes going to west and east, qazvin has always enjoyed military and political significance in both the pre-islamic and the islamic period. after the muslim arabs’ conquest of persia, qazvin became one of the borders of...

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 ...

Mustafa Kamal, Abu-Bakr El-BediwiTamer Dawod* and Adel. S. Waqlan** Metal Physics Lab. Physics Department, Faculty of Science –Mansoura University, Egypt. * Medical Physics Unit, Clinical Oncology and Nuclear Medicine Dept., Faculty of Medicine, Mansoura University **On leave, M.sc student, Ministry of Higher Education, Yemen. [email protected], [email protected] [email protected]...

Touraj Banirostam, Kamal Mirzaie, Mehdi N. Fesharaki Department of Computer Engineering, Central Tehran Branch, Islamic Azad University, IRAN Email: [email protected] Department of Computer Engineering, Maybod Branch, Islamic Azad University, IRAN Email: [email protected] Department of Computer Engineering, Science and research Branch, Islamic Azad University, IRAN Email: fesharak...

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...