Broad research interests and related applications: My research is in the area of stochastic systems, computational methods for sensing, estimation, and control problems, with a focus on robotic systems. In real-world systems, uncertainty (both in the system model and sensory readings) is omnipresent. A few of the vast set of applications for this research include (i) Motion planning for mobile ...

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].

| 2017 | 1 Seyed-Hossein Abtahi1,2, Mohammad-Ali Abtahi1,2, Seyed Ali Akbar Mortazavi1,2, Hamidreza Jahanbani-Ardakani2,3,4, Mehdi Mazloumi5 1Department of Ophthalmology, School of Medicine, Isfahan University of Medical Sciences, 2Isfahan Eye Research Center, Isfahan University of Medical Sciences, 3Medical School, Isfahan University of Medical Sciences, 4Isfahan Medical Students Research Cent...

We prove that a certain series defines a constant function using Wolpert’s formula for the variation of the length of a geodesic along a Fenchel Nielsen twist. Subsequently we determine the value viewing it as function on the the Deligne Mumford compactification M1,1 and evaluating it at the stable curve at infinity. Conventions: 1. For γ an essential closed curve on a surface lγ(x) is the leng...

We compute explicitly the anisotropy eeect in the H 1 term, generated in the approximation of the Mumford-Shah functional by nite element spaces deened on structured triangulations.

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