Calculus of Variations and Geometric Measure Theory
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Reconstruction of domains from slices using phase-field approximation.

Francois Dayrens

created by pluda on 21 Oct 2015

28 oct 2015 -- 15:30   [open in google calendar]

Aula Seminari, Dipartimento di Matematica di Pisa

Abstract.

How can we reconstruct a domain when we know it only on a finite number of slices? In the plane, given a family of segments, we search the "best" set inclosing these segments. In the usual space, the question is the same with a family of planar sections. First, by "the best set" we mean one which minimises one of the following geometrical energies: its perimeter or the Willmore energy of its boundary. We will see that the theorical problem is not well posed but a numerical phase-field approximation seems to give an answer... an unexpected solution. For the perimeter, this solution does not "really" fit the slices. I will explain why we have this solution and how we can slighty modify the phase field scheme to have what we expect. I will give all (intuitive) definitions of concepts I use in this talk, especially the phase-field model, and we will apply this reconstruction to movie interpolation...

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