Calculus of Variations and Geometric Measure Theory
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R. Hladky - S. Pauls

Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model

created by scott on 27 Sep 2005

[BibTeX]

Submitted Paper

Inserted: 27 sep 2005

Year: 2005

Abstract:

We investigate solutions to the minimal surface problem with Dirichlet boundary conditions in the roto-translation group equipped with a subRiemannian metric. By work of G. Citti and A. Sarti, such solutions are amodal completions of occluded visual data when using a model of the first layer of the visual cortex. Using a characterization of smooth minimal surfaces as ruled surfaces, we give a method to compute a minimal spanning surface given fixed boundary data presuming such a surface exists. Moreover, we describe a number of obstructions to existence and uniqueness but also show that under suitable conditions, smooth minimal spanning surfaces with good properties exist. Not only does this provide an explicit realization of the disocclusion process for the neurobiological model, but it also has application to contructing disocclusion algorithms in digital image processing.

Keywords: minimal surfaces, Roto-translation group, Visual cortex


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