期刊
JOURNAL OF MATHEMATICAL IMAGING AND VISION
卷 36, 期 1, 页码 1-27出版社
SPRINGER
DOI: 10.1007/s10851-009-0167-9
关键词
Minimal surfaces; Sub-Riemannian geometry; Roto-translation group; Visual cortex; Image reconstruction
类别
资金
- NSF [DMS-0306752]
We investigate solutions to the minimal surface problem with Dirichlet boundary conditions in the roto-translation group equipped with a sub-Riemannian metric. By work of G. Citti and A. Sarti, such solutions are completions of occluded visual data when using a model of the first layer of the visual cortex. Using a characterization of smooth non-characteristic 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 constructing disocclusion algorithms in digital image processing.
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