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Parallel Algorithm and Software for Image Inpainting via Sub-Riemannian Minimizers on the Group of Rototranslations

Published online by Cambridge University Press:  28 May 2015

Alexey P. Mashtakov ,
Andrei A. Ardentov  and
Yuri L. Sachkov
Alexey P. Mashtakov*
Affiliation:
Program Systems Institute, Pereslavl-Zalessky, Russia
Andrei A. Ardentov*
Affiliation:
Program Systems Institute, Pereslavl-Zalessky, Russia
Yuri L. Sachkov*
Affiliation:
Program Systems Institute, Pereslavl-Zalessky, Russia
*
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
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Abstract

The paper is devoted to an approach for image inpainting developed on the basis of neurogeometry of vision and sub-Riemannian geometry. Inpainting is realized by completing damaged isophotes (level lines of brightness) by optimal curves for the left-invariant sub-Riemannian problem on the group of rototranslations (motions) of a plane SE(2). The approach is considered as anthropomorphic inpainting since these curves satisfy the variational principle discovered by neurogeometry of vision. A parallel algorithm and software to restore monochrome binary or halftone images represented as series of isophotes were developed. The approach and the algorithm for computation of completing arcs are presented in detail.

Keywords

65M1078A48Image inpaintingsub-Riemannian geometry neurogeometry of visiongroup of rototranslations of a planeparallel software
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 95 - 115
Copyright
Copyright © Global Science Press Limited 2013

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