Volume 6, Issue 1
Parallel Algorithm and Software for Image Inpainting via Sub-Riemannian Minimizers on the Group of Rototranslations

Alexey P. Mashtakov, Andrei A. Ardentov & Yuri L. Sachkov

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 95-115.

Published online: 2013-06

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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

Image inpainting, sub-Riemannian geometry, neurogeometry of vision, group of rototranslations of a plane, parallel software.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-95, author = {}, title = {Parallel Algorithm and Software for Image Inpainting via Sub-Riemannian Minimizers on the Group of Rototranslations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {1}, pages = {95--115}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.mssvm05}, url = {http://global-sci.org/intro/article_detail/nmtma/5896.html} }
TY - JOUR T1 - Parallel Algorithm and Software for Image Inpainting via Sub-Riemannian Minimizers on the Group of Rototranslations JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 95 EP - 115 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.mssvm05 UR - https://global-sci.org/intro/article_detail/nmtma/5896.html KW - Image inpainting, sub-Riemannian geometry, neurogeometry of vision, group of rototranslations of a plane, parallel software. AB -

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.

Alexey P. Mashtakov, Andrei A. Ardentov & Yuri L. Sachkov. (2020). Parallel Algorithm and Software for Image Inpainting via Sub-Riemannian Minimizers on the Group of Rototranslations. Numerical Mathematics: Theory, Methods and Applications. 6 (1). 95-115. doi:10.4208/nmtma.2013.mssvm05
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