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)b...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.展开更多
A general(abstract)scheme of iterative improvement and optimization on the base of extension,localization principles which would help to generate new concrete methods and algorithms for new problems is proposed.Appli...A general(abstract)scheme of iterative improvement and optimization on the base of extension,localization principles which would help to generate new concrete methods and algorithms for new problems is proposed.Application to optimal control problems for continuous systems is considered.Visual example is given.展开更多
基金The authors acknowledge support by Russian Foundation for Basic Research,Project No.12-01-00913-aand by the Ministry of Education and Science of Russia within the Federal program"Scientific and Scientific-Pedagogical Personnel of Innovative Russia,"Agreement No.8209 of August 6,2012.
文摘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.
基金the Russian Foundation for Basic Research(No.15-01-01923A).
文摘A general(abstract)scheme of iterative improvement and optimization on the base of extension,localization principles which would help to generate new concrete methods and algorithms for new problems is proposed.Application to optimal control problems for continuous systems is considered.Visual example is given.
