38809

Автор(ы): 

Автор(ов): 

4

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Hypoelliptic Diffusion and Human Vision: A Semidiscrete New Twist

ISBN/ISSN: 

1936-4954

DOI: 

10.1137/130924731

Наименование источника: 

  • SIAM Journal on Imaging Sciences

Обозначение и номер тома: 

Vol. 7, No. 2

Город: 

  • United States

Издательство: 

  • Society for Industrial and Applied Mathematics

Год издания: 

2014

Страницы: 

669-695
Аннотация
This paper presents a semidiscrete alternative to the theory of neurogeometry of vision, due to Citti, Petitot, and Sarti. We propose a new ingredient, namely, working on the group of translations and discrete rotations SE(2,N). The theoretical side of our study relates the stochastic nature of the problem with the Moore group structure of SE(2,N). Harmonic analysis over this group leads to very simple finite dimensional reductions. We then apply these ideas to the inpainting problem which is reduced to the integration of a completely parallelizable finite set of Mathieu-type diffusions (indexed by the dual of SE(2,N) in place of the points of the Fourier plane, which is a drastic reduction). The integration of the the Mathieu equations can be performed by standard numerical methods for elliptic diffusions and leads to a very simple and efficient class of inpainting algorithms. We illustrate the performances of the method on a series of deeply corrupted images.

Библиографическая ссылка: 

Боскаин У.В., Готье Ж.-П.А., Ремизов А.О., Чертовских Р.А. Hypoelliptic Diffusion and Human Vision: A Semidiscrete New Twist // SIAM Journal on Imaging Sciences. 2014. Vol. 7, No. 2. С. 669-695.