Hypoelliptic Diffusion and Human Vision: A Semidiscrete New Twist

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Boscain, U (Author) Other; Chertovskih, RA (Author) Other; Gauthier, JP (Author) Other; Remizov, AO (Author) Other

Journal

Title: SIAM Journal on Imaging Sciences

Vol. 7

Pages: 669-695

ISSN: 1936-4954

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 37 Citations

Other information

Authenticus ID: P-009-ND4

DOI: 10.1137/130924731

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 27