58 citations · 100 across the 5 of their papers we have counts for
5 papers
Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion
Ugo Boscain, Roman Chertovskih, Jean-Paul Gauthier +2
In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In…
Highly corrupted image inpainting through hypoelliptic diffusion
Ugo Boscain, Roman Chertovskih, Jean-Paul Gauthier +2
We present a new image inpainting algorithm, the Averaging and Hypoelliptic Evolution (AHE) algorithm, inspired by the one presented in [SIAM J. Imaging Sci., vol. 7, no. 2, pp. 66…
On the local and global properties of geodesics in pseudo-Riemannian metrics
Alexey Remizov
The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investig…
Hypoelliptic diffusion and human vision: a semi-discrete new twist
Ugo Boscain, Roman Chertovskih, Jean-Paul Gauthier +1
This paper presents a semi-discrete alternative to the theory of neurogeometry of vision, due to Citti, Petitot and Sarti. We propose a new ingredient, namely working on the group…
On a class of vector fields with discontinuity of divide-by-zero type and its applications
Roberta Ghezzi, Alexey Remizov
We study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smoo…