33 citations · 53 across the 11 of their papers we have counts for
11 papers
Liouville integrability in a four-dimensional model of the visual cortex
Ivan Galyaev, Alexey Mashtakov
We consider a natural extension of the Petitot-Citti-Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taking into account such that occ…
Time minimization problem on the group of motions of a plane with admissible control in a half-disk
Alexey Mashtakov
We study a time minimization problem on the group of motions of a plane with admissible control in a half-disk. The considered control system describes a model of a car that can mo…
Geometrical Optical Illusion via Sub-Riemannian Geodesics in the Roto-Translation Group
Benedetta Franceschiello, Alexey Mashtakov, Giovanna Citti +1
We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual st…
Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to Linear Parabolic and (Hypo-)Elliptic PDEs
Remco Duits, Erik J. Bekkers, Alexey Mashtakov
Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics,…
Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space
Alexey Mashtakov, Anton Popov
For the sub-Riemannian problem on the group of motions of Euclidean space we present explicit formulas for extremal controls in a special case, when one of the initial momenta is f…
Vessel Tracking via Sub-Riemannian Geodesics on
E. J. Bekkers, R. Duits, A. Mashtakov +1
We study a data-driven sub-Riemannian (SR) curve optimization model for connecting local orientations in orientation lifts of images. Our model lives on the projective line bundle…
Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)
Alexey Mashtakov, Andrei Ardentov, Yuri Sachkov
In this note we describe a relation between Euler's elasticae and sub-Riemannian geodesics on SE(2). Analyzing the Hamiltonian system of Pontryagin maximum principle we show that t…
Sub-Riemannian Fast Marching in SE(2)
Gonzalo Sanguinetti, Erik Bekkers, Remco Duits +3
We propose a Fast Marching based implementation for computing sub-Riemanninan (SR) geodesics in the roto-translation group SE(2), with a metric depending on a cost induced by the i…
A PDE Approach to Data-driven Sub-Riemannian Geodesics in SE(2)
Erik J. Bekkers, Remco Duits, Alexey Mashtakov +1
We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group $SE(2) = \mathbb{R}^2 \rtim…
Superintegrability of Sub-Riemannian Problems on Unimodular 3D Lie Groups
Alexey P. Mashtakov, Yuri L. Sachkov
Left-invariant sub-Riemannian problems on unimodular 3D Lie groups are considered. For the Hamiltonian system of Pontryagin maximum principle for sub-Riemannian geodesics, the Liou…
Asymptotics of Maxwell time in the plate-ball problem
A. P. Mashtakov, A. Yu. Popov
The problem on rolling of a sphere on a plane without slipping or twisting is considered. One should roll the sphere from one contact configuration to another so that the length of…