Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Mashtakov, Alexey P."'
Autor:
Galyaev, Ivan, Mashtakov, Alexey
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 occluded contours are completed using sub-Riemannian geodesics in the fou
Externí odkaz:
http://arxiv.org/abs/2107.11602
Autor:
Mashtakov, Alexey
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 move forward on a plane and turn in place. Optimal trajectories of this
Externí odkaz:
http://arxiv.org/abs/2105.00232
Publikováno v:
Differential Geometry and its Applications, 2019
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 stimulus and its associated percept. They take place in the visual areas
Externí odkaz:
http://arxiv.org/abs/2002.08063
Fokker-Planck PDEs (incl. diffusions) for stable L\'{e}vy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exa
Externí odkaz:
http://arxiv.org/abs/1811.00363
Autor:
Mashtakov, Alexey, Popov, Anton
Publikováno v:
Mashtakov, A.P. & Popov, A.Y. Regul. Chaot. Dyn. (2017) 22: 949
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 fixed.
Comment: 8 pages, 0 figures
Comment: 8 pages, 0 figures
Externí odkaz:
http://arxiv.org/abs/1805.08537
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 these two curves coincide only in the case when they are segments of a
Externí odkaz:
http://arxiv.org/abs/1609.03704
Autor:
Sanguinetti, Gonzalo, Bekkers, Erik, Duits, Remco, Janssen, Michiel, Mashtakov, Alexey, Mirebeau, Jean-Marie
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 image data. The key ingredient is a Riemannian approximation of the SR-
Externí odkaz:
http://arxiv.org/abs/1508.02553
Publikováno v:
SIAM J Imaging Sci, 2015, 8(4), 2740-2770. (31 pages)
We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group $SE(2) = \mathbb{R}^2 \rtimes S^1$ with a metric tensor depending on a smooth external cost $\mat
Externí odkaz:
http://arxiv.org/abs/1503.01433
Autor:
Mashtakov, Alexey P., Sachkov, Yuri L.
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 Liouville integrability and superintegrability are proved.
Externí odkaz:
http://arxiv.org/abs/1405.1716
We consider the problem $\mathbf{P_{curve}}$ of minimizing $\int \limits_0^L \sqrt{\xi^2 + \kappa^2(s)} \, {\rm d}s$ for a curve $\mathbf{x}$ on $\mathbb R$ with fixed boundary points and directions. Here the total length $L\geq 0$ is free, $s$ denot
Externí odkaz:
http://arxiv.org/abs/1305.6061