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To model association fields that underly perceptional organization (gestalt) in psychophysics we consider the problem P curve of minimizing $\int _{0}^{\ell} \sqrt{\xi^{2} +\kappa^{2}(s)} {\rm d}s $ for a planar curve having fixed initial and final positions and directions. Here κ(s) is the curvature of the curve with free total length ℓ. This problem comes… (More)

We consider the problem of minimizing L 0 1 + K(t) 2 dt for a planar curve having fixed initial and final positions and directions. Here K(t) is the curvature of the curve and the total length L is free. This problem comes from a model of geometry of vision due to Petitot, Citti and Sarti. We study existence of local and global minimizers for this problem.… (More)

- Yuri Sachkov
- 2013

We compute two vector field models of the Carnot algebra with the growth vector (2, 3, 5, 8), and an infinitesimal symmetry of the corresponding sub-Riemannian structure.

- Yuri Sachkov
- 2013

We study the free nilpotent Lie algebra L with the growth vector (2, 3, 5, 8), and the corresponding connected simply connected Lie group G. In this situation, we compute explicitly the following objects important for the subsequent study of the left-invariant sub-Riemannian problem with the growth vector (2,3,5,8): (1) the product rule in the Lie group G,… (More)

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