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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)
In order to detect salient lines in spherical images, we consider the problem of minimizing the functional $$\int \limits _0^l \mathfrak {C}(\gamma (s)) \sqrt{\xi ^2 + k_g^2(s)} \, \mathrm{d}s$$ ∫ 0 l C ( γ ( s ) ) ξ 2 + k g 2 ( s ) d s for a curve $$\gamma $$ γ on a sphere with fixed boundary points and directions. The total length l is free, s denotes the(More)
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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