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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)

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