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Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space

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  • The functionality of the visual cortex has been described in [63] and in [50] as a contact manifold of dimension three and in [62] the Mumford and Shah functional has been proposed to segment lifting of an image in the three dimensional cortical space. Hence, we study here this functional and we provide a constructive approach to the problem, extending to the sub- Riemannian setting an approximation technique proposed by De Giorgi in the Euclidean case.
    Mathematics Subject Classification: Primary: 49J45,35R03; Secondary: 49M25, 35Q92.

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