The functionality of the visual cortex has been described by Peititot as a contact manifold of dimension three and in a previous paper of the authors 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.
Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space / Citti, G.; Manfredini, M.; Sarti, A.. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 9:(2010), pp. 905-927. [10.3934/cpaa.2010.9.905]
Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space
M. Manfredini;
2010
Abstract
The functionality of the visual cortex has been described by Peititot as a contact manifold of dimension three and in a previous paper of the authors 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.
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