# American Institute of Mathematical Sciences

July  2010, 9(4): 905-927. doi: 10.3934/cpaa.2010.9.905

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

 1 Dipartimento di Matematica, Piazza Porta S. Donato 5, 40126 Bologna, Italy, Italy 2 CREA, École Polytechnique, 32, Boulevard Victor, 75015 Paris, France

Received  December 2008 Revised  March 2010 Published  April 2010

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.
Citation: Giovanna Citti, Maria Manfredini, Alessandro Sarti. Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space. Communications on Pure & Applied Analysis, 2010, 9 (4) : 905-927. doi: 10.3934/cpaa.2010.9.905
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