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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