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.

G. Citti, M. Manfredini, A. Sarti (2010). Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 9, 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

CITTI, GIOVANNA;MANFREDINI, MARIA;SARTI, ALESSANDRO
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.
2010
G. Citti, M. Manfredini, A. Sarti (2010). Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 9, 905-927 [10.3934/cpaa.2010.9.905].
G. Citti; M. Manfredini; A. Sarti
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/93046
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
social impact