In this paper we reconsider the sub-Riemannian cortical model of image completion introduced in [G. Citti and A. Sarti, J. Math. Imaging Vision, 24 (2006), pp. 307–326]. This model combines two mechanisms, the sub-Riemannian diffusion and the concentration, giving rise to a diffusion driven motion by curvature. In this paper we give a formal proof of the existence of viscosity solutions of the sub-Riemannian motion by curvature. Furthermore we illustrate the sub-Riemannian finite difference scheme used to implement the model and we discuss some properties of the algorithm. Finally results of completion and enhancement on a number of natural images are shown and compared with other models.

Citti, G., Franceschiello, B., Sanguinetti, G., Sarti, A. (2016). Sub-riemannian mean curvature flow for image processing. SIAM JOURNAL ON IMAGING SCIENCES, 9(1), 212-237 [10.1137/15M1013572].

Sub-riemannian mean curvature flow for image processing

CITTI, GIOVANNA;Franceschiello, B.;
2016

Abstract

In this paper we reconsider the sub-Riemannian cortical model of image completion introduced in [G. Citti and A. Sarti, J. Math. Imaging Vision, 24 (2006), pp. 307–326]. This model combines two mechanisms, the sub-Riemannian diffusion and the concentration, giving rise to a diffusion driven motion by curvature. In this paper we give a formal proof of the existence of viscosity solutions of the sub-Riemannian motion by curvature. Furthermore we illustrate the sub-Riemannian finite difference scheme used to implement the model and we discuss some properties of the algorithm. Finally results of completion and enhancement on a number of natural images are shown and compared with other models.
2016
Citti, G., Franceschiello, B., Sanguinetti, G., Sarti, A. (2016). Sub-riemannian mean curvature flow for image processing. SIAM JOURNAL ON IMAGING SCIENCES, 9(1), 212-237 [10.1137/15M1013572].
Citti, Giovanna; Franceschiello, B.; Sanguinetti, G.; Sarti, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/554766
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