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.
Sub-riemannian mean curvature flow for image processing / Citti, Giovanna; Franceschiello, B.; Sanguinetti, G.; Sarti, A.. - In: SIAM JOURNAL ON IMAGING SCIENCES. - ISSN 1936-4954. - STAMPA. - 9:1(2016), pp. 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.File | Dimensione | Formato | |
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