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In this paper we reconsider the sub-Riemannian cortical model of image completion introduced in [16,61]. 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.A model expressed by a system of two equations, one responsible for boundary extraction, and one for figure completion was proposed by Bertalmio, Sapiro, Caselles, and Ballester in [3]. In Sarti et al [63] the role of the observer was considered, letting evolve by curvature in the Riemannian metric associated to the image a fixed surface called point of view surface.