Maurizio Falcone

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Abs t r ac t . A numerical scheme to solve the Dirichlet type problem for the first order Hamilton-Jacobi equation related to the shape-fromshading model is proposed. The algorithm computes the maximal solution of the problem provided a compatibility condition on the discretization steps is satisfied. This global formulation a~ows to include in the model(More)
Many algorithms have been suggested for the shape-from-shading problem, and some years have passed since the publication of the survey paper by Zhang et al. [1]. In this new survey paper, we try to update their presentation including some recent methods which seem to be particularly representative of three classes of methods: methods based on partial(More)
We present a new Fast Marching algorithm for a non-convex eikonal equation modeling front evolutions in the normal direction. The algorithm is an extension of the Fast Marching Method since the new scheme can deal with a time-dependent velocity without any restriction on its sign. We analyze the properties of the algorithm and we prove its convergence in(More)
We present a new Fast Marching algorithm for an eikonal equation with a velocity changing sign. This first order equation models a front propagation in the normal direction. The algorithm is an extension of the Fast Marching Method in two respects. The first is that the new scheme can deal with a time-dependent velocity and the second is that there is no(More)
In this paper we study a modern, perspective model for shape from shading and its numerical approximation. We show that a new form of the classic concave/convex ambiguity is still present, although the model has been shown to be well-posed under particular assumptions. This analytical result is confirmed by various numerical tests. Moreover, we present(More)