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- Maurizio Falcone, Manuela Sagona
- ICIAP
- 1997

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)

- Jean-Denis Durou, Maurizio Falcone, Manuela Sagona
- Computer Vision and Image Understanding
- 2008

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)

Several algorithms have been suggested for the shape from shading problem, and some years have passed since the publication of Horn and Brooks’ book [27]. In this survey paper, we try to update the approach in presenting some algorithms which seem to be particularly representative of three classes of methods: (i) methods based on partial differential… (More)

- Emiliano Cristiani, Maurizio Falcone
- SIAM J. Numerical Analysis
- 2007

- Elisabetta Carlini, Maurizio Falcone, Nicolas Forcadel, Régis Monneau
- SIAM J. Numerical Analysis
- 2008

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)

- Fabio Camilli, Maurizio Falcone
- ICIP
- 1996

- M W Falcone, J K Perloff, W C Roberts
- The American journal of cardiology
- 1972

- M W Falcone, W C Roberts, A G Morrow, J K Perloff
- Circulation
- 1971

- Michael Breuß, Emiliano Cristiani, Jean-Denis Durou, Maurizio Falcone, Oliver Vogel
- SIAM J. Imaging Sciences
- 2012

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)