We propose a new method for the Lambertian Shape From Shading (SFS) problem based on the notion of Crandall-Lions viscosity solution. This method has the advantage of requiring the knowledge of the solution (the surface to be reconstructed) only on some part of the boundary and/or of the singular set (the set of the points at maximal intensity). Moreover it unifies in an unique mathematical formulation the works of Rouy et al. [34, 50], Falcone et al. [21], Prados et al. [46, 48, 49], based on the notion of viscosity solutions and the work of Dupuis and Oliensis [17] dealing with classical solutions and value functions. Also, it allows to generalize their results to the "perspective SFS" problem recently simultaneously introduced in [13,46,55]. While the theoretical part has been developed in [44], in this paper we give some stability results and we describe numerical schemes for the SFS based on this method. We construct provably convergent and robust algorithms. Finally, we apply our SFS method to real images and we suggest some real-life applications.

A unifying and rigorous Shape-from-Shading method adapted to realistic data and applications / Camilli, Fabio; Fagueras, O; Prados, O.. - In: JOURNAL OF MATHEMATICAL IMAGING AND VISION. - ISSN 0924-9907. - STAMPA. - 25:(2006), pp. 307-328. [10.1007/s10851-006-6899-x]

A unifying and rigorous Shape-from-Shading method adapted to realistic data and applications

CAMILLI, FABIO;
2006

Abstract

We propose a new method for the Lambertian Shape From Shading (SFS) problem based on the notion of Crandall-Lions viscosity solution. This method has the advantage of requiring the knowledge of the solution (the surface to be reconstructed) only on some part of the boundary and/or of the singular set (the set of the points at maximal intensity). Moreover it unifies in an unique mathematical formulation the works of Rouy et al. [34, 50], Falcone et al. [21], Prados et al. [46, 48, 49], based on the notion of viscosity solutions and the work of Dupuis and Oliensis [17] dealing with classical solutions and value functions. Also, it allows to generalize their results to the "perspective SFS" problem recently simultaneously introduced in [13,46,55]. While the theoretical part has been developed in [44], in this paper we give some stability results and we describe numerical schemes for the SFS based on this method. We construct provably convergent and robust algorithms. Finally, we apply our SFS method to real images and we suggest some real-life applications.
shape from shading; hamilton-jacobi equations; viscosity solutions; states constraints; finite differences
01 Pubblicazione su rivista::01a Articolo in rivista
A unifying and rigorous Shape-from-Shading method adapted to realistic data and applications / Camilli, Fabio; Fagueras, O; Prados, O.. - In: JOURNAL OF MATHEMATICAL IMAGING AND VISION. - ISSN 0924-9907. - STAMPA. - 25:(2006), pp. 307-328. [10.1007/s10851-006-6899-x]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/43877
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? 26
  • Scopus 49
  • ???jsp.display-item.citation.isi??? 36
social impact