In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their "minimums"; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal. 29 ( 1992) 867-884], [Lions et al., Numer. Math. 64 (1993) 323-353], [Falcone and Sagona, Lect. Notes Math. 1310 (1997) 596-603], [Prados et al., Proc. 7th Eur. Conf. Computer Vision 2351 (2002) 790-804; Prados and Faugeras, IEEE Comput. Soc. Press 2 (2003) 826-831], based on the notion of viscosity solutions and the work of [Dupuis and Oliensis, Ann. Appl. Probab. 4 (1994) 287-346] dealing with classical solutions.

A viscosity method for Shape-from-Shading without boundary data, / E., Prados; Camilli, Fabio; O., Fagueras. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - STAMPA. - 40:(2006), pp. 393-412. [10.1051/m2an:2006018]

A viscosity method for Shape-from-Shading without boundary data,

CAMILLI, FABIO;
2006

Abstract

In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their "minimums"; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal. 29 ( 1992) 867-884], [Lions et al., Numer. Math. 64 (1993) 323-353], [Falcone and Sagona, Lect. Notes Math. 1310 (1997) 596-603], [Prados et al., Proc. 7th Eur. Conf. Computer Vision 2351 (2002) 790-804; Prados and Faugeras, IEEE Comput. Soc. Press 2 (2003) 826-831], based on the notion of viscosity solutions and the work of [Dupuis and Oliensis, Ann. Appl. Probab. 4 (1994) 287-346] dealing with classical solutions.
2006
Shape-from-shading; boundary data; unification of SFS theories; singular viscosity solutions; states constraints.
01 Pubblicazione su rivista::01a Articolo in rivista
A viscosity method for Shape-from-Shading without boundary data, / E., Prados; Camilli, Fabio; O., Fagueras. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - STAMPA. - 40:(2006), pp. 393-412. [10.1051/m2an:2006018]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/43880
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