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.
@article{M2AN_2006__40_2_393_0,
author = {Prados, Emmanuel and Camilli, Fabio and Faugeras, Olivier},
title = {A viscosity solution method for shape-from-shading without image boundary data},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {40},
year = {2006},
pages = {393-412},
doi = {10.1051/m2an:2006018},
mrnumber = {2241829},
zbl = {1112.49025},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2006__40_2_393_0}
}
Prados, Emmanuel; Camilli, Fabio; Faugeras, Olivier. A viscosity solution method for shape-from-shading without image boundary data. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 40 (2006) pp. 393-412. doi : 10.1051/m2an:2006018. http://gdmltest.u-ga.fr/item/M2AN_2006__40_2_393_0/
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