no. 2
A viscosity solution method for shape-from-shading without image boundary data
ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 2, pp. 393-412

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.

DOI : 10.1051/m2an:2006018
Classification : 35D99, 62H35, 65N06, 65N12, 68T45
Keywords: shape-from-shading, boundary data, unification of SFS theories, singular viscosity solutions, states constraints 
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     title = {A viscosity solution method for shape-from-shading without image boundary data},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {393--412},
     year = {2006},
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     url = {https://www.numdam.org/articles/10.1051/m2an:2006018/}
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Prados, Emmanuel; Camilli, Fabio; Faugeras, Olivier. A viscosity solution method for shape-from-shading without image boundary data. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 2, pp. 393-412. doi: 10.1051/m2an:2006018

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