Volume 40, Number 2, March-April 2006
|Page(s)||393 - 412|
|Published online||21 June 2006|
A viscosity solution method for Shape-From-Shading without image boundary data
Perception Team, INRIA Rhône-Alpes, France. Emmanuel.Prados@inrialpes.fr
2 Dipartimento di Matematica Pura e Applicata, Università dell'Aquila, Italy. email@example.com
3 Odyssée Lab., INRIA Sophia Antipolis, France. Olivier.Faugeras@sophia.inria.fr
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.
Mathematics Subject Classification: 35D99 / 62H35 / 65N06 / 65N12 / 68T45
Key words: Shape-from-shading / boundary data / unification of SFS theories / singular viscosity solutions / states constraints.
© EDP Sciences, SMAI, 2006
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