A Unifying and Rigorous Shape from Shading Method Adapted to Realistic Data and Applications
 Emmanuel Prados,
 Fabio Camilli,
 Olivier Faugeras
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We propose a new method for the Lambertian Shape From Shading (SFS) problem based on the notion of CrandallLions 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 reallife applications.
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 Title
 A Unifying and Rigorous Shape from Shading Method Adapted to Realistic Data and Applications
 Journal

Journal of Mathematical Imaging and Vision
Volume 25, Issue 3 , pp 307328
 Cover Date
 20061001
 DOI
 10.1007/s108510066899x
 Print ISSN
 09249907
 Online ISSN
 15737683
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Shape From Shading
 HamiltonJacobi equations
 viscosity solutions
 states constraints
 finite differences
 Industry Sectors
 Authors

 Emmanuel Prados ^{(1)}
 Fabio Camilli ^{(2)}
 Olivier Faugeras ^{(3)}
 Author Affiliations

 1. UCLA Vision Lab., USA
 2. Dipartimento di Matematica Pura e Applicata, Università dell'Aquila, Italy
 3. Odyssée Lab.  INRIA Sophia Antipolis, France