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3D shape from shading algorithm

The Odyssee research group has proposed a rigorous and realistic solution of the Lambertian Shape From Shading problem. The power of the approach is threefold.

First the work is based on a rigorous mathematical method: A "new'' notion of weak solutions (in the viscosity sense) is defined which does not necessarily requires boundary data (contrary to the work of well-known classical approaches (Rouy-Tourin:92, Camilli-Falcone:96, Falcone-Sagona-etal:01) and which allows to define a solution as soon as the image is (Lipschitz) continuous (contrary to the work of [Oliensis:91,Dupuis-Oliensis:94]). The existence and uniqueness of this (new) solution is proved and approximated by using a provably convergent algorithm.

Second it improves the applicability of the Shape From Shading to real images: The Odyssee research group completed the realistic work of [Prados-Faugeras:03,Tankus-Sochen-etal:03], by modelling the problem with a pinhole camera and with a single point light source located at the optical centre. This new modelization appeared very relevant for various applications. Moreover, the algorithm can deal with images containing discontinuities and black shadows. It is very robust to pixel noise and to errors on parameters. It is also generic: i.e. a unique algorithm, which can compute numerical solutions of the various perspective and orthographic Shape From Shading models.

Finally, the algorithm proposed by the Odyssee research group seems to be the most efficient iterative algorithm of the Shape From Shading literature. It has been successfully applied and validated in three different applications: face reconstruction, documents restoration and medical imaging.

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