Geodesic
Numerical algorithms for perspective shape from shading
Kybernetika, Tome 46 (2010) no. 2, pp. 207-225.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The Shape-From-Shading (SFS) problem is a fundamental and classic problem in computer vision. It amounts to compute the 3-D depth of objects in a single given 2-D image. This is done by exploiting information about the illumination and the image brightness. We deal with a recent model for Perspective SFS (PSFS) for Lambertian surfaces. It is defined by a Hamilton–Jacobi equation and complemented by state constraints boundary conditions. In this paper we investigate and compare three state-of-the-art numerical approaches. We begin with a presentation of the methods. Then we discuss the use of some acceleration techniques, including cascading multigrid, for all the tested algorithms. The main goal of our paper is to analyze and compare recent solvers for the PSFS problem proposed in the literature.
Classification : 35L60, 65D19, 65N06, 65N12, 68T45, 68U10
Keywords: hyperbolic partial differential equation; Hamilton–Jacobi equation; finite difference method; semi-Lagrangian scheme; Shape-from-Shading 
@article{KYB_2010__46_2_a1,
     author = {Breuss, Michael and Cristiani, Emiliano and Durou, Jean-Denis and Falcone, Maurizio and Vogel, Oliver},
     title = {Numerical algorithms for perspective shape from shading},
     journal = {Kybernetika},
     pages = {207--225},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2010},
     mrnumber = {2663598},
     zbl = {1198.68266},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_2_a1/}
}
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Breuss, Michael; Cristiani, Emiliano; Durou, Jean-Denis; Falcone, Maurizio; Vogel, Oliver. Numerical algorithms for perspective shape from shading. Kybernetika, Tome 46 (2010) no. 2, pp. 207-225. http://geodesic.mathdoc.fr/item/KYB_2010__46_2_a1/