Numerical algorithms for perspective shape from shading

Michael Breuss; Emiliano Cristiani; Jean-Denis Durou; Maurizio Falcone; Oliver Vogel

Kybernetika (2010)

  • Volume: 46, Issue: 2, page 207-225
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Breuss, Michael, et al. "Numerical algorithms for perspective shape from shading." Kybernetika 46.2 (2010): 207-225. <http://eudml.org/doc/196399>.

@article{Breuss2010,
abstract = {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.},
author = {Breuss, Michael, Cristiani, Emiliano, Durou, Jean-Denis, Falcone, Maurizio, Vogel, Oliver},
journal = {Kybernetika},
keywords = {hyperbolic partial differential equation; Hamilton–Jacobi equation; finite difference method; semi-Lagrangian scheme; Shape-from-Shading; finite difference method; hyperbolic partial differential equation; Hamilton-Jacobi equation; semi-Lagrangian scheme; shape-from-shading},
language = {eng},
number = {2},
pages = {207-225},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Numerical algorithms for perspective shape from shading},
url = {http://eudml.org/doc/196399},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Breuss, Michael
AU - Cristiani, Emiliano
AU - Durou, Jean-Denis
AU - Falcone, Maurizio
AU - Vogel, Oliver
TI - Numerical algorithms for perspective shape from shading
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 2
SP - 207
EP - 225
AB - 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.
LA - eng
KW - hyperbolic partial differential equation; Hamilton–Jacobi equation; finite difference method; semi-Lagrangian scheme; Shape-from-Shading; finite difference method; hyperbolic partial differential equation; Hamilton-Jacobi equation; semi-Lagrangian scheme; shape-from-shading
UR - http://eudml.org/doc/196399
ER -

References

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