BibTeX
@MISC{Ulich96aprovably,
author = {G. Ulich},
title = {A Provably Convergent Method for the Non-Linear Image Irradiance Equation},
year = {1996}
}
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Abstract
In this paper we present a provably convergent method for the Shape from Shading problem in the case of a Lambertian reflectance map. The non-linear image irradiance equation is approximated by a Taylor-expansion. The resulting linear PDE is solved numerically by an implicit, sequentiell method. We prove its convergence and present several test results. 1 Introduction The basic problem in Shape from Shading (SFS) is to recover the shape z(x,y) of a surface from its variation in brightness. If we denote the reflectance map by R(p,q), where (p,q) is the surface gradient with p = z x and q = z y at a point (x,y) and the image brightness at this point by E(x,y), then, under certain assumptions (see [2]) we have the image irradiance equation R(p; q) = E(x; y): (1) The reflectance map depends on the properties of the surface material of the object, and the distribution of light sources. For a Lambertian surface illuminated by a single point source far away from the object, we can use foll...
Keyphrases
non-linear image irradiance equation provably convergent method reflectance map linear pde surface gradient basic problem image brightness lambertian surface single point source surface material present several test result convergent method certain assumption lambertian reflectance map sequentiell method image irradiance equation light source
