@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...