Provably Convergent Methods for the Linear and Nonlinear Shape from Shading Problem

Authors:
Gabriele Ulich
Affiliations:
Fachbereich Mathematik, TU Berlin, MA 6-2, Straße des 17 Juni 136, 10623 Berlin, Germany. E-mail: ulich@math.tu-berlin.de
Venue:
Journal of Mathematical Imaging and Vision
Year:
1998

Citing 5
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Abstract

In this paper we present provably convergent algorithms forthe linear and nonlinear Shape from Shading problem in the case of aLambertian reflectance map. For the linear problem we discuss twoexplicit methods and one implicit method, for which we proveconvergence for certain light directions. The method for thenonlinear Shape from Shading problem is based on a linearapproximation of the image irradiance equation. For the resultinglinear PDE the implicit method for the linear problem can be applied.We prove convergence of this method for all light directions.