Evaluation of Algorithms for Linear Shape from Shading

Abstract

We analyse different sequential algorithms for the recovery of object shape from a single shading pattern generated under the assumption of a linear reflectance map. The algorithms are based on the finite difference approximation of the derivatives. They operate on a rectangular discrete image (or part of it) and use the height of the sought-after surface along a curve in the image (image boundary) as initial data. The evaluation of different numerical schemes is achieved by comparing stability, convergence, and domains of influence of each scheme in question. The relative difficulty of handling a linear case indicates that the case of non-linear reflectance maps is far from being trivial.