A Probabilistic Framework for Specular Shape-from-Shading

One of the problems that hinders conventional methods for shape-from-shading is the presence of local specularities which may be misidenti.ed as high curvature surface features. In this paper we address the problem of estimating the proportions of Lambertian and specular re1ection components in order to improve the quality of surface normal information recoverable using shape-from-shading. The framework for our study is provided by the iterated conditional modes algorithm. We develop a maximum a posteriori probability (MAP) estimation method for estimating the mixing proportions for Lambertian and specular re1ectance, and also, for recovering local surface normals. The MAP estimation scheme has two model ingredients. First, there are separate conditional measurement densities which describe the distributions of surface normal directions for the Lambertian and specular re1ectance components. We experimentally compare three di7erent models for the specular component. The second ingredient is a smoothness prior which models the distribution of surface normal directions over local image regions. We demonstrate the utility of method on real-world data. Ground truth data is provided by imagery obtained with crossed polaroid .lters. This reveals not only that the method accurately estimates the proportion of specular re1ection, but that it also results in good surface normal reconstruction in the proximity of specular highlights. ? 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.