A probabilistic framework for specular shape-from-shading

In this paper we address the problem of separating Lambertian and specular reflection 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 the two reflectances, 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 normals for the two reflectance components. The second ingredient is a smoothness prior which models the distribution of surface normals over local image regions. We experiment with the method on real-world data. Ground truth data are provided by the imagery obtained with crossed polaroid filters. This reveals not only that the method accurately estimates the proportion of specular reflection, but that it also results in good surface normal reconstruction in the proximity of specular highlights.