Reconstructing relief surfaces

This paper generalizes Markov Random Field (MRF) stereo methods to the generation of surface relief (height) fields rather than disparity or depth maps. This generalization enables the reconstruction of complete object models using the same algorithms that have been previously used to compute depth maps in binocular stereo. In contrast to traditional dense stereo where the parametrization is image based, here we advocate a parametrization by a height field over any base surface. In practice, the base surface is a coarse approximation to the true geometry, e.g., a bounding box, visual hull or triangulation of sparse correspondences, and is assigned or computed using other means. A dense set of sample points is defined on the base surface, each with a fixed normal direction and unknown height value. The estimation of heights for the sample points is achieved by a belief propagation technique. Our method provides a viewpoint independent smoothness constraint, a more compact parametrization and explicit handling of occlusions. We present experimental results on real scenes as well as a quantitative evaluation on an artificial scene.