Surface Geometric Constraints for Stereo in Belief Propagation

Belief propagation has been shown to be a powerful inference mechanism for stereo correspondence. However the classical formulation of belief propagation implicitly imposes the frontal parallel plane assumption in the compatibility matrix for exploiting contextual information, since the priors perfer no depth (disparity) change in surrounding neighborhoods. This results in systematic errors for slanted or curved surfaces. To eliminate these errors we propose to use contextual information geometrically, and show how to encode surface differential geometric properties in the compatibility matrix for stereo correspondence. This enforces consistency for both depth and surface normal, extending the traditional formulation beyond consistency for (constant) depth. With such geometric contextual information, the belief propagation algorithm shows dramatic improvement on generic non-frontal parallel scenes. Several such examples are provided.