A Bayesian framework for enhanced geometric reconstruction of complex objects by Helmholtz stereopsis

Helmholtz stereopsis is an advanced 3D reconstruction technique for objects with arbitrary reflectance properties that uniquely characterises surface points by both depth and normal. Traditionally, in Helmholtz stereopsis consistency of depth and normal estimates is assumed rather than explicitly enforced. Furthermore, conventional Helmholtz stereopsis performs maximum likelihood depth estimation without neighbourhood consideration. In this paper, we demonstrate that reconstruction accuracy of Helmholtz stereopsis can be greatly enhanced by formulating depth estimation as a Bayesian maximum a posteriori probability problem. In reformulating the problem we introduce neighbourhood support by formulating and comparing three priors: a depth-based, a normal-based and a novel depth-normal consistency enforcing one. Relative performance evaluation of the three priors against standard maximum likelihood Helmholtz stereopsis is performed on both real and synthetic data to facilitate both qualitative and quantitative assessment of reconstruction accuracy. Observed superior performance of our depth-normal consistency prior indicates a previously unexplored advantage in joint optimisation of depth and normal estimates.