A Maximum Likelihood Surface Normal Estimation Algorithm for Helmholtz Stereopsis

Helmholtz stereopsis is a relatively recent reconstruction technique which is able to reconstruct scenes with arbitrary and unknown surface reflectance properties. Conventional implementations of the method estimate surface normal direction at each surface point via an eigenanalysis, thereby optimising an algebraic distance. We develop a more physically meaningful radiometric distance whose minimisation is shown to yield a Maximum Likelihood surface normal estimate. The proposed method produces more accurate results than algebraic methods on synthetic imagery and yields excellent reconstruction results on real data. Our analysis explains why, for some imaging configurations, a sub-optimal algebraic distance can yield good results.