Bayesian Helmholtz Stereopsis with Integrability Prior

Abstract

Helmholtz Stereopsis is a 3D reconstruction method uniquely independent of surface reflectance. Yet, its sub-optimal maximum likelihood formulation with drift-prone normal integration limits performance. Via three contributions this paper presents a complete novel pipeline for Helmholtz Stereopsis. First, we propose a Bayesian formulation replacing the maximum likelihood problem by a maximum a posteriori one. Second, a tailored prior enforcing consistency between depth and normal estimates via a novel metric related to optimal surface integrability is proposed. Third, explicit surface integration is eliminated by taking advantage of the accuracy of prior and high resolution of the coarse-to-fine approach. The pipeline is validated quantitatively and qualitatively against alternative formulations, reaching sub-millimetre accuracy and coping with complex geometry and reflectance.