Bayesian Helmholtz Stereopsis with Integrability Prior

Nadejda Roubtsova,Jean-Yves Guillemaut

doi:10.1109/tpami.2017.2749373

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.

Highlights

Helmholtz Stereopsis (HS) [14] tackles photometric complexity by exclusively exploiting the generic BRDF symmetry of reciprocity instead of a specific reflectance model through tailored acquisition
The proposed integrability promoting dist.Depth-Normal Consistency Prior (DNprior) is more robust to noise than the earlier corr.DNprior resulting in depth accuracy improvements from just under 0.5 mm to 2-4 mm, though a similar normal error
We qualitatively evaluate the performance of the five reconstruction methods on eight real datasets from [49]: the three specular and one Lambertian with intricate geometry here as well as four others of varying complexity in the supplementary material, available online

Summary

Introduction

Helmholtz Stereopsis (HS) [14] tackles photometric complexity by exclusively exploiting the generic BRDF symmetry of reciprocity instead of a specific reflectance model through tailored acquisition. Its normal constraint is uniquely independent of the reflectance model which in addition provides a likelihood of the Manuscript received 24 Nov. 2016; revised 13 June 2017; accepted 29 Aug. 2017. The method’s surface characterisation is more complete, with an unexplored potential for further reconstruction improvements, than the one-sided depth maps of conventional stereo or the normal fields of photometric stereo. A noisy depth map obtained by independent per-point depth search indexes normals. Normal integration reveals a surface of a much higher resolution than the original depth map and camouflages the errors by enforcing integrability a posteriori. The result is incorrect as the integrated normal field is comprised of inaccurate spatially inconsistent normals reflecting the noise of the indexing depth maps, whose continuity is never enforced.

Methods

Results

Conclusion