Abstract
Many 3D reconstruction techniques are based on the assumption of prior knowledge of the object's surface reflectance, which severely restricts the scope of scenes that can be reconstructed. In contrast, Helmholtz Stereopsis (HS) employs Helmholtz Reciprocity to compute the scene geometry regardless of its Bidirectional Reflectance Distribution Function (BRDF). Despite this advantage, most HS implementations to date have been limited to 2.5D reconstruction, with the few extensions to full 3D being generally limited to a local refinement due to the nature of the optimisers they rely on. In this paper, we propose a novel approach to full 3D HS based on Markov Random Field (MRF) optimisation. After defining a solution space that contains the surface of the object, the energy function to be minimised is computed based on the HS quality measure and a normal consistency term computed across neighbouring surface points. This new method offers several key advantages with respect to previous work: the optimisation is performed globally instead of locally; a more discriminative energy function is used, allowing for better and faster convergence; a novel visibility handling approach to take advantage of Helmholtz reciprocity is proposed; and surface integration is performed implicitly as part of the optimisation process, thereby avoiding the need for an additional step. The approach is evaluated on both synthetic and real scenes, with an analysis of the sensitivity to input noise performed in the synthetic case. Accurate results are obtained on both types of scenes. Further, experimental results indicate that the proposed approach significantly outperforms previous work in terms of geometric and normal accuracy.