A Differential Volumetric Approach to Multi-View Photometric Stereo

Highly accurate 3D volumetric reconstruction is still an open research topic where the main difficulties are usually related to merging rough estimations with high frequency details. One of the most promising methods is the fusion between multi-view stereo and photometric imaging 3D shape reconstruction techniques. However, beside the intrinsic difficulties that multi-view stereo and photometric stereo have to make them working reliably, supplementary problems raise when considered together. Most importantly, the projection of the fine details usually retrievable with photometric stereo onto the rough multi-view stereo reconstruction is difficult to handle. In this work, we present a volumetric approach to the multi-view photometric stereo problem defined by a unified differential model. The key to our method is the signed distance field parameterisation which avoids the complex step of re-projecting high frequency details as the parameterisation of the whole volume allows a photometric modeling on the volume itself efficiently dealing with occlusions, discontinuities, etc. The relation between the surface normals and the gradient of the signed distance field leads to a homogeneous linear partial differential equation. A variational optimisation is adopted in order to combine multiple images from multiple points of view in a single system avoiding the need of merging depth maps. Our approach is evaluated on synthetic and real data-sets and achieves state-of-the-art results.