A Neural Height-Map Approach for the Binocular Photometric Stereo
  Problem
Fotios Logothetis Ignas Budvytis Roberto Cipolla
In this work we propose a novel, highly practical, binocular photometric
stereo (PS) framework, which has same acquisition speed as single view PS,
however significantly improves the quality of the estimated geometry.
  As in recent neural multi-view shape estimation frameworks such as NeRF,
SIREN and inverse graphics approaches to multi-view photometric stereo (e.g.
PS-NeRF) we formulate shape estimation task as learning of a differentiable
surface and texture representation by minimising surface normal discrepancy for
normals estimated from multiple varying light images for two views as well as
discrepancy between rendered surface intensity and observed images. Our method
differs from typical multi-view shape estimation approaches in two key ways.
First, our surface is represented not as a volume but as a neural heightmap
where heights of points on a surface are computed by a deep neural network.
Second, instead of predicting an average intensity as PS-NeRF or introducing
lambertian material assumptions as Guo et al., we use a learnt BRDF and perform
near-field per point intensity rendering.
  Our method achieves the state-of-the-art performance on the DiLiGenT-MV
dataset adapted to binocular stereo setup as well as a new binocular
photometric stereo dataset - LUCES-ST.