Variational Uncalibrated Photometric Stereo under General Lighting

Bjoern Haefner, Zhenzhang Ye, Maolin Gao, Tao Wu, Yvain Quéau, Daniel Cremers

Abstract:

Photometric stereo (PS) techniques nowadays remain
constrained to an ideal laboratory setup where modeling
and calibration of lighting is amenable. To eliminate such
restrictions, we propose an efficient principled variational
approach to uncalibrated PS under general illumination. To
this end, the Lambertian reflectance model is approximated
through a spherical harmonic expansion, which preserves
the spatial invariance of the lighting. The joint recovery
of shape, reflectance and illumination is then formulated as
a single variational problem. There the shape estimation
is carried out directly in terms of the underlying perspective depth map, thus implicitly ensuring integrability and
bypassing the need for a subsequent normal integration. To
tackle the resulting nonconvex problem numerically, we undertake a two-phase procedure to initialize a balloon-like
perspective depth map, followed by a “lagged” block coordinate descent scheme. The experiments validate efficiency
and robustness of this approach. Across a variety of evaluations, we are able to reduce the mean angular error consistently by a factor of 2–3 compared to the state-of-the-art.