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. * Authors contributed equally. 1 https://github.com/zhenzhangye/general_ups
Figure 1. Left: We present a novel approach for isometric multi-shape matching based on matching each shape to a (virtual) universe shape (shown semi-transparent). Our formulation represents point-to-point correspondences between shapes i and j as the composition of the shape-to-universe permutation matrix Pi and the universe-to-shape permutation matrix P T j . By doing so, the pairwise matchings Pij = PiP j are by construction cycle-consistent. Middle: Our formulation successfully solves isometric multi-matching of partial shapes. Right: Due to the cycle-consistency we can use our correspondences to faithfully transfer textures across a shape collection.
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