Solving Uncalibrated Photometric Stereo Using Fewer Images by Jointly Optimizing Low-rank Matrix Completion and Integrability

We introduce a new, integrated approach to uncalibrated photometric stereo. We perform 3D reconstruction of Lambertian objects using multiple images produced by unknown, directional light sources. We show how to formulate a single optimization that includes rank and integrability constraints, allowing also for missing data. We then solve this optimization using the Alternating Direction Method of Multipliers (ADMM). We conduct extensive experimental evaluation on real and synthetic data sets. Our integrated approach is particularly valuable when performing photometric stereo using as few as 4-6 images, since the integrability constraint is capable of improving estimation of the linear subspace of possible solutions. We show good improvements over prior work in these cases.