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We conduct a thorough study of photometric stereo under nearby point lightsource illumination, from modeling to numerical solution, through calibration.In the classical formulation of photometric stereo, the luminous fluxes areassumed to be directional, which is very difficult to achieve in practice.Rather, we use light-emitting diodes (LEDs) to illuminate the scene toreconstruct. Such point light sources are very convenient to use, yet theyyield a more complex photometric stereo model which is arduous to solve. Wefirst derive in a physically sound manner this model, and show how to calibrateits parameters. Then, we discuss two state-of-the-art numerical solutions. Thefirst one alternatingly estimates the albedo and the normals, and thenintegrates the normals into a depth map. It is shown empirically to beindependent from the initialization, but convergence of this sequentialapproach is not established. The second one directly recovers the depth, byformulating photometric stereo as a system of PDEs which are partiallylinearized using image ratios. Although the sequential approach is avoided,initialization matters a lot and convergence is not established either.Therefore, we introduce a provably convergent alternating reweightedleast-squares scheme for solving the original system of PDEs, without resortingto image ratios for linearization. Finally, we extend this study to the case ofRGB images.

LED-based Photometric Stereo: Modeling, Calibration and Numerical Solution