  We conduct a thorough study of photometric stereo under nearby point light
source illumination, from modeling to numerical solution, through calibration.
In the classical formulation of photometric stereo, the luminous fluxes are
assumed to be directional, which is very difficult to achieve in practice.
Rather, we use light-emitting diodes (LEDs) to illuminate the scene to
reconstruct. Such point light sources are very convenient to use, yet they
yield a more complex photometric stereo model which is arduous to solve. We
first derive in a physically sound manner this model, and show how to calibrate
its parameters. Then, we discuss two state-of-the-art numerical solutions. The
first one alternatingly estimates the albedo and the normals, and then
integrates the normals into a depth map. It is shown empirically to be
independent from the initialization, but convergence of this sequential
approach is not established. The second one directly recovers the depth, by
formulating photometric stereo as a system of PDEs which are partially
linearized 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 reweighted
least-squares scheme for solving the original system of PDEs, without resorting
to image ratios for linearization. Finally, we extend this study to the case of
RGB images.
