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

• Published in: Journal of mathematical imaging and vision Vol. 60; no. 3; pp. 313 - 340
• Main Authors: Quéau, Yvain, Durix, Bastien, Wu, Tao, Cremers, Daniel, Lauze, François, Durou, Jean-Denis
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2018; Springer Nature B.V; Springer Verlag
• Subjects: Albedo; Applications of Mathematics; Calibration; Color imagery; Computer Science; Computer Vision and Pattern Recognition; Convergence; Fluxes; Image Processing and Computer Vision; Light emitting diodes; Light sources; Mathematical Methods in Physics; Mathematical models; Nonlinear differential equations; Nonlinear equations; Organic light emitting diodes; Partial differential equations; Photometry; Signal,Image and Speech Processing; Variational methods; 3D-reconstruction; Photometric stereo; Point light sources; Alternating reweighted least-squares
• ISSN: 0924-9907; 1573-7683
• DOI: 10.1007/s10851-017-0761-1

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 to illuminate the scene to be reconstructed. 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 nonlinear partial differential equations (PDEs), which are 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 nonlinear PDEs. Finally, we extend this study to the case of RGB images.