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

Abstract

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 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

Optimisation of Classic Photometric Stereo by Non-convex Variational Minimisation

“…without employing ratios. Other methods [31,33] overcome the nonlinearity by absorbing it in the auxiliary albedo variable. Again, the solution is not that of the original problem (5) which remains, to the best of our knowledge, unsolved.…”

“…Observe that, if A(z, ρ) and b(z, ρ) were constant, problem (19) would be a linear least squares problem with respect to z. Let us remark that (19) can be easily extended to include more realistic reflectance [15,16] and lighting [28,31] models, as well as more robust estimators [14,33]: this only requires to change the definition of f , which stands for the global reprojection error E R .…”

Light Structure from Pin Motion: Geometric Point Light Source Calibration

“…Park et al (2014) and Ma et al (2019) handle non-isotropic lights and jointly estimate the light position and RID from imagery of shading and specular reflections on a planar calibration target. In the context of photometric stereo, Quéau et al (2018), Collins and Bartoli (2012), and Song et al (2018) proposed pipelines that first perform geometric calibration by specularity-based triangulation and then estimate the RID from shading on a planar target. Regarding the geometric calibration, these methods have shown to obtain a more accurate estimation compared to the plane-based methods of Park et al (2014) and Ma et al (2019).…”

Variational Reflectance Estimation from Multi-view Images

“…where ρ (x) and σ i denote, respectively, the colored reflectance and the i-th colored lighting vector, relatively to the response of the camera in channel . A more complete study of Model (13) is presented in [31].…”

“…Proving convergence of our scheme is beyond the scope of this paper, but the proof could certainly be derived from that in [31], where a similar alternating majorization-minimization called "alternating reweighted least-squares" is used. Note, however, that the convergence rate seems to be sublinear (see Figure 4), hence possibly faster numerical strategies could be explored in the future.…”