A Non-convex Variational Approach to Photometric Stereo under Inaccurate Lighting

Abstract

This paper tackles the photometric stereo problem in the presence of inaccurate lighting, obtained either by calibration or by an uncalibrated photometric stereo method. Based on a precise modeling of noise and outliers, a robust variational approach is introduced. It explicitly accounts for self-shadows, and enforces robustness to castshadows and specularities by resorting to redescending Mestimators. The resulting non-convex model is solved by means of a computationally efficient alternating reweighted least-squares algorithm. Since it implicitly enforces integrability, the new variational approach can refine both the intensities and the directions of the lighting.

Dynamic photometric stereo method using multi-tap CMOS image sensor

“…In addition to this assumption, classical photometric stereo method assumes the target object has Lambertian surface, the light sources are parallel illumination and uniform, the direction of incident illumination is known, there is no cast shadow or occlusions, and the target scene is static. There are numerous research tackling these assumptions, non-Lambertian reflectance [14][15][16][17], surface including specular [18][19][20], cast shadow problem [21], point light source [22][23][24], the non-uniform lighting [25][26][27] and unknown lighting direction [28][29][30]. In case of a point light source, we can rewrite the Equation (2) as follows:…”

Variational Uncalibrated Photometric Stereo Under General Lighting

“…It is indeed well-known that Cauchy's estimator, being nonconvex, is robust against outliers; see for instance [42] in the context of PS. The scaling parameter λ = 0.15 is used in all experiments.…”

Semi-calibrated Near-Light Photometric Stereo

“…In addition, the semi-calibrated PS approach from [6] lacks robustness, as it is based on non-robust least-squares. The recent method in [7] solves this issue by resorting to a non-convex variational formulation: in the present paper we use the same numerical framework, but extend it to the case of nearby sources. Apart from fully uncalibrated ones [2,3,4], methods for PS with nondistant sources do not refine the intensities, and sometimes lack robustness.…”

“…However, existing methods for semi-calibrated PS [6,7] are restricted to distant sources. In addition, the semi-calibrated PS approach from [6] lacks robustness, as it is based on non-robust least-squares.…”

“…Instead of estimating the albedoρ(p) in each pixel p, we follow [7] and rather estimate the following "pseudo"-albedo:…”