Numerical Reflectance Compensation for Non-Lambertian Photometric Stereo

The surface normal estimation from photometric stereo becomes less reliable when the surface reflectance deviates from the Lambertian assumption. The non-Lambertian effect can be explicitly addressed by physics modeling to the reflectance function, at the cost of introducing highly nonlinear optimization. This paper proposes a numerical compensation scheme that attempts to minimize the angular error to address the non-Lambertian photometric stereo problem. Due to the multifaceted influence in the modeling of non-Lambertian reflectance in photometric stereo, directly minimizing the angular errors of surface normal is a highly complex problem. We introduce an alternating strategy, in which the estimated reflectance can be temporarily regarded as a known variable, to simplify the formulation of angular error. To reduce the impact of inaccurately estimated reflectance in this simplification, we propose a numerical compensation scheme whose compensation weight is formulated to reflect the reliability of estimated reflectance. Finally, the solution for the proposed numerical compensation scheme is efficiently computed by using cosine difference to approximate the angular difference. The experimental results show that our method can significantly improve the performance of the state-of-the-art methods on both synthetic data and real data with small additive costs. Moreover, our method initialized by results from the baseline method (least-square-based) achieves the state-of-the-art performance on both synthetic data and real data with significantly smaller overall computation, i.e. , about eight times faster compared with the state-of-the-art methods.