Photometric Stereo Using Constrained Bivariate Regression for General Isotropic Surfaces

This paper presents a photometric stereo method that is purely pixelwise and handles general isotropic surfaces in a stable manner. Following the recently proposed sum-of-lobes representation of the isotropic reflectance function, we constructed a constrained bivariate regression problem where the regression function is approximated by smooth, bivariate Bernstein polynomials. The unknown normal vector was separated from the unknown reflectance function by considering the inverse representation of the image formation process, and then we could accurately compute the unknown surface normals by solving a simple and efficient quadratic programming problem. Extensive evaluations that showed the state-of-the-art performance using both synthetic and real-world images were performed.