Shape from Shading and Photometric Stereo Using Surface Approximation by Legendre Polynomials

Abstract

In this paper, a new iterative shape from shading (SFS) algorithm is proposed. In the proposed algorithm, the given 3D surface is approximated by Legendre polynomials and the relationships between the given surface and its derivatives are represented in matrix forms using a polynomial coefficient vector. Then the relative depth and its derivatives are iteratively computed by updating the coefficient vector. Also the proposed SFS algorithm is extended to a photometric stereo case. In the proposed photometric stereo algorithm, the reflectance map is linearized and the cost function expressed in quadratic matrix form is minimized. The relative depth and its derivatives are also obtained by updating them iteratively. Performance of the proposed SFS and photometric stereo algorithms is evaluated in terms of three different error measures: the brightness error, orientation error, and height error. In addition, a performance comparison of the proposed and conventional SFS algorithms is shown.