SHAPE FROM SHADING AND PHOTOMETRIC STEREO USING SURFACE APPROXIMATIONBY LEGENDRE POLYNOMIALS

In this paper, a new iterative shape from shading (SFS) algorithm is p roposed. In the proposed algorithm, the given 3D surface is approximat ed by Legendre polynomials and the relationships between the given sur face and its derivatives are represented in matrix forms using a polyn omial 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 th e proposed photometric stereo algorithm, the reflectance map is linear ized and the cost function expressed in quadratic matrix farm is minim ized. The relative depth and its derivatives are also obtained by upda ting them iteratively. Performance of the proposed SFS and photometric stereo algorithms is evaluated in terms of three different error meas ures: the brightness error, orientation error, and height error. In ad dition, a performance comparison of the proposed and conventional SFS algorithms is shown. (C) 1997 Academic Press.