Multi-image photometric stereo using surface approximation by Legendre polynomials

Abstract

This paper presents a photometric stereo algorithm that reconstructs object shapes from multiple images, in which given 3D surfaces are approximated by Legendre polynomials and the relationships between the given surface and its derivatives are represented in matrix forms in terms of a polynomial coefficient vector. The reflectance map is linearized and the cost function expressed in quadratic matrix form in terms of the polynomial coefficient vector is minimized. The relative depth and its derivatives are obtained by updating them iteratively. Computer simulation with various noiseless/noisy sets of test images shows that the performance of the presented two-image photometric stereo algorithm is comparable to that of the conventional methods in terms of three different error measures: brightness error, orientation error and height error. Also the performance comparison of the presented and conventional three-image photometric stereo algorithms for the noiseless/noisy sets of images is shown.