Pose Estimation of Quadratic Surfaces Using Range Image Data

Pose estimation of known quadratic surfaces from possibly noisy data is important in robotics, and there is room for generating improved algorithms which achieve global optinia, and if possible on line. Current algorithms frequently converge to local minima of the performance index and are unsuited for on line applications because of the intensive computer effort required. Algebraic solutions are first proposed based on a two stage optimization involving least squares estimation, or better the method of instrumental variables, and 3 x 3 matrix diagonalizations. The resulting estimates are optimal in a reasonable sense and can be implemented on line. In the noise free, finite data case, or in the infinite data, white noise case the results give zero error, and small error for the case of finite data and small noise. The first stage of the procedure ignores a priori knowledge of the surface shape and estimates the quadratic coefficient matrix via least squares or the method of instrumental variables. The second stage exploits the priori shape information to estimate the pose of the object using diagonalization of 3 x 3 matrices.