Rotational symmetry: the Lie group SO(3) and its representations

Abstract

The paper describes iterative algorithms to normalize coefficient vectors computed by expanding functions on the unit sphere into a series of surface harmonics. Typical applications of the normalization procedure are the matching of different three-dimensional images, orientation estimations in low-level image processing or robotics. The method uses general methods from the theory of Lie-groups and Lie-algebras to linearize the highly-nonlinear original problem and can therefore also be adapted to applications involving groups different from the group of three-dimensional rotations. The performance of the algorithm is illustrated with a few experiments involving random coefficient vectors.