Constructing iterative matching algorithms with the use of Lie theory: three-dimensional orientation example

Iterative algorithms are described for normalizing-coefficient vectors computed by expanding functions on the unit sphere into a series of spherical 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.