This paper analyses the computational complexity and stability of an online algorithm recently proposed for learning rotations. The proposed algorithm involves multiplicative updates that are matrix exponentials of skew-symmetric matrices comprising the Lie algebra of the rotation group. The rank-deficiency of the skewsymmetric matrices involved in the updates is exploited to reduce the updates to a simple quadratic form. The Lyapunov stability of the algorithm is established and the application of the algorithm to registration of pointclouds in n-dimensional Euclidean space is discussed.
Raman Arora, William A. Sethares