An Efficient and Stable Algorithm for Learning Rotations

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 skew-symmetric 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 point-clouds in n-dimensional Euclidean space is discussed.