On Averaging Rotations 
Claus Gramkow

Abstract  In this paper two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very often the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong to a nonlinear manifold and renormalization or orthogonalization must be applied to obtain proper rotations. These latter steps have been viewed as ad hoc corrections for the errors introduced by assuming a vector space. The article shows that the two approximative methods can be derived from natural approximations to the Riemannian metric, and that the subsequent corrections are inherent in the least squares estimation 
Keywords  averaging rotations, Riemannian metric; matrix; quaternion 
Type  Journal paper [With referee] 
Journal  Journal of Mathematical Imaging and Vision 
Editors  
Year  2002 Vol. 15 No. 12 pp. 716 
ISBN / ISSN  09249907 
BibTeX data  [bibtex] 
IMM Group(s)  Image Analysis & Computer Graphics 