Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Least-Squares Estimation of Transformation Parameters Between Two Point Patterns
IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature-Based Registration of Medical Images: Estimation and Validation of the Pose Accuracy
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention
Distributed consensus on camera pose
IEEE Transactions on Image Processing
4D shape registration for dynamic electrophysiological cardiac mapping
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
On averaging in clifford groups
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Averaging complex subspaces via a Karcher mean approach
Signal Processing
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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 non-linear manifold and re-normalization 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.