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
Optimal Lower Bound for Generalized Median Problems in Metric Space
Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
An orientation update message filtering algorithm in collaborative virtual environments
Journal of Computer Science and Technology
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Real-Time 3D Body Pose Tracking from Multiple 2D Images
AMDO '08 Proceedings of the 5th international conference on Articulated Motion and Deformable Objects
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
Hopping odometry: motion estimation with selective vision
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
IPCAI'10 Proceedings of the First international conference on Information processing in computer-assisted interventions
Proceedings of the ACM workshop on 3D object retrieval
Efficient Video Rectification and Stabilisation for Cell-Phones
International Journal of Computer Vision
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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.