Means and Averaging in the Group of Rotations

  title={Means and Averaging in the Group of Rotations},
  author={Maher Moakher},
  journal={SIAM J. Matrix Analysis Applications},
In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to the usual arithmetic mean of the given rotation matrices. The mean rotation associated with the intrinsic metric on SO(3) is the Riemannian center of mass of the given rotation matrices. We show that… CONTINUE READING
Highly Influential
This paper has highly influenced 37 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 345 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper


Publications citing this paper.
Showing 1-10 of 224 extracted citations

Geometric Science of Information

Lecture Notes in Computer Science • 2017
View 8 Excerpts
Highly Influenced

Non-iterative, fast SE(3) path smoothing

2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) • 2016
View 5 Excerpts
Highly Influenced

Prediction of apparent trabecular bone stiffness through fourth-order fabric tensors.

Biomechanics and modeling in mechanobiology • 2016
View 4 Excerpts
Highly Influenced

Underground Incrementally Deployed Magneto-Inductive 3-D Positioning Network

IEEE Transactions on Geoscience and Remote Sensing • 2016
View 4 Excerpts
Highly Influenced

Distances and Means of Direct Similarities

International Journal of Computer Vision • 2014
View 4 Excerpts
Highly Influenced

Riemannian Means on Special Euclidean Group and Unipotent Matrices Group

TheScientificWorldJournal • 2013
View 7 Excerpts
Highly Influenced

346 Citations

Citations per Year
Semantic Scholar estimates that this publication has 346 citations based on the available data.

See our FAQ for additional information.


Publications referenced by this paper.
Showing 1-10 of 23 references

Differential Geometry: Manifolds

M. Berger, B. Gostiaux
Curves, and Surfaces, Springer-Verlag, New York • 1988
View 4 Excerpts
Highly Influenced

Maximum likelihood estimation for the matrix von Mises-Fisher and Bingham distributions

P. E. Jupp, K. V. Mardia
Ann. Statist., 7 • 1979
View 5 Excerpts
Highly Influenced

The von Mises-Fisher matrix distribution in orientation statistics

C. G. Khatri, K. V. Mardia
J. R. Stat. Soc. Ser. B, 39 • 1977
View 5 Excerpts
Highly Influenced

Jacobi fields and Finsler metrics on compact Lie groups with an application to differentiable pinching problem

K. Grove, H. Karcher, E. A. Ruh
Math. Ann., 211 • 1974
View 3 Excerpts
Highly Influenced

Lie-group methods

A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett, A. Zanna
Acta Numerica, 9 • 2000
View 1 Excerpt

Geometrical Methods in Robotics

Monographs in Computer Science • 1996
View 2 Excerpts

Optimization and Dynamical Systems

Proceedings of the IEEE • 1996
View 1 Excerpt

Similar Papers

Loading similar papers…