Means and Averaging in the Group of Rotations

@article{Moakher2002MeansAA,
  title={Means and Averaging in the Group of Rotations},
  author={Maher Moakher},
  journal={SIAM J. Matrix Analysis Applications},
  year={2002},
  volume={24},
  pages={1-16}
}
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
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