Abstract
In this article two common approaches to averaging rotations are
compared to a more advanced approach based on a Riemannian metric.
Very offten 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
renromalization 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 inherient in the least squares
estimation. Keywords: averaging rotations, Riemannian metric,
matrix, quaternion
Original language | English |
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Title of host publication | Proceedings from The 11th. Scandinavian Conference on Image Analysis |
Place of Publication | Lyngby |
Publication date | 1999 |
Pages | 615-620 |
Publication status | Published - 1999 |
Event | 11th Scandinavian Conference on Image Analysis (SCIA) - Kangerlussuaq, Greenland Duration: 7 Jun 1999 → 11 Jun 1999 Conference number: 11 |
Conference
Conference | 11th Scandinavian Conference on Image Analysis (SCIA) |
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Number | 11 |
Country/Territory | Greenland |
City | Kangerlussuaq |
Period | 07/06/1999 → 11/06/1999 |