Sampling Rotation Groups Using Successive Orthogonal Images

Julie Mitchell

Math Department, University of Wisconsin-Madison

The ability to construct uniform deterministic samples of rotation groups is useful in many contexts, but there are inherent mathematical difficulties preventing an exact solution. Here, we present Successive Orthogonal Images, an effective means for uniform deterministic sampling of orthogonal groups. The method is valid in any dimension, and analytic bounds are provided on the sampling uniformity. Numerical comparisons with other sampling methods are given for the three-dimensional case. We make use of non-Riemannian distance metrics that are group invariant, and locally compatible with the Haar measure. In addition, our results make use of a semi-unique decomposition of any orthogonal matrix into the product of simple planar rotations.

Deepak Ramachandran

Last modified: Mon Mar 27 11:36:13 CST 2006