Point Estimation of the Central Direction of Random Rotations in SO(3)

• Activity Number: 513
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Bryan Stanfill*+ and Ulrike Genschel and Heike Hofmann and Dan Nordman
• Companies: Iowa State University and Iowa State University and Iowa State University and Iowa State University
• Keywords: Random rotations ; Central direction ; Uniform-axis random spin distributions ; Distance metrics

Abstract

Random rotations in SO(3) (the space of 3x3 orthogonal matrices with determinant 1) are used to model three-dimensional orientations in fields such as computer science, kinesiology, material science, and even astrophysics. Currently, several estimators of the central direction are suggested in the literature but little attention has been paid to a comparison study examining which provides the best estimate. We compare four favorable estimators across three commonly used uniform-axis random spin distributions. Three of the estimators have been studied in the literature thus far at varying depths whereas the fourth estimator is adapted to rotation matrices for the first time. For the von Mises distribution the normalized spatial median yields preferable results whereas for the Cayley and Fisher distributions an estimator based on the L2 norm is preferred. These findings, when applied to pu