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Proceedings Paper

Optimal estimation and tracking of general rotations using geometric algebra with applications in computer vision
Author(s): Sahan S. Hiniduma Udugama Gamage; Joan Lasenby
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Paper Abstract

In this paper we discuss an alternative approach to optimal and near optimal tracking and estimation of rotations with applications in vision systems. The technique used here will be that of Geometric Algebra (GA) which provides a very elegant and efficient framework for dealing with geometric entities and transformations. It is coordinate-free and has associated with it a well-developed calculus and multi-linear algebra. Much of the power of GA lies in the way it represents and interprets rotations. Estimation and tracking of geometric entities are important in many fields -- e.g. 3D object tracking, multi-camera systems, space and terrestrial navigation etc., and to date Kalman filter techniques have provided a fast and efficient means of solving such problems. We will show how Kalman filters with conventional type state- spaces are derived in a GA setting and then extend these ideas to deal with a state-space consisting of rotors. Taking advantage of the fact that we are able to write down a minimally parameterized cost function and differentiate with respect to rotors in the GA framework, a solution to the tracking and optimal orientation estimation problem can be obtained efficiently. The resulting algorithm is applied to a variety of real and simulated data using articulated models. In particular, we will look at tracking human motion data from an optical motion capture unit. The extraction, interpolation, modification and classification of the underlying motion is also discussed with reference to future research directions.

Paper Details

Date Published: 23 October 2000
PDF: 11 pages
Proc. SPIE 4117, Vision Geometry IX, (23 October 2000); doi: 10.1117/12.404828
Show Author Affiliations
Sahan S. Hiniduma Udugama Gamage, Cambridge Univ. (United Kingdom)
Joan Lasenby, Cambridge Univ. (United Kingdom)

Published in SPIE Proceedings Vol. 4117:
Vision Geometry IX
Longin Jan Latecki; David M. Mount; Angela Y. Wu, Editor(s)

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