Optimal estimation and tracking of general rotations using geometric algebra with applications in computer vision

Sahan S. Hiniduma Udugama Gamage; Joan Lasenby

doi:10.1117/12.404828

23 October 2000 Optimal estimation and tracking of general rotations using geometric algebra with applications in computer vision

Sahan S. Hiniduma Udugama Gamage, Joan Lasenby

Author Affiliations +

Proceedings Volume 4117, Vision Geometry IX; (2000) https://doi.org/10.1117/12.404828
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

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.

Citation Download Citation

Sahan S. Hiniduma Udugama Gamage and Joan Lasenby "Optimal estimation and tracking of general rotations using geometric algebra with applications in computer vision", Proc. SPIE 4117, Vision Geometry IX, (23 October 2000); https://doi.org/10.1117/12.404828

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available