On quaternion based parameterization of orientation in computer vision and robotics

The problem of orientation parameterization for applications in computer vision and robotics is examined in detail herein. The necessary intuition and formulas are provided for direct practical use in any existing algorithm that seeks to minimize a cost function in an iterative fashion. Two distin...

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Bibliographic Details
Main Authors:	G. Terzakis, P. Culverhouse, G. Bugmann, S. Sharma, R. Sutton
Format:	Article
Language:	English
Published:	Eastern Macedonia and Thrace Institute of Technology 2014-04-01
Series:	Journal of Engineering Science and Technology Review
Subjects:	Orientation rotation matrix quaternions axis-angle parameters stereographic projection.
Online Access:	http://www.jestr.org/downloads/Volume7Issue1/fulltext147114.pdf

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spelling	doaj-28e96e3b9c2f40d78c84a39e9f2659ae2020-11-25T01:45:40ZengEastern Macedonia and Thrace Institute of TechnologyJournal of Engineering Science and Technology Review1791-23771791-23772014-04-01718293On quaternion based parameterization of orientation in computer vision and roboticsG. Terzakis0P. Culverhouse1G. Bugmann2S. Sharma3R. Sutton4Centre for Robotics and Neural Systems, Plymouth University, Drake Circus, Plymouth, PL4 8AA, UK Centre for Robotics and Neural Systems, Plymouth University, Drake Circus, Plymouth, PL4 8AA, UK Centre for Robotics and Neural Systems, Plymouth University, Drake Circus, Plymouth, PL4 8AA, UK School of Marine Science and Engineerinyg, Plymouth University, Drake Circus, Plymouth, PL4 8AA, UKSchool of Marine Science and Engineerinyg, Plymouth University, Drake Circus, Plymouth, PL4 8AA, UKThe problem of orientation parameterization for applications in computer vision and robotics is examined in detail herein. The necessary intuition and formulas are provided for direct practical use in any existing algorithm that seeks to minimize a cost function in an iterative fashion. Two distinct schemes of parameterization are analyzed: The first scheme concerns the traditional axis-angle approach, while the second employs stereographic projection from unit quaternion sphere to the 3D real projective space. Performance measurements are taken and a comparison is made between the two approaches. Results suggests that there exist several benefits in the use of stereographic projection that include rational expressions in the rotation matrix derivatives, improved accuracy, robustness to random starting points and accelerated convergence.http://www.jestr.org/downloads/Volume7Issue1/fulltext147114.pdfOrientationrotation matrixquaternionsaxis-angle parametersstereographic projection.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	G. Terzakis P. Culverhouse G. Bugmann S. Sharma R. Sutton
spellingShingle	G. Terzakis P. Culverhouse G. Bugmann S. Sharma R. Sutton On quaternion based parameterization of orientation in computer vision and robotics Journal of Engineering Science and Technology Review Orientation rotation matrix quaternions axis-angle parameters stereographic projection.
author_facet	G. Terzakis P. Culverhouse G. Bugmann S. Sharma R. Sutton
author_sort	G. Terzakis
title	On quaternion based parameterization of orientation in computer vision and robotics
title_short	On quaternion based parameterization of orientation in computer vision and robotics
title_full	On quaternion based parameterization of orientation in computer vision and robotics
title_fullStr	On quaternion based parameterization of orientation in computer vision and robotics
title_full_unstemmed	On quaternion based parameterization of orientation in computer vision and robotics
title_sort	on quaternion based parameterization of orientation in computer vision and robotics
publisher	Eastern Macedonia and Thrace Institute of Technology
series	Journal of Engineering Science and Technology Review
issn	1791-2377 1791-2377
publishDate	2014-04-01
description	The problem of orientation parameterization for applications in computer vision and robotics is examined in detail herein. The necessary intuition and formulas are provided for direct practical use in any existing algorithm that seeks to minimize a cost function in an iterative fashion. Two distinct schemes of parameterization are analyzed: The first scheme concerns the traditional axis-angle approach, while the second employs stereographic projection from unit quaternion sphere to the 3D real projective space. Performance measurements are taken and a comparison is made between the two approaches. Results suggests that there exist several benefits in the use of stereographic projection that include rational expressions in the rotation matrix derivatives, improved accuracy, robustness to random starting points and accelerated convergence.
topic	Orientation rotation matrix quaternions axis-angle parameters stereographic projection.
url	http://www.jestr.org/downloads/Volume7Issue1/fulltext147114.pdf
work_keys_str_mv	AT gterzakis onquaternionbasedparameterizationoforientationincomputervisionandrobotics AT pculverhouse onquaternionbasedparameterizationoforientationincomputervisionandrobotics AT gbugmann onquaternionbasedparameterizationoforientationincomputervisionandrobotics AT ssharma onquaternionbasedparameterizationoforientationincomputervisionandrobotics AT rsutton onquaternionbasedparameterizationoforientationincomputervisionandrobotics
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On quaternion based parameterization of orientation in computer vision and robotics

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