Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registration

No proper norm exists to measure the distance between two object poses essentially because a general pose is defined by a rotation and a translation, and thus it involves magnitudes with different units. As a means to solve this dimensional-inhomogeneity problem, the concept of characteristic length...

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Detalles Bibliográficos
Autores: Sarabandi, Soheil, Thomas, Federico
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/295772
Acceso en línea:http://hdl.handle.net/10261/295772
Access Level:acceso abierto
Palabra clave:Characteristic length
Dual quaternions
3-D pointcloud registration
Quaternions
3-D rigid displacements
4-D rotations
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spelling Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registrationSarabandi, SoheilThomas, FedericoCharacteristic lengthDual quaternions3-D pointcloud registrationQuaternions3-D rigid displacements4-D rotationsNo proper norm exists to measure the distance between two object poses essentially because a general pose is defined by a rotation and a translation, and thus it involves magnitudes with different units. As a means to solve this dimensional-inhomogeneity problem, the concept of characteristic length has been put forward in the area of kinematics. The idea consists in scaling translations according to this characteristic length and then approximating the corresponding displacement defining the object pose in R^3 by a rotation in R^4, for which a norm exists. This paper sheds new light on this kind of approximations which permits simplifying optimization problem whose cost functions involve translations and rotations simultaneously. A good example of this kind of problems is the pointcloud registration problem in which the optimal rotation and translation between two sets of corresponding 3D point data, so that they are aligned/registered, have to be found. As a result, a simple closed-form formula for solving this problem is presented which is shown to be an attractive alternative to the previous approaches.This work was partially supported by the Spanish Ministry of Economy and Competitiveness through the projects DPI2017-88282-P, PID2020-117509GBI00, and MDM-2016-0656.Institute of Electrical and Electronics EngineersMinisterio de Ciencia, Innovación y Universidades (España)Agencia Estatal de Investigación (España)Ministerio de Economía y Competitividad (España)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2023202320222023info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Postprintinfo:eu-repo/semantics/acceptedVersionhttp://hdl.handle.net/10261/295772reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/DPI2017-88282-Pinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-117509GB-I00info:eu-repo/grantAgreement/MINECO//MDM-2016-0656http://dx.doi.org/10.1109/TRO.2021.3128328Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/2957722026-05-22T06:33:51Z
dc.title.none.fl_str_mv Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registration
title Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registration
spellingShingle Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registration
Sarabandi, Soheil
Characteristic length
Dual quaternions
3-D pointcloud registration
Quaternions
3-D rigid displacements
4-D rotations
title_short Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registration
title_full Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registration
title_fullStr Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registration
title_full_unstemmed Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registration
title_sort Approximating displacements in R^3 by rotations in R^4 and its application to pointcloud registration
dc.creator.none.fl_str_mv Sarabandi, Soheil
Thomas, Federico
author Sarabandi, Soheil
author_facet Sarabandi, Soheil
Thomas, Federico
author_role author
author2 Thomas, Federico
author2_role author
dc.contributor.none.fl_str_mv Ministerio de Ciencia, Innovación y Universidades (España)
Agencia Estatal de Investigación (España)
Ministerio de Economía y Competitividad (España)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Characteristic length
Dual quaternions
3-D pointcloud registration
Quaternions
3-D rigid displacements
4-D rotations
topic Characteristic length
Dual quaternions
3-D pointcloud registration
Quaternions
3-D rigid displacements
4-D rotations
description No proper norm exists to measure the distance between two object poses essentially because a general pose is defined by a rotation and a translation, and thus it involves magnitudes with different units. As a means to solve this dimensional-inhomogeneity problem, the concept of characteristic length has been put forward in the area of kinematics. The idea consists in scaling translations according to this characteristic length and then approximating the corresponding displacement defining the object pose in R^3 by a rotation in R^4, for which a norm exists. This paper sheds new light on this kind of approximations which permits simplifying optimization problem whose cost functions involve translations and rotations simultaneously. A good example of this kind of problems is the pointcloud registration problem in which the optimal rotation and translation between two sets of corresponding 3D point data, so that they are aligned/registered, have to be found. As a result, a simple closed-form formula for solving this problem is presented which is shown to be an attractive alternative to the previous approaches.
publishDate 2022
dc.date.none.fl_str_mv 2022
2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Postprint
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/295772
url http://hdl.handle.net/10261/295772
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/DPI2017-88282-P
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-117509GB-I00
info:eu-repo/grantAgreement/MINECO//MDM-2016-0656
http://dx.doi.org/10.1109/TRO.2021.3128328
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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