Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds

We propose the Taubin-Weingarten algorithm to compute second-order geometric features in 3D point clouds. This method is well-suited for working with large-scale 3D datasets due to its embarrassingly parallel nature. The speedup of our open-source C++ implementation is systematically above 30 for a...

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Detalles Bibliográficos
Autores: Esmorís Pena, Alberto Manuel, García-Martínez, Xabier, Ladra González, Manuel, Cabaleiro Domínguez, José Carlos, Fernández Rivera, Francisco
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:dnet:minerva_____::21a037b15fd2142b8194dc580cee229f
Acceso en línea:https://hdl.handle.net/10347/47590
Access Level:acceso abierto
Palabra clave:Algorithms
Geometric descriptors
3D point clouds
Semantic segmentation
Machine learning
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spelling Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point cloudsEsmorís Pena, Alberto ManuelGarcía-Martínez, XabierLadra González, ManuelCabaleiro Domínguez, José CarlosFernández Rivera, FranciscoAlgorithmsGeometric descriptors3D point cloudsSemantic segmentationMachine learningWe propose the Taubin-Weingarten algorithm to compute second-order geometric features in 3D point clouds. This method is well-suited for working with large-scale 3D datasets due to its embarrassingly parallel nature. The speedup of our open-source C++ implementation is systematically above 30 for a high-performance CPU with 32 cores. It provides reliable estimates for standard quantifications in differential geometry, such as the Gaussian and mean curvatures of a surface, when compared to other approaches. Additionally, it achieves improvements of between 1.6% and 10% in F1-score compared to the standard first-order approach in point-wise classification tasks, such as object part segmentation and large-scale semantic scene segmentation. The results demonstrate that the Taubin-Weingarten algorithm is both efficient and robust, enabling consistent improvements in machine learning performance across various tasks.ElsevierUniversidade de Santiago de Compostela. Centro de Investigación en Tecnoloxías Intelixentes da USC (CiTIUS)Universidade de Santiago de Compostela. Departamento de Electrónica e ComputaciónUniversidade de Santiago de Compostela. Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)Universidade de Santiago de Compostela. Departamento de Matemáticas20262026-03-1720262026-03-17journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10347/47590reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-115155GB-I00 HOMOLOGIA, HOMOTOPIA E INVARIANTES CATEGORICOS EN GRUPOS Y ALGEBRAS NO ASOCIATIVASAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-141623NB-I00 COMPUTACION DE ALTAS PRESTACIONES, HETEROGENEA Y EN LA NUBE PARA APLICACIONES DE ALTA DEMANDAAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2024-2027 PID2024-155502NB HOMOLOGIA, HOMOTOPIA E INVARIANTES CATEGORICOS EN GRUPOS Y ALGEBRAS NO ASOCIATIVASopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:dnet:minerva_____::21a037b15fd2142b8194dc580cee229f2026-06-15T12:47:27Z
dc.title.none.fl_str_mv Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds
title Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds
spellingShingle Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds
Esmorís Pena, Alberto Manuel
Algorithms
Geometric descriptors
3D point clouds
Semantic segmentation
Machine learning
title_short Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds
title_full Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds
title_fullStr Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds
title_full_unstemmed Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds
title_sort Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds
dc.creator.none.fl_str_mv Esmorís Pena, Alberto Manuel
García-Martínez, Xabier
Ladra González, Manuel
Cabaleiro Domínguez, José Carlos
Fernández Rivera, Francisco
author Esmorís Pena, Alberto Manuel
author_facet Esmorís Pena, Alberto Manuel
García-Martínez, Xabier
Ladra González, Manuel
Cabaleiro Domínguez, José Carlos
Fernández Rivera, Francisco
author_role author
author2 García-Martínez, Xabier
Ladra González, Manuel
Cabaleiro Domínguez, José Carlos
Fernández Rivera, Francisco
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Universidade de Santiago de Compostela. Centro de Investigación en Tecnoloxías Intelixentes da USC (CiTIUS)
Universidade de Santiago de Compostela. Departamento de Electrónica e Computación
Universidade de Santiago de Compostela. Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)
Universidade de Santiago de Compostela. Departamento de Matemáticas
dc.subject.none.fl_str_mv Algorithms
Geometric descriptors
3D point clouds
Semantic segmentation
Machine learning
topic Algorithms
Geometric descriptors
3D point clouds
Semantic segmentation
Machine learning
description We propose the Taubin-Weingarten algorithm to compute second-order geometric features in 3D point clouds. This method is well-suited for working with large-scale 3D datasets due to its embarrassingly parallel nature. The speedup of our open-source C++ implementation is systematically above 30 for a high-performance CPU with 32 cores. It provides reliable estimates for standard quantifications in differential geometry, such as the Gaussian and mean curvatures of a surface, when compared to other approaches. Additionally, it achieves improvements of between 1.6% and 10% in F1-score compared to the standard first-order approach in point-wise classification tasks, such as object part segmentation and large-scale semantic scene segmentation. The results demonstrate that the Taubin-Weingarten algorithm is both efficient and robust, enabling consistent improvements in machine learning performance across various tasks.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-03-17
2026
2026-03-17
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10347/47590
url https://hdl.handle.net/10347/47590
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-115155GB-I00 HOMOLOGIA, HOMOTOPIA E INVARIANTES CATEGORICOS EN GRUPOS Y ALGEBRAS NO ASOCIATIVAS
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-141623NB-I00 COMPUTACION DE ALTAS PRESTACIONES, HETEROGENEA Y EN LA NUBE PARA APLICACIONES DE ALTA DEMANDA
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2024-2027 PID2024-155502NB HOMOLOGIA, HOMOTOPIA E INVARIANTES CATEGORICOS EN GRUPOS Y ALGEBRAS NO ASOCIATIVAS
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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