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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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Main Authors: Esmorís Pena, Alberto M. (Author) , Garcia-Albeniz, Xabier (Author) , Ladra, Manuel (Author) , Cabaleiro, José Carlos (Author) , Fernández-Rivera, Francisco (Author)
Format: Article (Journal)
Language:English
Published: 15 October 2026
In: Journal of computational and applied mathematics
Year: 2026, Volume: 485, Pages: 1-19
ISSN:1879-1778
DOI:10.1016/j.cam.2026.117569
Online Access:Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.cam.2026.117569
Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S0377042726002177
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Author Notes:Alberto M. Esmorís, Xabier García-Martínez, Manuel Ladra, José Carlos Cabaleiro, Francisco Fernández Rivera
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Summary: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.
Item Description:Online veröffentlicht: 17. März 2026, Artikelversion: 20. März 2026
Gesehen am 23.03.2026
Physical Description:Online Resource
ISSN:1879-1778
DOI:10.1016/j.cam.2026.117569

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