Complete and Efficient Covariants for 3D Point Configurations

Hartmut Maennel
Proceedings of the Geometry, Topology, and Machine Learning Workshop, PMLR 325:46-68, 2026.

Abstract

We investigate the question: “How can we efficiently describe equivalence classes of finite sets of (colored) points in $\BR^3$, where (colored) point sets are equivalent if they can be transformed into each other by a rotation?” It sounds very simple, but we will see it leads to some interesting mathematical structures. However, they only become a part of the picture when we have to take into account some application specific constraints: We want to characterize these configurations by features that do not depend on the number of points in the set, and that are fast to evaluate.

Cite this Paper

BibTeX
@InProceedings{pmlr-v325-maennel26a, title = {Complete and Efficient Covariants for 3D Point Configurations}, author = {Maennel, Hartmut}, booktitle = {Proceedings of the Geometry, Topology, and Machine Learning Workshop}, pages = {46--68}, year = {2026}, editor = {Bleher, Michael and Jensen, Freya and Maier, Levin and Taha, Diaaeldin and Wienhard, Anna}, volume = {325}, series = {Proceedings of Machine Learning Research}, month = {10--14 Nov}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v325/main/assets/maennel26a/maennel26a.pdf}, url = {https://proceedings.mlr.press/v325/maennel26a.html}, abstract = {We investigate the question: “How can we efficiently describe equivalence classes of finite sets of (colored) points in $\BR^3$, where (colored) point sets are equivalent if they can be transformed into each other by a rotation?” It sounds very simple, but we will see it leads to some interesting mathematical structures. However, they only become a part of the picture when we have to take into account some application specific constraints: We want to characterize these configurations by features that do not depend on the number of points in the set, and that are fast to evaluate.} }
Endnote
%0 Conference Paper %T Complete and Efficient Covariants for 3D Point Configurations %A Hartmut Maennel %B Proceedings of the Geometry, Topology, and Machine Learning Workshop %C Proceedings of Machine Learning Research %D 2026 %E Michael Bleher %E Freya Jensen %E Levin Maier %E Diaaeldin Taha %E Anna Wienhard %F pmlr-v325-maennel26a %I PMLR %P 46--68 %U https://proceedings.mlr.press/v325/maennel26a.html %V 325 %X We investigate the question: “How can we efficiently describe equivalence classes of finite sets of (colored) points in $\BR^3$, where (colored) point sets are equivalent if they can be transformed into each other by a rotation?” It sounds very simple, but we will see it leads to some interesting mathematical structures. However, they only become a part of the picture when we have to take into account some application specific constraints: We want to characterize these configurations by features that do not depend on the number of points in the set, and that are fast to evaluate.
APA
Maennel, H.. (2026). Complete and Efficient Covariants for 3D Point Configurations. Proceedings of the Geometry, Topology, and Machine Learning Workshop, in Proceedings of Machine Learning Research 325:46-68 Available from https://proceedings.mlr.press/v325/maennel26a.html.

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