BiEquiFormer: Bi-Equivariant Representations for Global Point Cloud Registration

Stefanos Pertigkiozoglou, Evangelos Chatzipantazis, Kostas Daniilidis
Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, PMLR 282:1136-1161, 2026.

Abstract

The goal of this paper is to address the problem of \textit{global} point cloud registration (PCR) i.e., finding the optimal alignment between point clouds irrespective of the initial poses of the scans. This problem is notoriously challenging for classical optimization methods due to computational constraints. First, we show that many state-of-the-art deep learning methods suffer from huge performance degradation when the point clouds are arbitrarily placed in space. We propose that \textit{equivariant deep learning} should be utilized for solving this task and we characterize the specific type of bi-equivariance of PCR. Then, we design BiEquiformer a novel and scalable \textit{bi-equivariant} pipeline i.e. equivariant to the independent transformations of the input point clouds. While a naive approach would process the point clouds independently we design expressive bi-equivariant layers that fuse the information from both point clouds. This allows us to extract high-quality superpoint correspondences and in turn, robust point-cloud registration. Extensive comparisons against state-of-the-art methods show that our method achieves comparable performance in the canonical setting and superior performance in the robust setting in both the 3DMatch and the challenging low-overlap 3DLoMatch dataset.

Cite this Paper

BibTeX
@InProceedings{pmlr-v282-pertigkiozoglou26a, title = {BiEquiFormer: Bi-Equivariant Representations for Global Point Cloud Registration}, author = {Pertigkiozoglou, Stefanos and Chatzipantazis, Evangelos and Daniilidis, Kostas}, booktitle = {Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations}, pages = {1136--1161}, year = {2026}, editor = {Acosta, Francisco and Azeglio, Simone and Tolooshams, Bahareh and van de Geijn, Chase and Shewmake, Christian and Sanborn, Sophia and Miolane, Nina}, volume = {282}, series = {Proceedings of Machine Learning Research}, month = {14 Dec 2024--07 Dec 2025}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v282/main/assets/pertigkiozoglou26a/pertigkiozoglou26a.pdf}, url = {https://proceedings.mlr.press/v282/pertigkiozoglou26a.html}, abstract = {The goal of this paper is to address the problem of \textit{global} point cloud registration (PCR) i.e., finding the optimal alignment between point clouds irrespective of the initial poses of the scans. This problem is notoriously challenging for classical optimization methods due to computational constraints. First, we show that many state-of-the-art deep learning methods suffer from huge performance degradation when the point clouds are arbitrarily placed in space. We propose that \textit{equivariant deep learning} should be utilized for solving this task and we characterize the specific type of bi-equivariance of PCR. Then, we design BiEquiformer a novel and scalable \textit{bi-equivariant} pipeline i.e. equivariant to the independent transformations of the input point clouds. While a naive approach would process the point clouds independently we design expressive bi-equivariant layers that fuse the information from both point clouds. This allows us to extract high-quality superpoint correspondences and in turn, robust point-cloud registration. Extensive comparisons against state-of-the-art methods show that our method achieves comparable performance in the canonical setting and superior performance in the robust setting in both the 3DMatch and the challenging low-overlap 3DLoMatch dataset.} }
Endnote
%0 Conference Paper %T BiEquiFormer: Bi-Equivariant Representations for Global Point Cloud Registration %A Stefanos Pertigkiozoglou %A Evangelos Chatzipantazis %A Kostas Daniilidis %B Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2026 %E Francisco Acosta %E Simone Azeglio %E Bahareh Tolooshams %E Chase van de Geijn %E Christian Shewmake %E Sophia Sanborn %E Nina Miolane %F pmlr-v282-pertigkiozoglou26a %I PMLR %P 1136--1161 %U https://proceedings.mlr.press/v282/pertigkiozoglou26a.html %V 282 %X The goal of this paper is to address the problem of \textit{global} point cloud registration (PCR) i.e., finding the optimal alignment between point clouds irrespective of the initial poses of the scans. This problem is notoriously challenging for classical optimization methods due to computational constraints. First, we show that many state-of-the-art deep learning methods suffer from huge performance degradation when the point clouds are arbitrarily placed in space. We propose that \textit{equivariant deep learning} should be utilized for solving this task and we characterize the specific type of bi-equivariance of PCR. Then, we design BiEquiformer a novel and scalable \textit{bi-equivariant} pipeline i.e. equivariant to the independent transformations of the input point clouds. While a naive approach would process the point clouds independently we design expressive bi-equivariant layers that fuse the information from both point clouds. This allows us to extract high-quality superpoint correspondences and in turn, robust point-cloud registration. Extensive comparisons against state-of-the-art methods show that our method achieves comparable performance in the canonical setting and superior performance in the robust setting in both the 3DMatch and the challenging low-overlap 3DLoMatch dataset.
APA
Pertigkiozoglou, S., Chatzipantazis, E. & Daniilidis, K.. (2026). BiEquiFormer: Bi-Equivariant Representations for Global Point Cloud Registration. Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 282:1136-1161 Available from https://proceedings.mlr.press/v282/pertigkiozoglou26a.html.

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