PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification

Xinxing Yu, Liying Yang, Hao Mo, Hui Ma, Fang Kai, Ajian Liu, Yanyan Liang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:151501-151518, 2026.

Abstract

High-curvature regions in 3D point clouds encapsulate critical fine-grained geometric semantics yet exhibit a distinct long-tail sparsity in their spatial distribution. The inherent limitations of polynomial volume growth in Euclidean space frequently render these intricate geometric features challenging to adequately resolve within a uniform-scale feature space. Consequently, these regions are frequently overshadowed by smooth global features dominated by low-curvature regions, thereby limiting the discriminative capacity of the network. To address this issue, we propose PointCHR, a curvature-aware hyperbolic rectification (CHR) for point cloud analysis. Utilising the property of exponential volume expansion in the vicinity of hyperbolic manifolds, CHR presents a learnable curvature-guided radial rectification mechanism. By adaptively projecting high-curvature points towards boundary regions endowed with larger effective embedding capacities, PointCHR effectively mitigates the representation crowding problem inherent in Euclidean settings. Extensive experimentation has demonstrated that PointCHR significantly enhances the ability of backbone to capture fine-grained geometric details, achieving state-of-the-art performance across multiple benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-yu26bj, title = {{P}oint{CHR}: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification}, author = {Yu, Xinxing and Yang, Liying and Mo, Hao and Ma, Hui and Kai, Fang and Liu, Ajian and Liang, Yanyan}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {151501--151518}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/yu26bj/yu26bj.pdf}, url = {https://proceedings.mlr.press/v306/yu26bj.html}, abstract = {High-curvature regions in 3D point clouds encapsulate critical fine-grained geometric semantics yet exhibit a distinct long-tail sparsity in their spatial distribution. The inherent limitations of polynomial volume growth in Euclidean space frequently render these intricate geometric features challenging to adequately resolve within a uniform-scale feature space. Consequently, these regions are frequently overshadowed by smooth global features dominated by low-curvature regions, thereby limiting the discriminative capacity of the network. To address this issue, we propose PointCHR, a curvature-aware hyperbolic rectification (CHR) for point cloud analysis. Utilising the property of exponential volume expansion in the vicinity of hyperbolic manifolds, CHR presents a learnable curvature-guided radial rectification mechanism. By adaptively projecting high-curvature points towards boundary regions endowed with larger effective embedding capacities, PointCHR effectively mitigates the representation crowding problem inherent in Euclidean settings. Extensive experimentation has demonstrated that PointCHR significantly enhances the ability of backbone to capture fine-grained geometric details, achieving state-of-the-art performance across multiple benchmarks.} }
Endnote
%0 Conference Paper %T PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification %A Xinxing Yu %A Liying Yang %A Hao Mo %A Hui Ma %A Fang Kai %A Ajian Liu %A Yanyan Liang %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-yu26bj %I PMLR %P 151501--151518 %U https://proceedings.mlr.press/v306/yu26bj.html %V 306 %X High-curvature regions in 3D point clouds encapsulate critical fine-grained geometric semantics yet exhibit a distinct long-tail sparsity in their spatial distribution. The inherent limitations of polynomial volume growth in Euclidean space frequently render these intricate geometric features challenging to adequately resolve within a uniform-scale feature space. Consequently, these regions are frequently overshadowed by smooth global features dominated by low-curvature regions, thereby limiting the discriminative capacity of the network. To address this issue, we propose PointCHR, a curvature-aware hyperbolic rectification (CHR) for point cloud analysis. Utilising the property of exponential volume expansion in the vicinity of hyperbolic manifolds, CHR presents a learnable curvature-guided radial rectification mechanism. By adaptively projecting high-curvature points towards boundary regions endowed with larger effective embedding capacities, PointCHR effectively mitigates the representation crowding problem inherent in Euclidean settings. Extensive experimentation has demonstrated that PointCHR significantly enhances the ability of backbone to capture fine-grained geometric details, achieving state-of-the-art performance across multiple benchmarks.
APA
Yu, X., Yang, L., Mo, H., Ma, H., Kai, F., Liu, A. & Liang, Y.. (2026). PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:151501-151518 Available from https://proceedings.mlr.press/v306/yu26bj.html.

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