PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification
2026-07-27 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors address a problem in 3D point cloud analysis where tiny, detailed shapes (high-curvature regions) are hard to capture because usual methods focus more on smooth, less detailed parts. They propose PointCHR, which uses a special type of geometry called hyperbolic space that expands faster and can better represent these detailed areas. PointCHR guides the detailed points to areas in the space where they can be better distinguished, improving how well the network understands fine details. Experiments show that this method helps models perform better on several standard tests.
3D point cloudshigh-curvature regionsEuclidean spacehyperbolic spacefeature representationcurvature-guided projectionembedding capacityvolume growthgeometric semanticspoint cloud analysis
Authors
Xinxing Yu, Liying Yang, Hao Mo, Hui Ma, Fang Kai, Ajian Liu, Yanyan Liang
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.