PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification

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.

High-curvature regions, such as edges and corners, are crucial for understanding 3D point clouds, but they are often sparse and easily dominated by smoother regions. This makes it difficult for standard Euclidean feature spaces to represent fine geometric details effectively. We propose PointCHR, a curvature-aware hyperbolic rectification method that adaptively assigns high-curvature points to regions with larger representation capacity in hyperbolic space. This helps reduce feature crowding and enables the network to better capture subtle geometric structures. Experiments show that PointCHR consistently improves point cloud representation learning and achieves strong results across multiple benchmarks.