PointCHR：通过曲率感知双曲整流进行点云分析
PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification
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中文总结 AI 辅助
针对三维点云中高曲率区域难以解析的问题，提出PointCHR方法，利用双曲流形指数体积膨胀特性，通过曲率引导径向整流机制，有效缓解表示拥挤问题，提升主干网络捕捉细节能力，在多基准测试中达最优性能。
中文摘要 AI 辅助
三维点云中的高曲率区域蕴含关键的细粒度几何语义，但其空间分布呈现出明显的长尾稀疏性。欧几里得空间中多项式体积增长的固有局限性使得这些复杂几何特征在统一尺度特征空间中难以充分解析。我们提出PointCHR，一种用于点云分析的曲率感知双曲整流方法。利用双曲流形附近指数体积膨胀的特性，提出可学习的曲率引导径向整流机制。通过将高曲率点自适应投影到具有更大有效嵌入能力的边界区域，有效缓解了欧几里得环境中固有的表示拥挤问题。实验表明PointCHR显著增强了主干网络捕捉细粒度几何细节的能力，在多个基准测试中达到了当前最优性能。
英文摘要
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.
