# PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification

arXiv: https://arxiv.org/abs/2607.24052 · HTML: https://mlsanity.com/paper/2607.24052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 63 of its 81 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 30 of 63)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Point Transformer V2: Grouped Vector Attention and Partition-based Pooling](https://mlsanity.com/paper/2210.05666/) (2022)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [Point-M2AE: Multi-scale Masked Autoencoders for Hierarchical Point Cloud Pre-training](https://mlsanity.com/paper/2205.14401/) (2022)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [RPVNet: A Deep and Efficient Range-Point-Voxel Fusion Network for LiDAR Point Cloud Segmentation](https://mlsanity.com/paper/2103.12978/) (2021)
- [Walk in the Cloud: Learning Curves for Point Clouds Shape Analysis](https://mlsanity.com/paper/2105.01288/) (2021)
- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [Swin3D: A Pretrained Transformer Backbone for 3D Indoor Scene Understanding](https://mlsanity.com/paper/2304.06906/) (2023)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Sonata: Self-Supervised Learning of Reliable Point Representations](https://mlsanity.com/paper/2503.16429/) (2025)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [OneFormer3D: One Transformer for Unified Point Cloud Segmentation](https://mlsanity.com/paper/2311.14405/) (2023)
- [Surface Representation for Point Clouds](https://mlsanity.com/paper/2205.05740/) (2022)
- [Open3DSG: Open-Vocabulary 3D Scene Graphs from Point Clouds with Queryable Objects and Open-Set Relationships](https://mlsanity.com/paper/2402.12259/) (2024)
- [Learning Geometry-Disentangled Representation for Complementary Understanding of 3D Object Point Cloud](https://mlsanity.com/paper/2012.10921/) (2020)

## Abstract (arXiv)

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.