mlsanityData to 7 Oct 2026

Rethinking the compositionality of point clouds through regularization in the hyperbolic space

arXiv 2209.10318 ↗First posted 21 Sep 2022cs.CV eess.IVcited by 18

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Abstract (arXiv)

Point clouds of 3D objects exhibit an inherent compositional nature where simple parts can be assembled into progressively more complex shapes to form whole objects. Explicitly capturing such part-whole hierarchy is a long-sought objective in order to build effective models, but its tree-like nature has made the task elusive. In this paper, we propose to embed the features of a point cloud classifier into the hyperbolic space and explicitly regularize the space to account for the part-whole hierarchy. The hyperbolic space is the only space that can successfully embed the tree-like nature of the hierarchy. This leads to substantial improvements in the performance of state-of-art supervised models for point cloud classification.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 34 of its 43 references that are in the map. First posted on arXiv 21 Sep 2022.

Builds on

34 of 43 references.

References · 34

  1. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  2. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  3. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  4. 2020Point Transformercited by 1,462
  5. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,133
  6. 2018PointCNN: Convolution On X-Transformed Pointscited by 764
  7. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  8. 2018PointConv: Deep Convolutional Networks on 3D Point Cloudscited by 656
  9. 2019Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Datacited by 532
  10. 2022PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategiescited by 432
  11. 2018Hyperbolic Neural Networkscited by 393
  12. 2022Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Frameworkcited by 376
22 more
  1. 2019Relation-Shape Convolutional Neural Network for Point Cloud Analysiscited by 346
  2. 2020Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloudcited by 335
  3. 2019Hyperbolic Image Embeddingscited by 219
  4. 2021PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Cloudscited by 211
  5. 2018Riemannian Adaptive Optimization Methodscited by 187
  6. 2021Spatio-temporal Self-Supervised Representation Learning for 3D Point Cloudscited by 180
  7. 2021Walk in the Cloud: Learning Curves for Point Clouds Shape Analysiscited by 172
  8. 2021Revisiting Point Cloud Shape Classification with a Simple and Effective Baselinecited by 145
  9. 2020MVTN: Multi-View Transformation Network for 3D Shape Recognitioncited by 140
  10. 2020Geoopt: Riemannian Optimization in PyTorchcited by 109
  11. 2022Hyperbolic Vision Transformers: Combining Improvements in Metric Learningcited by 109
  12. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  13. 2020Global-Local Bidirectional Reasoning for Unsupervised Representation Learning of 3D Point Cloudscited by 75
  14. 2020Info3D: Representation Learning on 3D Objects using Mutual Information Maximization and Contrastive Learningcited by 68
  15. 2021PRA-Net: Point Relation-Aware Network for 3D Point Cloud Analysiscited by 58
  16. 2021Self-Contrastive Learning with Hard Negative Sampling for Self-supervised Point Cloud Learningcited by 52
  17. 2020End-to-End Learning Local Multi-view Descriptors for 3D Point Cloudscited by 47
  18. 2021Unsupervised Discovery of the Long-Tail in Instance Segmentation Using Hierarchical Self-Supervisioncited by 39
  19. 2018PVNet: A Joint Convolutional Network of Point Cloud and Multi-View for 3D Shape Recognitioncited by 36
  20. 2020Capturing implicit hierarchical structure in 3D biomedical images with self-supervised hyperbolic representationscited by 24
  21. 2022Distillation with Contrast is All You Need for Self-Supervised Point Cloud Representation Learningcited by 19
  22. 2022Unsupervised Point Cloud Pre-Training via Contrasting and Clusteringcited by 9

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 6; 2024: 5; 2025: 3; 2026: 3.

18 papers.

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  1. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 72
  2. 2023HypLiLoc: Towards Effective LiDAR Pose Regression with Hyperbolic Fusioncited by 24
  3. 2023Transfer Learning in Robotics: An Upcoming Breakthrough? A Review of Promises and Challengescited by 17
  4. 2023Hyperbolic Contrastive Learningcited by 15
  5. 2023Dynamic Hyperbolic Attention Network for Fine Hand-object Reconstructioncited by 10
  6. 2024Understanding Hyperbolic Metric Learning through Hard Negative Samplingcited by 10
  7. 2022Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifoldscited by 9
  8. 2024HyperSDFusion: Bridging Hierarchical Structures in Language and Geometry for Enhanced 3D Text2Shape Generationcited by 8
  9. 2024Hyperbolic-constraint Point Cloud Reconstruction from Single RGB-D Imagescited by 8
  10. 2023GPr-Net: Geometric Prototypical Network for Point Cloud Few-Shot Learningcited by 7
  11. 2024GeoFormer: Learning Point Cloud Completion with Tri-Plane Integrated Transformercited by 7
  12. 2024Hyperbolic Image-and-Pointcloud Contrastive Learning for 3D Classificationcited by 3
6 more
  1. 2025Graph-Convolutional-Beta-VAE for Synthetic Abdominal Aorta Aneurysm Generationcited by 2
  2. 2025Geometry-aware Distance Measure for Diverse Hierarchical Structures in Hyperbolic Spacescited by 2
  3. 2025HyPCV-Former: Hyperbolic Spatio-Temporal Transformer for 3D Point Cloud Video Anomaly Detectioncited by 1
  4. 2026Mamba Learns in Context: Structure-Aware Domain Generalization for Multi-Task Point Cloud Understandingcited by 0
  5. 2026Curvature-Aware Captioning:Leveraging Geodesic Attention for 3D Scene Understandingcited by 0
  6. 2026PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectificationcited by 0