# CanonNet: Canonical Ordering and Curvature Learning for Point Cloud Analysis

arXiv: https://arxiv.org/abs/2504.02763 · HTML: https://mlsanity.com/paper/2504.02763/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 45 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 29 of 29)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [3D Object Detection with Pointformer](https://mlsanity.com/paper/2012.11409/) (2020)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [D3Feat: Joint Learning of Dense Detection and Description of 3D Local Features](https://mlsanity.com/paper/2003.03164/) (2020)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [SpinNet: Learning a General Surface Descriptor for 3D Point Cloud Registration](https://mlsanity.com/paper/2011.12149/) (2020)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [Deep Learning for LiDAR Point Clouds in Autonomous Driving: A Review](https://mlsanity.com/paper/2005.09830/) (2020)
- [PointCloud Saliency Maps](https://mlsanity.com/paper/1812.01687/) (2018)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [Surface Representation for Point Clouds](https://mlsanity.com/paper/2205.05740/) (2022)
- [Covariant Compositional Networks For Learning Graphs](https://mlsanity.com/paper/1801.02144/) (2018)
- [End-to-End Learning Local Multi-view Descriptors for 3D Point Clouds](https://mlsanity.com/paper/2003.05855/) (2020)
- [Learning Compact Geometric Features](https://mlsanity.com/paper/1709.05056/) (2017)
- [DeepFit: 3D Surface Fitting via Neural Network Weighted Least Squares](https://mlsanity.com/paper/2003.10826/) (2020)
- [Natural Graph Networks](https://mlsanity.com/paper/2007.08349/) (2020)
- [Benchmarking Positional Encodings for GNNs and Graph Transformers](https://mlsanity.com/paper/2411.12732/) (2024)
- [Self-Ordering Point Clouds](https://mlsanity.com/paper/2304.00961/) (2023)

## Built on by (most cited first, 2 of 2)

- [Transport, Don't Generate: Deterministic Geometric Flows for Combinatorial Optimization](https://mlsanity.com/paper/2602.10794/) (2026)
- [PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification](https://mlsanity.com/paper/2607.24052/) (2026)

## Abstract (arXiv)

Point cloud processing poses two fundamental challenges: establishing consistent point ordering and effectively learning fine-grained geometric features. Current architectures rely on complex operations that limit expressivity while struggling to capture detailed surface geometry. We present CanonNet, a lightweight neural network composed of two complementary components: (1) a preprocessing pipeline that creates a canonical point ordering and orientation, and (2) a geometric learning framework where networks learn from synthetic surfaces with precise curvature values. This modular approach eliminates the need for complex transformation-invariant architectures while effectively capturing local geometric properties. Our experiments demonstrate state-of-the-art performance in curvature estimation and competitive results in geometric descriptor tasks with significantly fewer parameters (100X) than comparable methods. CanonNet's efficiency makes it particularly suitable for real-world applications where computational resources are limited, demonstrating that mathematical preprocessing can effectively complement neural architectures for point cloud analysis. The code for the project is publicly available hyperlinkhttps://benjyfri.github.io/CanonNet/https://benjyfri.github.io/CanonNet/.