CanonNet: Canonical Ordering and Curvature Learning for Point Cloud Analysis

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 (\textbf{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 \hyperlink{this https URL}{this https URL}.

@article{friedmann2025_2504.02763,
  title={ CanonNet: Canonical Ordering and Curvature Learning for Point Cloud Analysis },
  author={ Benjy Friedmann and Michael Werman },
  journal={arXiv preprint arXiv:2504.02763},
  year={ 2025 }
}