CanonNet: Canonical Ordering and Curvature Learning for Point Cloud Analysis

2025-04-03

AI Summary

Point cloud analysis faces two key challenges: point-order ambiguity and difficulty in learning fine-grained geometric features. To address these, we propose a lightweight dual-module architecture. First, geometric preprocessing—comprising coordinate normalization and PCA-based alignment—establishes a canonical point ordering and globally consistent orientation. Second, a differentiable MLP-based geometric encoder is trained on synthetically generated surfaces with controllable curvature, using differential-geometric priors (i.e., curvature) as supervision to learn expressive local geometric representations. Our approach avoids complex permutation-invariant networks and is the first to explicitly embed curvature into supervised geometric learning, achieving both geometric interpretability and computational efficiency. Experiments demonstrate state-of-the-art curvature estimation accuracy, competitive performance on geometric descriptor benchmarks, and a parameter count merely 1% of those in comparable models—significantly enhancing feasibility for edge deployment.

Technology Category

• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

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 ( extbf{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{https://benjyfri.github.io/CanonNet/}{https://benjyfri.github.io/CanonNet/}.

Problem

• Establishes consistent point ordering for point cloud analysis
• Learns fine-grained geometric features effectively
• Reduces computational complexity for real-world applications

Innovation

• Canonical point ordering preprocessing pipeline
• Geometric learning from synthetic curvature surfaces
• Lightweight network with fewer parameters