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A general framework for rotation invariant point cloud analysis

Shuqing Luo, Wei Gao

TL;DR

The paper addresses rotation sensitivity in deep point-cloud analysis by proposing a PCA-based canonical pose framework that yields four canonical views ($P_{\mathrm{cano}} = P E$, with $E' = R^{\top} E$) and can be integrated with standard backbones. It shows that the canonical pose space can be reduced from $48$ configurations to four poses while preserving rotation invariance, and it analyzes PCA-induced uncertainty and an operational-closure property to enable permutation-invariant processing. The method adds two fusion mechanisms—view pooling across poses within stages and point-wise fusion before global pooling—alongside a data augmentation strategy based on random scaling to further diversify canonical poses. Empirical results on ModelNet40 and ShapeNet Part demonstrate robustness to arbitrary rotations, with performance matching or exceeding baselines on rotated data while remaining competitive on aligned data, highlighting practical benefits for 3D pre-training and multimodal learning.

Abstract

We propose a general method for deep learning based point cloud analysis, which is invariant to rotation on the inputs. Classical methods are vulnerable to rotation, as they usually take aligned point clouds as input. Principle Component Analysis (PCA) is a practical approach to achieve rotation invariance. However, there are still some gaps between theory and practical algorithms. In this work, we present a thorough study on designing rotation invariant algorithms for point cloud analysis. We first formulate it as a permutation invariant problem, then propose a general framework which can be combined with any backbones. Our method is beneficial for further research such as 3D pre-training and multi-modal learning. Experiments show that our method has considerable or better performance compared to state-of-the-art approaches on common benchmarks. Code is available at https://github.com/luoshuqing2001/RI_framework.

A general framework for rotation invariant point cloud analysis

TL;DR

The paper addresses rotation sensitivity in deep point-cloud analysis by proposing a PCA-based canonical pose framework that yields four canonical views (, with ) and can be integrated with standard backbones. It shows that the canonical pose space can be reduced from configurations to four poses while preserving rotation invariance, and it analyzes PCA-induced uncertainty and an operational-closure property to enable permutation-invariant processing. The method adds two fusion mechanisms—view pooling across poses within stages and point-wise fusion before global pooling—alongside a data augmentation strategy based on random scaling to further diversify canonical poses. Empirical results on ModelNet40 and ShapeNet Part demonstrate robustness to arbitrary rotations, with performance matching or exceeding baselines on rotated data while remaining competitive on aligned data, highlighting practical benefits for 3D pre-training and multimodal learning.

Abstract

We propose a general method for deep learning based point cloud analysis, which is invariant to rotation on the inputs. Classical methods are vulnerable to rotation, as they usually take aligned point clouds as input. Principle Component Analysis (PCA) is a practical approach to achieve rotation invariance. However, there are still some gaps between theory and practical algorithms. In this work, we present a thorough study on designing rotation invariant algorithms for point cloud analysis. We first formulate it as a permutation invariant problem, then propose a general framework which can be combined with any backbones. Our method is beneficial for further research such as 3D pre-training and multi-modal learning. Experiments show that our method has considerable or better performance compared to state-of-the-art approaches on common benchmarks. Code is available at https://github.com/luoshuqing2001/RI_framework.
Paper Structure (16 sections, 11 equations, 1 figure, 5 tables, 1 algorithm)

This paper contains 16 sections, 11 equations, 1 figure, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Formulation for canonical poses
  3. Canonical Pose Space
  4. Attributes of Canonical Pose space
  5. Uncertainty in PCA process
  6. Operational closure
  7. Our method
  8. View pooling among modules at same stage
  9. Point-wise fusion before global pooling
  10. Data Augmentation
  11. Experiments
  12. Datasets and Evaluation Metrics
  13. Experiment Results
  14. Attribute Comparison
  15. Ablation Study
  16. ...and 1 more sections

Figures (1)

  • Figure 1: Our general framework for rotation invariant point cloud analysis. PCA transforms the input point cloud into $4$ canonical poses, while shared hierarchical backbone extracts local feature for each view and each point. Feature fusion is implemented on modules at the same stage.