[Paper Review] PRIN: Pointwise Rotation-Invariant Network.

Yang You, Yujing Lou+5 more|arXiv (Cornell University)|Nov 23, 2018

3D Shape Modeling and Analysis9 references16 citations

TL;DR

PRIN introduces a novel pointwise rotation-invariant network for 3D point cloud analysis that achieves rotation invariance through spherical signal construction via Density Aware Adaptive Sampling, spherical voxel convolution, and point re-sampling. It outperforms state-of-the-art methods on rotated point clouds without data augmentation, with theoretical justification for invariance.

ABSTRACT

Point cloud analysis without pose priors is very challenging in real applications, as the orientations of point clouds are often unknown. In this paper, we propose a brand new point-set learning framework PRIN, namely, Pointwise Rotation-Invariant Network, focusing on rotation-invariant feature extraction in point clouds analysis. We construct spherical signals by Density Aware Adaptive Sampling to deal with distorted point distributions in spherical space. In addition, we propose Spherical Voxel Convolution and Point Re-sampling to extract rotation-invariant features for each point. Our network can be applied to tasks ranging from object classification, part segmentation, to 3D feature matching and label alignment. We show that, on the dataset with randomly rotated point clouds, PRIN demonstrates better performance than state-of-the-art methods without any data augmentation. We also provide theoretical analysis for the rotation-invariance achieved by our methods.

Motivation & Objective

• To address the challenge of point cloud analysis under unknown or random orientations in real-world applications.
• To develop a deep learning framework that learns rotation-invariant features directly from unordered point clouds.
• To eliminate reliance on data augmentation or pose priors for achieving robustness to rotation.
• To enable consistent performance across diverse 3D tasks including classification, part segmentation, and feature matching.

Proposed method

• Construct spherical signals using Density Aware Adaptive Sampling to normalize distorted point distributions in spherical space.
• Introduce Spherical Voxel Convolution to extract local, rotation-invariant features by aggregating spherical neighborhoods.
• Apply Point Re-sampling to refine feature representations and enhance invariance through spatial reorganization.
• Design a pointwise network architecture that processes each point independently with rotation-equivariant operations.
• Leverage spherical coordinate transformation to embed geometric invariance into the feature learning process.
• Provide theoretical analysis proving the rotation-invariance of the proposed feature extraction pipeline.

Experimental results

Research questions

• RQ1 Can a point cloud network achieve rotation invariance without relying on data augmentation or pose supervision?
• RQ2 How can spherical signal construction mitigate distortions from non-uniform point distributions?
• RQ3 What architectural components enable effective rotation-invariant feature learning in point clouds?
• RQ4 How does the proposed method compare to state-of-the-art approaches on rotated point cloud benchmarks?
• RQ5 What is the theoretical basis for the rotation invariance of the proposed network components?

Key findings

• PRIN achieves superior performance on rotated point cloud datasets compared to state-of-the-art methods without any data augmentation.
• The network maintains high accuracy across diverse 3D tasks, including object classification, part segmentation, and 3D feature matching.
• Spherical Voxel Convolution and Point Re-sampling significantly improve feature robustness to rotation.
• Density Aware Adaptive Sampling effectively reduces geometric distortion in spherical representations.
• Theoretical analysis confirms that the network's design ensures rotation invariance in feature learning.
• Empirical results demonstrate consistent gains on standard benchmarks under random rotation settings.