[Paper Review] PRIN/SPRIN: On Extracting Point-wise Rotation Invariant Features

Yang You, Yujing Lou+6 more|arXiv (Cornell University)|Feb 24, 2021

3D Shape Modeling and Analysis47 references4 citations

TL;DR

This paper proposes PRIN/SPRIN, a novel point-wise rotation invariant network for 3D point cloud analysis that uses density-aware adaptive sampling, spherical voxel convolution, and point re-sampling to extract rotation-invariant features without data augmentation. SPRIN achieves state-of-the-art performance on part segmentation, outperforming prior methods on rotated ShapeNet and ModelNet40 datasets.

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, Point-wise 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. Spherical Voxel Convolution and Point Re-sampling are proposed to extract rotation invariant features for each point. In addition, we extend PRIN to a sparse version called SPRIN, which directly operates on sparse point clouds. Both PRIN and SPRIN can be applied to tasks ranging from object classification, part segmentation, to 3D feature matching and label alignment. Results show that, on the dataset with randomly rotated point clouds, SPRIN demonstrates better performance than state-of-the-art methods without any data augmentation. We also provide thorough theoretical proof and analysis for point-wise rotation invariance achieved by our methods. Our code is available on https://github.com/qq456cvb/SPRIN.

Motivation & Objective

• To address the challenge of point cloud analysis under arbitrary rotations, where existing methods fail without pose priors or extensive data augmentation.
• To design a deep learning framework that extracts point-wise rotation-invariant features directly from sparse, randomly rotated point clouds.
• To ensure theoretical rigor by proving point-wise rotation invariance under specific conditions for both PRIN and SPRIN.
• To extend the framework to a sparse version (SPRIN) that operates directly on raw point clouds without intermediate grid conversion.
• To demonstrate broad applicability across tasks including classification, part segmentation, 3D feature matching, and label alignment.

Proposed method

• Proposes Density Aware Adaptive Sampling (DAAS) to construct spherical signals that reduce bias from non-uniform point distributions in spherical space.
• Introduces Spherical Voxel Convolution (SVC), a rotation-equivariant convolution on spherical voxel grids that preserves geometric structure and captures concave features.
• Employs a Point Re-sampling module to extract per-point features from spherical voxel representations, enabling one-to-one correspondence between input and output points.
• Extends PRIN to SPRIN, a sparse variant that treats input points as Dirac delta functions and applies rotation-invariant filtering on the left coset of z-axis rotations.
• Uses correlation features and triangle invariants as rotation-invariant representations in SPRIN to enhance feature robustness.
• Provides rigorous theoretical proof of point-wise rotation invariance for both PRIN and SPRIN under defined filter and sampling conditions.

Experimental results

Research questions

• RQ1 Can a deep learning framework extract point-wise rotation-invariant features from arbitrary rotated point clouds without data augmentation?
• RQ2 How can spherical voxel convolution preserve rotation invariance while handling non-convex and concave 3D shapes?
• RQ3 What sampling strategy minimizes bias in spherical signal construction from sparse and non-uniform point clouds?
• RQ4 To what extent does the sparse variant SPRIN maintain performance on low-density point clouds compared to dense PRIN?
• RQ5 Can the proposed framework generalize across diverse 3D tasks such as classification, segmentation, feature matching, and label alignment?

Key findings

• SPRIN achieves 92.08% accuracy and 82.67% mIoU on the rotated ShapeNet part dataset, outperforming state-of-the-art methods without data augmentation.
• PRIN with DAAS achieves 85.99% accuracy and 71.20% mIoU on the same dataset, with a 16.04% relative improvement in accuracy when bandwidth increases from 4 to 32.
• DAAS sampling outperforms uniform sampling by 2.86% in accuracy and 3.73% in mIoU, confirming its effectiveness in reducing sampling bias.
• Both PRIN and SPRIN maintain high performance under extreme point density reduction, with SPRIN achieving 64.17% accuracy and 51.38% mIoU at 256 points.
• Feature visualization confirms that DAAS maintains better correspondence in feature space across rotated point clouds than uniform sampling.
• The ablation study shows that combining correlation and triangle-based features in SPRIN yields the best performance, with 92.08% accuracy and 82.67% mIoU.