# Endowing Deep 3D Models with Rotation Invariance Based on Principal Component Analysis

arXiv: https://arxiv.org/abs/1910.08901 · HTML: https://mlsanity.com/paper/1910.08901/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2019.

## Built on by (most cited first, 17 of 17)

- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Frame Averaging for Equivariant Shape Space Learning](https://mlsanity.com/paper/2112.01741/) (2021)
- [RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learning](https://mlsanity.com/paper/2409.00353/) (2024)
- [Invariance-Aware Randomized Smoothing Certificates](https://mlsanity.com/paper/2211.14207/) (2022)
- [Local-consistent Transformation Learning for Rotation-invariant Point Cloud Analysis](https://mlsanity.com/paper/2403.11113/) (2024)
- [MaskLRF: Self-supervised Pretraining via Masked Autoencoding of Local Reference Frames for Rotation-invariant 3D Point Set Analysis](https://mlsanity.com/paper/2403.00206/) (2024)
- [Learning a Task-specific Descriptor for Robust Matching of 3D Point Clouds](https://mlsanity.com/paper/2210.14899/) (2022)
- [Disentangling Geometric Deformation Spaces in Generative Latent Shape Models](https://mlsanity.com/paper/2103.00142/) (2021)
- [A Simple Strategy to Provable Invariance via Orbit Mapping](https://mlsanity.com/paper/2209.11916/) (2022)
- [TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis](https://mlsanity.com/paper/2211.14456/) (2022)
- [General Rotation Invariance Learning for Point Clouds via Weight-Feature Alignment](https://mlsanity.com/paper/2302.09907/) (2023)
- [Self-supervised Learning of Rotation-invariant 3D Point Set Features using Transformer and its Self-distillation](https://mlsanity.com/paper/2308.04725/) (2023)
- [Rotation-Invariant Random Features Provide a Strong Baseline for Machine Learning on 3D Point Clouds](https://mlsanity.com/paper/2308.06271/) (2023)
- [DifAttack++: Query-Efficient Black-Box Adversarial Attack via Hierarchical Disentangled Feature Space in Cross-Domain](https://mlsanity.com/paper/2406.03017/) (2024)
- [Cloud-RAIN: Point Cloud Analysis with Reflectional Invariance](https://mlsanity.com/paper/2305.07814/) (2023)
- [Hierarchical Direction Perception via Atomic Dot-Product Operators for Rotation-Invariant Point Clouds Learning](https://mlsanity.com/paper/2511.08240/) (2025)
- [REVNET: Rotation-Equivariant Point Cloud Completion via Vector Neuron Anchor Transformer](https://mlsanity.com/paper/2601.08558/) (2026)

## Abstract (arXiv)

In this paper, we propose a simple yet effective method to endow deep 3D models with rotation invariance by expressing the coordinates in an intrinsic frame determined by the object shape itself. Key to our approach is to find such an intrinsic frame which should be unique to the identical object shape and consistent across different instances of the same category, e.g. the frame axes of desks should be all roughly along the edges. Interestingly, the principal component analysis exactly provides an effective way to define such a frame, i.e. setting the principal components as the frame axes. As the principal components have direction ambiguity caused by the sign-ambiguity of eigenvector computation, there exist several intrinsic frames for each object. In order to achieve absolute rotation invariance for a deep model, we adopt the coordinates expressed in all intrinsic frames as inputs to obtain multiple output features, which will be further aggregated as a final feature via a self-attention module. Our method is theoretically rotation-invariant and can be flexibly embedded into the current network architectures. Comprehensive experiments demonstrate that our approach can achieve near state-of-the-art performance on rotation-augmented dataset for ModelNet40 classification and outperform other models on SHREC'17 perturbed retrieval task.