# Learning an Effective Equivariant 3D Descriptor Without Supervision

arXiv: https://arxiv.org/abs/1909.06887 · HTML: https://mlsanity.com/paper/1909.06887/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2019.

## Built on by (most cited first, 14 of 14)

- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [Learning general and distinctive 3D local deep descriptors for point cloud registration](https://mlsanity.com/paper/2105.10382/) (2021)
- [Learning Rotation-Invariant Representations of Point Clouds Using Aligned Edge Convolutional Neural Networks](https://mlsanity.com/paper/2101.00483/) (2021)
- [RefRec: Pseudo-labels Refinement via Shape Reconstruction for Unsupervised 3D Domain Adaptation](https://mlsanity.com/paper/2110.11036/) (2021)
- [Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives](https://mlsanity.com/paper/2303.15385/) (2023)
- [WSDesc: Weakly Supervised 3D Local Descriptor Learning for Point Cloud Registration](https://mlsanity.com/paper/2108.02740/) (2021)
- [ZeroReg: Zero-Shot Point Cloud Registration with Foundation Models](https://mlsanity.com/paper/2312.03032/) (2023)
- [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)
- [Equivariant Local Reference Frames for Unsupervised Non-rigid Point Cloud Shape Correspondence](https://mlsanity.com/paper/2404.00959/) (2024)
- [Augmenting Imitation Experience via Equivariant Representations](https://mlsanity.com/paper/2110.07668/) (2021)
- [View Transformation Robustness for Multi-View 3D Object Reconstruction with Reconstruction Error-Guided View Selection](https://mlsanity.com/paper/2412.11428/) (2024)
- [Neural TMDlayer: Modeling Instantaneous flow of features via SDE Generators](https://mlsanity.com/paper/2108.08891/) (2021)
- [Registering Image Volumes using 3D SIFT and Discrete SP-Symmetry](https://mlsanity.com/paper/2205.15456/) (2022)
- [Attention-guided reference point shifting for Gaussian-mixture-based partial point set registration](https://mlsanity.com/paper/2512.02496/) (2025)

## Abstract (arXiv)

Establishing correspondences between 3D shapes is a fundamental task in 3D Computer Vision, typically addressed by matching local descriptors. Recently, a few attempts at applying the deep learning paradigm to the task have shown promising results. Yet, the only explored way to learn rotation invariant descriptors has been to feed neural networks with highly engineered and invariant representations provided by existing hand-crafted descriptors, a path that goes in the opposite direction of end-to-end learning from raw data so successfully deployed for 2D images. In this paper, we explore the benefits of taking a step back in the direction of end-to-end learning of 3D descriptors by disentangling the creation of a robust and distinctive rotation equivariant representation, which can be learned from unoriented input data, and the definition of a good canonical orientation, required only at test time to obtain an invariant descriptor. To this end, we leverage two recent innovations: spherical convolutional neural networks to learn an equivariant descriptor and plane folding decoders to learn without supervision. The effectiveness of the proposed approach is experimentally validated by outperforming hand-crafted and learned descriptors on a standard benchmark.