# Cross-Domain 3D Equivariant Image Embeddings

arXiv: https://arxiv.org/abs/1812.02716 · HTML: https://mlsanity.com/paper/1812.02716/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2018.

## Built on by (most cited first, 12 of 12)

- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold](https://mlsanity.com/paper/2106.05965/) (2021)
- [Wide-Baseline Relative Camera Pose Estimation with Directional Learning](https://mlsanity.com/paper/2106.03336/) (2021)
- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [Image to Sphere: Learning Equivariant Features for Efficient Pose Prediction](https://mlsanity.com/paper/2302.13926/) (2023)
- [Leveraging Equivariant Features for Absolute Pose Regression](https://mlsanity.com/paper/2204.02163/) (2022)
- [Equivariant Single View Pose Prediction Via Induced and Restricted Representations](https://mlsanity.com/paper/2307.03704/) (2023)
- [Explicit Discovery of Nonlinear Symmetries from Dynamic Data](https://mlsanity.com/paper/2510.01855/) (2025)
- [Semi-supervised Viewpoint Estimation with Geometry-aware Conditional Generation](https://mlsanity.com/paper/2104.01103/) (2021)
- [ViewNet: Unsupervised Viewpoint Estimation from Conditional Generation](https://mlsanity.com/paper/2212.00435/) (2022)
- [Learning Implicit Probability Distribution Functions for Symmetric Orientation Estimation from RGB Images Without Pose Labels](https://mlsanity.com/paper/2211.11394/) (2022)
- [Iterative collaborative routing among equivariant capsules for transformation-robust capsule networks](https://mlsanity.com/paper/2210.11095/) (2022)

## Abstract (arXiv)

Spherical convolutional networks have been introduced recently as tools to learn powerful feature representations of 3D shapes. Spherical CNNs are equivariant to 3D rotations making them ideally suited to applications where 3D data may be observed in arbitrary orientations. In this paper we learn 2D image embeddings with a similar equivariant structure: embedding the image of a 3D object should commute with rotations of the object. We introduce a cross-domain embedding from 2D images into a spherical CNN latent space. This embedding encodes images with 3D shape properties and is equivariant to 3D rotations of the observed object. The model is supervised only by target embeddings obtained from a spherical CNN pretrained for 3D shape classification. We show that learning a rich embedding for images with appropriate geometric structure is sufficient for tackling varied applications, such as relative pose estimation and novel view synthesis, without requiring additional task-specific supervision.