# Canonical Fields: Self-Supervised Learning of Pose-Canonicalized Neural Fields

arXiv: https://arxiv.org/abs/2212.02493 · HTML: https://mlsanity.com/paper/2212.02493/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 76 references that are in the map.
- First posted on arXiv 5 Dec 2022.

## Builds on (most cited first, 30 of 57)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [In-Place Scene Labelling and Understanding with Implicit Scene Representation](https://mlsanity.com/paper/2103.15875/) (2021)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [Animatable Neural Radiance Fields for Modeling Dynamic Human Bodies](https://mlsanity.com/paper/2105.02872/) (2021)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [NeRF in the Dark: High Dynamic Range View Synthesis from Noisy Raw Images](https://mlsanity.com/paper/2111.13679/) (2021)

## Built on by (most cited first, 9 of 9)

- [A Canonicalization Perspective on Invariant and Equivariant Learning](https://mlsanity.com/paper/2405.18378/) (2024)
- [Laplacian Canonization: A Minimalist Approach to Sign and Basis Invariant Spectral Embedding](https://mlsanity.com/paper/2310.18716/) (2023)
- [SOCS: Semantically-aware Object Coordinate Space for Category-Level 6D Object Pose Estimation under Large Shape Variations](https://mlsanity.com/paper/2303.10346/) (2023)
- [Neural Radiance Field-based Visual Rendering: A Comprehensive Review](https://mlsanity.com/paper/2404.00714/) (2024)
- [SYM3D: Learning Symmetric Triplanes for Better 3D-Awareness of GANs](https://mlsanity.com/paper/2406.06432/) (2024)
- [FedMeNF: Privacy-Preserving Federated Meta-Learning for Neural Fields](https://mlsanity.com/paper/2508.06301/) (2025)
- [Toward Efficient Generalization in 3D Human Pose Estimation via a Canonical Domain Approach](https://mlsanity.com/paper/2501.16146/) (2025)
- [Learning Positive-Incentive Point Sampling in Neural Implicit Fields for Object Pose Estimation](https://mlsanity.com/paper/2602.19937/) (2026)
- [CANIS: Generation-Assisted 3D Canonicalization via an Image-Semantic Bridge](https://mlsanity.com/paper/2608.07256/) (2026)

## Abstract (arXiv)

Coordinate-based implicit neural networks, or neural fields, have emerged as useful representations of shape and appearance in 3D computer vision. Despite advances, however, it remains challenging to build neural fields for categories of objects without datasets like ShapeNet that provide "canonicalized" object instances that are consistently aligned for their 3D position and orientation (pose). We present Canonical Field Network (CaFi-Net), a self-supervised method to canonicalize the 3D pose of instances from an object category represented as neural fields, specifically neural radiance fields (NeRFs). CaFi-Net directly learns from continuous and noisy radiance fields using a Siamese network architecture that is designed to extract equivariant field features for category-level canonicalization. During inference, our method takes pre-trained neural radiance fields of novel object instances at arbitrary 3D pose and estimates a canonical field with consistent 3D pose across the entire category. Extensive experiments on a new dataset of 1300 NeRF models across 13 object categories show that our method matches or exceeds the performance of 3D point cloud-based methods.