# ConDor: Self-Supervised Canonicalization of 3D Pose for Partial Shapes

arXiv: https://arxiv.org/abs/2201.07788 · HTML: https://mlsanity.com/paper/2201.07788/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 63 references that are in the map.
- First posted on arXiv 19 Jan 2022.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstruction](https://mlsanity.com/paper/2109.00512/) (2021)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [DeepGMR: Learning Latent Gaussian Mixture Models for Registration](https://mlsanity.com/paper/2008.09088/) (2020)
- [BAE-NET: Branched Autoencoder for Shape Co-Segmentation](https://mlsanity.com/paper/1903.11228/) (2019)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [6-PACK: Category-level 6D Pose Tracker with Anchor-Based Keypoints](https://mlsanity.com/paper/1910.10750/) (2019)
- [C3DPO: Canonical 3D Pose Networks for Non-Rigid Structure From Motion](https://mlsanity.com/paper/1909.02533/) (2019)
- [Learning to Reconstruct Shapes from Unseen Classes](https://mlsanity.com/paper/1812.11166/) (2018)
- [A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels](https://mlsanity.com/paper/2010.10952/) (2020)

## Built on by (most cited first, 30 of 31)

- [LEGO-Net: Learning Regular Rearrangements of Objects in Rooms](https://mlsanity.com/paper/2301.09629/) (2023)
- [Zero-Shot Category-Level Object Pose Estimation](https://mlsanity.com/paper/2204.03635/) (2022)
- [Open-Universe Indoor Scene Generation using LLM Program Synthesis and Uncurated Object Databases](https://mlsanity.com/paper/2403.09675/) (2024)
- [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)
- [4D Panoptic Segmentation as Invariant and Equivariant Field Prediction](https://mlsanity.com/paper/2303.15651/) (2023)
- [Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariance](https://mlsanity.com/paper/2305.16314/) (2023)
- [EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision](https://mlsanity.com/paper/2303.15440/) (2023)
- [Shape-Pose Disentanglement using SE(3)-equivariant Vector Neurons](https://mlsanity.com/paper/2204.01159/) (2022)
- [HyP-NeRF: Learning Improved NeRF Priors using a HyperNetwork](https://mlsanity.com/paper/2306.06093/) (2023)
- [OV9D: Open-Vocabulary Category-Level 9D Object Pose and Size Estimation](https://mlsanity.com/paper/2403.12396/) (2024)
- [Canonical Fields: Self-Supervised Learning of Pose-Canonicalized Neural Fields](https://mlsanity.com/paper/2212.02493/) (2022)
- [SC3K: Self-supervised and Coherent 3D Keypoints Estimation from Rotated, Noisy, and Decimated Point Cloud Data](https://mlsanity.com/paper/2308.05410/) (2023)
- [SCARP: 3D Shape Completion in ARbitrary Poses for Improved Grasping](https://mlsanity.com/paper/2301.07213/) (2023)
- [PaRot: Patch-Wise Rotation-Invariant Network via Feature Disentanglement and Pose Restoration](https://mlsanity.com/paper/2302.02535/) (2023)
- [Vitruvio: 3D Building Meshes via Single Perspective Sketches](https://mlsanity.com/paper/2210.13634/) (2022)
- [Approximately Piecewise E(3) Equivariant Point Networks](https://mlsanity.com/paper/2402.08529/) (2024)
- [ESCAPE: Equivariant Shape Completion via Anchor Point Encoding](https://mlsanity.com/paper/2412.00952/) (2024)
- [Category-Level Global Camera Pose Estimation with Multi-Hypothesis Point Cloud Correspondences](https://mlsanity.com/paper/2209.14419/) (2022)
- [Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learning](https://mlsanity.com/paper/2306.11406/) (2023)
- [Improving Equivariance in State-of-the-Art Supervised Depth and Normal Predictors](https://mlsanity.com/paper/2309.16646/) (2023)
- [A Simple Strategy to Provable Invariance via Orbit Mapping](https://mlsanity.com/paper/2209.11916/) (2022)
- [3D Surface Reconstruction in the Wild by Deforming Shape Priors from Synthetic Data](https://mlsanity.com/paper/2302.12883/) (2023)
- [Grasp Transfer based on Self-Aligning Implicit Representations of Local Surfaces](https://mlsanity.com/paper/2308.07807/) (2023)
- [Learning Generalizable Shape Completion with SIM(3) Equivariance](https://mlsanity.com/paper/2509.26631/) (2025)
- [Symmetry-Robust 3D Orientation Estimation](https://mlsanity.com/paper/2410.02101/) (2024)
- [CanoVerse: 3D Object Scalable Canonicalization and Dataset for Generation and Pose](https://mlsanity.com/paper/2603.07144/) (2026)
- [Towards Foundation Models for Cryo-ET Subtomogram Analysis](https://mlsanity.com/paper/2509.24311/) (2025)
- [Every9D-21M: Large-Scale Real-World 9D Canonicalization of Everyday Objects](https://mlsanity.com/paper/2605.28270/) (2026)
- [Annotation-Free Furniture Codes: What They Encode, and How Far They Transfer](https://mlsanity.com/paper/2607.10461/) (2026)

## Abstract (arXiv)

Progress in 3D object understanding has relied on manually canonicalized shape datasets that contain instances with consistent position and orientation (3D pose). This has made it hard to generalize these methods to in-the-wild shapes, eg., from internet model collections or depth sensors. ConDor is a self-supervised method that learns to Canonicalize the 3D orientation and position for full and partial 3D point clouds. We build on top of Tensor Field Networks (TFNs), a class of permutation- and rotation-equivariant, and translation-invariant 3D networks. During inference, our method takes an unseen full or partial 3D point cloud at an arbitrary pose and outputs an equivariant canonical pose. During training, this network uses self-supervision losses to learn the canonical pose from an un-canonicalized collection of full and partial 3D point clouds. ConDor can also learn to consistently co-segment object parts without any supervision. Extensive quantitative results on four new metrics show that our approach outperforms existing methods while enabling new applications such as operation on depth images and annotation transfer.