# Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learning

arXiv: https://arxiv.org/abs/2306.11406 · HTML: https://mlsanity.com/paper/2306.11406/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 150 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 30 of 59)

- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Self-Calibrating Neural Radiance Fields](https://mlsanity.com/paper/2108.13826/) (2021)
- [Tangent Convolutions for Dense Prediction in 3D](https://mlsanity.com/paper/1807.02443/) (2018)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [PointMixer: MLP-Mixer for Point Cloud Understanding](https://mlsanity.com/paper/2111.11187/) (2021)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [C3DPO: Canonical 3D Pose Networks for Non-Rigid Structure From Motion](https://mlsanity.com/paper/1909.02533/) (2019)
- [Future Video Synthesis with Object Motion Prediction](https://mlsanity.com/paper/2004.00542/) (2020)
- [Rebooting ACGAN: Auxiliary Classifier GANs with Stable Training](https://mlsanity.com/paper/2111.01118/) (2021)
- [Deep Hough Voting for Robust Global Registration](https://mlsanity.com/paper/2109.04310/) (2021)
- [CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations](https://mlsanity.com/paper/2008.02792/) (2020)
- [Learning Debiased Classifier with Biased Committee](https://mlsanity.com/paper/2206.10843/) (2022)
- [Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation](https://mlsanity.com/paper/2111.00190/) (2021)
- [Quaternion Equivariant Capsule Networks for 3D Point Clouds](https://mlsanity.com/paper/1912.12098/) (2019)
- [Rotation-Invariant Local-to-Global Representation Learning for 3D Point Cloud](https://mlsanity.com/paper/2010.03318/) (2020)
- [StudioGAN: A Taxonomy and Benchmark of GANs for Image Synthesis](https://mlsanity.com/paper/2206.09479/) (2022)
- [Fill-Up: Balancing Long-Tailed Data with Generative Models](https://mlsanity.com/paper/2306.07200/) (2023)

## Built on by (most cited first, 3 of 3)

- [Learning SO(3)-Invariant Semantic Correspondence via Local Shape Transform](https://mlsanity.com/paper/2404.11156/) (2024)
- [Combinative Matching for Geometric Shape Assembly](https://mlsanity.com/paper/2508.09780/) (2025)
- [Symmetry-Robust 3D Orientation Estimation](https://mlsanity.com/paper/2410.02101/) (2024)

## Abstract (arXiv)

Learning to predict reliable characteristic orientations of 3D point clouds is an important yet challenging problem, as different point clouds of the same class may have largely varying appearances. In this work, we introduce a novel method to decouple the shape geometry and semantics of the input point cloud to achieve both stability and consistency. The proposed method integrates shape-geometry-based SO(3)-equivariant learning and shape-semantics-based SO(3)-invariant residual learning, where a final characteristic orientation is obtained by calibrating an SO(3)-equivariant orientation hypothesis using an SO(3)-invariant residual rotation. In experiments, the proposed method not only demonstrates superior stability and consistency but also exhibits state-of-the-art performances when applied to point cloud part segmentation, given randomly rotated inputs.