# A Laplace-inspired Distribution on SO(3) for Probabilistic Rotation Estimation

arXiv: https://arxiv.org/abs/2303.01743 · HTML: https://mlsanity.com/paper/2303.01743/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 58 references that are in the map.
- First posted on arXiv 3 Mar 2023.

## Builds on (most cited first, 30 of 31)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [Geometric Loss Functions for Camera Pose Regression with Deep Learning](https://mlsanity.com/paper/1704.00390/) (2017)
- [DeMoN: Depth and Motion Network for Learning Monocular Stereo](https://mlsanity.com/paper/1612.02401/) (2016)
- [On the uncertainty of self-supervised monocular depth estimation](https://mlsanity.com/paper/2005.06209/) (2020)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Human Pose Regression with Residual Log-likelihood Estimation](https://mlsanity.com/paper/2107.11291/) (2021)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Volumetric Grasping Network: Real-time 6 DOF Grasp Detection in Clutter](https://mlsanity.com/paper/2101.01132/) (2021)
- [An Analysis of SVD for Deep Rotation Estimation](https://mlsanity.com/paper/2006.14616/) (2020)
- [Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold](https://mlsanity.com/paper/2106.05965/) (2021)
- [Viewpoints and Keypoints](https://mlsanity.com/paper/1411.6067/) (2014)
- [Deep Directional Statistics: Pose Estimation with Uncertainty Quantification](https://mlsanity.com/paper/1805.03430/) (2018)
- [Deep Bingham Networks: Dealing with Uncertainty and Ambiguity in Pose Estimation](https://mlsanity.com/paper/2012.11002/) (2020)
- [Tangent Space Backpropagation for 3D Transformation Groups](https://mlsanity.com/paper/2103.12032/) (2021)
- [Spherical Regression: Learning Viewpoints, Surface Normals and 3D Rotations on n-Spheres](https://mlsanity.com/paper/1904.05404/) (2019)
- [Probabilistic orientation estimation with matrix Fisher distributions](https://mlsanity.com/paper/2006.09740/) (2020)
- [Projective Manifold Gradient Layer for Deep Rotation Regression](https://mlsanity.com/paper/2110.11657/) (2021)
- [Deep-6DPose: Recovering 6D Object Pose from a Single RGB Image](https://mlsanity.com/paper/1802.10367/) (2018)
- [A Mixed Classification-Regression Framework for 3D Pose Estimation from 2D Images](https://mlsanity.com/paper/1805.03225/) (2018)
- [Robust Neural Routing Through Space Partitions for Camera Relocalization in Dynamic Indoor Environments](https://mlsanity.com/paper/2012.04746/) (2020)
- [FisherMatch: Semi-Supervised Rotation Regression via Entropy-based Filtering](https://mlsanity.com/paper/2203.15765/) (2022)
- [Bayesian Attitude Estimation with the Matrix Fisher Distribution on SO(3)](https://mlsanity.com/paper/1710.03746/) (2017)
- [Occlusion Resistant Object Rotation Regression from Point Cloud Segments](https://mlsanity.com/paper/1808.05498/) (2018)
- [Towards Accurate Active Camera Localization](https://mlsanity.com/paper/2012.04263/) (2020)
- [Maximum Likelihood Uncertainty Estimation: Robustness to Outliers](https://mlsanity.com/paper/2202.03870/) (2022)

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

- [Reloc3r: Large-Scale Training of Relative Camera Pose Regression for Generalizable, Fast, and Accurate Visual Localization](https://mlsanity.com/paper/2412.08376/) (2024)
- [Confronting Ambiguity in 6D Object Pose Estimation via Score-Based Diffusion on SE(3)](https://mlsanity.com/paper/2305.15873/) (2023)
- [Delving into Discrete Normalizing Flows on SO(3) Manifold for Probabilistic Rotation Modeling](https://mlsanity.com/paper/2304.03937/) (2023)
- [Equivariant Single View Pose Prediction Via Induced and Restricted Representations](https://mlsanity.com/paper/2307.03704/) (2023)
- [3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction](https://mlsanity.com/paper/2411.00543/) (2024)
- [Semi-Supervised Unconstrained Head Pose Estimation in the Wild](https://mlsanity.com/paper/2404.02544/) (2024)
- [Alignist: CAD-Informed Orientation Distribution Estimation by Fusing Shape and Correspondences](https://mlsanity.com/paper/2409.06683/) (2024)
- [On the power of data augmentation for head pose estimation](https://mlsanity.com/paper/2407.05357/) (2024)
- [HACMatch Semi-Supervised Rotation Regression with Hardness-Aware Curriculum Pseudo Labeling](https://mlsanity.com/paper/2603.21583/) (2026)

## Abstract (arXiv)

Estimating the 3DoF rotation from a single RGB image is an important yet challenging problem. Probabilistic rotation regression has raised more and more attention with the benefit of expressing uncertainty information along with the prediction. Though modeling noise using Gaussian-resembling Bingham distribution and matrix Fisher distribution is natural, they are shown to be sensitive to outliers for the nature of quadratic punishment to deviations. In this paper, we draw inspiration from multivariate Laplace distribution and propose a novel Rotation Laplace distribution on SO(3). Rotation Laplace distribution is robust to the disturbance of outliers and enforces much gradient to the low-error region, resulting in a better convergence. Our extensive experiments show that our proposed distribution achieves state-of-the-art performance for rotation regression tasks over both probabilistic and non-probabilistic baselines. Our project page is at https://pku-epic.github.io/RotationLaplace.