# Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distribution arXiv: https://arxiv.org/abs/2305.10465 ยท HTML: https://mlsanity.com/paper/2305.10465/ ## Key facts - Cited by 5 papers in the map (data through 14 Oct 2026). - Builds on 40 of its 86 references that are in the map. - First posted on arXiv 17 May 2023. ## Builds on (most cited first, 30 of 40) - [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016) - [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017) - [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015) - [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) - [BOP Challenge 2020 on 6D Object Localization](https://mlsanity.com/paper/2009.07378/) (2020) - [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) - [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016) - [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) - [Explaining the Ambiguity of Object Detection and 6D Pose From Visual Data](https://mlsanity.com/paper/1812.00287/) (2018) - [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) - [ROAD: The ROad event Awareness Dataset for Autonomous Driving](https://mlsanity.com/paper/2102.11585/) (2021) - [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) - [GeoNet++: Iterative Geometric Neural Network with Edge-Aware Refinement for Joint Depth and Surface Normal Estimation](https://mlsanity.com/paper/2012.06980/) (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) ## Built on by (most cited first, 5 of 5) - [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) - [Z-FLoc: Zero-Shot Floorplan Localization via Geometric Primitives](https://mlsanity.com/paper/2606.04788/) (2026) - [HACMatch Semi-Supervised Rotation Regression with Hardness-Aware Curriculum Pseudo Labeling](https://mlsanity.com/paper/2603.21583/) (2026) - [InCaRPose: In-Cabin Relative Camera Pose Estimation Model and Dataset](https://mlsanity.com/paper/2604.03814/) (2026) ## Abstract (arXiv) Estimating the 3DoF rotation from a single RGB image is an important yet challenging problem. As a popular approach, probabilistic rotation modeling additionally carries prediction uncertainty information, compared to single-prediction rotation regression. For modeling probabilistic distribution over SO(3), it is natural to use Gaussian-like Bingham distribution and matrix Fisher, however they are shown to be sensitive to outlier predictions, e.g. 180^circ error and thus are unlikely to converge with optimal performance. In this paper, we draw inspiration from multivariate Laplace distribution and propose a novel rotation Laplace distribution on SO(3). Our rotation Laplace distribution is robust to the disturbance of outliers and enforces much gradient to the low-error region that it can improve. In addition, we show that our method also exhibits robustness to small noises and thus tolerates imperfect annotations. With this benefit, we demonstrate its advantages in semi-supervised rotation regression, where the pseudo labels are noisy. To further capture the multi-modal rotation solution space for symmetric objects, we extend our distribution to rotation Laplace mixture model and demonstrate its effectiveness. Our extensive experiments show that our proposed distribution and the mixture model achieve state-of-the-art performance in all the rotation regression experiments over both probabilistic and non-probabilistic baselines.