# Deep Directional Statistics: Pose Estimation with Uncertainty Quantification

arXiv: https://arxiv.org/abs/1805.03430 · HTML: https://mlsanity.com/paper/1805.03430/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2018.

## Built on by (most cited first, 30 of 45)

- [Riemannian Score-Based Generative Modelling](https://mlsanity.com/paper/2202.02763/) (2022)
- [RelPose: Predicting Probabilistic Relative Rotation for Single Objects in the Wild](https://mlsanity.com/paper/2208.05963/) (2022)
- [SceneGen: Learning to Generate Realistic Traffic Scenes](https://mlsanity.com/paper/2101.06541/) (2021)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold](https://mlsanity.com/paper/2106.05965/) (2021)
- [Continuous 3D Multi-Channel Sign Language Production via Progressive Transformers and Mixture Density Networks](https://mlsanity.com/paper/2103.06982/) (2021)
- [Wide-Baseline Relative Camera Pose Estimation with Directional Learning](https://mlsanity.com/paper/2106.03336/) (2021)
- [Hierarchical Kinematic Probability Distributions for 3D Human Shape and Pose Estimation from Images in the Wild](https://mlsanity.com/paper/2110.00990/) (2021)
- [Probabilistic 3D Human Shape and Pose Estimation from Multiple Unconstrained Images in the Wild](https://mlsanity.com/paper/2103.10978/) (2021)
- [PoseContrast: Class-Agnostic Object Viewpoint Estimation in the Wild with Pose-Aware Contrastive Learning](https://mlsanity.com/paper/2105.05643/) (2021)
- [Image to Sphere: Learning Equivariant Features for Efficient Pose Prediction](https://mlsanity.com/paper/2302.13926/) (2023)
- [Orienting Novel 3D Objects Using Self-Supervised Learning of Rotation Transforms](https://mlsanity.com/paper/2105.14246/) (2021)
- [Confronting Ambiguity in 6D Object Pose Estimation via Score-Based Diffusion on SE(3)](https://mlsanity.com/paper/2305.15873/) (2023)
- [FisherMatch: Semi-Supervised Rotation Regression via Entropy-based Filtering](https://mlsanity.com/paper/2203.15765/) (2022)
- [SpyroPose: SE(3) Pyramids for Object Pose Distribution Estimation](https://mlsanity.com/paper/2303.05308/) (2023)
- [Delving into Discrete Normalizing Flows on SO(3) Manifold for Probabilistic Rotation Modeling](https://mlsanity.com/paper/2304.03937/) (2023)
- [Toward Reliable Human Pose Forecasting with Uncertainty](https://mlsanity.com/paper/2304.06707/) (2023)
- [The Role of Predictive Uncertainty and Diversity in Embodied AI and Robot Learning](https://mlsanity.com/paper/2405.03164/) (2024)
- [HHP-Net: A light Heteroscedastic neural network for Head Pose estimation with uncertainty](https://mlsanity.com/paper/2111.01440/) (2021)
- [A Laplace-inspired Distribution on SO(3) for Probabilistic Rotation Estimation](https://mlsanity.com/paper/2303.01743/) (2023)
- [Diverse Multimedia Layout Generation with Multi Choice Learning](https://mlsanity.com/paper/2301.06629/) (2023)
- [Lifting 2D Object Locations to 3D by Discounting LiDAR Outliers across Objects and Views](https://mlsanity.com/paper/2109.07945/) (2021)
- [Ki-Pode: Keypoint-based Implicit Pose Distribution Estimation of Rigid Objects](https://mlsanity.com/paper/2209.09659/) (2022)
- [An Uncertainty-aware Loss Function for Training Neural Networks with Calibrated Predictions](https://mlsanity.com/paper/2110.03260/) (2021)
- [Equivariant Single View Pose Prediction Via Induced and Restricted Representations](https://mlsanity.com/paper/2307.03704/) (2023)
- [Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distribution](https://mlsanity.com/paper/2305.10465/) (2023)
- [Shape Completion with Prediction of Uncertain Regions](https://mlsanity.com/paper/2308.00377/) (2023)
- [3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction](https://mlsanity.com/paper/2411.00543/) (2024)
- [SE(3)-PoseFlow: Estimating 6D Pose Distributions for Uncertainty-Aware Robotic Manipulation](https://mlsanity.com/paper/2511.01501/) (2025)
- [Learning to Predict Diverse Human Motions from a Single Image via Mixture Density Networks](https://mlsanity.com/paper/2109.05776/) (2021)

## Abstract (arXiv)

Modern deep learning systems successfully solve many perception tasks such as object pose estimation when the input image is of high quality. However, in challenging imaging conditions such as on low-resolution images or when the image is corrupted by imaging artifacts, current systems degrade considerably in accuracy. While a loss in performance is unavoidable, we would like our models to quantify their uncertainty in order to achieve robustness against images of varying quality. Probabilistic deep learning models combine the expressive power of deep learning with uncertainty quantification. In this paper, we propose a novel probabilistic deep learning model for the task of angular regression. Our model uses von Mises distributions to predict a distribution over object pose angle. Whereas a single von Mises distribution is making strong assumptions about the shape of the distribution, we extend the basic model to predict a mixture of von Mises distributions. We show how to learn a mixture model using a finite and infinite number of mixture components. Our model allows for likelihood-based training and efficient inference at test time. We demonstrate on a number of challenging pose estimation datasets that our model produces calibrated probability predictions and competitive or superior point estimates compared to the current state-of-the-art.