# Probabilistic orientation estimation with matrix Fisher distributions

arXiv: https://arxiv.org/abs/2006.09740 · HTML: https://mlsanity.com/paper/2006.09740/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2020.

## Built on by (most cited first, 30 of 36)

- [RelPose: Predicting Probabilistic Relative Rotation for Single Objects in the Wild](https://mlsanity.com/paper/2208.05963/) (2022)
- [Deep Regression on Manifolds: A 3D Rotation Case Study](https://mlsanity.com/paper/2103.16317/) (2021)
- [Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold](https://mlsanity.com/paper/2106.05965/) (2021)
- [Hierarchical Kinematic Probability Distributions for 3D Human Shape and Pose Estimation from Images in the Wild](https://mlsanity.com/paper/2110.00990/) (2021)
- [Extreme Rotation Estimation using Dense Correlation Volumes](https://mlsanity.com/paper/2104.13530/) (2021)
- [Equivariant Adaptation of Large Pretrained Models](https://mlsanity.com/paper/2310.01647/) (2023)
- [Probabilistic 3D Human Shape and Pose Estimation from Multiple Unconstrained Images in the Wild](https://mlsanity.com/paper/2103.10978/) (2021)
- [HuManiFlow: Ancestor-Conditioned Normalising Flows on SO(3) Manifolds for Human Pose and Shape Distribution Estimation](https://mlsanity.com/paper/2305.06968/) (2023)
- [Image to Sphere: Learning Equivariant Features for Efficient Pose Prediction](https://mlsanity.com/paper/2302.13926/) (2023)
- [XVO: Generalized Visual Odometry via Cross-Modal Self-Training](https://mlsanity.com/paper/2309.16772/) (2023)
- [FisherMatch: Semi-Supervised Rotation Regression via Entropy-based Filtering](https://mlsanity.com/paper/2203.15765/) (2022)
- [Delving into Discrete Normalizing Flows on SO(3) Manifold for Probabilistic Rotation Modeling](https://mlsanity.com/paper/2304.03937/) (2023)
- [SimpleEgo: Predicting Probabilistic Body Pose from Egocentric Cameras](https://mlsanity.com/paper/2401.14785/) (2024)
- [A Laplace-inspired Distribution on SO(3) for Probabilistic Rotation Estimation](https://mlsanity.com/paper/2303.01743/) (2023)
- [Ki-Pode: Keypoint-based Implicit Pose Distribution Estimation of Rigid Objects](https://mlsanity.com/paper/2209.09659/) (2022)
- [Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distribution](https://mlsanity.com/paper/2305.10465/) (2023)
- [Unified framework for diffusion generative models in SO(3): applications in computer vision and astrophysics](https://mlsanity.com/paper/2312.11707/) (2023)
- [3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction](https://mlsanity.com/paper/2411.00543/) (2024)
- [ZeroVO: Visual Odometry with Minimal Assumptions](https://mlsanity.com/paper/2506.08005/) (2025)
- [Efficient Molecular Conformer Generation with SO(3)-Averaged Flow Matching and Reflow](https://mlsanity.com/paper/2507.09785/) (2025)
- [Probabilistic Regression with Huber Distributions](https://mlsanity.com/paper/2111.10296/) (2021)
- [Stable Object Reorientation using Contact Plane Registration](https://mlsanity.com/paper/2208.08962/) (2022)
- [Learning Implicit Probability Distribution Functions for Symmetric Orientation Estimation from RGB Images Without Pose Labels](https://mlsanity.com/paper/2211.11394/) (2022)
- [Semi-Supervised Unconstrained Head Pose Estimation in the Wild](https://mlsanity.com/paper/2404.02544/) (2024)
- [Are Euler angles a useful rotation parameterisation for pose estimation with Normalizing Flows?](https://mlsanity.com/paper/2511.02277/) (2025)
- [MOSS: Motion-based 3D Clothed Human Synthesis from Monocular Video](https://mlsanity.com/paper/2405.12806/) (2024)
- [Riemannian Neural Geodesic Interpolant](https://mlsanity.com/paper/2504.15736/) (2025)
- [RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization](https://mlsanity.com/paper/2505.13289/) (2025)
- [Matching the Optimal Denoiser in Point Cloud Diffusion with (Improved) Rotational Alignment](https://mlsanity.com/paper/2510.03335/) (2025)
- [MimiCAT: Mimic with Correspondence-Aware Cascade-Transformer for Category-Free 3D Pose Transfer](https://mlsanity.com/paper/2511.18370/) (2025)

## Abstract (arXiv)

This paper focuses on estimating probability distributions over the set of 3D rotations (SO(3)) using deep neural networks. Learning to regress models to the set of rotations is inherently difficult due to differences in topology between ℝN and SO(3). We overcome this issue by using a neural network to output the parameters for a matrix Fisher distribution since these parameters are homeomorphic to ℝ9. By using a negative log likelihood loss for this distribution we get a loss which is convex with respect to the network outputs. By optimizing this loss we improve state-of-the-art on several challenging applicable datasets, namely Pascal3D+, ModelNet10-SO(3) and UPNA head pose.