# Probabilistic Rotation Representation With an Efficiently Computable Bingham Loss Function and Its Application to Pose Estimation

arXiv: https://arxiv.org/abs/2203.04456 · HTML: https://mlsanity.com/paper/2203.04456/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 9 Mar 2022.

## Builds on (most cited first, 10 of 10)

- [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)
- [Geometry-Aware Learning of Maps for Camera Localization](https://mlsanity.com/paper/1712.03342/) (2017)
- [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)
- [Deep Bingham Networks: Dealing with Uncertainty and Ambiguity in Pose Estimation](https://mlsanity.com/paper/2012.11002/) (2020)
- [6D Camera Relocalization in Ambiguous Scenes via Continuous Multimodal Inference](https://mlsanity.com/paper/2004.04807/) (2020)
- [Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC](https://mlsanity.com/paper/1805.12279/) (2018)
- [When Regression Meets Manifold Learning for Object Recognition and Pose Estimation](https://mlsanity.com/paper/1805.06400/) (2018)
- [Maximum likelihood estimation of the Fisher-Bingham distribution via efficient calculation of its normalizing constant](https://mlsanity.com/paper/2004.14660/) (2020)

## Built on by (most cited first, 1 of 1)

- [Uncertainty Quantification with Deep Ensembles for 6D Object Pose Estimation](https://mlsanity.com/paper/2403.07741/) (2024)

## Abstract (arXiv)

In recent years, a deep learning framework has been widely used for object pose estimation. While quaternion is a common choice for rotation representation of 6D pose, it cannot represent an uncertainty of the observation. In order to handle the uncertainty, Bingham distribution is one promising solution because this has suitable features, such as a smooth representation over SO(3), in addition to the ambiguity representation. However, it requires the complex computation of the normalizing constants. This is the bottleneck of loss computation in training neural networks based on Bingham representation. As such, we propose a fast-computable and easy-to-implement loss function for Bingham distribution. We also show not only to examine the parametrization of Bingham distribution but also an application based on our loss function.