# A Probabilistic Rotation Representation for Symmetric Shapes With an Efficiently Computable Bingham Loss Function

arXiv: https://arxiv.org/abs/2305.18947 · HTML: https://mlsanity.com/paper/2305.18947/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 12 of 12)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [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)
- [EPro-PnP: Generalized End-to-End Probabilistic Perspective-n-Points for Monocular Object Pose Estimation](https://mlsanity.com/paper/2303.12787/) (2023)
- [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)
- [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)
- [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, 2 of 2)

- [Deterministic Object Pose Confidence Region Estimation](https://mlsanity.com/paper/2506.22720/) (2025)
- [Aleatoric Uncertainty from AI-based 6D Object Pose Predictors for Object-relative State Estimation](https://mlsanity.com/paper/2509.01583/) (2025)

## 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, it cannot represent the ambiguity of the observation. In order to handle the ambiguity, the Bingham distribution is one promising solution. However, it requires complicated calculation when yielding the negative log-likelihood (NLL) loss. An alternative easy-to-implement loss function has been proposed to avoid complex computations but has difficulty expressing symmetric distribution. In this paper, we introduce a fast-computable and easy-to-implement NLL loss function for Bingham distribution. We also create the inference network and show that our loss function can capture the symmetric property of target objects from their point clouds.