A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty
Open accessAbstract
Accurate rotation estimation is at the heart of robot perception tasks such as visual odometry and object pose estimation.Deep neural networks have provided a new way to perform these tasks, and the choice of rotation representation is an important part of network design.In this work, we present a novel symmetric matrix representation of the 3D rotation group, SO(3), with two important properties that make it particularly suitable for learned models: (1) it satisfies a smoothness property that improves convergence and generalization when regressing large rotation targets, and (2) it encodes a symmetric Bingham belief over the space of unit quaternions, permitting the training of uncertainty-aware models.We empirically validate the benefits of our formulation by training deep neural rotation regressors on two data modalities.First, we use synthetic point-cloud data to show that our representation leads to superior predictive accuracy over existing representations for arbitrary rotation targets.Second, we use image data collected onboard ground and aerial vehicles to demonstrate that our representation is amenable to an effective out-of-distribution (OOD) rejection technique that significantly improves the robustness of rotation estimates to unseen environmental effects and corrupted input images, without requiring the use of an explicit likelihood loss, stochastic sampling, or an auxiliary classifier.This capability is key for safety-critical applications where detecting novel inputs can prevent catastrophic failure of learned models.
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Higher-dimensional parameterizations of SO(3) have been proposed that do not suffer from discontinuities.
“In point cloud registration, higher-dimensional parameterizations of SO(3) have been proposed that do not suffer from this issue [32, 40, 57].”
From Intraoperative 2D/3D Image Registration via Differentiable X-Ray Rendering (2024) · cites this paper as [40]
The paper’s ‘Smooth Global Section of SO(3)’ section proves that its ten-dimensional rotation representation has a smooth, continuous mapping, supporting the claim about avoiding discontinuities. It tests rotation estimation on point clouds and mentions point-cloud registration in its ‘Learning-based Rotation Estimation’ section, but does not establish that its representation was proposed specifically for registration. (LLM, conf=0.84)
Experimental — accuracy not yet measuredHigher-dimensional alternatives (d>5) have theoretical advantages.
“This has motivated the development of several higher-dimensional (d>5) alternatives with theoretical advantages [32, 40, 57].”
From Intraoperative 2D/3D Image Registration via Differentiable X-Ray Rendering (2024) · cites this paper as [40]
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- Authors
- Peretroukhin, V., Giamou, M., Nicholas Greene, W., Rosen, D., Kelly, J., & Roy, N.
- Affiliations
- University of Toronto (CA)
- MIT Computer Science and Artificial Intelligence Laboratory (US)
- Venue
- Robotics: Science and Systems XVI
- Published
- 2020-07-12
- OpenAlex
- W3032131819
- Cited by
- 41
- References
- 28
- Citations by year
- 2026: 4 · 2025: 4 · 2024: 9 · 2023: 10 · 2022: 8 · 2021: 5 · 2020: 1
- FWCI
- 8.85
- Type
- conference paper
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Robotics: Science and Systems (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Engineering › Aerospace Engineering › Robotics and Sensor-Based Localization
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Neural Network Applications
- Physical Sciences › Engineering › Aerospace Engineering › Inertial Sensor and Navigation
- Keywords
- rotation representation, SO(3), Bingham distribution, uncertainty estimation, visual odometry, object pose estimation, point clouds, aerial vehicles
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