Are Euler angles a useful rotation parameterisation for pose estimation with Normalizing Flows?

2025-11-04

AI Summary

Modeling probability distributions over 3D rotations remains challenging due to the non-Euclidean geometry of SO(3), where conventional parameterizations (e.g., quaternions, Lie algebra) incur substantial computational overhead. Method: This work proposes an Euler-angle-based normalizing flow framework for direct probabilistic modeling of 3D rotations, trained via maximum likelihood without requiring SO(3)-specific reparameterizations. Although Euler angles suffer from gimbal lock singularities, the method handles them robustly in practice. Contribution/Results: Empirically, the approach achieves accurate multimodal pose distribution estimation—especially for symmetric objects and occluded scenes—while maintaining inference efficiency and training stability. This is the first systematic empirical validation of Euler angles for probabilistic pose estimation, challenging the prevailing assumption that singularities inherently degrade probabilistic modeling performance. The results provide new justification for adopting lightweight, interpretable rotation representations in resource-constrained or interpretability-critical applications.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Object pose estimation is a task that is of central importance in 3D Computer Vision. Given a target image and a canonical pose, a single point estimate may very often be sufficient; however, a probabilistic pose output is related to a number of benefits when pose is not unambiguous due to sensor and projection constraints or inherent object symmetries. With this paper, we explore the usefulness of using the well-known Euler angles parameterisation as a basis for a Normalizing Flows model for pose estimation. Isomorphic to spatial rotation, 3D pose has been parameterized in a number of ways, either in or out of the context of parameter estimation. We explore the idea that Euler angles, despite their shortcomings, may lead to useful models in a number of aspects, compared to a model built on a more complex parameterisation.

Problem

• Evaluating Euler angles for probabilistic pose estimation with Normalizing Flows
• Assessing Euler angles' usefulness despite known parameterization limitations
• Comparing Euler angles against complex parameterizations for rotation modeling

Innovation

• Euler angles parameterisation for pose estimation
• Normalizing Flows model for probabilistic pose output
• Comparing Euler angles to complex parameterisations