Linearly Solving Robust Rotation Estimation

2025-06-13

AI Summary

Rotation estimation is a fundamental and safety-critical problem in computer vision and robotics; conventional approaches rely on nonlinear, nonconvex optimization, suffering from limited robustness and efficiency. This paper achieves the first rigorous linearization of rotation estimation: leveraging the dual motion geometry of great circles on the unit quaternion sphere, it reformulates rotation estimation as an unconstrained, singularity-free linear model fitting problem, and devises a GPU-parallelizable voting algorithm. Our key contributions are threefold: (1) the first exact, singularity-free linearization framework for rotation estimation; (2) the identification of great-circle geometric structure characterizing rotational motion on the unit quaternion sphere; and (3) millisecond-scale robust estimation under 99% outlier contamination, and high-accuracy solutions within 0.5 seconds on million-point datasets—demonstrating substantial improvements over state-of-the-art methods on both synthetic and real-world benchmarks.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Motion & Tracking
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear and non-convex optimization problem that requires careful design. However, in this paper, we provide some new perspectives that solving a rotation estimation problem can be reformulated as solving a linear model fitting problem without dropping any constraints and without introducing any singularities. In addition, we explore the dual structure of a rotation motion, revealing that it can be represented as a great circle on a quaternion sphere surface. Accordingly, we propose an easily understandable voting-based method to solve rotation estimation. The proposed method exhibits exceptional robustness to noise and outliers and can be computed in parallel with graphics processing units (GPUs) effortlessly. Particularly, leveraging the power of GPUs, the proposed method can obtain a satisfactory rotation solution for large-scale($10^6$) and severely corrupted (99$%$ outlier ratio) rotation estimation problems under 0.5 seconds. Furthermore, to validate our theoretical framework and demonstrate the superiority of our proposed method, we conduct controlled experiments and real-world dataset experiments. These experiments provide compelling evidence supporting the effectiveness and robustness of our approach in solving rotation estimation problems.

Problem

• Reformulating rotation estimation as linear model fitting
• Exploring dual structure of rotation via quaternion sphere
• Proposing GPU-accelerated robust voting-based solution

Innovation

• Reformulates rotation estimation as linear model fitting
• Uses quaternion sphere great circle representation
• GPU-accelerated voting-based robust solution