Linearly Solving Robust Rotation Estimation

TL;DR

This paper introduces a novel linear reformulation of rotation estimation problems, enabling robust, fast, and parallelizable solutions even with high outlier ratios, validated through experiments.

Contribution

It presents a new perspective that rotation estimation can be solved as a linear problem without constraints, improving robustness and computational efficiency.

Findings

Robust rotation estimation achieved with linear model fitting.

Method handles 99% outliers effectively.

Solution computed in under 0.5 seconds on large-scale problems.

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.