A 5-Point Minimal Solver for Event Camera Relative Motion Estimation

TL;DR

The paper addresses the challenge of estimating camera displacement from events produced by line features in event cameras. It introduces eventails, a geometric manifold that tightly couples line geometry and motion, and derives a minimal 5-point solver that jointly estimates line parameters and observable velocity components with known rotation. A velocity averaging scheme fuses partial observations from multiple eventails to produce a robust, full linear velocity estimate, improving stability and inlier recovery over plane-based methods. Experiments on synthetic and real data show a substantial boost in robustness and velocity estimation accuracy, including a 100% success rate on velocity estimation in real-world benchmarks, suggesting eventails as a foundational tool for future event-based motion estimation.

Abstract

Event-based cameras are ideal for line-based motion estimation, since they predominantly respond to edges in the scene. However, accurately determining the camera displacement based on events continues to be an open problem. This is because line feature extraction and dynamics estimation are tightly coupled when using event cameras, and no precise model is currently available for describing the complex structures generated by lines in the space-time volume of events. We solve this problem by deriving the correct non-linear parametrization of such manifolds, which we term eventails, and demonstrate its application to event-based linear motion estimation, with known rotation from an Inertial Measurement Unit. Using this parametrization, we introduce a novel minimal 5-point solver that jointly estimates line parameters and linear camera velocity projections, which can be fused into a single, averaged linear velocity when considering multiple lines. We demonstrate on both synthetic and real data that our solver generates more stable relative motion estimates than other methods while capturing more inliers than clustering based on spatio-temporal planes. In particular, our method consistently achieves a 100% success rate in estimating linear velocity where existing closed-form solvers only achieve between 23% and 70%. The proposed eventails contribute to a better understanding of spatio-temporal event-generated geometries and we thus believe it will become a core building block of future event-based motion estimation algorithms.

Figures (5)

• Figure 1: An event camera observing two non-parallel lines and moving with constant linear and angular velocity. The events triggered by each line lie on a manifold, which we call an eventail. We derive a minimal 5-point solver to estimate the parameters of the manifold, which includes both camera motion and scene geometry. Clustering these events based on spatio-temporal planes as done in previous work le2020idolpeng2021continuous generates many spurious clusters (colorful points) with many outliers (grey points). Instead, eventails result in two large clusters with fewer outliers, and a velocity direction error of only 0.01rad.
• Figure 2: Incidence relationship between the line $\mathbf{L}$ with the two-point-two-plane parametrization, and the event with the bearing vector $\mathbf{f}_{j}'$. Camera velocity is given in the line-dependent reference frame $\mathbf{R}_{\ell}=[\mathbf{e}^\ell_{1} \, \mathbf{e}^\ell_{2} \, \mathbf{e}^\ell_{3}]$.
• Figure 3: The chosen elimination template for our 5-point solver.
• Figure 4: Results for the directional accuracy of the partially observed camera velocity as a function of noise in the event timestamps, the measured angular velocity, and the event locations. Each box denotes the range from the first quartile to the third quartile of the error distribution. The median is marked as the black line in the middle.
• Figure 5: Average directional errors of fully estimated linear velocity over ten éventails. Results are evaluated for clean and noisy data, and different violations of the motion model assumptions.