A Height-Constrained 2-Point Minimal Solver for Pose Estimation from Active LED Markers with Event Cameras
Authors: Runze Yuan, Alexander Kappler, Jun Zhang, Kuangyi Chen, Fabio Morbidi, Pascal Vasseur, Cédric Demonceaux, Friedrich Fraundorfer
Organizations: Institute of Visual Computing, Graz University of Technology · MIS laboratory, University of Picardie Jules Verne · ICB laboratory, University of Burgundy Europe
Abstract
In many autonomous applications requiring real-time localization, active marker-based systems are preferred due to their low latency and ease of deployment compared to computationally demanding feature-based methods. Event~\mbox{cameras} offer high temporal resolution and minimal delay and are commonly used with active LED markers for robust real-time localization. Existing methods typically rely on Perspective-n-Point (PnP) solvers for pose estimation. However, structured marker layouts can be challenging to deploy in space-constrained scenarios, while partial self-motion information (e.g., gravity direction and altitude) is readily available from onboard sensors. We derive a robust and accurate minimal solver that estimates camera pose from only two LED markers by incorporating known tilt angle and camera height measured by an onboard sensor, such as an IMU or an altimeter. The proposed formulation uniquely determines the camera pose through both a closed-form and a linear least-squares solution. We further analyze degenerate configurations and characterize the conditions under which height information does not contribute to rotation estimation. For evaluation, we developed an event-based active marker system to collect real-world data with ground truth from a motion capture system. Experiments on both synthetic and real data demonstrate improved accuracy over the state-of-the-art P2P solver and competitive performance relative to P3P.
This paper presents a new algorithm to estimate absolute camera pose given an axis of the camera's rotation matrix. Current algorithms solve the problem via algebraic solutions on limited input domains. This paper shows that the problem can be solved efficiently by finding the intersection points of a hyperbola and the unit circle. The solution can flexibly accommodate combinations of point and line features in minimal and overconstrained configurations. In addition, the two special cases of planar and minimal configurations are identified to yield simpler closed-form solutions. Extensive experiments validate the approach.
Despite the rapid advancements in event-based motion estimation, current geometric methods primarily focus on velocity estimation. However, absolute pose estimation, which is equally crucial for key applications such as robotic navigation and augmented reality, remains relatively underexplored. Consequently, the simultaneous recovery of absolute pose and velocity from event streams remains an open and challenging problem. To address this gap, we propose a geometric framework for absolute pose and velocity estimation by leveraging 3D lines in the scene and the events they trigger. At the core of the framework lie two key geometric constraints: the orthogonality between a 3D line and the normal vector of its corresponding event plane, and the collinearity of an event with the 2D projection of its associated line. Based on these constraints, we present both linear and polynomial solvers for absolute pose estimation. The former enables efficient computation, while the latter provides a globally optimal solution for rotation. For velocity estimation, we develop an efficient linear solver and a more accurate optimization-based solver to recover both angular and linear velocities. Notably, our methods require a minimum of three event-line correspondences to determine the 6-DoF absolute pose or velocities independently. Extensive experiments in simulation and on real-world datasets demonstrate that our methods achieve state-of-the-art performance, with significant improvements in accuracy and computational efficiency compared to existing methods. The demo code is publicly available at https://github.com/Zibin6/EventPoseVelocity.
With the advancement of visual sensing systems, computer vision is playing an increasingly important role in autonomous driving and robot navigation. Relative pose estimation in multi-camera systems is essential for accurate vehicle localization and environment perception, demanding high real-time performance and robustness. Existing methods, however, often involve high computational costs and rely heavily on abundant feature matches, limiting their applicability in time-sensitive driving scenarios. To address these limitations, this paper introduces a unified framework for efficient relative pose estimation, built upon a novel translation parameterization and first-order rotation approximation. Within this framework, we propose three efficient minimal solvers specifically designed for autonomous vehicles. The first solver integrates the vertical direction prior from Inertial Measurement Units (IMUs), the second utilizes the rotation axis direction prior during steering maneuvers, and the third is designed for planar motion - a realistic assumption for ground vehicles operating on structured roads. By reducing both the minimal number of point correspondences and the algebraic complexity, our methods enable faster hypothesis generation within RANSAC-based pipelines, improving suitability for real-time systems. Extensive experiments on synthetic datasets and the KITTI autonomous driving benchmark demonstrate that the proposed solvers achieve a favorable balance between speed and accuracy compared to existing state-of-the-art algorithms.