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.

翻译：事件相机非常适合基于直线的运动估计，因为它们主要对场景中的边缘做出响应。然而，基于事件精确确定相机位移仍然是一个未解决的问题。这是因为在使用事件相机时，直线特征提取与动力学估计紧密耦合，且目前尚无精确模型描述直线在事件时空体积中产生的复杂结构。我们通过推导此类流形的正确非线性参数化（称为事件尾流）解决了该问题，并演示了其在基于事件的线性运动估计中的应用，其中惯性测量单元已知旋转信息。利用该参数化，我们提出了一种新颖的5点最小求解器，可联合估计直线参数和线性相机速度投影；当考虑多条直线时，这些投影可融合为单个平均线性速度。我们在合成数据和真实数据上均证明，我们的求解器能生成比其他方法更稳定的相对运动估计，同时比基于时空平面的聚类方法捕获更多内点。特别地，我们的方法在线性速度估计中始终达到100%的成功率，而现有闭式求解器的成功率仅为23%至70%。所提出的事件尾流有助于更深入地理解时空事件生成几何结构，因此我们相信它将成为未来基于事件的运动估计算法的核心构建模块。