We tackle the problem of bundle adjustment (i.e., simultaneous refinement of camera poses and scene map) for a purely rotating event camera. Starting from first principles, we formulate the problem as a classical non-linear least squares optimization. The photometric error is defined using the event generation model directly in the camera rotations and the semi-dense scene brightness that triggers the events. We leverage the sparsity of event data to design a tractable Levenberg-Marquardt solver that handles the very large number of variables involved. To the best of our knowledge, our method, which we call Event-based Photometric Bundle Adjustment (EPBA), is the first event-only photometric bundle adjustment method that works on the brightness map directly and exploits the space-time characteristics of event data, without having to convert events into image-like representations. Comprehensive experiments on both synthetic and real-world datasets demonstrate EPBA's effectiveness in decreasing the photometric error (by up to 90%), yielding results of unparalleled quality. The refined maps reveal details that were hidden using prior state-of-the-art rotation-only estimation methods. The experiments on modern high-resolution event cameras show the applicability of EPBA to panoramic imaging in various scenarios (without map initialization, at multiple resolutions, and in combination with other methods, such as IMU dead reckoning or previous event-based rotation estimation methods). We make the source code publicly available. https://github.com/tub-rip/epba

翻译：本文研究纯旋转事件相机的光束法平差问题（即同时优化相机位姿与场景地图）。我们从基本原理出发，将该问题表述为经典的非线性最小二乘优化问题。摄影测量误差直接依据相机旋转运动与触发事件的半稠密场景亮度所对应的事件生成模型进行定义。我们利用事件数据的稀疏特性，设计了一种可处理的列文伯格-马夸尔特求解器，以应对所涉及的海量变量。据我们所知，我们提出的方法——基于事件的摄影测量光束法平差（EPBA）——是首个直接处理亮度图、利用事件数据时空特性、且无需将事件转换为类图像表示的事件专用摄影测量光束法平差方法。在合成数据集和真实数据集上的综合实验表明，EPBA能有效降低摄影测量误差（最高达90%），并产生无与伦比的质量结果。优化后的地图揭示了先前最先进的纯旋转估计方法所隐藏的细节。在现代高分辨率事件相机上的实验证明了EPBA在各种场景下全景成像的适用性（无需地图初始化、支持多分辨率、并能与其他方法结合使用，如IMU航位推算或先前基于事件的旋转估计方法）。我们已公开源代码。https://github.com/tub-rip/epba