Event cameras are bio-inspired sensors that perform well in challenging illumination conditions and have high temporal resolution. However, their concept is fundamentally different from traditional frame-based cameras. The pixels of an event camera operate independently and asynchronously. They measure changes of the logarithmic brightness and return them in the highly discretised form of time-stamped events indicating a relative change of a certain quantity since the last event. New models and algorithms are needed to process this kind of measurements. The present work looks at several motion estimation problems with event cameras. The flow of the events is modelled by a general homographic warping in a space-time volume, and the objective is formulated as a maximisation of contrast within the image of warped events. Our core contribution consists of deriving globally optimal solutions to these generally non-convex problems, which removes the dependency on a good initial guess plaguing existing methods. Our methods rely on branch-and-bound optimisation and employ novel and efficient, recursive upper and lower bounds derived for six different contrast estimation functions. The practical validity of our approach is demonstrated by a successful application to three different event camera motion estimation problems.

We present a new solution to tracking and mapping with an event camera. The motion of the camera contains both rotation and translation displacements in the plane, and the displacements happen in an arbitrarily structured environment. As a result, the image matching may no longer be represented by a low-dimensional homographic warping, thus complicating an application of the commonly used Image of Warped Events (IWE). We introduce a new solution to this problem by performing contrast maximization in 3D. The 3D location of the rays cast for each event is smoothly varied as a function of a continuous-time motion parametrization, and the optimal parameters are found by maximizing the contrast in a volumetric ray density field. Our method thus performs joint optimization over motion and structure. The practical validity of our approach is supported by an application to AGV motion estimation and 3D reconstruction with a single vehicle-mounted event camera. The method approaches the performance obtained with regular cameras and eventually outperforms in challenging visual conditions.

Vision-based localization is a cost-effective and thus attractive solution for many intelligent mobile platforms. However, its accuracy and especially robustness still suffer from low illumination conditions, illumination changes, and aggressive motion. Event-based cameras are bio-inspired visual sensors that perform well in HDR conditions and have high temporal resolution, and thus provide an interesting alternative in such challenging scenarios. While purely event-based solutions currently do not yet produce satisfying mapping results, the present work demonstrates the feasibility of purely event-based tracking if an alternative sensor is permitted for mapping. The method relies on geometric 3D-2D registration of semi-dense maps and events, and achieves highly reliable and accurate cross-modal tracking results. Practically relevant scenarios are given by depth camera-supported tracking or map-based localization with a semi-dense map prior created by a regular image-based visual SLAM or structure-from-motion system. Conventional edge-based 3D-2D alignment is extended by a novel polarity-aware registration that makes use of signed time-surface maps (STSM) obtained from event streams. We furthermore introduce a novel culling strategy for occluded points. Both modifications increase the speed of the tracker and its robustness against occlusions or large view-point variations. The approach is validated on many real datasets covering the above-mentioned challenging conditions, and compared against similar solutions realised with regular cameras.

Traditional visual-inertial state estimation targets absolute camera poses and spatial landmark locations while first-order kinematics are typically resolved as an implicitly estimated substate. However, this poses a risk in velocity-based control scenarios, as the quality of the estimation of kinematics depends on the stability of absolute camera and landmark coordinates estimation. To address this issue, we propose a novel solution to tight visual–inertial fusion directly at the level of first-order kinematics by employing a dynamic vision sensor instead of a normal camera. More specifically, we leverage trifocal tensor geometry to establish an incidence relation that directly depends on events and camera velocity, and demonstrate how velocity estimates in highly dynamic situations can be obtained over short-time intervals. Noise and outliers are dealt with using a nested two-layer random sample consensus (RANSAC) scheme. In addition, smooth velocity signals are obtained from a tight fusion with preintegrated inertial signals using a sliding window optimizer. Experiments on both simulated and real data demonstrate that the proposed tight event-inertial fusion leads to continuous and reliable velocity estimation in highly dynamic scenarios independently of absolute coordinates. Furthermore, in extreme cases, it achieves more stable and more accurate estimation of kinematics than traditional, point-position-based visual-inertial odometry.

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an $n-1$ dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to four fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, point set registration, and rotation and focal length estimation. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios.