Despite the promise of superior performance under challenging conditions, event-based motion estimation remains a hard problem owing to the difficulty of extracting and tracking stable features from event streams. In order to robustify the estimation, it is generally believed that fusion with other sensors is a requirement. In this work, we demonstrate reliable, purely event-based visual odometry on planar ground vehicles by employing the constrained non-holonomic motion model of Ackermann steering platforms. We extend single feature n-linearities for regular frame-based cameras to the case of quasi time-continuous event-tracks, and achieve a polynomial form via variable degree Taylor expansions. Robust averaging over multiple event tracks is simply achieved via histogram voting. As demonstrated on both simulated and real data, our algorithm achieves accurate and robust estimates of the vehicle's instantaneous rotational velocity, and thus results that are comparable to the delta rotations obtained by frame-based sensors under normal conditions. We furthermore significantly outperform the more traditional alternatives in challenging illumination scenarios. The code is available at \url{https://github.com/gowanting/NHEVO}.
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.
Event cameras are emerging vision sensors and their advantages are suitable for various applications such as autonomous robots. Contrast maximization (CMax), which provides state-of-the-art accuracy on motion estimation using events, may suffer from an overfitting problem called event collapse. Prior works are computationally expensive or cannot alleviate the overfitting, which undermines the benefits of the CMax framework. We propose a novel, computationally efficient regularizer based on geometric principles to mitigate event collapse. The experiments show that the proposed regularizer achieves state-of-the-art accuracy results, while its reduced computational complexity makes it two to four times faster than previous approaches. To the best of our knowledge, our regularizer is the only effective solution for event collapse without trading off runtime. We hope our work opens the door for future applications that unlocks the advantages of event cameras.
Contrast maximization (CMax) is a framework that provides state-of-the-art results on several event-based computer vision tasks, such as ego-motion or optical flow estimation. However, it may suffer from a problem called event collapse, which is an undesired solution where events are warped into too few pixels. As prior works have largely ignored the issue or proposed workarounds, it is imperative to analyze this phenomenon in detail. Our work demonstrates event collapse in its simplest form and proposes collapse metrics by using first principles of space-time deformation based on differential geometry and physics. We experimentally show on publicly available datasets that the proposed metrics mitigate event collapse and do not harm well-posed warps. To the best of our knowledge, regularizers based on the proposed metrics are the only effective solution against event collapse in the experimental settings considered, compared with other methods. We hope that this work inspires further research to tackle more complex warp models.
Contrast maximisation estimates the motion captured in an event stream by maximising the sharpness of the motion compensated event image. To carry out contrast maximisation, many previous works employ iterative optimisation algorithms, such as conjugate gradient, which require good initialisation to avoid converging to bad local minima. To alleviate this weakness, we propose a new globally optimal event-based motion estimation algorithm. Based on branch-and-bound (BnB), our method solves rotational (3DoF) motion estimation on event streams, which supports practical applications such as video stabilisation and attitude estimation. Underpinning our method are novel bounding functions for contrast maximisation, whose theoretical validity is rigorously established. We show concrete examples from public datasets where globally optimal solutions are vital to the success of contrast maximisation. Despite its exact nature, our algorithm is currently able to process a 50,000 event input in 300 seconds (a locally optimal solver takes 30 seconds on the same input), and has the potential to be further speeded-up using GPUs.
Star trackers are state-of-the-art attitude estimation devices which function by recognising and tracking star patterns. Most commercial star trackers use conventional optical sensors. A recent alternative is to use event sensors, which could enable more energy efficient and faster star trackers. However, this demands new algorithms that can efficiently cope with high-speed asynchronous data, and are feasible on resource-constrained computing platforms. To this end, we propose an event-based processing approach for star tracking. Our technique operates on the event stream from a star field, by using multiresolution Hough Transforms to time-progressively integrate event data and produce accurate relative rotations. Optimisation via rotation averaging is then used to fuse the relative rotations and jointly refine the absolute orientations. Our technique is designed to be feasible for asynchronous operation on standard hardware. Moreover, compared to state-of-the-art event-based motion estimation schemes, our technique is much more efficient and accurate.