Aggregation Functions for Simultaneous Attitude and Image Estimation With Event Cameras at High Angular Rates

Abstract

For fast-moving event cameras, projection of events onto the image frame exhibits smearing of events analogous to high motion blur. For camera attitude estimation, this presents a causality dilemma where motion prior is required to unsmear events, but an image prior is required to estimate motion. This dilemma is typically circumvented by including an IMU to provide motion priors. However, IMUs limited dynamic range of ±2000 • /s are shown to be insufficient for high angular rate rotorcrafts. Contrast Maximization is an event-only optimization framework that computes the optimal motion compensation parameter while generating an event image simultaneously. This paper analyses the performance of existing aggregation functions of the contrast maximization framework and proposes a nonconvolution-based aggregation function that outperforms existing implementations. The use of discrete event images for optimizers is discussed, demonstrating alternate avenues of the framework to exploit. The effect of motion blur in motion-compensated images is defined and studied for Contrast Maximisation at high angular rates. Lastly, the framework is applied to rotation datasets with angular rates exceeding 2000 • /s to demonstrate high angular rate motion estimation without motion priors.

Event Collapse in Contrast Maximization Frameworks

“…Each IWE pixel sums the values of the warped events that fall within it: if polarity is used or if polarity is not used. The Dirac delta is in practice replaced by a smooth approximation [ 33 ], such as a Gaussian, with pixel. A popular objective function is the visual contrast of the IWE ( 3 ), given by the variance with mean and image domain .…”

Formulating Event-based Image Reconstruction as a Linear Inverse Problem with Deep Regularization using Optical Flow

“…The delta δ in ( 5) is an idealized model amenable for integration. In practice it is replaced by a kernel, such as a Gaussian δ(x) ≈ N (x; 0, 2 Id), where ≈ 1 pixel and Id is the identity matrix [26], [36]. For speed-up, it is implemented using bilinear voting and Gaussian convolution [37].…”

Design, Modeling and Control of a Two Flight Mode Capable Single Wing Rotorcraft With Mid-Air Transition Ability

“…The spinning nature of the platform also helped in passively scanning and mapping the surrounding environment using Simultaneous Localization and Mapping (SLAM) in [12]. Similarly, in [13] and [14], the authors have shown applications for the monocopter for simultaneous image and onboard state estimation and LiDAR inertial odometry, respectively. On the other hand, a bicopter UAV uses two motors to generate collective lift force and torque in the roll axis using differential thrust.…”

“…Moreover, recent research has also demonstrated that the rotating wing platform has superior power efficiency compared to other platforms [22]. Monocopters can be employed for various applications where the spinning nature of the platform can be utilized, for example, passively scanning and mapping the surrounding environment as done in [12], [13]. However, even though the monocopter platform is based on a single wing, the physical footprint of the spinning drone is large enough to hinder its mobility.…”