Labits: Layered Bidirectional Time Surfaces Representation for Event Camera-based Continuous Dense Trajectory Estimation

Event cameras provide a compelling alternative to traditional frame-based sensors, capturing dynamic scenes with high temporal resolution and low latency. Moving objects trigger events with precise timestamps along their trajectory, enabling smooth continuous-time estimation. However, few works have attempted to optimize the information loss during event representation construction, imposing a ceiling on this task. Fully exploiting event cameras requires representations that simultaneously preserve fine-grained temporal information, stable and characteristic 2D visual features, and temporally consistent information density, an unmet challenge in existing representations. We introduce Labits: Layered Bidirectional Time Surfaces, a simple yet elegant representation designed to retain all these features. Additionally, we propose a dedicated module for extracting active pixel local optical flow (APLOF), significantly boosting the performance. Our approach achieves an impressive 49% reduction in trajectory end-point error (TEPE) compared to the previous state-of-the-art on the MultiFlow dataset. The code will be released upon acceptance.

A Riemannian Take on Distance Fields and Geodesic Flows in Robotics

Distance functions are crucial in robotics for representing spatial relationships between the robot and the environment. It provides an implicit representation of continuous and differentiable shapes, which can seamlessly be combined with control, optimization, and learning techniques. While standard distance fields rely on the Euclidean metric, many robotic tasks inherently involve non-Euclidean structures. To this end, we generalize the use of Euclidean distance fields to more general metric spaces by solving a Riemannian eikonal equation, a first-order partial differential equation, whose solution defines a distance field and its associated gradient flow on the manifold, enabling the computation of geodesics and globally length-minimizing paths. We show that this \emph{geodesic distance field} can also be exploited in the robot configuration space. To realize this concept, we exploit physics-informed neural networks to solve the eikonal equation for high-dimensional spaces, which provides a flexible and scalable representation without the need for discretization. Furthermore, a variant of our neural eikonal solver is introduced, which enables the gradient flow to march across both task and configuration spaces. As an example of application, we validate the proposed approach in an energy-aware motion generation task. This is achieved by considering a manifold defined by a Riemannian metric in configuration space, effectively taking the property of the robot's dynamics into account. Our approach produces minimal-energy trajectories for a 7-axis Franka robot by iteratively tracking geodesics through gradient flow backpropagation.