# Continuous Event-Line Constraint for Closed-Form Velocity Initialization

arXiv: https://arxiv.org/abs/2109.04313 · HTML: https://mlsanity.com/paper/2109.04313/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 10 of 10)

- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [Ultimate SLAM? Combining Events, Images, and IMU for Robust Visual SLAM in HDR and High Speed Scenarios](https://mlsanity.com/paper/1709.06310/) (2017)
- [Focus Is All You Need: Loss Functions For Event-based Vision](https://mlsanity.com/paper/1904.07235/) (2019)
- [Continuous-Time Visual-Inertial Odometry for Event Cameras](https://mlsanity.com/paper/1702.07389/) (2017)
- [Event-based, 6-DOF Camera Tracking from Photometric Depth Maps](https://mlsanity.com/paper/1607.03468/) (2016)
- [Globally Optimal Contrast Maximisation for Event-based Motion Estimation](https://mlsanity.com/paper/2002.10686/) (2020)
- [IDOL: A Framework for IMU-DVS Odometry using Lines](https://mlsanity.com/paper/2008.05749/) (2020)
- [Spatiotemporal Registration for Event-based Visual Odometry](https://mlsanity.com/paper/2103.05955/) (2021)
- [Hough2Map -- Iterative Event-based Hough Transform for High-Speed Railway Mapping](https://mlsanity.com/paper/2102.08145/) (2021)
- [cilantro: A Lean, Versatile, and Efficient Library for Point Cloud Data Processing](https://mlsanity.com/paper/1807.00399/) (2018)

## Built on by (most cited first, 11 of 11)

- [Line-based 6-DoF Object Pose Estimation and Tracking With an Event Camera](https://mlsanity.com/paper/2408.03225/) (2024)
- [A 5-Point Minimal Solver for Event Camera Relative Motion Estimation](https://mlsanity.com/paper/2309.17054/) (2023)
- [An N-Point Linear Solver for Line and Motion Estimation with Event Cameras](https://mlsanity.com/paper/2404.00842/) (2024)
- [Full-DoF Egomotion Estimation for Event Cameras Using Geometric Solvers](https://mlsanity.com/paper/2503.03307/) (2025)
- [Tight Fusion of Events and Inertial Measurements for Direct Velocity Estimation](https://mlsanity.com/paper/2401.09296/) (2024)
- [EVIT: Event-based Visual-Inertial Tracking in Semi-Dense Maps Using Windowed Nonlinear Optimization](https://mlsanity.com/paper/2408.01370/) (2024)
- [A Linear N-Point Solver for Structure and Motion from Asynchronous Tracks](https://mlsanity.com/paper/2507.22733/) (2025)
- [Continuous-Time Gaussian Process Motion-Compensation for Event-vision Pattern Tracking with Distance Fields](https://mlsanity.com/paper/2303.02672/) (2023)
- [Event-Based Visual Odometry on Non-Holonomic Ground Vehicles](https://mlsanity.com/paper/2401.09331/) (2024)
- [A Geometric Framework for Absolute Pose and Velocity Estimation with Event Cameras](https://mlsanity.com/paper/2606.09139/) (2026)
- [Event-driven dynamic trajectories reconstruction and measurement of mechanical parameters for fragments](https://mlsanity.com/paper/2606.09208/) (2026)

## Abstract (arXiv)

Event cameras trigger events asynchronously and independently upon a sufficient change of the logarithmic brightness level. The neuromorphic sensor has several advantages over standard cameras including low latency, absence of motion blur, and high dynamic range. Event cameras are particularly well suited to sense motion dynamics in agile scenarios. We propose the continuous event-line constraint, which relies on a constant-velocity motion assumption as well as trifocal tensor geometry in order to express a relationship between line observations given by event clusters as well as first-order camera dynamics. Our core result is a closed-form solver for up-to-scale linear camera velocity {with known angular velocity}. Nonlinear optimization is adopted to improve the performance of the algorithm. The feasibility of the approach is demonstrated through a careful analysis on both simulated and real data.