# An N-Point Linear Solver for Line and Motion Estimation with Event Cameras

arXiv: https://arxiv.org/abs/2404.00842 · HTML: https://mlsanity.com/paper/2404.00842/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 47 references that are in the map.
- First posted on arXiv 1 Apr 2024.

## Builds on (most cited first, 21 of 21)

- [Event-based Vision: A Survey](https://mlsanity.com/paper/1904.08405/) (2019)
- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (2016)
- [Event-based Vision meets Deep Learning on Steering Prediction for Self-driving Cars](https://mlsanity.com/paper/1804.01310/) (2018)
- [A Unifying Contrast Maximization Framework for Event Cameras, with Applications to Motion, Depth, and Optical Flow Estimation](https://mlsanity.com/paper/1804.01306/) (2018)
- [Ultimate SLAM? Combining Events, Images, and IMU for Robust Visual SLAM in HDR and High Speed Scenarios](https://mlsanity.com/paper/1709.06310/) (2017)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [Event-based Stereo Visual Odometry](https://mlsanity.com/paper/2007.15548/) (2020)
- [Event-aided Direct Sparse Odometry](https://mlsanity.com/paper/2204.07640/) (2022)
- [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)
- [VECtor: A Versatile Event-Centric Benchmark for Multi-Sensor SLAM](https://mlsanity.com/paper/2207.01404/) (2022)
- [Event-Based Angular Velocity Regression with Spiking Networks](https://mlsanity.com/paper/2003.02790/) (2020)
- [DEVO: Depth-Event Camera Visual Odometry in Challenging Conditions](https://mlsanity.com/paper/2202.02556/) (2022)
- [Globally Optimal Contrast Maximisation for Event-based Motion Estimation](https://mlsanity.com/paper/2002.10686/) (2020)
- [Globally-Optimal Contrast Maximisation for Event Cameras](https://mlsanity.com/paper/2206.05127/) (2022)
- [IDOL: A Framework for IMU-DVS Odometry using Lines](https://mlsanity.com/paper/2008.05749/) (2020)
- [UV-SLAM: Unconstrained Line-based SLAM Using Vanishing Points for Structural Mapping](https://mlsanity.com/paper/2112.13515/) (2021)
- [High Speed Event Camera TRacking](https://mlsanity.com/paper/2010.02771/) (2020)
- [A 5-Point Minimal Solver for Event Camera Relative Motion Estimation](https://mlsanity.com/paper/2309.17054/) (2023)
- [Continuous Event-Line Constraint for Closed-Form Velocity Initialization](https://mlsanity.com/paper/2109.04313/) (2021)

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

- [Recent Event Camera Innovations: A Survey](https://mlsanity.com/paper/2408.13627/) (2024)
- [Full-DoF Egomotion Estimation for Event Cameras Using Geometric Solvers](https://mlsanity.com/paper/2503.03307/) (2025)
- [Event Camera Meets Mobile Embodied Perception: Abstraction, Algorithm, Acceleration, Application](https://mlsanity.com/paper/2503.22943/) (2025)
- [Minimal Solvers for Full DoF Motion Estimation from Asynchronous Tracks](https://mlsanity.com/paper/2508.17537/) (2025)
- [E-MoFlow: Learning Egomotion and Optical Flow from Event Data via Implicit Regularization](https://mlsanity.com/paper/2510.12753/) (2025)
- [Odometry Without Correspondence from Inertially Constrained Ruled Surfaces](https://mlsanity.com/paper/2512.00327/) (2025)
- [RoEL: Robust Event-based 3D Line Reconstruction](https://mlsanity.com/paper/2602.18258/) (2026)
- [Single-View Rolling-Shutter SfM](https://mlsanity.com/paper/2603.11888/) (2026)
- [A Geometric Framework for Absolute Pose and Velocity Estimation with Event Cameras](https://mlsanity.com/paper/2606.09139/) (2026)
- [Minimal Solvers for Full-DoF Motion Estimation from Asynchronous Differential SfM](https://mlsanity.com/paper/2606.09218/) (2026)
- [Event-Based Motion Estimation via Oriented Distance Fields](https://mlsanity.com/paper/2608.24223/) (2026)

## Abstract (arXiv)

Event cameras respond primarily to edges--formed by strong gradients--and are thus particularly well-suited for line-based motion estimation. Recent work has shown that events generated by a single line each satisfy a polynomial constraint which describes a manifold in the space-time volume. Multiple such constraints can be solved simultaneously to recover the partial linear velocity and line parameters. In this work, we show that, with a suitable line parametrization, this system of constraints is actually linear in the unknowns, which allows us to design a novel linear solver. Unlike existing solvers, our linear solver (i) is fast and numerically stable since it does not rely on expensive root finding, (ii) can solve both minimal and overdetermined systems with more than 5 events, and (iii) admits the characterization of all degenerate cases and multiple solutions. The found line parameters are singularity-free and have a fixed scale, which eliminates the need for auxiliary constraints typically encountered in previous work. To recover the full linear camera velocity we fuse observations from multiple lines with a novel velocity averaging scheme that relies on a geometrically-motivated residual, and thus solves the problem more efficiently than previous schemes which minimize an algebraic residual. Extensive experiments in synthetic and real-world settings demonstrate that our method surpasses the previous work in numerical stability, and operates over 600 times faster.