# A 5-Point Minimal Solver for Event Camera Relative Motion Estimation

arXiv: https://arxiv.org/abs/2309.17054 · HTML: https://mlsanity.com/paper/2309.17054/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 52 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 19 of 19)

- [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)
- [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)
- [VECtor: A Versatile Event-Centric Benchmark for Multi-Sensor SLAM](https://mlsanity.com/paper/2207.01404/) (2022)
- [Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm](https://mlsanity.com/paper/1906.02290/) (2019)
- [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)
- [High Speed Event Camera TRacking](https://mlsanity.com/paper/2010.02771/) (2020)
- [Continuous Event-Line Constraint for Closed-Form Velocity Initialization](https://mlsanity.com/paper/2109.04313/) (2021)
- [Globally-Optimal Event Camera Motion Estimation](https://mlsanity.com/paper/2203.03914/) (2022)
- [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, 13 of 13)

- [AE-NeRF: Augmenting Event-Based Neural Radiance Fields for Non-ideal Conditions and Larger Scene](https://mlsanity.com/paper/2501.02807/) (2025)
- [Motion and Structure from Event-based Normal Flow](https://mlsanity.com/paper/2407.12239/) (2024)
- [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)
- [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)
- [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)
- [Event-based Facial Keypoint Alignment via Cross-Modal Fusion Attention and Self-Supervised Multi-Event Representation Learning](https://mlsanity.com/paper/2509.24968/) (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)
- [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)

## Abstract (arXiv)

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.