# Globally Optimal Contrast Maximisation for Event-based Motion Estimation

arXiv: https://arxiv.org/abs/2002.10686 · HTML: https://mlsanity.com/paper/2002.10686/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2020.

## Built on by (most cited first, 30 of 33)

- [Recent Event Camera Innovations: A Survey](https://mlsanity.com/paper/2408.13627/) (2024)
- [Ev-NeRF: Event Based Neural Radiance Field](https://mlsanity.com/paper/2206.12455/) (2022)
- [DEVO: Depth-Event Camera Visual Odometry in Challenging Conditions](https://mlsanity.com/paper/2202.02556/) (2022)
- [Event Collapse in Contrast Maximization Frameworks](https://mlsanity.com/paper/2207.04007/) (2022)
- [Globally-Optimal Contrast Maximisation for Event Cameras](https://mlsanity.com/paper/2206.05127/) (2022)
- [CMax-SLAM: Event-based Rotational-Motion Bundle Adjustment and SLAM System using Contrast Maximization](https://mlsanity.com/paper/2403.08119/) (2024)
- [Deep Event Visual Odometry](https://mlsanity.com/paper/2312.09800/) (2023)
- [The Spatio-Temporal Poisson Point Process: A Simple Model for the Alignment of Event Camera Data](https://mlsanity.com/paper/2106.06887/) (2021)
- [Real-Time Optical Flow for Vehicular Perception with Low- and High-Resolution Event Cameras](https://mlsanity.com/paper/2112.10591/) (2021)
- [Comparing Representations in Tracking for Event Camera-based SLAM](https://mlsanity.com/paper/2104.09887/) (2021)
- [Spatiotemporal Registration for Event-based Visual Odometry](https://mlsanity.com/paper/2103.05955/) (2021)
- [Event-based Simultaneous Localization and Mapping: A Comprehensive Survey](https://mlsanity.com/paper/2304.09793/) (2023)
- [EV-Catcher: High-Speed Object Catching Using Low-latency Event-based Neural Networks](https://mlsanity.com/paper/2304.07200/) (2023)
- [EF-3DGS: Event-Aided Free-Trajectory 3D Gaussian Splatting](https://mlsanity.com/paper/2410.15392/) (2024)
- [Visual Odometry with an Event Camera Using Continuous Ray Warping and Volumetric Contrast Maximization](https://mlsanity.com/paper/2107.03011/) (2021)
- [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)
- [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)
- [Asynchronous Optimisation for Event-based Visual Odometry](https://mlsanity.com/paper/2203.01037/) (2022)
- [Globally Optimal Event-Based Divergence Estimation for Ventral Landing](https://mlsanity.com/paper/2209.13168/) (2022)
- [Cross-Modal Semi-Dense 6-DoF Tracking of an Event Camera in Challenging Conditions](https://mlsanity.com/paper/2401.08043/) (2024)
- [E3NeRF: Efficient Event-Enhanced Neural Radiance Fields from Blurry Images](https://mlsanity.com/paper/2408.01840/) (2024)
- [Out of the Room: Generalizing Event-Based Dynamic Motion Segmentation for Complex Scenes](https://mlsanity.com/paper/2403.04562/) (2024)
- [Tight Fusion of Events and Inertial Measurements for Direct Velocity Estimation](https://mlsanity.com/paper/2401.09296/) (2024)
- [Event Camera Meets Mobile Embodied Perception: Abstraction, Algorithm, Acceleration, Application](https://mlsanity.com/paper/2503.22943/) (2025)
- [Density Invariant Contrast Maximization for Neuromorphic Earth Observations](https://mlsanity.com/paper/2304.14125/) (2023)
- [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)

## Abstract (arXiv)

Contrast maximisation estimates the motion captured in an event stream by maximising the sharpness of the motion compensated event image. To carry out contrast maximisation, many previous works employ iterative optimisation algorithms, such as conjugate gradient, which require good initialisation to avoid converging to bad local minima. To alleviate this weakness, we propose a new globally optimal event-based motion estimation algorithm. Based on branch-and-bound (BnB), our method solves rotational (3DoF) motion estimation on event streams, which supports practical applications such as video stabilisation and attitude estimation. Underpinning our method are novel bounding functions for contrast maximisation, whose theoretical validity is rigorously established. We show concrete examples from public datasets where globally optimal solutions are vital to the success of contrast maximisation. Despite its exact nature, our algorithm is currently able to process a 50,000 event input in 300 seconds (a locally optimal solver takes 30 seconds on the same input), and has the potential to be further speeded-up using GPUs.