# Globally-Optimal Contrast Maximisation for Event Cameras

arXiv: https://arxiv.org/abs/2206.05127 · HTML: https://mlsanity.com/paper/2206.05127/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 87 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 28 of 28)

- [High Speed and High Dynamic Range Video with an Event Camera](https://mlsanity.com/paper/1906.07165/) (2019)
- [Unsupervised Event-based Learning of Optical Flow, Depth, and Egomotion](https://mlsanity.com/paper/1812.08156/) (2018)
- [EV-FlowNet: Self-Supervised Optical Flow Estimation for Event-based Cameras](https://mlsanity.com/paper/1802.06898/) (2018)
- [The Event-Camera Dataset and Simulator: Event-based Data for Pose Estimation, Visual Odometry, and SLAM](https://mlsanity.com/paper/1610.08336/) (2016)
- [A Unifying Contrast Maximization Framework for Event Cameras, with Applications to Motion, Depth, and Optical Flow Estimation](https://mlsanity.com/paper/1804.01306/) (2018)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [Bringing a Blurry Frame Alive at High Frame-Rate with an Event Camera](https://mlsanity.com/paper/1811.10180/) (2018)
- [Event-based Moving Object Detection and Tracking](https://mlsanity.com/paper/1803.04523/) (2018)
- [Event-based Stereo Visual Odometry](https://mlsanity.com/paper/2007.15548/) (2020)
- [Spike-FlowNet: Event-based Optical Flow Estimation with Energy-Efficient Hybrid Neural Networks](https://mlsanity.com/paper/2003.06696/) (2020)
- [Focus Is All You Need: Loss Functions For Event-based Vision](https://mlsanity.com/paper/1904.07235/) (2019)
- [Event-Based Motion Segmentation by Motion Compensation](https://mlsanity.com/paper/1904.01293/) (2019)
- [Semi-Dense 3D Reconstruction with a Stereo Event Camera](https://mlsanity.com/paper/1807.07429/) (2018)
- [Continuous-Time Visual-Inertial Odometry for Event Cameras](https://mlsanity.com/paper/1702.07389/) (2017)
- [Event-Based Angular Velocity Regression with Spiking Networks](https://mlsanity.com/paper/2003.02790/) (2020)
- [Globally Optimal Contrast Maximisation for Event-based Motion Estimation](https://mlsanity.com/paper/2002.10686/) (2020)
- [Realtime Time Synchronized Event-based Stereo](https://mlsanity.com/paper/1803.09025/) (2018)
- [GOGMA: Globally-Optimal Gaussian Mixture Alignment](https://mlsanity.com/paper/1603.00150/) (2016)
- [Simultaneous Optical Flow and Segmentation (SOFAS) using Dynamic Vision Sensor](https://mlsanity.com/paper/1805.12326/) (2018)
- [End-to-end Learning of Object Motion Estimation from Retinal Events for Event-based Object Tracking](https://mlsanity.com/paper/2002.05911/) (2020)
- [The Alignment of the Spheres: Globally-Optimal Spherical Mixture Alignment for Camera Pose Estimation](https://mlsanity.com/paper/1812.01232/) (2018)
- [Globally-Optimal Inlier Set Maximisation for Simultaneous Camera Pose and Feature Correspondence](https://mlsanity.com/paper/1709.09384/) (2017)
- [Neuromorphic Visual Odometry System for Intelligent Vehicle Application with Bio-inspired Vision Sensor](https://mlsanity.com/paper/1909.02490/) (2019)
- [Globally-Optimal Event Camera Motion Estimation](https://mlsanity.com/paper/2203.03914/) (2022)
- [Unsupervised Learning of Dense Optical Flow, Depth and Egomotion from Sparse Event Data](https://mlsanity.com/paper/1809.08625/) (2018)
- [Efficient Globally-Optimal Correspondence-Less Visual Odometry for Planar Ground Vehicles](https://mlsanity.com/paper/2203.00291/) (2022)
- [Globally optimal point set registration by joint symmetry plane fitting](https://mlsanity.com/paper/2002.07988/) (2020)
- [Improved Fourier Mellin Invariant for Robust Rotation Estimation with Omni-cameras](https://mlsanity.com/paper/1811.05306/) (2018)

## Built on by (most cited first, 30 of 31)

- [Secrets of Event-Based Optical Flow](https://mlsanity.com/paper/2207.10022/) (2022)
- [Event Collapse in Contrast Maximization Frameworks](https://mlsanity.com/paper/2207.04007/) (2022)
- [CMax-SLAM: Event-based Rotational-Motion Bundle Adjustment and SLAM System using Contrast Maximization](https://mlsanity.com/paper/2403.08119/) (2024)
- [Multi-Event-Camera Depth Estimation and Outlier Rejection by Refocused Events Fusion](https://mlsanity.com/paper/2207.10494/) (2022)
- [Event-based Simultaneous Localization and Mapping: A Comprehensive Survey](https://mlsanity.com/paper/2304.09793/) (2023)
- [A Fast Geometric Regularizer to Mitigate Event Collapse in the Contrast Maximization Framework](https://mlsanity.com/paper/2212.07350/) (2022)
- [Implicit Event-RGBD Neural SLAM](https://mlsanity.com/paper/2311.11013/) (2023)
- [EF-3DGS: Event-Aided Free-Trajectory 3D Gaussian Splatting](https://mlsanity.com/paper/2410.15392/) (2024)
- [Accelerating Globally Optimal Consensus Maximization in Geometric Vision](https://mlsanity.com/paper/2304.05156/) (2023)
- [A 5-Point Minimal Solver for Event Camera Relative Motion Estimation](https://mlsanity.com/paper/2309.17054/) (2023)
- [Event-based Background-Oriented Schlieren](https://mlsanity.com/paper/2311.00434/) (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)
- [Cross-Modal Semi-Dense 6-DoF Tracking of an Event Camera in Challenging Conditions](https://mlsanity.com/paper/2401.08043/) (2024)
- [Tight Fusion of Events and Inertial Measurements for Direct Velocity Estimation](https://mlsanity.com/paper/2401.09296/) (2024)
- [Instance-Level Moving Object Segmentation from a Single Image with Events](https://mlsanity.com/paper/2502.12975/) (2025)
- [Event-based Mosaicing Bundle Adjustment](https://mlsanity.com/paper/2409.07365/) (2024)
- [Simultaneous Motion And Noise Estimation with Event Cameras](https://mlsanity.com/paper/2504.04029/) (2025)
- [A Survey of 3D Reconstruction with Event Cameras](https://mlsanity.com/paper/2505.08438/) (2025)
- [Temporal Up-Sampling for Asynchronous Events](https://mlsanity.com/paper/2208.08721/) (2022)
- [Density Invariant Contrast Maximization for Neuromorphic Earth Observations](https://mlsanity.com/paper/2304.14125/) (2023)
- [Event-based Photometric Bundle Adjustment](https://mlsanity.com/paper/2412.14111/) (2024)
- [A Linear N-Point Solver for Structure and Motion from Asynchronous Tracks](https://mlsanity.com/paper/2507.22733/) (2025)
- [Event-Based Visual Odometry on Non-Holonomic Ground Vehicles](https://mlsanity.com/paper/2401.09331/) (2024)
- [ClearSight: Human Vision-Inspired Solutions for Event-Based Motion Deblurring](https://mlsanity.com/paper/2501.15808/) (2025)
- [Iterative Event-based Motion Segmentation by Variational Contrast Maximization](https://mlsanity.com/paper/2504.18447/) (2025)
- [Optical Flow-Guided 6DoF Object Pose Tracking with an Event Camera](https://mlsanity.com/paper/2512.21053/) (2025)
- [Geometric-Photometric Event-based 3D Gaussian Ray Tracing](https://mlsanity.com/paper/2512.18640/) (2025)
- [LECalib: Line-Based Event Camera Calibration](https://mlsanity.com/paper/2512.22441/) (2025)
- [Global Truncated Loss Minimization for Robust and Threshold-Resilient Geometric Estimation](https://mlsanity.com/paper/2603.14796/) (2026)

## Abstract (arXiv)

Event cameras are bio-inspired sensors that perform well in challenging illumination conditions and have high temporal resolution. However, their concept is fundamentally different from traditional frame-based cameras. The pixels of an event camera operate independently and asynchronously. They measure changes of the logarithmic brightness and return them in the highly discretised form of time-stamped events indicating a relative change of a certain quantity since the last event. New models and algorithms are needed to process this kind of measurements. The present work looks at several motion estimation problems with event cameras. The flow of the events is modelled by a general homographic warping in a space-time volume, and the objective is formulated as a maximisation of contrast within the image of warped events. Our core contribution consists of deriving globally optimal solutions to these generally non-convex problems, which removes the dependency on a good initial guess plaguing existing methods. Our methods rely on branch-and-bound optimisation and employ novel and efficient, recursive upper and lower bounds derived for six different contrast estimation functions. The practical validity of our approach is demonstrated by a successful application to three different event camera motion estimation problems.