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A Unifying Contrast Maximization Framework for Event Cameras, with Applications to Motion, Depth, and Optical Flow Estimation
Guillermo Gallego, Henri Rebecq, Davide Scaramuzza
TL;DR
Event cameras require methods suited to asynchronous, sparse event streams and limited appearance information. This paper introduces a unified contrast-maximization framework that aligns event trajectories across depth, optical flow, and motion estimation, achieving accurate motion recovery, including approximately 3% rotational-motion error.
Problem
Event cameras produce asynchronous, sparse brightness-change events, making data association and visual-information processing different from conventional image sequences.
Method
The framework estimates image-plane point trajectories by maximizing the contrast of warped events, using groups of events and their spatiotemporal and polarity information without additional scene appearance.
Results
The framework addresses 3D reconstruction, optical flow, and motion estimation; rotational-motion estimation achieves approximately 3% error relative to peak excursions of 670 °/s.
Takeaways & Limitations
A single principled event-alignment strategy can process several event-camera vision problems without additional appearance information about the scene.
Takeaways & Limitations
Planar-scene motion estimation has a scale ambiguity: homography decomposition provides translation direction but not its magnitude without additional information.
Abstract
from arXiv · showhide
We present a unifying framework to solve several computer vision problems with event cameras: motion, depth and optical flow estimation. The main idea of our framework is to find the point trajectories on the image plane that are best aligned with the event data by maximizing an objective function: the contrast of an image of warped events. Our method implicitly handles data association between the events, and therefore, does not rely on additional appearance information about the scene. In addition to accurately recovering the motion parameters of the problem, our framework produces motion-corrected edge-like images with high dynamic range that can be used for further scene analysis. The proposed method is not only simple, but more importantly, it is, to the best of our knowledge, the first method that can be successfully applied to such a diverse set of important vision tasks with event cameras.
1. Introduction
Event cameras generate asynchronous, sparse brightness-change events, motivating methods that process temporal event groups without relying on conventional appearance images. The paper introduces a unifying framework that exploits temporal information across several estimation problems.
- Motivation: Event cameras report intensity changes asynchronously, producing a fundamentally different visual signal from fixed-rate intensity images.Each event includes spatiotemporal coordinates and polarity, while event cameras offer microsecond latency, high dynamic range, and low power consumption.
- Existing approaches: Event-camera algorithms include event-by-event methods and group-based methods that either discard or exploit event timing.Event-by-event approaches rely on additional appearance data, whereas group-based methods aggregate events to estimate unknowns.
- Contribution: The paper presents the first unifying framework for processing groups of events while exploiting their temporal information.It targets optical flow, depth, rotational motion, and planar-scene motion estimation.
- Contribution: The framework finds image-plane point trajectories that best fit event data and recovers parameters describing relative camera–scene motion without additional appearance information.It also implicitly handles event data association and produces motion-corrected event images for further scene analysis.
- Core idea: The approach warps events according to candidate trajectories and measures their agreement through the contrast of the resulting event image.
2. Contrast Maximization Framework
The framework estimates motion-related parameters by finding point trajectories that best align events, using contrast maximization on warped-event images. This process implicitly establishes event correspondences and produces motion-corrected edge-like images.
- Motivation: Event trajectories are chosen to align events generated by the same moving edge, addressing data association without additional scene appearance information.Under constant illumination, events require relative motion and sufficient texture; corresponding events are expected along shared image-plane trajectories.
- Optical Flow: For optical flow, the correct motion vector is the one producing the highest-contrast warped-event image.In the illustrated example, θ* = argmaxθ f(θ) ≈ (−40,0)^⊤ pixel/s.
- Framework: The method warps events to a reference time according to a geometric trajectory model, then forms an image or histogram from event counts or polarities.For the optical-flow example, locally straight trajectories use candidate velocity θ = v, and each pixel accumulates contributions from warped events.
- Framework: The objective is the variance of the warped-event image, interpreted as contrast, and maximizing it selects parameters that best fit the event data.The score measures the dispersion of warped events under candidate parameters; higher contrast corresponds to better alignment.
- Optimization: Optimization methods such as gradient ascent or Newton’s method obtain the model parameters, while the framework does not require a specific optimizer.Its three stages are event warping, score computation, and objective optimization.
- Outputs: Optimal trajectories yield motion-corrected edge-like images representing brightness-increment patterns and approximating gradients of the brightness pattern that caused the events.For optimal trajectories, the brightness increment is proportional to ∇I · v under the optical-flow constraint.
3. Sample Applications
The framework applies contrast maximization to depth estimation, rotational motion estimation, and planar-scene motion, using event alignment to recover parameters and produce motion-corrected images.
- The framework is flexible and generic, applying contrast maximization to several important vision problems.
- 3.1. Depth Estimation: Depth is estimated by warping events to a reference view under candidate depths and selecting the depth producing maximum contrast.Known camera poses and intrinsics define the warp; contrast is measured by variance and maximized over depth.
- 3.1. Depth Estimation: Correct depth aligns transferred events, while incorrect depths place corresponding events at different image locations.The method compares candidate depths in front of, at, and behind an object; only the correct value aligns the transferred points.
- 3.1. Depth Estimation: For two analyzed patches, the contrast curves vary smoothly with depth and have clear maxima; highest-contrast warped patches resemble grayscale edgemaps.This indicates that the event data recover an approximation to the scene edges that triggered the events.
- 3.1. Depth Estimation: Repeating the patch procedure across the reference view yields a semi-dense depth map, while iterative contrast optimization can produce continuous depth values.The reconstruction selects high-contrast points as more reliable, uses adaptive thresholding and median filtering, and can refine beyond discrete voxelized depths.
- 3.3. Motion Estimation in Planar Scenes: For planar scenes, homography-based alignment produces sharper motion-corrected edges and improves the resulting visual-inertial reconstruction.The homography parameters include angular velocity, translation scaled by plane depth, and plane orientation; the translation scale has an inherent ambiguity.
4. Conclusion
The framework addresses 3D reconstruction, optical flow, and motion estimation by maximizing event alignment along image-plane point trajectories. The authors position this approach as a step toward leveraging event cameras’ low latency, high dynamic range, and low power consumption.
- The framework tackles 3D reconstruction, optical flow, and motion estimation with event cameras.
- It processes events without additional scene appearance information by maximizing alignment along point trajectories on the image plane.
- The authors identify low latency, very high dynamic range, and low power consumption as event-camera advantages.
A Unifying Contrast Maximization Framework for Event Cameras, with Applications to Motion, Depth, and Optical Flow Estimation – Supplementary Material –
The supplementary material identifies Guillermo Gallego, Henri Rebecq, and Davide Scaramuzza as authors affiliated with the University of Zurich and ETH Zurich.
- The authors are Guillermo Gallego, Henri Rebecq, and Davide Scaramuzza.
- Their listed affiliations are the Department of Informatics and Neuroinformatics at the University of Zurich and ETH Zurich.
5. Multimedia Material
A video demonstrating the framework’s applications to several computer-vision problems with event cameras is available online.
- The multimedia material includes a video showing the framework applied to several computer-vision problems with event cameras.
6. Optical Flow Estimation
For optical-flow estimation, the framework uses polarity-aware warped-event patches and selects image-plane trajectories by maximizing their contrast. Polarity preserves approximately the same optimum while making the objective peak narrower and more pronounced for thin edges.
- The framework incorporates event polarity when creating image patches of warped events.
- An intensity frame may illustrate the event patch, but it is not used by the framework.
- Candidate optical-flow vectors define trajectories whose warped-event images and contrast objective are compared.
- Polarity-aware patches encode absent events in green and positive or negative event accumulation in red or blue, respectively.
- Both objectives yield approximately the same optimal velocity, θ ≡ v ≈ (−40,0) pixel/s.
- Using polarity makes the optimum’s basin of attraction slightly narrower and more pronounced because overlapping opposite-polarity edges cancel.
7. Depth Estimation
Depth reconstruction becomes more accurate as more events are processed, while optical flow is estimated by maximizing the contrast of warped events.
- Depth Estimation: As more events are processed, corresponding to a larger camera baseline, the reconstructed depth point cloud becomes more accurate.The experiment varies the processed events from 20,000 to 1 million.
- Optical Flow: Candidate optical-flow velocities are compared using an intensity frame showing the corresponding event patch.
- Optical Flow: Optical flow is estimated by finding the parameters that maximize the contrast objective f(θ) of warped events.
8. Rotational Motion Estimation
Warping events with estimated motion increases image contrast relative to per-pixel accumulation, with or without event polarity. Rotational motion estimation remains accurate at increasing speeds, while polarity has little effect in the reported scenario.
- Warped Event Images: Estimated motion produces sharper, higher-contrast warped-event images than per-pixel accumulation because events align along candidate point trajectories.
- Depth Visualization: Depth visualizations show color-coded values from 0.45 m to 2.4 m across depth maps and reconstructed point clouds.
- Warped Event Images: The higher-contrast warped-event image has a larger value range and a distribution shifted toward larger positive values.
- Event Polarity: With polarity, optimal-parameter warping yields more contrast, reflected by larger value ranges and more bright and dark pixels.
- Rotational Motion: 25.96 °/s without polarity and 24.39 °/s with polarity are the reported RMS angular velocity errors over the full rotational sequence.The two settings do not significantly change the results in this scenario.