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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

arXiv:1804.01306v1cs.CVcs.RO

TL;DR

Prior group-of-events methods offered ad hoc solutions for each problem. This paper presents a contrast-maximization framework that aligns image-plane trajectories with events and demonstrates it on 3D reconstruction, optical flow, and motion estimation.

  • Problem

    Prior group-of-events methods offered ad hoc solutions for each problem, with no unifying framework exploiting event temporal information across tasks.

    Source: §1 · p. 2

  • Method

    The framework maximizes contrast in images of warped events to select aligned image-plane point trajectories, implicitly handling data association without additional scene appearance information.

    Source: §1 · p. 2, §2.2.1 · p. 4

  • Results

    The framework is demonstrated on 3D reconstruction, optical flow, and motion estimation.

    Source: §4 · p. 8

  • Takeaways & Limitations

    A single principled approach can process events across these problems without additional scene appearance information.

    Source: §4 · p. 8

    For planar-scene motion estimation, translation magnitude remains ambiguous without additional information because homography decomposition yields only translation direction.

    Source: §3.3 · p. 8

Abstract

from arXiv · show

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

The paper introduces a unified approach for event cameras that estimates motion by fitting image-plane point trajectories to groups of events. It exploits event timing without relying on additional appearance information and applies to tasks ranging from optical flow to monocular depth estimation.

Motivation

  • Event cameras produce asynchronous, sparse streams of intensity-change events rather than fixed-rate intensity images, motivating methods designed for this different visual representation.Their event-driven sampling and sparse stream call for new processing methods.Source: §1 · p. 1

Related work

  • Among group-based methods, the paper identifies a gap: approaches exploiting event timing had problem-specific solutions, whereas its framework unifies this category.Group-based methods aggregate events and do not rely on prior appearance data.Source: §1 · p. 2

Contribution

  • The framework fits image-plane point trajectories to event data by maximizing the contrast of a warped-event image, implicitly handling event data association without additional appearance information.It uses the events’ spatiotemporal and polarity information to recover parameters describing relative camera-scene motion.Source: §1 · p. 2, Figure 2 · p. 2
  • The same framework applies to optical flow with short characteristic times and monocular depth estimation with longer estimation times.It also addresses rotational motion estimation and motion estimation in planar scenes.Source: §1 · p. 2
  • The method produces motion-corrected event images that approximate the image gradients causing events and can support further processing such as recognition or visual-inertial data fusion.Source: §1 · p. 2

2. Contrast Maximization Framework

Event cameras capture brightness changes caused by apparent motion of textured edges, so the framework estimates image-plane trajectories that fit the events and implicitly establishes correspondences between them.

2.1. Example: Optical Flow Estimation

  • For optical flow, locally straight point trajectories are tested by summing event counts or polarities after warping, and the best flow maximizes the resulting image variance.In the illustrated example, the maximum occurs near (−40,0) pixel/s; the method uses event counts by default.Source: §2.1 · pp. 2–3

2.2.1. Steps of the Method.

  • The method warps events along candidate model trajectories to a reference time, builds an image or histogram, computes its dispersion score, and optimizes the model parameters.The variance of the warped-event image is the contrast score; the framework does not require a specific optimizer.Source: §2.2.1 · p. 4

2.2. General Description of the Framework

  • The framework maximizes the variance, or contrast, of a warped-event image to find trajectories that align corresponding events with the event data.It assumes model parameters are shared across events and observable, then optimizes them to maximize the alignment score.Source: §2.2 · pp. 3–4, §2.2.1 · p. 4

2.2.2. Contrast Maximization.

  • Higher contrast corresponds to sharper alignment, producing a motion-corrected edge-like image that represents the brightness-increment patterns that caused the events.For optimal optical-flow trajectories, the image patch’s brightness increment is proportional to ∇I · v.Source: §2.1 · p. 3, §2.2.2 · p. 4

2.2.3. Computational Complexity.

  • Computing the warped-event image has complexity linear in the number of events, while contrast computation is typically negligible relative to warping.Overall cost also depends on the application-dependent optimization algorithm.Source: §2.2.3 · p. 4, §2.2.1 · p. 4

3. Sample Applications

The framework applies contrast maximization to depth estimation, rotational motion estimation, and motion estimation in planar scenes. In each application, it aligns warped events using trajectories constrained by the problem geometry.

3.1. Depth Estimation

  • For depth estimation, the candidate depth that maximizes warped-event contrast aligns events best; repeating the procedure yields a semi-dense depth map, most reliable at strong brightness edges.The method transfers events to a reference view using a depth-dependent planar homography, then scores the warped-event patch by variance; the resulting edge-like image approximates the scene patch’s grayscale edgemap. Depth values can be iteratively refined continuously rather than being limited to discrete voxelized disparity-space slices.Source: §3.1 · pp. 5–6

3.2. Rotational Motion Estimation

  • RMS rotational-motion error is approximately 20 °/s against peak excursions of 670 °/s (3% error), without requiring a scene map or prior optical flow.The method estimates motion by maximizing contrast over trajectories compatible with constant-velocity rotation in a small temporal window; the authors describe it as a visual event-based gyroscope.Source: Figure 9 · p. 7, §3.2 · p. 7

3.3. Motion Estimation in Planar Scenes

  • In planar scenes, maximizing contrast over 8-DOF homography trajectories estimates motion and plane parameters, and motion-corrected event images sharpen edges and improve a visual-inertial reconstruction.The homography parameterization uses angular velocity, translation divided by plane distance, and two plane-normal parameters; translation magnitude remains scale-ambiguous without additional information.Source: §3.3 · pp. 7–8, Figure 11 · p. 8

4. Conclusion

The framework addresses 3D reconstruction, optical flow, and motion estimation with event cameras by maximizing event alignment along image-plane point trajectories, without additional scene appearance information. The authors describe this as a step toward leveraging event cameras’ advantages in real-world scenarios.

4. Conclusion

  • The framework tackles 3D reconstruction, optical flow, and motion estimation with event cameras.The authors identify this breadth of applications as the framework’s most remarkable characteristic.Source: §4 · p. 8
  • It processes events without additional scene appearance information by maximizing alignment along image-plane point trajectories.Source: §4 · p. 8
  • The authors see the work as a step toward real-world use of event cameras’ low latency, high dynamic range, and low power consumption.Source: §4 · p. 8

5. Multimedia Material

The section points to a video demonstrating the framework on several computer-vision problems with event cameras.

5. Multimedia Material

  • An accompanying video shows the framework applied to several computer-vision problems with event cameras.https://youtu.be/KFMZFhi-9AwSource: §5 · p. 11

6. Optical Flow Estimation

The framework estimates optical flow by fitting point trajectories to event data, incorporating event polarity in warped-event patches. In the example, using polarity preserves the optimal velocity while making the objective’s attraction basin narrower and more pronounced.

6. Optical Flow Estimation

  • The framework fits point trajectories using event space-time coordinates and polarity, which is incorporated when creating warped-event image patches.The intensity frame shown to illustrate the event patch is not used by the framework.Source: §6 · p. 11
  • Both objectives yield approximately the same optimal velocity, θ ≡ v ≈ (−40,0) pixel/s, but using polarity produces a narrower, more pronounced basin of attraction.For thin edges, overlapping nearby events of opposite polarity cancel and sharply reduce contrast; without polarity, this cancellation does not occur, so contrast decreases more slowly.Source: §6 · p. 11

7. Depth Estimation

In the slider depth sequence, processing more events improved the reconstructed point cloud, with the same trend visible in semi-dense depth maps overlaid on the reference view.

7. Depth Estimation

  • Processing 20,000 to 1 million events showed that depth reconstruction improves as more events are processed, corresponding to a larger camera baseline.The experiment used the slider depth sequence [1].Source: §7 · p. 11
  • As more events were processed, the reconstructed point cloud became more accurate and less noisy.Source: §7 · p. 11
  • The improvement with more processed events was also visible in semi-dense depth maps overlaid on the grayscale reference-view frame.Source: §7 · p. 11

8. Rotational Motion Estimation

For rotational motion estimation, warped-event images are sharper and higher-contrast than per-pixel accumulations, while using event polarity does not significantly change the motion results. The framework’s estimates closely track ground truth, including during fast rotations.

Rotational Motion Estimation

  • Warping events with estimated rotational motion yields sharper, higher-contrast images than per-pixel accumulation, with broader value distributions both with and without polarity.The polarity-based warped image also contains more bright and dark pixels than the polarity-accumulation image.Source: §8 · pp. 12–13
  • The evaluation used one-minute rotational-motion sequences with 100–200 million events each and sub-millimeter motion-capture ground truth.Sequences include rotations around each camera axis followed by rotations in all three degrees of freedom, with motion speed increasing over time.Source: §8 · p. 13
  • 25.96°/s without polarity and 24.39°/s with polarity are the full-sequence RMS angular-velocity errors; both are about 2.5% of peak velocities near 1000°/s.The two polarity settings produced no significant difference in this scenario.Source: §8 · p. 14

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