Receding-Horizon Maximum-Likelihood Estimation of Neural-ODE Dynamics and Thresholds from Event Cameras

TL;DR

This work model events with a history-dependent marked point process whose conditional intensity is a smooth surrogate of contrast-threshold triggering, treating the contrast threshold as an unknown parameter and proposed receding-horizon estimator that performs a few gradient steps per update on a receding horizon window.

Abstract

Event cameras emit asynchronous brightness-change events where each pixel triggers an event when the last event exceeds a threshold, yielding a history-dependent measurement model. We address online maximum-likelihood identification of continuous-time dynamics from such streams. The latent state follows a Neural ODE and is mapped to predicted log-intensity through a differentiable state-to-image model. We model events with a history-dependent marked point process whose conditional intensity is a smooth surrogate of contrast-threshold triggering, treating the contrast threshold as an unknown parameter. The resulting log-likelihood consists of an event term and a compensator integral. We propose a receding-horizon estimator that performs a few gradient steps per update on a receding horizon window. For streaming evaluation, we store two scalars per pixel (last-event time and estimated log-intensity at that time) and approximate the compensator via Monte Carlo pixel subsampling. Synthetic experiments demonstrate joint recovery of dynamics parameters and the contrast threshold, and characterize accuracy--latency trade-offs with respect to the window length.

Figures (9)

• Figure 1: Illustration of the proposed framework.
• Figure 2: Surrogate intensity \ref{['eq:intensity']} as a function of the distance-to-threshold $d=\left|\varphi\right|$. Increasing $\gamma$ concentrates events closer to $d=0$ (here shown for $\gamma\in\{30,60,120\}$; log-scale on the $y$-axis).
• Figure 3: True pixel dependent threshold map $C(\cdot)$.
• Figure 4: Representative snapshots from the synthetic event-camera sequence. Top: rendered intensity frames. Bottom: corresponding event images in polarity mode (yellow: $p=+1$, purple: $p=-1$, white arrow: approximated motion).
• Figure 5: Learning curves for a fixed horizon $H=15$. Top:$\hat{\alpha}$ versus episode $e$. Bottom:$\hat{\omega}$ versus episode $e$. Dashed lines indicate the ground truth.