Neural Networks for Threshold Dynamics Reconstruction
This work addresses the problem of modeling threshold dynamics from video data for applications such as environmental monitoring, but it is incremental as it builds on existing MBO and CNN methods.
The authors tackled the problem of reconstructing threshold dynamics for front evolution from video data by introducing two CNN architectures inspired by the MBO algorithm and cellular automatons, with results showing effective reconstruction and extrapolation of evolving boundaries on synthetic and real-world videos like ice melting and fire front propagation.
We introduce two convolutional neural network (CNN) architectures, inspired by the Merriman-Bence-Osher (MBO) algorithm and by cellular automatons, to model and learn threshold dynamics for front evolution from video data. The first model, termed the (single-dynamics) MBO network, learns a specific kernel and threshold for each input video without adapting to new dynamics, while the second, a meta-learning MBO network, generalizes across diverse threshold dynamics by adapting its parameters per input. Both models are evaluated on synthetic and real-world videos (ice melting and fire front propagation), with performance metrics indicating effective reconstruction and extrapolation of evolving boundaries, even under noisy conditions. Empirical results highlight the robustness of both networks across varied synthetic and real-world dynamics.