将密集人群建模为带随机力的活性物质，实现高密度人群动态分析与预测。
Learning Extremely High Density Crowds as Active Matters
- 用活性物质物理模型描述人群，引入随机力模拟复杂行为。
- 在低质量视频上仍能准确分析和预测极密人群动态，优于现有方法。
- 连续时间模型具可解释性，适合仿真与可视化，区别于黑箱深度学习。
基于视频的高密度人群分析与预测是计算机视觉中的长期难题，主要因高质量数据稀缺及人群动力学复杂所致。本文提出新方法，直接从野外低质量视频中学习，难以追踪个体或数头。核心创新在于引入新的物理先验：将高密度人群视为具有随机力作用的活性物质，称为“人群材料”。该物理模型与神经网络结合，构建神经随机微分方程系统，可有效模拟复杂人群动态。由于同类研究较少，我们采用多种相近方法进行对比。通过全面评估，验证了本模型在分析与预测极密人群方面显著优于现有方法。此外，作为连续时间物理模型，其具备强可解释性，可用于仿真与分析，这与大多数离散时间、黑箱化的深度学习方法有本质区别。
原文摘要 · Abstract (English)
Video-based high-density crowd analysis and prediction has been a long-standing topic in computer vision. It is notoriously difficult due to, but not limited to, the lack of high-quality data and complex crowd dynamics. Consequently, it has been relatively under studied. In this paper, we propose a new approach that aims to learn from in-the-wild videos, often with low quality where it is difficult to track individuals or count heads. The key novelty is a new physics prior to model crowd dynamics. We model high-density crowds as active matter, a continumm with active particles subject to stochastic forces, named 'crowd material'. Our physics model is combined with neural networks, resulting in a neural stochastic differential equation system which can mimic the complex crowd dynamics. Due to the lack of similar research, we adapt a range of existing methods which are close to ours for comparison. Through exhaustive evaluation, we show our model outperforms existing methods in analyzing and forecasting extremely high-density crowds. Furthermore, since our model is a continuous-time physics model, it can be used for simulation and analysis, providing strong interpretability. This is categorically different from most deep learning methods, which are discrete-time models and black-boxes.
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