Exemplar-AMMs: Recognizing Crowd Movements From Pedestrian Trajectories

In this paper, we present a novel method to recognize the types of crowd movement from crowd trajectories using agent-based motion models (AMMs). Our idea is to apply a number of AMMs, referred to as exemplar-AMMs, to describe the crowd movement. Specifically, we propose an optimization framework that filters out the unknown noise in the crowd trajectories and measures their similarity to the exemplar-AMMs to produce a crowd motion feature. We then address our real-world crowd movement recognition problem as a multi-label classification problem. Our experiments show that the proposed feature outperforms the state-of-the-art methods in recognizing both simulated and real-world crowd movements from their trajectories. Finally, we have created a synthetic dataset, SynCrowd, which contains 2D crowd trajectories in various scenarios, generated by various crowd simulators. This dataset can serve as a training set or benchmark for crowd analysis work

Topological Data Analysis of Biological Aggregation Models

We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D'Orsogna. These models are dynamical systems describing the movement of agents who interact via alignment, attraction, and/or repulsion. Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure of these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti numbers count connected components, topological circles, and trapped volumes present in the data. To interpret our results, we introduce a visualization that displays Betti numbers over simulation time and topological persistence scale. We compare our topological results to order parameters typically used to quantify the global behavior of aggregations, such as polarization and angular momentum. The topological calculations reveal events and structure not captured by the order parameters.Comment: 25 pages, 12 figures; second version contains typo corrections, minor textual additions, and a brief discussion of computational complexity; third version fixes one typo and adds small paragraph about topological stabilit