An Eigenvalue Approach to Detect Flows and Events in Crowd Videos

Abstract

Analysis of flows in crowd videos is a remarkable topic with practical implementations in many different areas. In this paper, we present a wide overview of this topic along with our own approach to this problem. Our approach treats the difficulty of crowd flow analysis by distinguishing single versus multiple flows in a scene. Spatiotemporal features of two consecutive frames are extracted by optical flows to create a three-dimensional tensor, which retains appearance and velocity information. Tensor’s upper left minor matrix captures intensity structure. A normalized continuous rank-increase measure for each frame is calculated by a generalized interlacing property of the eigenvalues of these matrices. In essence, measure values put through the knowledge of existing flows. Yet they do not go into effect desirably due to optical flow estimation error and some other factors. A proper set of the degree of polynomial fitting functions decodes their existence. But how can we estimate that set? Its detailed study is performed. Zero flow, single flow, multiple flows, and interesting events are detected as frame basis using thresholds on the polynomial fitting measure values. Plausible mean outputs of recall rate (88.9%), precision rate (86.7%), area under the receiver operating characteristic curve (98.9%), and accuracy (92.9%) reported from conducted experiments on PETS2009 and UMN benchmark datasets make clear and visible that our method gains high-quality results to detect flows and events in crowd videos in terms of both robustness and potency.