A Measurement Method for Speed Distribution of Collective Motion with Optical Flow and its Application to Estimation of Rotation Curve

We propose a measurement method for the mean speed distribution of collective motions of highly dense groups with optical flow in this paper. This measurement is fundamental for ecological investigations and mathematical modeling of collective animal behaviors, including human crowds. Our method is applicable to highly dense homogeneous groups wherein individual movements are approximately uniform locally. To measure speed distributions, we partition a group into regions and estimate mean speeds in each region by extracting only flows that are relevant to collective motions and averaging them over a period of time. We experimentally find that our method works well even when we cannot reliably track individuals. We specifically apply our method to schools of sardines to measure a kind of speed distribution called rotation curve (RC). Experimental results obtained by simulation demonstrate that our method can estimate flows and RCs accurately. We also performed experiments with videos of real fish. The RCs were estimated by manual tracking and by our method. The results are approximately equal, and the average difference is less than 4% of the mean body length of fish in the observed schools. These results indicate that our method is practically useful for measuring RCs.