Measuring Flow Complexity in Videos

In this paper a notion of flow complexity that measures the amount of interaction among objects is introduced and an approach to compute it directly from a video sequence is proposed. The approach employs particle trajectories as the input representation of motion and maps it into a `braid´ based representation. The mapping is based on the observation that 2D trajectories of particles take the form of a braid in space-time due to the intermingling among particles over time. As a result of this mapping, the problem of estimating the flow complexity from particle trajectories becomes the problem of estimating braid complexity, which in turn can be computed by measuring the topological entropy of a braid. For this purpose recently developed mathematical tools from braid theory are employed which allow rapid computation of topological entropy of braids. The approach is evaluated on a dataset consisting of open source videos depicting variations in terms of types of moving objects, scene layout, camera view angle, motion patterns, and object densities. The results show that the proposed approach is able to quantify the complexity of the flow, and at the same time provides useful insights about the sources of the complexity.