Abstract
Recently, point cloud data have been analyzed to estimate their population dynamics model. Such attempts arise in many fields, including behavior prediction with GPS data, multi-target tracking and density observation in meteorology. When predicting the trajectory of each point, typical methods are to track each point over multiple time periods and to recover a population dynamics model. However, these methods are difficult to apply when the same point cloud cannot be tracked in time series due to observational constraints or privacy issues. To address this problem, our research aims to estimate the population dynamics behind a point cloud snapshot at a single time. In this case, the trajectory of each point is estimated only from its coordinates without time information. In our method, the prediction process is formulated as an optimal transport problem, and is further formulated as an optimization problem by introducing the smoothness of the movement as a regularization term. Experiments show that our method can predict the correct trajectories from a single-time point cloud snapshot with high accuracy, using point cloud data created from several typical vector fields.
