Online Identification of Dwell Regions for Moving Objects

A region R is a dwell region for a moving object O if, given a threshold distance d and duration t, every point of R remains within distance d of O for at least time t. Clearly, points within R are likely to be of interest to O, so identification of O and R has applications in areas such as monitoring and surveillance, as well as to trajectory simplification. We propose an online algorithm to solve this problem, which can handle dynamic addition and deletion of data in logarithmic time. We assume an incoming stream of object positions, and maintain the upper and lower bounds for the radius of the smallest circle enclosing these positions, as points are added and deleted. These bounds allow us to greatly reduce the number of trajectory points we need to consider in the query, as well as to defer query evaluation. Our method can approximate the radius of the smallest circle enclosing a given sub trajectory within an arbitrarily small user defined factor. Our experiments show that the proposed method can scale up to hundreds of thousands of trajectories.