A generative statistical model for tracking multiple smooth trajectories

We present a general model for tracking smooth trajectories of multiple targets in complex data sets, where tracks potentially cross each other many times. As the number of overlapping trajectories grows, exploiting smoothness becomes increasingly important to disambiguate the association of successive points. However, in many important problems an effective parametric model for the trajectories does not exist. Hence we propose modeling trajectories as independent realizations of Gaussian processes with kernel functions which allow for arbitrary smooth motion. Our generative statistical model accounts for the data as coming from an unknown number of such processes, together with expectations for noise points and the probability that points are missing. For inference we compare two methods: A modified version of the Markov chain Monte Carlo data association (MCMCDA) method, and a Gibbs sampling method which is much simpler and faster, and gives better results by being able to search the solution space more efficiently. In both cases, we compare our results against the smoothing provided by linear dynamical systems (LDS). We test our approach on videos of birds and fish, and on 82 image sequences of pollen tubes growing in a petri dish, each with up to 60 tubes with multiple crossings. We achieve 93% accuracy on image sequences with up to ten trajectories (35 sequences) and 88% accuracy when there are more than ten (42 sequences). This performance surpasses that of using an LDS motion model, and far exceeds a simple heuristic tracker.