Visual target tracking using improved and computationally efficient particle filtering

In this paper, we present a new particle filtering (PF) algorithm for visual target tracking where Galerkin's projection method is used to generate the proposal distribution. Galerkin's method is a numerical approach to approximate the solution of a partial differential equation (PDE). By leveraging this method in concert with L-2 theory and the FFT, we obtain a new proposal which directly approximates the true state posterior distribution and is fundamentally different from various local linearizations or Kalman filter-based proposals. We apply this improved PF algorithm to track a human head in a video sequence. As predicted by theory and demonstrated by our experimental results, this new algorithm is highly effective for tracking targets which exhibit complex kinematics. The new proposal distribution given here captures the high probability area in the state space, thereby gleaning increased support from the true posterior distribution.