Histogram-Based Partial Differential Equation for Object Tracking

Traditional object tracking based on color histograms can only represent objects with rectangles or ellipses, thus having very limited ability to follow objects with complex shapes or with highly non-rigid motion. In addressing this problem, we formulate histogram-based tracking as a functional optimization problem based on Jesson-Shannon divergence that is bounded, symmetric and a true metric. Optimization of the functional consists in searching for a candidate image region of possibly very complex shape, whose color distribution is the most similar to the known, target distribution. By using two different techniques of shape derivative and variational derivative (in section 2 and appendix respectively), we derive the partial differential equation (PDE) that describes the evolution of the object contour. Level set algorithm is used to compute the solution of the PDE. Experiments show that the proposed work is globally convergent and can track objects with complex shapes and/or with highly non-rigid motion.