Provably fast algorithms for contour tracking

A new tracker is presented. Two sets are identified: one which contains all possible curves as found in the image, and a second which contains all curves which characterize the object of interest. The former is constructed out of edge-points in the image, while the latter is learned prior to running. The tracked curve is taken to be the element of the first set which is near-est the second set. The formalism for the learned set of curves allows for mathematically well understood groups of transformations (e.g. affine, projective) to be treated on the same footing as less well understood deformations, which may be learned from training curves. An algorithm is proposed to solve the tracking problem, and its properties are theoretically demonstrated: it solves the global optimization problem, and does so with certain complexity bounds. Experimental results applying the proposed algorithm to the tracking of a moving finger are presented, and compared with the results of a condensation approach.