Fast track matching and event detection

This paper addresses the problems of track stitching and dynamic event detection in a sequence of frames. The input data consists of tracks, possibly fragmented due to occlusion, belonging to multiple targets. The goals are to (i) establish track identity across occlusion, and (ii) detect points where the motion of these targets undergo substantial changes. The main result of the paper is a simple, computationally inexpensive approach that achieves these goals in a unified way. Given a continuous track, the main idea is to detect changes in the dynamics by parsing it into segments according to the complexity of the model required to explain the observed data. Intuitively, changes in this complexity correspond to points where the dynamics change. Since the problem of estimating the complexity of the underlying model can be reduced to estimating the rank of a matrix constructed from the observed data, these changes can be found with a simple algorithm, computationally no more expensive that a sequence of SVDs. Proceeding along the same lines, fragmented tracks corresponding to multiple targets can be linked by searching for sets corresponding to minimal complexity joint models. As we show in the paper, this problem can be reduced to a semi-definite optimization and efficiently solved with commonly available software.