Using circular statistics for trajectory shape analysis

The analysis of patterns of movement is a crucial task for several surveillance applications, for instance to classify normal or abnormal people trajectories on the basis of their occurrence. This paper proposes to model the shape of a single trajectory as a sequence of angles described using a mixture of Von Mises (MoVM) distribution. A complete EM (expectation maximization) algorithm is derived for MoVM parameters estimation and an on-line version proposed to meet real time requirement. Maximum-A-Posteriori is used to encode the trajectory as a sequence of symbols corresponding to the MoVM components. Iterative k-medoids clustering groups trajectories in a variable number of similarity classes. The similarity is computed aligning (with dynamic programming) two sequences and considering as symbol-to-symbol distance the Bhattacharyya distance between von Mises distributions. Extensive experiments have been performed on both synthetic and real data.