This paper proposes the exploitation of a dynamic programming technique for efficiently comparing people trajectories adopting an encoding scheme that jointly takes into account both the direction and the velocity of movement. With this approach, each pair of trajectories in the training set is compared and the corresponding distance computed. Clustering is achieved by using the k-medoids algorithm and each cluster is modeled with a 1-D Gaussian over the distance from the medoid. A MAP framework is adopted for the testing phase. The reported results are encouraging.