Classifying spatiotemporal object trajectories using unsupervised learning of basis function coefficients

This paper proposes a novel technique for clustering and classification of object trajectory-based video motion clips using spatiotemporal functional approximations. A Mahalanobis classifier is then used for the detection of anomalous trajectories. Motion trajectories are considered as time series and modeled using the leading Fourier coefficients obtained by a Discrete Fourier Transform. Trajectory clustering is then carried out in the Fourier coefficient feature space to discover patterns of similar object motions. The coefficients of the basis functions are used as input feature vectors to a Self-Organising Map which can learn similarities between object trajectories in an unsupervised manner. Encoding trajectories in this way leads to efficiency gains over existing approaches that use discrete point-based flow vectors to represent the whole trajectory. Experiments are performed on two different datasets -- synthetic and pedestrian object tracking - to demonstrate the effectiveness of our approach. Applications to motion data mining in video surveillance databases are envisaged.