Classifying spatiotemporal object trajectories using unsupervised learning in the coefficient feature space

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This paper proposes a novel technique for clustering and classification of object trajectory-based video motion clips using spatiotemporal function approximations. Assuming the clusters of trajectory points are distributed normally in the coefficient feature space, we propose a Mahalanobis classifier for the detection of anomalous trajectories. Motion trajectories are considered as time series and modelled using orthogonal basis function representations. We have compared three different function approximations --- least squares polynomials, Chebyshev polynomials and Fourier series obtained by Discrete Fourier Transform (DFT). Trajectory clustering is then carried out in the chosen 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. Our proposed techniques are validated on three different datasets --- Australian sign language, hand-labelled object trajectories from video surveillance footage and real-time tracking data obtained in the laboratory. Applications to event detection and motion data mining for multimedia video surveillance systems are envisaged.