Parametric Trajectory Representations for Behaviour Classification

This paper presents an empirical comparison of strategies for representing motion trajectories with fixed-length vectors. We compare four techniques, which have all previously been adopted in the trajectory classification literature: least-squares cubic spline approximation, the Discrete Fourier Transform, Chebyshev polynomial approximation, and the Haar wavelet transform. We measure the class separability of five different trajectory datasets ranging from vehicle trajectories to pen trajectories when described in terms of these representations. Results obtained over a range of dimensionalities indicate that the different representations yield similar levels of class separability, with marginal improvements provided by Chebyshev and Spline representations. For the datasets considered here, each representation appears to yield better results when used in conjunction with a curve parametrisation strategy based on arc-length, rather than time. However, we illustrate a situation pertinent to surveillance applications where the converse is true.