Motion Trajectory Learning in the DFT-Coefficient Feature Space

Abstract

Techniques for understanding video object motion activity are becoming increasingly important with the widespread adoption of CCTV surveillance systems. In this paper we propose a novel vision system for clustering and classification of object-based video motion clips using spatiotemporal models. Object trajectories are modeled as motion time series using the lowest order Fourier coefficients obtained by Discrete Fourier Transform. Trajectory clustering is then carried out in the DFT-coefficient feature space to discover patterns of similar object motion activity. The DFT coefficients 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. Assuming the clusters of trajectory points are distributed normally in the coefficient feature space, we propose a simple Mahalanobis classifier for the detection of anomalous trajectories. Our proposed techniques are validated on three different datasets -Australian sign language, handlabelled object trajectories from video surveillance footage and real-time tracking data obtained in the laboratory. Applications to event detection and motion data mining for visual surveillance systems are envisaged.

Trajectory-Based Video Retrieval Using Dirichlet Process Mixture Models

“…Following the observation [8] that the DFT-coefficient feature is more robust than the original point-based feature, DFT coefficients are used to represent the object trajectories in our framework. In order to precisely characterize time-varying information of a trajectory, it is necessary to segment a trajectory into atomic subtrajectories.…”

“…In the off-line learning stage, object trajectories are first extracted using an existing method [9]. Following the observation in [8], we employ DFT coefficients to represent the object trajectories. Then the extracted object trajectories are clustered into several clusters by learning the full trajectories using DPMM in the DFT-coefficient feature space.…”

“…As a result, ISC is capable of identifying the number of subtrajectories automatically. After the trajectory segmentation, the DFT-coefficient feature [8] is extracted for each subtrajectory, leading to an E-dimensional DFT-coefficient representation so (E = 18 in the experiments). As a result, the trajectory is represented by a DFT-coefficient sequence…”

“…Sahouria [6] applied a wavelet transform using Harr basis to analyze object trajectory's spatio-temporal information in multiple scales. Naftel and Khalid [8] showed that the Discrete Fourier Transform (DFT) coefficient based trajectory representation performed better than polynomial-based trajectory representation in video retrieval. Bashir et al [18] proposed a principal component analysis based approach to model object trajectories in a video clip.…”

“…In this case, the problem of trajectorybased video retrieval is reduced to how to make trajectory learning more effective and efficient. In [8], motion trajectories are learned through self-organizing map (SOM) in the DFT-Coefficient feature space. Johnson and Hogg [2] used two competitive neural networks connected by a leaky neuron layer to model the probabilistic distribution of flow vectors and the trajectories.…”