Recognition of motions and activities of objects in videos requires effective representations for analysis and matching of motion trajectories. In this paper, we introduce a new representation speciï¬cally aimed at matching motion trajectories. We model a trajectory as a continuous dense ï¬‚ow ï¬eld from a sparse set of vector sequences using Gaussian Process Regression. Furthermore, we introduce a random sampling strategy for learning stable classes of motions from limited data. Our representation allows for incrementally predicting possible paths and detecting anomalous events from online trajectories. This representation also supports matching of complex motions with acceleration changes and pauses or stops within a trajectory. We use the proposed approach for classifying and predicting motion trajectories in trafï¬c monitoring domains and test on several data sets. We show that our approach works well on various types of complete and incomplete trajectories from a variety of video data sets with different frame rates.
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