Dynamic updating and downdating matrix SVD and tensor HOSVD for adaptive indexing and retrieval of motion trajectories

Motion information is regarded as one of the most important cues for developing semantics in video data. Yet it is extremely challenging to build indexing and browsing tools for video data, particularly when it involves interactive motions of multiple objects. The problem is further complicated when the video archives are dynamically updated, and/or queries contains partial information. An efficient solution would require that the feature space used to represent the data be dynamically updated or downdated to allow frequent additions/deletions and matching of queries. Assuming tensor HOSVD as the feature space, in this paper, we propose two novel algorithms, namely, dynamic tensor HOSVD updating algorithm (DTSV D⁺) and dynamic tensor HOSVD downdating algorithm (DTSV D^-), for dynamically updating and downdating existing tensor HOSVD, without recalculating it from the raw data. The proposed algorithms are robustly applied to both full and partial multiple motion trajectories events with varying number of objects, trajectory lengths, and sampling rates. Simulations on real-world multiple motion trajectories data demonstrate the robustness and accuracy of the proposed algorithms.