| Motion information is regarded as one of the most important cues for developing semantics in video data. Yet it is extremely challenging to build semantics of video clips particularly when it involves interactive motion of multiple objects.;We present a novel framework for compact representation of multi-object motion trajectories. Three efficient multi-trajectory indexing and retrieval algorithms based on tensor analysis are proposed. These include: (i) geometrical multiple-trajectory indexing and retrieval (GMIR), (ii) unfolded multiple-trajectory indexing and retrieval (UMIR), and (iii) concentrated multiple-trajectory indexing and retrieval (CMIR). The proposed tensor-based representations not only remarkably reduce the dimensionality of the indexing space but also enable the realization of fast retrieval systems.;We propose a novel solution to an arbitrary non-causal, multi-dimensional hidden Markov model (HMM) for image and video classification. We provide a solution for the non-causal model by splitting it into multiple causal HMMs that are analytically solvable in a fully synchronous distributed computing framework, therefore referred to as distributed HMMs.;We propose methods for dynamically updating and downdating them matrix SVD and tensor HOSVD, without the need to recalculate it from raw data. Specifically, we provide a robust and efficient indexing and retrieval system of multiple interacting motion trajectories by addressing three fundamental problems: (i) Dynamic insertion and deletion of entries in multiple motion trajectory databases, (ii) Dynamic matching of query and entries in multiple motion trajectory databases with different number of trajectories, (iii) Dynamic matching of query and entries in multiple motion trajectory databases with different temporal lengths. |
