Mixed-State Models for Nonstationary Multiobject Activities
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Research Article Mixed-State Models for Nonstationary Multiobject Activities Naresh P. Cuntoor and Rama Chellappa Department of Electrical and Computer Engineering, Center for Automation Research, University of Maryland, A. V. Williams Building, College Park, MD 20742, USA Received 13 June 2006; Revised 20 October 2006; Accepted 30 October 2006 Recommended by Francesco G. B. De Natale We present a mixed-state space approach for modeling and segmenting human activities. The discrete-valued component of the mixed state represents higher-level behavior while the continuous state models the dynamics within behavioral segments. A basis of behaviors based on generic properties of motion trajectories is chosen to characterize segments of activities. A Viterbi-based algorithm to detect boundaries between segments is described. The usefulness of the proposed approach for temporal segmentation and anomaly detection is illustrated using the TSA airport tarmac surveillance dataset, the bank monitoring dataset, and the UCF database of human actions. Copyright © 2007 N.P. Cuntoor and R. Chellappa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Modeling complex activities involves extracting spatiotemporal descriptors associated with objects moving in a scene. It is natural to think of activities as a sequence of segments in which each segment possesses coherent motion properties. There exists a hierarchical relationship extending from observed features to higher-level behaviors of moving objects. Features such as motion trajectories and optical flow are continuous-valued variables, whereas behaviors such as start/stop, split/merge, and move along a straight line are discrete-valued. Mixed-state models provide a way to encapsulate both continuous and discrete-valued states. In general, the activity structure, that is, the number of behaviors and their sequence, may not be known a priori. It requires an activity model that cannot only adapt to changing behaviors but also one that can learn incrementally and “on the fly.” Many existing approaches assume that the structure of activities is known; and a fixed number of free parameters is determined based on experience or by estimating the model order. The structure then remains fixed. This may be a reasonable assumption for activities such as walking and running, but becomes a serious limitation when modeling complex activities in surveillance and other scenarios. We are interested in these classes of activities. Instead of assuming a fixed global model order, local complexity is constrained using dynamical primitives within short-time seg-
ments. We choose a basis of behaviors that reflects generic motion properties to model these primitives. For example, the basis elements represent motion with constant velocity along a straight line, curved motion, and so forth. Using the basis of behaviors, we p
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