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We provide an alternative to both of these approaches

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Unformatted text preview: . We provide an alternative to both of these approaches by proposing that our method of two-dimensional successive di erencing of the centroids of the head eliminates the need to construct three-dimensional models as a prerequisite for recognition. Our methodology, like Rosario and Pentland 12 , uses the Bayesian framework for modeling human actions. Given the correct probability density functions, Bayes theory is optimal in the sense of producing minimal classi cation errors. State space models have been widely used to detect, predict and estimate time series over a long period of time. Many state space systems use the hidden Markov model HMM, a probabilistic model for the study of discrete time series. In 12, 15 , HMMs have been applied to human activity recognition. However, our approach, unlike 12, 15 , computes statistical data about the human subject and models the actions based on the mean and covariance matrix of the di erence in co-ordinates of the centroid of the head obtained from di erent frames in each monocular grayscale sequence. Thus we are able to design a system that is simple in design, but robust in recognition. Human action recognition nds application in security and surveillance. A great deal of work has centered on developing systems that can be trained to alert authorities about individuals whose actions appear questionable. For instance, in an airport a system could be trained to recognize a person bending down to leave some baggage and then walking o , leaving it unattended, as a cause for concern and requiring investigation. Similarly, in a department store, a person picking up an article and leaving without paying could be interpreted as a suspicious activity. Thus, an intelligent, e cient recognition system could make manual surveillance redundant or, at any rate, reduce the need for human monitoring. This paper is structured as follows: Section 2 presents our modeling and classi cation algorithm, section 3 describes the techniques for segmentation and tracking of the head of the subject, and section 4 describes the system implementation. Section 5 presents the experimental results obtained, while section 6 summarizes the main conclusions and sketches our future directions of research. 2 Modeling & Classi cation In this section we describe the various steps in modeling our system and our procedure for identifying the test sequences. 2.1 Extracting feature vectors The motion of the head forms the basis of our detection and matching algorithm. The head of the person moves in a characteristic manner while walking, sitting, standing, hugging, falling down, etc. Thus each action is distinguished by the distinctive movement of the head in the execution of that particular action. By modeling the movement of the head for each of the individual actions, we have means of recognizing the type of action. To do this, we proceed by estimating the centroid of the head in each frame. The centroids of the head for the di erent frames of each sequence are given as x1 ; y1 : : : xn+1 ; yn+...
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