A new method for the representation, recognition, and interpretation of parameterized gesture is presented. By parameterized gesture we mean gestures that exhibit a meaningful variation; one example is a point gesture where the important parameter is direction. Our approach is to extend the standard hidden Markov model method of gesture recognition by including a global parametric variation in the output probabilities of the states of the HMM. Using a linear model to derive the theory, we formulate an expectation-maximization (EM) method for training the parametric HMM. During testing, the parametric HMM simultaneously recognizes the gesture and estimates the quantifying parameters. Using visually-derived and directly measured 3-dimensional hand position measurements as input, we present results on two different movements --- a size gesture and a point gesture --- and show robustness with respect to noise in the input features.
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