Hand gestures are examples of fast and complex motions.Computers fail to track these in fast video, but sleight of hand fools humans as well: what happens too quickly we just cannot see. We show a 3D tracker for these types of motions that relies on the recognition of familiar configurations in 2D images (classification), and fills the gaps in-between (interpolation). We illustrate this idea with experiments on hand motions similar to finger spelling. The penalty for a recognition failure is often small: if two configurations are confused, they are often similar to each other, and the illusion works well enough, for instance, to drive a graphics animation of the moving hand. We contribute advances in both feature design and classifier training: our image features are invariant to image scale, translation, and rotation, and we propose a classification method that combines VQPCA with discrimination trees.

Abstrucf -In this paper we carry out a detailed analysis of the multiple time scale behavior of singularly perturbed linear systems of the formwhere A ( < ) is analytic in the small parameter e. Our basic result is a uniform asymptotic approximation to exp A ( e ) r that we obtain under a certain multiple semistability condition.This asymptotic approximation gives a complete multiple time scale decomposition of the above system and specifies a set of reduced order models valid at each time scale.Our contribution is threefold. 1) We do not require that the state variables be chosen so as to display the time scale structure of the system.2) Our formulation can handle systems with multiple ( > 2) time scales and we obtain uniform asymptotic expansions for their behavior on [0,00]. 3) We give an aggregation method to produce increasingly simplified models valid at progressively slower time scales.

We study the asymptotic behavior of the closed loop eigenvalues (root loci) of a strictly proper, linear, time-invariant control system as loop gain goes to . The formulae are stated in terms of the eigenvalues of nested restricted linear maps of the form A(mod S2)Is where S and S2 are subspaces of complementary dimension.Additional geometrical insight into the formulae is obtained by mechanizing the formulae using orthogonal projections.Our method and formulae are useful in other asymptotic calculations as well e.g. hierarchical multiple-time scales aggregation of Markov chains with some infrequent transitions.