Modeling complex actions using Differential Geometry and coupled hidden Markov models

Recent interest in the encoding, tracking and recognition of human actions such as hand, facial gestures, complex limb motions, raises fundamental questions about how such fully 3D actions of reasonably long duration can be appropriately encoded, learned and interpreted in ways which are unique but also invariant to specified transformations in space or time. Of particular interest is the use of curvature-torsion phase space to encode trajectory shapes, velocity-acceleration phase space to encode dynamics and the implementation of a screw decomposition model for the symbolic description of actions recording from 3D magnetic field sensors. In addition to this we have also explored how such encoding methods can then be integrated with a specific type of Dynamical Bayesian Network (in the form of coupled hidden Markov models) for the learning, recognition and prediction of such complex actions. Estimation solutions and empirical results are presented.
New Zealand