Hidden Markov Model on a unit hypersphere space for gesture trajectory recognition

• Gesture trajectory is modeled on a unit-hypersphere for scale-invariancy.
• A Mixture of von Mises-Fisher (MvMF) distribution is incorporated into an HMM.
• The parameter estimation formulae for MvMF-HMM are derived in a closed form.

In this paper, a Mixture of von Mises-Fisher (MvMF) Probability Density Function (PDF) is incorporated into a Hidden Markov Model (HMM) in order to model spatio-temporal data in a unit-hypersphere space. The parameter estimation formulae for MvMF-HMM are derived in a closed form. As an application for the proposed MvMF-HMM, hands gesture trajectory recognition task is considered. Modeling gesture trajectory on a unit-hypersphere inherently removes bias from a subject’s arm length or distance between a subject and camera. In experiments with public datasets, InteractPlay and UCF Kinect, the proposed MvMF-HMM showed superior recognition performance compared to current state-of-the-art techniques.