Gesture Modeling by Hanklet-based Hidden Markov Model

In this paper we propose a novel approach for gesture modeling. We aim at decomposing a gesture into sub-trajectories that are the output of a sequence of atomic linear time invariant (LTI) systems, and we use a Hidden Markov Model to model the transitions from the LTI system to another. For this purpose, we represent the human body motion in a temporal window as a set of body joint trajectories that we assume are the output of an LTI system. We describe the set of trajectories in a temporal window by the corresponding Hankel matrix (Hanklet), which embeds the observability matrix of the LTI system that produced it. We train a set of HMMs (one for each gesture class) with a discriminative approach. To account for the sharing of body motion templates we allow the HMMs to share the same state space. We demonstrate by means of experiments on two publicly available datasets that, even with just considering the trajectories of the 3D joints, our method achieves state-of-the-art accuracy while competing well with methods that employ more complex models and feature representations.