Activity recognition using a supervised non-parametric hierarchical HMM

• Hierarchical composition of poses enables information sharing and model simplification.
• The non-parametric nature estimates Markov states automatically from data.
• Inference procedure suitable for sequence classification.

The problem of classifying human activities occurring in depth image sequences is addressed. The 3D joint positions of a human skeleton and the local depth image pattern around these joint positions define the features. A two level hierarchical Hidden Markov Model (H-HMM), with independent Markov chains for the joint positions and depth image pattern, is used to model the features. The states corresponding to the H-HMM bottom level characterize the granular poses while the top level characterizes the coarser actions associated with the activities. Further, the H-HMM is based on a Hierarchical Dirichlet Process (HDP), and is fully non-parametric with the number of pose and action states inferred automatically from data. This is a significant advantage over classical HMM and its extensions. In order to perform classification, the relationships between the actions and the activity labels are captured using multinomial logistic regression. The proposed inference procedure ensures alignment of actions from activities with similar labels. Our construction enables information sharing, allows incorporation of unlabelled examples and provides a flexible factorized representation to include multiple data channels. Experiments with multiple real world datasets show the efficacy of our classification approach.