Continuous Hidden Markov Models for Depth Map-Based Human Activity Recognition

Abstract

There is an enormous volume of literature on the applications of Hidden Markov Models (HMMs) to a broad range of pattern recognition tasks. The first practical application of HMMs is much based on the work of Rabiner et al (Lawrence & Rabiner, 1989) for speech recognition. Since then, HMMs have been extensively used in various scientific fields such as computational biology, biomedical signal interpretation, image classification and segmentation, etc. An HMM can be described as a stochastic finite-state automation that can be used to model time sequential data. In general, there are four basic parts involved in the HMM: namely states, initial state distribution, state transition matrix, and state observation matrix. A state represents a property or condition that an HMM might have at a particular time. Initial state distribution indicates each state probability of an HMM at the time of starting the modeling procedure of an event. The state transition matrix represents the probabilities among the states. The observation matrix contains the observation probabilities from each state. Once the architecture of an HMM is defined with the four essential components, training of the HMM is required. To train, the first step is to classify features into a specific number of clusters, generating a codebook. Then from the codebook, symbol sequences are generated through vector quantization. These symbol sequences later are used to model spatiotemporal patterns in an HMM. The number of states and initial state distribution of HMM are empirically determined in general. The state transition and observation probabilities from each state are usually initialized with uniform distributions and later adapted according to the training symbol sequences. In practice, there are some wellestablished training algorithms available to automatically optimize the parameters of the HMM. The Baum–Welch (Baum et al., 1970) training procedure is a standard algorithm which uses the Maximum Likelihood Estimation (MLE) criterion. In this training algorithm, the training symbol sequences are used to estimate the HMM parameters. Finally, a testing sequence gets analyzed by the trained HMMs to be recognized. In an HMM, the underlying processes are usually not observable, but they can be observed through another set of stochastic processes that produces continuous or discrete observations (Lawrence & Rabiner, 1989), which lead to discrete or continuous HMMs respectively. In the discrete HMMs, the observation sequences are vector-quantized using a codebook to select discrete symbols. Though the discrete symbols for the observations