The most widely used recognition algorithm for gesture recognition is Hidden Markov Models (HMMs). Hidden Markov Models are mathematical models of the stochastic process which generates a sequence of observations according to the previously stored information. Statistical approach has many advantages in HMMs like rich mathematical framework, powerful learning and decoding methods, good sequences handling capabilities, flexible topology for the statistical phonology and the syntax. The disadvantages lie in the poor discrimination between the models and in unrealistic assumptions that must be made to construct the HMMs theory, namely the independence of the successive feature frames (i.e. input vectors) and the first order Markov process. The developed algorithms in the statistical framework which uses HMMs are rich and powerful in real-time situations. In addition, Hidden Markov Models are the widely used in practice to implement gesture recognition and understanding systems.
In the Markov chain, every state of the model can only observe a single symbol. However, all states in Hidden Markov Models topology can observe one symbol out of a distinct gesture. The probability of observing a symbol for each state is stored in the observation probability distribution matrix. For example, the observation probability of a symbol in the state s1 is considered as the probability to emit the symbol. So, in other words the observation probability distribution is named emission distribution in the recognition task. Furthermore, HMMs states are called hidden for the following reasons. Firstly, the decision of observing a symbol represents the second process. Secondly, the emitter of an HMM only emits the observed symbol. Finally, the emitting states are unknown since the current states are based on the previous states. In the gesture recognition, HMMs are very well known and more flexible due to their stochastic nature.