An Efficient and Robust Technique for Facial Expression Recognition Using Modified Hidden Markov Model

2. Basics Of Hmm

Markov process is used for time series data modelling. This model is applicable for situations where there is a dependability of present state to previous state. For example, bowler bowls the ball in cricket game; ball first hit the ground then hit the bat or pad. This situation can be easily modelled by time series data modelling. In other example such as in a spoken sentence, the present pronounced word is depending on the previous pronounced word. Markov process effectively handles such situations (see Figure 1).

Figure 1.

A Markov Model for 3 observations variables

When an observation variable is dependent only on previous observation variable in a markov model is called first order markov chain. The joint probability distribution is given byp(X₁, X₂,----,X_N) = p(X₁) Л p(X_N|X_N-1)(1) where p(X₁, X₂,------,X_N) is the joint probability distribution of states X₁, X₂,----,X_N and p(X1) is the probability of state X₁ and p(X_N|X_N-1) is the probability of state X_N given state X_N-1 .