5-8 Maximum Likelihood Classifier

Maximum likelihood classifier is one of the most popular methods for thematic mapping with satellite multispectral imagery.

An unknown pixel X with multispectral values (n bands) will be classified into the class (k) that has the maximum likelihood
{ max Lk (X) }.

The likelihood function is given as follows on the assumption that the ground truth data of class k will form the Gaussian (normal) distribution (see Figure 5.11).

where:

: mean vector of the ground truth data in class k
: Variance-covariance matrix of K class produced from the ground truth data
: determinant of Sk

For practical computation, the above likelihood is converted to the discriminant function in the form of logarithm.

Gk (X) = In |Sk| + d2k

where : d2k =

Instead of maximum Lk (X), class k that makes Gk (X) minimum is searched for among the classes.

The maximum likelihood classifier is popular because of its robustness and simplicity. But there will be some errors in the results if the number of sample data is not sufficient, the distributions of the population does not follow the Gaussian distribution and/or the classes have much overlap in their distribution resulting in poor Separability.