309.

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Figure 2.9 Example of minimum distance classification criteria. See text for details.

2.3.4.3 Maximum likelihood classifier

The Maximum Likelihood (ML) procedure is a supervised statistical approach to pattern recognition. The probability of a pixel belonging to each of a predefined set of classes is calculated, and the pixel is then assigned to the class for which the probability is the highest. ML is based on the Bayesian probability formula:

(2.18)

where x and w are generally called ‘events’. P(x, w) is the probability of co-existence (or intersection) of events x and w, P(x) and P(w) are the prior probabilities of events x and w, and P(w|x) is the conditional probability of event x given event w. P(w|x) is interpreted in the same manner. If event x_i is the ith pattern vector and w_j is information class j then, according to Equation (2.18), the probability that x_i belongs to class w_j is given by:

(2.19)

Since, in general, P(x) is set to be uniformly distributed (i.e. the probability of occurrence is the same for all pixel features), Equation (2.19) can be rewritten as:

(2.20)

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