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Figure 2.9 Example of minimum distance classification criteria. See text for details.
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 xi is the ith pattern vector and wj is information class j then, according to Equation (2.18), the probability that xi belongs to class wj 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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