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divided in a ‘fuzzy’ fashion, the rule set is then generated. The general form of fuzzy rule is as follows: ‘If the pixel is in fuzzy partition A then the pixel belongs to class j with certainty w’.

The creation of rules and certainty parameters w (which are a function of membership value) is performed automatically. The user has only to define the membership function and to select training samples. Details of the procedure are given in Chapter 4.

2.4 Combining classifiers

The different approaches to pattern recognition that are presented in Section 2.3 are often viewed as alternative methods, and many researchers have published comparisons between the various procedures in order to demonstrate that one is ‘better’ than the other in some way. It appears that many of the methods are complementary; some are ‘better’ in resolving one aspect of the labelling problem, while another method may be superior in another respect. Hence, some interest has been shown in combining the results obtained using different decision rules in order to improve the overall labelling. Brief details of combination methods known as voting rules, Bayesian formalism, evidential reasoning, and multiple ANN are given in the following paragraphs. Vieira (2000) presents a more detailed survey.

The procedure using voting rules is quite simple. The labels output by a number of classifiers for a given pixel are collected, and the majority label is selected. This is known as the majority vote rule. A more stringent requirement is that all classifiers agree on a single label, and this approach uses the conservative voting rule. The latter rule is unlikely to produce a fully labelled thematic image if the number of classifiers used is more than two. On the other hand, the former rule may produce conflicts similar to the 2000 US Presidential election, in that the winner may have only a few votes more than the loser. In order to avoid the possibility of choosing label A when the evidence supporting A is not much greater than the evidence supporting label B, the method of comparative majority voting can be used. This method requires that the ‘winning’ vote should exceed the runner-up vote by a specified amount, thus ensuring a clear winner. Pixels that are not labelled because no clear winner emerges are labelled as ‘unknown’. See Hansen and Salomon (1990) for a discussion of combining artificial neural network classifiers. Brodley and Friedl (1999) consider the question of classifier combination and voting methods in the context of filtering training data (Section 2.6.3).

Bayesian formalism can involve a process as simple as averaging. It is used with multiple classifiers that output a probability (or probability-like) estimate of the likelihood of pixel A belonging to class j. Such classifiers include the maximum likelihood method and the artificial neural network. The probabilities (or pseudo-probabilities) for a pixel for each possible

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