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Figure 4.17 Example of using fuzzy membership functions to tackle mixture problem. MF1 and MF2 denote membership function 1 and 2, respectively. See text for further discussion.

bership grades for a given pixel over all classes must sum to one, it follows that the overlap area between membership functions should also sum to unity. The second issue is concerned with the dimensions of the images. The greater the dimensionality of the input data, the greater the number of fuzzy rules that will result. One possible solution is to use data dimension reduction techniques. Currently, the investigation of fuzzy rule base methods is still at an early stage. Further investigation is needed before an adequate method of dealing with mixed pixels is produced.

A method similar to the fuzzy set approach is known as linear discriminant analysis (Marsh et al., 1980). These authors use Landsat MSS four band images to construct a discriminant function. This function maps a four-dimensional input pattern on to a single discriminant value, which represents the distance of the pattern from the hyperplane representing the discriminant function. The class proportions are then estimated in proportion to this distance.

4.6.2 Use of artificial neural networks

Artificial neural network classifiers are described in Chapter 3. Chapter 3 also shows how a neural network can be trained to recognise linear features (Section 3.6). In this section, we consider the use of neural networks to resolve the pixel mixture problem.

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