286.

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nology, alternative strategies have been proposed, particularly the use of artificial neural networks, decision trees, methods derived from fuzzy set theory, and the incorporation of secondary information such as texture, context and terrain features.

This chapter introduces the principles of pattern recognition, starting from the concept of feature space and its manipulation using feature selection and orthogonalising techniques. Details of the statistical classifiers are then described. Algorithms based on artificial neural networks, decision trees, the fuzzy rule base concept and the incorporation of secondary information are discussed in later chapters, and are reviewed only briefly in this chapter, while the mixed pixel problem is considered in Chapter 4, in the context of fuzzy classification.

2.1 Feature space manipulation

Image coordinates give the relative location of a pixel in the spatial domain and, given the origin of the coordinate system and the pixel spacing (Δx and Δy), geometrical calculations, such as inter-pixel distance, can be performed. When we take into account the values associated with a pixel, which form a vector of measurements on a set of selected features, we can think of a space defined not by the x and y or row and column spatial coordinates, but by the features on which the pixel values are measured. These features may be image pixel values in separate wavebands, context or texture measurements, or geographical attributes of the area represented by the pixel, such as mean elevation, slope angle, or slope azimuth. Feature space is multidimensional and as such cannot be visualised. Nevertheless, standard geometrical measures such as the Euclidean distance as the shortest distance between two points are still valid (Alt, 1990, gives a non-mathematical description of hyperspace).

Figure 2.1a shows that the spatial domain coordinates of the shaded pixel (in row-column representation) are (5, 4). Figure 2.1b shows three co-registered images, perhaps representing reflectance in the green, red, and near-IR wavebands. The quantised pixel values in these wavebands are {35, 20, 46}, respectively. Figure 2.1c shows a plot of the position of the pixel in a feature space that has three axes defined by these three bands. The pattern recognition process involves the subdivision of feature space into homogeneous regions separated by decision boundaries. The various statistical, neural and knowledge-based methods discussed in this book use different decision rules to define or specify these boundaries. In the fuzzy classification approach (Chapter 4), decision boundaries can overlap. A number of techniques can be used to manipulate or transform the axes of the feature space in order to facilitate classification, for example by determining a subspace that contains most of the information present in

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