328.

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an influence on observed variability both within and between classes. If a sample is to be representative then its size should be related to the variance of the class. Scale of observation is generally proportional to variability; for example, consider the difference between two images with spatial resolutions of 1 km and 1 m, respectively. The latter shows more ‘detail’, in the sense that what appear to be homogeneous regions at 1 km resolution become fragmented and more variable as resolution increases (Woodcock and Strahler, 1987). Other pertinent references on the importance (and influence) of scale are Benson and Mackenzie (1995), Cushnie (1987), Foody and Curran (1994), Marceau et al. (1994), Marceau and Hay (1999) and contributions to Quattrochi and Goodchild (1997).

There is also an obvious link between the concept of ‘spatial variability’, mentioned in the preceding paragraph, and image texture. One can, in fact, consider the dependence between spatial scale/resolution and spatial variance from a number of aspects. For example, the multifractal dimension is based on the concept of sets each with its own fractal dimension (Pecknold et al., 1997). The use of fractal and multifractal dimension as measures of texture are described in Chapter 5. The discrete wavelet transform is a second example of a hierarchical or multiscale procedure. Unlike the Fourier transform, which decomposes an image into its frequency components, the wavelet transform takes into account both the spatial and the frequency characteristics of an image. In other words, the wavelet transform can deal with non-stationary series. It is described as ‘multiscale’ because it operates by decomposing the image into scale components in a recursive fashion. The applications of wavelets in remote sensing are described in detail in Starck et al. (1998). Zhu and Yang (1998) use wavelets to characterise image texture and demonstrate the utility of such texture measures in classification. See Chapter 5 for an extended discussion of the derivation of texture measures from remotely sensed images.

2.6.3 Adequacy of training data

Since training data sets are used to ‘teach’ a supervised classifier, it is important to ensure that the training data are adequate in the sense that no erroneous or unrepresentative samples are included. The presence of such outliers will have a lesser impact on supervised classifiers that are based on mean values alone, as one outlier will not have a particularly large influence on the value of the mean of a large sample (‘large’ means greater than thirty measurements on the given feature or variable). However, the variances and covariances are likely to be more badly affected because their computation includes the square of the difference between a given observation and the mean of its class. Artificial neural networks train directly on the sample data themselves, and are thus likely to be signifi

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