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HRV), to 0–1023 (10-bit representation, as used for AVHRR data) to more complex formats. For example, raw synthetic aperture radar data are commonly represented in terms of two 16-bit integers per pixel, with the first integer representing the real part and the second integer representing the imaginary part of a complex number. Whatever the precision (8, 10 or 16 bit) these pixel values are stored as rectangular rasters, and can be held in a computer in the form of a two-dimensional array. The data set used in pattern recognition consists of a number of co-registered raster images representing, for example, the measurements in the individual bands of a multispectral or hyperspectral image, the ground elevation (DEM), or some other spatial property of interest. The number of features used to represent terrain conditions is known as the ‘dimensionality’ of the data. Multispectral data have a low dimensionality; for instance, SPOT HRV produces three bands of data, and Landsat-7 ETM+ generates seven bands in wavelengths ranging from the optical to the thermal infrared, plus a panchromatic band. Hyperspectral sensors such as AVIRIS, CASI and DAIS have the ability to collect data in tens or hundreds of narrow spectral bands. One problem in the classification of high-dimensional remotely sensed data is the paucity of samples (‘training data’) relative to the dimensionality of the feature space. This problem leads to difficulties in estimating statistical parameters such as the mean and covariance matrix.

The aim of pattern recognition in the context of remote sensing is to link each object or pixel in the study area to one or more elements of a user-defined label set, so that the radiometric information contained in the image is converted to thematic information, such as vegetation type. The process can be regarded as a mapping function, which constructs a linkage between the raw data and the user-defined label set. A simple example is shown in Figure 1.1. Normally, each object or pixel is linked to a single label. However, it is also possible to perform a ‘one-to-many’ mapping, so that a given pixel can be associated with more than one label, with the differing degrees of association between the pixel and each label being expressed as probabilities of membership. Alternatively, a ‘many-to-one’ scheme will link groups of pixels to a single label. This approach can be used, for example, to give the same label to all of the pixels in a single agricultural field.

Each application generally requires a different methodology, and each methodology is likely to generate different results. If reliable results are to be obtained, the analyst should understand the behaviour of the method being used in order to achieve a satisfactory performance. For instance, the performance of a statistical procedure is strongly affected by the accuracy of the estimates of parameters such as the mean vector and the variance-covariance matrix for each class that are obtained from samples of pixels, called training data sets. Equally, the design of the architecture of a feed-

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