311.

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alanobis distance (Equation (2.10)). Thus, the geometrical shape of the cloud formed by a set of pixels belonging to a given class can be described by an ellipsoid. The shape of the ellipsoid depends on the covariance among the features belonging to a feature space. In a two-dimensional feature space the maximum-likelihood function delineates ellipsoidal ‘equiprobability contours’, which can be viewed as decision boundaries.

Two parameters, the mean vector and the covariance matrix, are used to characterise each class. The importance of choosing a sample size that is adequate to provide for an unbiased and efficient estimate of these parameters is considerable (see the discussion above, Section 2.1, and below, Section 2.6).

The ML classifier assumes that the information class prior probability P(w) is uniformly distributed. However, if one can model P(w) in a suitable way, the classification accuracy could be increased. For example, one may model prior probability as different weights associated with each class. A higher weight for a given class implies that there is a higher probability of a pixel receiving the label associated with that class. The effects of modelling P(w) are discussed by Swain and Davis (1978), Strahler (1980), and Mather (1985). In recent years, there has been a trend towards modelling the prior probability using a ‘smoothness’ assumption based on the concept of context. This method is called the smoothness prior. By using the smoothness prior together with the class conditional probability P(x|]w), one can attempt to perform a MAP classification. The use of statistically robust methods is the main topic of Chapter 6.

2.3.5 Artificial neural networks

Artificial neural networks (ANN) have been studied for many years in such fields as speech and handwriting recognition and in image analysis. In recent years, the use of ANN in pattern recognition applied to remotely sensed images has significantly increased, largely because ANN is believed to provide improved accuracy.

A typical ANN consists of a series of layers, each containing a number of processing units or neurones. All neurones on a given layer are linked to all neurones on the previous and subsequent layers (Figure 2.10). Hence, these methods are sometimes given the name ‘connectionist’. The design of the topology (or structure) of an ANN is based on our understanding of the way in which the human brain functions. From this perspective, parallel operation and a high computation rate are required to modify the weights and values associated with the neurones. The values (termed activities) of the neurones are determined via a linear or non-linear mapping function, which generally takes the sum of the product of both weights and values of previous computation elements as input (Section 3.1). In some cases, a

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