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correlation matrix. These matrices have different eigenvectors, and thus the resulting principal component images will also be different. In the case of land cover/use change detection, the standardised method is preferred by Fung and LeDrew (1987), who claim that the use of standardised PCA can minimise differences due to atmospheric conditions in multitemporal images. If the images subjected into PCA are not measured in the same scale, the standardised method is also a better choice than the unstandardised method because the correlation matrix normalises the data on to the same scale (i.e. each spectral band is given unit variance, hence inter-band variation is ignored). Users should be aware of the fact that the use of the correlation matrix implies the equalisation of within-band variance, and should also note that the technique does not differentiate between ‘information’ and ‘noise’. In some image sets (for example, hyperspectral data sets) there may be considerable noise present, and this noise may have a variance that is greater than some of the information sources.

2.1.3 Minlmax autocorrelation factors (MAP)

A somewhat different approach to the orthogonalisation of specifically spatial data is presented by Switzer and Green (1984), who argue that PCA does not differentiate between signal and noise, that it is not explicitly spatial (in the sense that the image data could be rearranged randomly without affecting the results), and that it is scale-dependent. They propose a method of distinguishing between signal and noise, and suggest that their approach should be preferred to filtering because it does not blur the data.

Their method is based on the principle that information, or ‘signal’, is spatially autocorrelated (in the sense that pixels in a neighbourhood will tend to have similar values because they represent some geographical object such as a lake or a forest). Conversely, noise will have a low spatial autocorrelation, if systematic noise such as banding is excluded. The MAP procedure is based on the ordering of set of orthogonal functions in such a way that autocorrelation decreases from the low-order to the high-order functions, i.e. autocorrelation is minimised rather than variance being maximised, as is the case with PCA. The lower-order functions may therefore be expected to contain mainly non-autocorrelated noise while the higher-order components would represent information. The procedure is scale-free in the sense that the same result is achieved irrespective of the scale of measurement used for each feature. This is because the procedure maximises a ratio—that of signal to noise.

A detailed account of the computational procedures involved in the MAF transform is provided by Neilsen (1994). The variance-covariance of the total data set, C, is derived, together with the corresponding eigenvalues and eigenvectors P. Next, the variance-covariance of the noise component, C_Δ, is computed. Switzer and Green (1984) suggest that the original

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