289.

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hence there is no redundancy. The synthetic features are defined by linear combinations of the observed features, and much of the information content of the observed features is reproduced by m synthetic features, where m<k. In the following subsections, four orthogonalising procedures are described. The Tasselled Cap transform differs from the remaining three methods as it uses three or four predefined linear combinations of Landsat MSS or TM bands. Principal components analysis (PCA) is a well known method of orthogonalising a data set and of ordering the synthetic features (in this case, the principal components) in terms of their contribution to total variance. However, it is sensitive to the scale of measurement used for each feature, and there is no reason to believe that lower-order principal components represent noise or unwanted information. The MAP (min/max autocorrelation factors) transform and the MNF (maximum noise fractions) procedures aim specifically to separate information and noise and, unlike PCA, are independent of measurement scale.

These four transforms are described in the following subsections.

2.1.1 Tasselled Cap transform

The Tasselled Cap transform was derived by Kauth and Thomas (1976) using four-band Landsat MSS images. The axes of this four-dimensional feature space are transformed into new four-dimensional coordinates defined by the concepts of ‘brightness’, ‘greenness’, ‘yellowness’ and ‘none-such’. The transformation involves rotation of the axes of feature space and translation of the origin of the coordinate system. For example, one of the axes could be moved to a position such that pixels with a low value of the ratio of infrared to red reflectance take low (near zero) values, while pixels that have a high infrared:red ratio take high values. Since the infrared:red ratio is correlated with vegetation vigour, then this ‘new’ axis could be described by the term ‘greenness’.

The first transformed axis, ‘brightness’, is based on soil reflectance values (e.g. for dry and wet soil) to form a ‘soil line’. The second and the third axes are based on pixels of green vegetation and senescent vegetation, respectively. The fourth axis, ‘nonesuch’ has been interpreted as being related to atmospheric conditions.

To construct such a new coordinate system, the user selects at least two representative pixel values for each coordinate because the definition of a line requires at least two points. Each representative pixel value can be obtained by taking the average of pixels belonging to the same group. For instance, in the case of soil line construction, one can select several pixels belonging to wet soil class then take the average as one end of soil line. The other end can be obtained based on the average of dry soil pixels. Once these candidates have been selected, an orthogonalisation process is carried out in order to make the coordinates perpendicular to each other.

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