ABSTRACT
This chapter considers more abstract representations which are useful in image interpretation and analysis. It explores the pixel values in a given spectral band to linear combinations of orthogonal functions of spatial frequency and distance. The principal components, minimum noise fraction and maximum autocorrelation factor transformations create at each pixel location new linear combinations of the pixel intensities from all of the spectral bands and can properly be called spectral transformations. Unlike the Fourier transform, which represents an array of pixel intensities in terms of pure frequency functions, the wavelet transform expresses an image array in terms of functions which are restricted both in terms of frequency and spatial extent. In many image processing applications, this turns out to be particularly efficient and useful. The principal components transformation, also called principal components analysis, generates linear combinations of multispectral pixel intensities which are mutually uncorrelated and which have maximum variance.
