ABSTRACT

This chapter is somewhat of a catch-all, intended mainly to consolidate and extend material presented in the preceding chapters and to help lay the foundation for the rest of the book. In Sections 4.1 and 4.2, building on the discrete Fourier transform introduced in Chapter 3, the concept of discrete convolution is introduced and filtering, both in the spatial and in the frequency domain, is discussed. Frequent reference to filtering will be made in Chapter 5 when we treat enhancement and geometric and radiometric correction of multispectral and SAR imagery. In Section 4.3 it is shown that the discrete wavelet transform of Chapter 3 is equivalent to a recursive application of low-and high-pass filters (a filter bank) and a pyramid algorithm for multiscale image representation is described and programmed in IDL and Python. Wavelet pyramid representations are applied in Chapter 5 for panchromatic sharpening and in Chapter 8 for contextual clustering. Section 4.4 introduces so-called kernelization, in which the dual representations of linear problems described in Chapters 2 and 3 can be modified to treat nonlinear data. Kernel methods are illustrated with a nonlinear version of the principal components transformation, for which both an ENVI/IDL extension and a Python script are provided. Kernel methods will be met again in Chapter 6 when we consider support vector machines for supervised classification, in Chapter 7 in connection with anomaly detection, in Chapter 8 in the form of a kernel Kmeans clustering algorithm and in Chapter 9 to illustrate nonlinear change detection. The present chapter closes in Section 4.5 with a brief introduction to Gibbs-Markov random fields, which are invoked in Chapter 8 in order to include spatial context in unsupervised image classification.