CHAPTER 6 – Spatial Transforms

Publisher Summary This chapter focuses on spatial transforms, which can be combined with spectral transforms for certain applications such as image fusion and feature extraction for classification. Spatial transforms provide tools to extract or modify the spatial information in remote-sensing images. Some transforms such as convolution use only local image information, that is, within relatively small neighborhoods of a given pixel. Others, for example, the Fourier transform, use global spatial content. Between these two extremes, the increasingly important category of scale-space filters, including Gaussian and Laplacian pyramids and the wavelet transform provide data representations that allow access to spatial information over a wide range of scales, from local to global. The chapter concludes the following points: convolution and Fourier transform filtering are equivalent global processing techniques, except in the border region; a wide range of processing can be performed with small neighborhood windows, including noise removal and edge detection; scale-space filters allow access to image features according to their size, which is not possible with linear convolution or Fourier filters; and the resolution pyramid provides a unified description of scale-space filters, for example, Gaussian, Laplacian, and wavelet pyramids.