ABSTRACT
The frequency/sequency transforms discussed in this chapter include the Fourier, cosine and Walsh–Hadamard and provide information regarding the rate at which the gray levels change within an image. Additionally, the wavelet and the Haar transforms are discussed and are unique in that they retain both frequency and spatial information. One transform that is not frequency related, the principal components transform, is included here and its primary purpose is to decorrelate the data between image bands. The discrete form of the frequency/sequency transforms is created by sampling the continuous form of the functions on which these transforms are based, that is, the basis functions. The basis functions used for these transforms are typically sinusoidal or rectangular, and the transforms are implemented by projecting the basis functions onto the images via an inner product. Equations, both forward and inverse, are given with numerous analytical and visual examples. The transforms can use the entire image or can be used on black by black basis. Along with the text are 32 illustrative figures and 71 associated monochrome and color images. The end of chapter exercises include problems and programming exercises.
