This is a major revision of the author’s successful book Mathematics of Computer Graphics. It still focuses on foundations and proofs, but now exhibits a shift towards digital image compression, restoration, and recognition. Topology is replaced by Probability and Information Theory (with Shannon’s source and channel encoding Theorems) which are used throughout. Several fractal methods are given in the service of Compression, along with linear transforms (hence FFT, DCT, JPEG, wavelets etc), recent neural methods, and the ubiquitous vector quantisation. Optimising for the Human Visual System is a subtheme. The superiority of Pyramid methods with respect to entropy is proved. Restoration offers convolution/deconvolution against noise and blurr. Recognition explores not only the Hough and Radon transforms, Statistical feature extraction, and Neural classification, but also Tomography, the recovery of 3-D images from 2-D data. It extends finally to multiple fractal dimensions in medical and other nature-related images.
