E-Book Overview
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.
E-Book Content
This page intentionally left blank MATHEMATICS OF DIGITAL IMAGES Creation, Compression, Restoration, Recognition Compression, restoration and recognition are three of the key components of digital imaging. The mathematics needed to understand and carry out all these components is here explained in a textbook that is at once rigorous and practical with many worked examples, exercises with solutions, pseudocode, and sample calculations on images. The introduction lists fast tracks to special topics such as Principal Component Analysis, and ways into and through the book, which abounds with illustrations. The first part describes plane geometry and pattern-generating symmetries, along with some text on 3D rotation and reflection matrices. Subsequent chapters cover vectors, matrices and probability. These are applied to simulation, Ba