Synopses & Reviews
This major revision of the author's popular book still focuses on foundations and proofs, but now exhibits a shift away from Topology to Probability and Information Theory (with Shannon's source and channel encoding theorems) which are used throughout. Three vital areas for the digital revolution are tackled (compression, restoration and recognition), establishing not only what is true, but why, to facilitate education and research. It will remain a valuable book for computer scientists, engineers and applied mathematicians.
Synopsis
This unique textbook, which is based on courses taught by the author to students in the US, UK and Europe, introduces the geometry, analysis and topology necessary to understand the mathematical framework for computer graphics. The topics covered range from symmetry and tilings to chaos and fractals, and the applications from computational geometry through numerical analysis to geometric modelling. Consequently it will be welcomed by mathematicians, computer scientists and engineers, whether students or professionals.
Synopsis
This textbook , based on courses taught by the author to students in the USA and Europe, introduces the geometry, analysis and topology necessary to understand the mathematical framework for computer graphics. Topics range from symmetry and tiling to chaos and fractals. Applications include computational geometry, numerical analysis and geometrical modelling.
Synopsis
This unique textbook introduces the geometry, analysis and topology necessary to understand the mathematical framework for computer graphics.
Synopsis
Compression, restoration and recognition are three of the key components of digital imaging. The mathematics needed to understand and carry them out are explained here in a style that is rigorous and practical, with many worked examples, exercises with solutions, pseudocode, and sample calculations on images. The book abounds with illustrations and is suited for course use or for self-study. It will appeal to all those working in biomedical imaging and diagnosis, computer graphics, machine vision, remote sensing, image processing and information theory and its applications.
About the Author
Dr S. G. Hoggar is a Research Fellow and formerly a Senior Lecturer in Mathematics at the University of Glasgow.
Table of Contents
1. Isometries; 2. How isometries combine; 3. The braid patterns; 4. Plane patterns and their symmetries; 5. The 17 plane patterns; 6. More plane truth; 7. Matrix and vector algebra; 8. Isometrics in 3-space; 9. Quaternions and rotations; 10. Fractals and nature; 11. Basic topology; 12. Compact sets, connected sets, holes and homeomorphisms; 13. The existence and uniqueness of fractals; 14. Iterated function systems; 15. Addresses, measures, and the Random Iteration Algorithm; 16. Julia and Mandelbrot and beyond.