Mathematics of Digital Images: Creation, Compression, Restoration, Recognition (Hardcover)

Description

Compression, restoration and recognition are three of the key components of digital imaging. The mathematics needed to understand and carry out all these components are explained here in a style 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 on 3D rotation and reflection matrices. Subsequent chapters cover vectors, matrices and probability. These are applied to simulation, Bayesian methods, Shannon's information theory, compression, filtering and tomography. The book will be suited for advanced courses 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.

• Written to be understood not only by engineers but by all concerned with digital image issues
• Builds up the required probability and information theory from scratch
• Draws on material from author's successful earlier book

Table of Contents

Introduction; 1. Isometries; 2. How isometries combine; 3. The braid patterns; 4. Plane patterns and symmetries; 5. The 17 plane patterns; 6. More plane truth; 7. Vectors and matrices; 8. Matrix algebra; 9. Probability; 10. Random vectors; 11. Sampling and inference; 12. Entropy and coding; 13. Information and error-correction; 14. The Fourier transform; 15. Transforming images; 16. Scaling; 17. B-spline wavelets; 18. Further methods; References; Symbols; Selected answers; Index.