This book contains a lot of interesting mathematics, most of it related to digital images, but it is not really a book about digital images. It does not even contain a definition of what a digital image is. Digital images are only really discussed in the last three chapters, which start on page 560. Before that, any discussion of the applications of the mathematics to actual problems related to digital images is almost incidental. There are brief discussions of the application of principal component analysis in image compression and reconstruction near page 300, Bayesian image restoration on page 372, Bayesian nets in computer vision on page 516. Those wishing to learn about digital images should start with the classics, such as Digital Image Processing by Gonzalez and Woods.
Nevertheless, the book is well written and might be good as a reference: it contains over 800 pages of text, with many examples and exercises, and over 10 pages of references to books and papers on specific topics.
Luiz Henrique de Figueiredo is a researcher at IMPA in Rio de Janeiro, Brazil. His main interests are numerical methods in computer graphics, but he remains an algebraist at heart. He is also one of the designers of the Lua language.
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.