Mathematics of Digital Images: Creation, Compression, Restoration, Recognition (Hoggar, S.G.; 2006) [Book Review]

This 854-page book covers the foundational mathematics essential to many modern image processing techniques and applications. It is impressively comprehensive and nearly encyclopedic in scope. The text itself is divided into 18 chapters arranged into six parts covering, respectively, plane-based symmetries, vector- and matrix-based algebra, probability theory, information theory, image transformation, and B-spline curves. The mathematics are rigorous, accurate, and accessible. It is important to note that this is a book on mathematics, and not a book on image processing, per se. Mathematics drive the discourse. The presentation of the book is very good. There are numerous illustrations - both diagrams and imagery - throughout the text that serve to illuminate key issues. Each chapter contains a number of exercises; both pencil-and-paper as well as implementation-base exercises are included. The book may find a niche for its unique mathematical focus by aiding mathematicians to converse with signal and image processing practitioners. It is also likely to find use as a reference for the latter, particularly for those engaged in mathematically based research.