Foundations of Image Science

Drs. Barrett and Myers are certainly well qualified to write such an ambitious book that spawns a multitude of subjects. It is a challenge to write a book that will satisfy the multidimensional needs of the practitioners of image science. This is a book for advanced students who have developed maturity in mathematical methods, physics, and systems analysis. The treatment of various subjects is often scholarly in nature punctuated by historical perspectives and, at times, an injection of humor. This book is definitely not for the ‘‘faint of heart.’’ The book is divided into seventeen chapters followed by three appendices and an extensive bibliography. The first chapter is meant to be a refresher in vector and operators and consists of eight subsections. An exposure to real and complex analysis and algebra, such as in classic works by Rudin, Lang, and Birkhoff, may be necessary in order to navigate these sections. I disagree with the authors that an elementary understanding of calculus and matrix algebra is sufficient to navigate this section. The authors do provide an extensive bibliography spawning a multitude of references. However, many of these references are not cited in the main body of the textbook. It would have been helpful to the student to cite a few key references at the beginning of each chapter. The material in this section as well as some of the other sections appears to be an exposition of the scholarliness of both authors as well as their knowledge of the history of mathematicians such as Banach. This historical perspective is a refreshing punctuation that occurs frequently in this book. The treatment in the first section covers aspects of vector analysis such as Hilbert spaces, eigenanalysis, and pseudoinverses. The authors devote two subsections to pseudoinverses including a special treatment of the MoorePenrose pseudoinverse. The treatment of certain subjects, at times, seems lopsided and seems to be a recurring theme in the rest of the book. The second chapter is treatment of delta