The first two texts in this series [1,2] were designed to give a reasonably complete introduction to the theory and practice of digital image processing. The authors made the good decision to produce three books of manageable size instead of one monster volume. This is the third and final book in the series. The three could be used in sequence for courses of varying degrees of depth: the first for a very introductory hands-on course, the second to make the course a little more complete, and the third for some more advanced material, and possibly also as an introduction to research.

There is much to admire in all three books. Digital image processing is such a vast field--with so many applications and algorithms, some generic and others more specific--that authors must decide what to include and what to omit. Burger and Burge have succeeded in providing a very good range of topics.

One potential problem with a multi-volume text is that many cross-references will refer to previous volumes, which means juggling multiple books. However, I would expect that any reader of this final volume would already be conversant with most of the preceding material.

This third volume investigates thresholding, methods of automatically choosing the optimal threshold, color filtering and edge detection, edge-preserving smoothing filters, Fourier shape descriptors, and the scale-invariant feature transform (SIFT) algorithm. The authors’ website includes an additional chapter on the synthesis of gradient noise images. The text contains a good mix of appropriately rigorous mathematics, pseudocode descriptions of algorithms, and plenty of examples. The example images are all appropriate for their algorithms, although at times the reproductions are a little small.

Each chapter contains a summary of its content, a careful mathematical exposition, pseudocode, and diagrams, many of which are in color. The authors have made every effort to ensure the clarity of their material. However, the pseudocode is at times difficult to follow, especially with the use of arcane symbols (such as a smile symbol for list concatenation). There is some discussion of the use of the Java library ImageJ, which is the authors’ preferred implementation platform. Java is a high enough level language to be read as pseudocode if properly written, which prompts me to wonder if some of the pseudocode could have been replaced with properly commented ImageJ code. At the end of each chapter, the authors provide an implementation section that consists of lists of the methods of the relevant Java classes. I would have preferred to see some complete example programs showing the methods in actual use.

Aside from these complaints, the exposition is in general first class, including the different automatic thresholding methods; different color spaces and their uses for image filtering; edge detection algorithms, including a very complete and excellent description of the Canny detector; and a delightful table that presents a number of binary images and the differences between them as computed by Fourier descriptors.

Another problem with this text is the paucity of exercises. The SIFT chapter, which is the longest because of the complexity of the material (the pseudocode description of the complete algorithm takes eight pages), has only two exercises. This severely limits the text’s usefulness as a textbook, and students or instructors who might hope to be carefully led through the material with scaffolded exercises will be disappointed.

I also think that, in their efforts to be mathematically precise, the authors have chosen notation that is sometimes confusing. For example, different accents are used on symbols: a dot for a particular value, a smile for an extreme value, and a tilde for a vector, as well as a bar. In the smaller font used for captions, these accents can be almost indistinguishable. This is especially a problem in the SIFT chapter, which requires the deepest mathematics.

I also found some of the diagrams confusing. The authors sometimes include so much detail that it threatens to obscure the main points. Figure 6.12, in the chapter on Fourier descriptors, is one such example, with curves, ellipses of different colors, and different colored points. The overall effect is confusion rather than elucidation. In Figure 7.15 (part of the SIFT chapter), 3D neighborhoods are shown as small cubes, which partly overlap each other. In fact, a simple wireframe diagram would have been much clearer and less complex.

Although the authors consider these textbooks, the lack of exercises means that I would not use them as such. However, in spite of my caveats, I really like these books and they will form part of my standard reference library from now on. As references for modern approaches to fundamental image processing, they are very good indeed and deserve to be widely read.