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Reviewer: Christian Ronse

The reputation of mathematical morphology in image processing can be considered somewhat analogous to that of operating systems in computer science: everyone uses it, few people understand it in depth, and its designers are a breed apart. This explains the great interest aroused by the publication, in 1999, of the first edition of this book. The first edition was a very rare instance of a presentation of the field requiring nearly no technical prerequisite, but, at the same time, going a long way beyond the elementary expositions, describing many elaborate methods and algorithms presented in recent works. This was achieved by the progressiveness of its discourse (starting from the well-known elementary concepts and operations, and going progressively through more elaborate tools), and its strict restriction to the digital framework. Faced with the success of his book, the author felt the need to revise and expand it. As it stands now, this second edition contains 12 chapters: (1) Introduction (2) Background Notions (3) Erosion and Dilation (4) Opening and Closing (5) Hit-or-miss and Skeletons (6) Geodesic Transformations (7) Geodesic Metrics (8) Filtering (9) Segmentation (10) Classification (11) Texture Analysis (12) Application Fields Only chapter 11 has been added to the top-level contents. However, the size of the book has increased by one-fourth, which means that most chapters have been lengthened. There are more algorithms and more applications, several of them coming from the author's own works. Many added illustrations improve the clarity of the explanations of the morphological theory, and the bibliography at the end of each chapter has become impressive. Some deeper notions have also been introduced, such as the lattice-theoretical structure of images and operators, connected filters, and activity ordering. Despite its increased size, this book cannot cover all the practical aspects of mathematical morphology, which have appeared in many books and articles for 40 years. In particular, probabilistic methods based on models of random sets are not discussed. Also, non-flat structuring elements are neglected, and the exposition of digital topology is superficial, and mostly restricted to two dimensions. A comprehensive book on mathematical morphology, however, would probably require a few thousand pages, and would be partially obsolete from its publication day. To a large extent, my review of the first edition ( Mathematical Reviews 2000b:68262) remains true for this second edition. The topics covered are basically the same, and the only prerequisites for entering this book are elementary set theory, the notions of a graph and an image histogram, and an informal understanding of linear filters, especially low-/high-/band-pass filters in the frequency domain. With its increased size and complexity, however, and in its deeper presentation of the abstract aspects of mathematical morphology, the nature and purpose of the book has somewhat changed. It is no longer suited for sequential reading by a beginner. An instructor could select, depending on the type of audience, some sections from several chapters to be read in a given order. It would be advisable to keep a copy of both editions: the first one for starters (typically, students at the master's degree level) and the second one for more experienced readers (namely, students starting their Ph.D. theses). I hope that there will be another printing, where the misprints and minor mistakes will be corrected. Online Computing Reviews Service