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Book review

Author(s) Alexandrov, V.V.
Gorsky, N.D.
Publisher Kluwer Academic Publishers
Year of publication 1993
Reviewed by Andrea Selinger

Interest in image processing techniques dates back to the early 1920's, but applications did not become widespread until the middle 1960's. Computer facilities are now highly developed, making it apparently possible to design special hardware that will help to solve every difficult problem. However, the large memory volume or fast memory needed for image processing is still a problem. That's why, from the authors' point of view, the representation and processing of images should be realized through parallel control of storage and computations.

The book investigates new structural forms of visual information which enables combining memory and structural control, such as pyramids and quad- and oct-trees, approached through self-similarity and space filling curves.

A new image representation is added to the classical ones (the full perception, the problem oriented perception and the reflex perception). This is the recursive approach based on pyramidal-recursive structures. The term covers the corresponding data structures having such common features as hierarchy and regularity. In the case of a pyramidal-recursive representation, the processed image is described by the ordered sequence of images of different resolution which converge to the original one. These are arranged and drawn usually one under another (hence the term "pyramid" of images). The interrelations of pixels of all images from the pyramid are described through recursion: it is sufficient to indicate the elementary cell and the law of transition to the next level.

After Chapter 1 introduce the reader briefly to image representation methods, Chapter 2 presents the basic theoretical results of the book, describing the mathematical apparatus for the operation with pyramidal-recursive structures. The meaning of recursion is analyzed through recursive definitions and recursive calculations. The main properties of pyramidal-recursive image representation are discussed in Chapter 3. The interrelation of the pyramidal-recursive representation and some widely used orthogonal two-dimensional transforms is considered. This is followed by the description of theoretical and experimental research into the pyramidal model of a greyscale image. The coding and compression algorithms presented in Chapter 4 provide a final form of data representation which might be useful for further processing. The authors deal with the problems of image data compression on the basis of the elimination of their statistical and, to some extent, semantic redundancy and of data transmission based on the level-by-level processing of an image pyramid. The primary purpose of Chapter 5, devoted to the processing of images represented by pyramidal recursive structures, is to show that various operations with images may be performed not based on their initial description, but by considering the hierarchical data structure. The chapter concludes with an identification for an arbitrarily oriented plane object which is based on image and object representations by regular hierarchical structures. Chapter 6 deals with applications of image processing algorithms and image models based on pyramidal-recursive structures for optical character recognition and for the processing of a mineral ore to forecast the ore enrichment process. Some parallels are presented between human visual perception and image analysis with pyramidal structures. The volume concludes with a comprehensive bibliography.

The book may be considered as a synthesis of some results of the authors, many of them already published.

The book is basic to any newcomer to the subject and may be of interest for any applied mathematicians and computer scientists whose work involves computer vision, information theory and other aspects of image representation techniques because it presents two original mathematical models of greyscale and binary images represented by recursive structures and includes expert systems and special computer architecture for pictorial data processing.

It is accurate and efficient and presents many useful algorithms. A thorough reading would, however, involve considerable effort on the part of the reader.