Recently, much attention has been paid to image processing with multiresolution and hierarchical structures such as pyramids and trees. This volume deals with recursive pyramids, which combine the advantages of available multiresolution structures and which are convenient both for global and local image processing. Recursive pyramids are based on regular hierarchical (recursive) structures containing data on image fragments of different sizes. Such an image representation technique enables the effective manipulation of pictorial information as well as the development of special hardware or data structures. The major aspects of this book are two original mathematical models of greyscale and binary images represented by recursive structures. Image compression, transmission and processing are discussed using these models. A number of applications are presented, including optical character recognition, expert systems and special computer architecture for pictorial data processing. The majority of results are presented as algorithms applicable to discrete information fields of arbitrary dimensions (e.g. 2-D or 3-D images). The book is divided into six chapters: Chapter 1 provides a brief introduction. Chapter 2 then deals with recursive structures and their properties. Chapter 3 introduces pyramidal image models. Image coding and the progressive transmission of images with gradual refinement are discussed in Chapter 4. Chapters 5 and 6 are devoted to image processing with pyramidal-recursive structures and applications. The volume concludes with a comprehensive bibliography. For applied mathematicians and computer scientists whose work involves computer vision, information theory and other aspects of image representation techniques.

One service mathematics has rendered the "Et moi, .... si j'a\'ait su comment en revenir, human race. It has put common sense back je n'y scrais point alit: Jules Verne where it belongs, on the topmost shelf next to the dusty canister labc\led 'discarded non The series is divergent; therefore we may be sense'. Eric T. 8c\l able to do something with it. O. Hcaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

One service mathematics has rendered the "Et moi, .... si j'a\'ait su comment en revenir, human race. It has put common sense back je n'y scrais point alit: Jules Verne where it belongs, on the topmost shelf next to the dusty canister labc\led 'discarded non The series is divergent; therefore we may be sense'. Eric T. 8c\l able to do something with it. O. Hcaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

Recently, much attention has been paid to image processing with multi-resolution and hierarchical structures such as pyramids and trees. This volume deals with recursive pyramids, which combine the advantages of available multiresolution structures and which are convenient both for global and local image processing. Recursive pyramids are based on regular hierarchical (recursive) structures containing data on image fragments of different sizes. Such an image representation technique enables the effective manipulation of pictorial information as well as the development of special hardware or data structures. The major aspects of this book are two original mathematical models of greyscale and binary images represented by recursive structures. Image compression, transmission and processing are discussed using these models. A number of applications are presented, including optical character recognition, expert systems and special computer architecture for pictorial data processing. The majority of results are presented as algorithms applicable to discrete information fields of arbitrary dimensions (e.g. 2-D or 3-D images). The book is divided into six chapters: Chapter 1 provides a brief introduction. Chapter 2 then deals with recursive structures and their properties. Chapter 3 introduces pyramidal image models. Image coding and the progressive transmission of images with gradual refinement are discussed in Chapter 4. Chapters 5 and 6 are devoted to image processing with pyramidal-recursive structures and applications. The volume concludes with a comprehensive bibliography. This work should interest applied mathematicians and computer scientists whose work involves computer vision, information theory and other aspects of image representation techniques.