Image Representation and Processing: A Recursive Approach

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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 ...

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Overview

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.

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Product Details

Table of Contents

Preface
1 Introduction 1
1.1 Human and Machine Perception 1
1.2 Representation of an Information Field 6
1.3 Recursive Approach to Image Representation 11
2 Recursive Structures and Their Properties 21
2.1 Recursive Descriptions and Recursive Structures 22
2.2 Representation of Some Mathematical Objects by Recursive Structures 28
2.3 The Enumeration of Cells in a Discrete Space 37
2.4 Cartesian and Positional Coordinates. Operations with Positional Coordinates 42
2.5 The Representation of Images with Pyramidal-Recursive Structures 51
3 Pyramidal Image Models 59
3.1 Comparison of Pyramidal-Recursive Structures and Two-dimensional Transforms 59
3.2 The Model of Greyscale Image 68
3.3 The Model of the Binary Image 77
4 Image Coding and Progressive Transmission With Gradual Refinement 87
4.1 Coding of Greyscale Images 88
4.2 Comparison of Some Image Coding Algorithms 94
4.3 Transmission of Greyscale Images with Gradual Refinement 98
4.4 Compression and Transmission of Binary Images 106
5 Image Processing With Pyramidal-Recursive Structures 111
5.1 Simple Operations with Images Represented by Truncated Trees 112
5.2 Fast Template Matching 123
5.3 Hierarchical Matching of Arbitrary-Oriented Template 124
6 Applications of Pyramidal-Recursive Structures and Algorithms 143
6.1 Data Flow Organization in Image Processing Systems 144
6.2 Optical Character Recognition 148
6.3 Modelling of Ore Milling 155
6.4 Special Devices for Image Processing 159
6.5 On Expert Systems Simulating Human Visual Perception 166
Bibliography 177
Index 187
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