Fundamentals of Three-dimensional Digital Image Processing / Edition 1

Fundamentals of Three-dimensional Digital Image Processing / Edition 1

by Junichiro Toriwaki, Hiroyuki Yoshida
     
 

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ISBN-10: 184800172X

ISBN-13: 9781848001725

Pub. Date: 05/28/2009

Publisher: Springer London

There are many areas of science and engineering where three-dimensional (3-D) discrete data are collected and analyzed, such as medical imaging and geoscience. To design and to prove the validity of computational procedures for processing and analysis of such data, the need for a mathematical theory and algorithms for image processing is essential

Self-contained,

Overview

There are many areas of science and engineering where three-dimensional (3-D) discrete data are collected and analyzed, such as medical imaging and geoscience. To design and to prove the validity of computational procedures for processing and analysis of such data, the need for a mathematical theory and algorithms for image processing is essential

Self-contained, accessible, and mathematically precise, this book serves as an introduction to the field of 3-D digital image processing, providing information that can be used immediately in practical algorithms for the analysis of 3-D data sets. By presenting problems of processing and analysis of practical 3-D data sets, readers will find the descriptions clear and accessible as concepts and methods are carefully introduced, defined, and illustrated with examples

A key textbook for graduates and resource for all working in areas of multidimensional image processing and analysis, this book is also excellent for self-study for practitioners in the field of 3-D digital image processing

Product Details

ISBN-13:
9781848001725
Publisher:
Springer London
Publication date:
05/28/2009
Edition description:
2009
Pages:
269
Product dimensions:
6.30(w) x 9.50(h) x 1.00(d)

Table of Contents

1 Introduction 1

1.1 Overview 1

1.1.1 3D continuous images 1

1.1.2 3D digital images 1

1.2 What does "3D image" mean 3

1.2.1 Dimensionality of the media and of the subject 3

1.2.2 Types of 3D images 3

1.2.3 Cues for 3D information 5

1.2.4 Specific examples of 3D images 5

1.3 Types and characteristics of 3D image processing 12

1.3.1 Examples of 3D image processing 12

1.3.2 Virtual spaces as 3D digital images 13

1.3.3 Characteristics of 3D image processing 14

1.3.4 Objectives in 3D image processing 15

1.4 The contents of this book 18

2 Models of Images and Image Operations 21

2.1 Introduction 21

2.2 Continuous and digitized images 22

2.2.1 Continuous images 22

2.2.2 Digitized images 22

2.2.3 Three-dimensional images 24

2.2.4 3D line figures and digitization 26

2.2.5 Cross section and projection 29

2.2.6 Relationships among images 31

2.3 Model of image operations 32

2.3.1 Formulation of image operations 33

2.3.2 Relations between image operators 34

2.3.3 Binary operators between images 34

2.3.4 Composition of image operations 35

2.3.5 Basic operators 38

2.4 Algorithm of image operations 40

2.4.1 General form of image operations 41

2.4.2 Important types of algorithms 41

3 Local Processing of 3D Images 49

3.1 Classification of local operations 49

3.1.1 General form 49

3.1.2 Classification by functions of filters 50

3.1.3 Classification by the form of a local function 50

3.2 Smoothing filter 51

3.2.1 Linear smoothing filter 51

3.2.2 Median filter and order statistics filter 52

3.2.3 Edge-preserving smoothing 53

3.2.4 Morphology filter 54

3.3 Difference filter 56

3.3.1 Significance 56

3.3.2 Differentials incontinuous space 57

3.3.3 Derivatives in digitized space 58

3.3.4 Basic characteristics of difference filter 59

3.3.5 Omnidirectionalization 60

3.3.6 1D difference filters and their combinations 61

3.3.7 3D Laplacian 62

3.3.8 2D difference filters and their combination 62

3.4 Differential features of a curved surface 66

3.5 Region growing (region merging) 69

3.5.1 Outline 69

3.5.2 Region expansion 69

4 Geometrical Properties of 3D Digitized Images 73

4.1 Neighborhood and connectivity 73

4.1.1 Neighborhood 73

4.1.2 Connectivity and connected component 75

4.2 Simplex and simplicial decomposition 78

4.3 Euler number 80

4.4 Local feature of a connected component and topology of a figure 81

4.5 Local patterns and their characterization 85

4.5.1 2 x 2 x 2 local patterns 86

4.5.2 3 x 3 x 3 local patterns 87

4.5.3 Classification of the voxel state 89

4.5.4 Voxel state and connectivity index 90

4.6 Calculation of connectivity index and connectivity number 92

4.6.1 Basic ideas 92

4.6.2 Calculation of the connectivity index 92

4.6.3 Calculation of the connectivity number 93

4.7 Calculation of the Euler number 94

4.7.1 Triangulation method 95

4.7.2 Simplex counting method 97

4.8 Algorithm of deletability test 101

4.9 Path and distance functions 103

4.9.1 Path 103

4.9.2 Distance function 105

4.9.3 Distance function in applications 109

4.9.4 Improvement in distance metric 110

4.10 Border surface 113

5 Algorithm of Binary Image Processing 115

5.1 Introduction 115

5.2 Labeling of a connected component 116

5.3 Shrinking 117

5.4 Surface thinning and axis thinning 120

5.4.1 Definition 120

5.4.2 Requirements of thinning 122

5.4.3 Realization - the sequential type 122

5.4.4 Examples of surface/axis thinning algorithms (sequential type) 124

5.4.5 Surface thinning algorithm accompanying the Euclidean distance transformation 127

5.4.6 Use of a 1D list for auxiliary information 131

5.4.7 Examples of surface/axis thinning algorithm (parallel type) 136

5.4.8 Experimental results 137

5.4.9 Points in algorithm construction 138

5.5 Distance transformation and skeleton 144

5.5.1 Definition 144

5.5.2 Significance of DT and skeleton 146

5.5.3 Classification of algorithms 147

5.5.4 Example of an algorithm - (1) squared Euclidean DT 147

5.5.5 Example of algorithms - (2) variable neighborhood DT (parallel type) 153

5.5.6 Supplementary comments on algorithms of DT 156

5.5.7 Skeleton 158

5.5.8 Reverse distance transformation 161

5.5.9 Example of RDT algorithms - (1) Euclidean squared RDT 162

5.5.10 Example of RDT algorithm - (2) fixed neighborhood (6-, 18-, or 26-neighborhood) RDT (sequential type) 167

5.5.11 Extraction of skeleton 170

5.5.12 Distance transformation of a line figure 176

5.6 Border surface following 176

5.6.1 Outline 176

5.6.2 Examples of algorithm 179

5.6.3 Restoration of a figure 181

5.7 Knot and link 182

5.7.1 Outline 182

5.7.2 Reduction of a digital knot 184

5.8 Voronoi division of a digitized image 186

6 Algorithms for Processing Connected Components with Gray Values 191

6.1 Distance transformation of a gray-tone image 191

6.1.1 Definition 191

6.1.2 An example of algorithm 192

6.2 Thinning of a gray-tone image 194

6.2.1 Basic idea 194

6.2.2 Requirements 195

6.2.3 Principles of thinning 195

6.3 Examples of algorithms - (1) integration of information concerning density values 197

6.3.1 Algorithm 197

6.3.2 Experimental results 200

6.4 Examples of algorithms - (2) ridgeline following 203

6.4.1 Meanings of a ridgeline 203

6.4.2 Algorithm 204

6.4.3 Experiments 207

7 Visualization of 3D Gray-Tone Images 209

7.1 Formulation of visualization problem 209

7.2 Voxel data and the polygon model 211

7.2.1 Voxel surface representation 211

7.2.2 Marching cubes algorithm 211

7.3 Cross section, surface, and projection 214

7.3.1 Cross section 214

7.3.2 Surface 215

7.3.3 Projection 216

7.4 The concept of visualization based on ray casting - (1) projection of a point 218

7.4.1 Displaying a point 218

7.4.2 Displaying lines 221

7.4.3 Displaying surfaces 221

7.5 The concept of visualization based on ray casting - (2) manipulation of density values 222

7.6 Rendering surfaces based on ray casting - surface rendering 222

7.6.1 Calculation of the brightness of a surface 223

7.6.2 Smooth shading 225

7.6.3 Depth coding 227

7.6.4 Ray tracing 227

7.7 Photorealistic rendering and rendering for visualization 230

7.8 Displaying density values based on ray casting - volume rendering 231

7.8.1 The algorithm of volume rendering 231

7.8.2 Selection of parameters 233

7.8.3 Front-to-back algorithm 235

7.8.4 Properties of volume rendering and surface rendering 236

7.8.5 Gradient shading 240

References 243

Index 261

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