The Insight Toolkit (ITK) is an open source library of object-oriented software components for image processing, data segmentation, and registration; it provides advanced algorithms for filtering, segmentation, and registration of volumetric data. This book describes the principles of all methods implemented in the Toolkit including greater background on the theory behind the methods and as such is an extended reference for ITK. The book can also be the basis for a graduate course on medical image processing. The Insight Software Consortium (ISC) is dedicated to developing, maintaining, disseminating, and promoting open-source, medical image analysis software, data, and publications.

Foreword

xi

I Introduction and Basics

1

(118)

1 Introduction

3

(16)

1.1 Medical Image Processing

4

(1)

1.2 A Brief Retrospective on 3D Medical Imaging

5

(1)

1.3 Medical Imaging Technology

6

(10)

1.4 Acquisition, Analysis, and Visualization

16

(1)

1.5 Summary

17

(2)

2 Basic Image Processing and Linear Operators

19

(28)

2.1 Introduction

19

(1)

2.2 Images

20

(1)

2.3 Point Operators

21

(4)

2.4 Linear Filtering

25

(12)

2.5 The Fourier Transform

37

(8)

2.6 Summary

45

(2)

3 Statistics of Pattern Recognition

47

(56)

3.1 Introduction

47

(2)

3.2 Background

49

(7)

3.3 Quantitative Comparison of Classifiers

56

(3)

3.4 Classification Systems

59

(25)

3.5 Summary of Classifiers' Performance

84

(3)

3.6 Goodness-of-Fit

87

(5)

3.7 Conclusion

92

(1)

3.8 Appendix: Extruded Gaussian Distributions

93

(10)

4 Nonlinear Image Filtering with Partial Differential Equations

103

(16)

4.1 Introduction

103

(1)

4.2 Gaussian Blurring and the Heat Equation

103

(7)

4.3 Numerical Implementations

110

(9)

II Segmentation

119

(118)

5 Segmentation Basics

121

(10)

5.1 Introduction

121

(2)

5.2 Statistical Pattern Recognition

123

(1)

5.3 Region Growing

124

(2)

5.4 Active Surfaces/Front Evolution

126

(1)

5.5 Combining Segmentation Techniques

127

(1)

5.6 Looking Ahead

128

(3)

6 Fuzzy Connectedness

131

(50)

6.1 Background

131

(2)

6.2 Outline of the Chapter

133

(3)

6.3 Basic Notations and Definitions

136

(2)

6.4 Theory

138

(13)

6.5 Methods and Algorithms

151

(10)

6.6 Applications

161

(10)

6.7 Concluding Remarks

171

(10)

7 Markov Random Field Models

181

(12)

7.1 Markov Random Field Models: Introduction and Previous Work

181

(1)

7.2 Gibbs Prior Model Theories

182

(3)

7.3 Bayesian Framework and Posterior Energy Function

185

(1)

7.4 Energy Minimization

186

(1)

7.5 Experiments and Results

186

(7)

8 Isosurfaces and Level Sets

193

(26)

8.1 Introduction

193

(2)

8.2 Deformable Surfaces

195

(4)

8.3 Numerical Methods

199

(9)

8.4 Applications

208

(6)

8.5 Summary

214

(5)

9 Deformable Models

219

(18)

9.1 Introduction

219

(1)

9.2 Previous Work

220

(2)

9.3 Deformable Model Theories

222

(8)

9.4 Experiments, Results, and Applications in ITK

230

(7)

III Registration

237

(112)

10 Medical Image Registration: Concepts and Implementation

239

(68)

10.1 Introduction

239

(1)

10.2 Image Registration Concepts

240

(2)

10.3 A Generic Software Framework for Image to Image Registration

242

(53)

10.4 Examples

295

(12)

11 Non-Rigid Image Registration

307

(42)

11.1 Introduction

307

(5)

11.2 Optical Flow: Fast Mono-Modality Non-Rigid Registration

312

(9)

11.3 Variational Framework for Computational Anatomy

321

(17)

11.4 Review

338

(11)

IV Hybrid Methods - Mixed Approaches to Segmentation

349

(40)

12 Hybrid Segmentation Methods

351

(24)

12.1 Introduction

351

(2)

12.2 Review of Segmentation Methods

353

(4)

12.3 Hybrid Segmentation Engine

357

(1)

12.4 Hybrid Segmentation: Integration of FC, VD, and DM

358

(7)

12.5 Evaluation of Segmentation

365

(2)

12.6 Results

367

(8)

12.7 Conclusions

375

(14)

Index

389

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