Medical Image Processing, Reconstruction and Restoration: Concepts and Methods ppt

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Medical Image
Processing,
Reconstruction
and Restoration
Boca Raton London New York Singapore
A CRC title, part of the Taylor & Francis imprint, a member of the
Taylor & Francis Group, the academic division of T&F Informa plc.
Concepts and Methods
Jiˇrí Jan
© 2006 by Taylor & Francis Group, LLC
Signal Processing and Communications
Editorial Board
Maurice G. Bellanger,
Conservatoire National
des Arts et Métiers (CNAM), Paris
Ezio Biglieri,
Politecnico di Torino, Italy
Sadaoki Furui,
Tokyo Institute of Technology
Yih-Fang Huang,
University of Notre Dame
Nikil Jayant,
Georgia Institute of Technology
Aggelos K. Katsaggelos,
Northwestern University
Mos Kaveh,
University of Minnesota
P. K. Raja Rajasekaran,
Texas Instruments
John Aasted Sorenson,

IT University of Copenhagen
1. Digital Signal Processing for Multimedia Systems, edited by Keshab K. Parhi
and Takao Nishitani
2. Multimedia Systems, Standards, and Networks, edited by Atul Puri
and Tsuhan Chen
3. Embedded Multiprocessors: Scheduling and Synchronization, Sundararajan Sriram
and Shuvra S. Bhattacharyya
4. Signal Processing for Intelligent Sensor Systems, David C. Swanson
5. Compressed Video over Networks, edited by Ming-Ting Sun and Amy R. Reibman
6. Modulated Coding for Intersymbol Interference Channels, Xiang-Gen Xia
7. Digital Speech Processing, Synthesis, and Recognition: Second Edition,
Revised and Expanded, Sadaoki Furui
8. Modern Digital Halftoning, Daniel L. Lau and Gonzalo R. Arce
9. Blind Equalization and Identification, Zhi Ding and Ye (Geoffrey) Li
10. Video Coding for Wireless Communication Systems, King N. Ngan, Chi W. Yap,
and Keng T. Tan
11. Adaptive Digital Filters: Second Edition, Revised and Expanded,
Maurice G. Bellanger
12. Design of Digital Video Coding Systems, Jie Chen, Ut-Va Koc, and K. J. Ray Liu
13. Programmable Digital Signal Processors: Architecture, Programming,
and Applications, edited by Yu Hen Hu
14. Pattern Recognition and Image Preprocessing: Second Edition, Revised
and Expanded, Sing-Tze Bow
15. Signal Processing for Magnetic Resonance Imaging and Spectroscopy,
edited by Hong Yan
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17. Speech Processing: A Dynamic and Optimization-Oriented Approach, Li Deng
18. Multidimensional Discrete Unitary Transforms: Representation: Partitioning

and Algorithms, Artyom M. Grigoryan, Sos S. Agaian, S.S. Agaian
19. High-Resolution and Robust Signal Processing, Yingbo Hua, Alex B. Gershman
and Qi Cheng
20. Domain-Specific Processors: Systems, Architectures, Modeling, and Simulation,
Shuvra Bhattacharyya; Ed Deprettere; Jurgen Teich
21. Watermarking Systems Engineering: Enabling Digital Assets Security
and Other Applications, Mauro Barni, Franco Bartolini
22. Biosignal and Biomedical Image Processing: MATLAB-Based Applications,
John L. Semmlow
23. Broadband Last Mile Technologies: Access Technologies for Multimedia
Communications, edited by Nikil Jayant
24. Image Processing Technologies: Algorithms, Sensors, and Applications,
edited by Kiyoharu Aizawa, Katsuhiko Sakaue and Yasuhito Suenaga
25. Medical Image Processing, Reconstruction and Restoration: Concepts
and Methods, Jirˇí Jan
26. Multi-Sensor Image Fusion and Its Applications, edited by Rick Blum
and Zheng Liu
27. Advanced Image Processing in Magnetic Resonance Imaging, edited by
Luigi Landini, Vincenzo Positano and Maria Santarelli
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Jan, Jirí.
Medical image processing, reconstruction and restoration : concepts and methods / by Jirí Jan.
p . cm. (Signal processing and communications ; 24)
Includes bibliographical references and index.
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1. Diagnostic imaging Digital techniques. I. Title. II. Series.
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v

Preface

Beginning with modest initial attempts in roughly the 1960s, digital
image processing has become a recognized field of science, as well
as a broadly accepted methodology, to solve practical problems in
many different kinds of human activities. The applications encom-
pass an enormous range, starting perhaps with astronomy, geology,
and physics, via medical, biological, and ecological imaging and
technological exploitation, up to the initially unexpected use in
humane sciences, e.g., archaeology or art history. The results
obtained in the area of digital image acquisition, synthesis, process-
ing, and analysis are impressive, though it is often not generally
known that digital methods have been applied. The basic concepts
and theory are, of course, common to the spectrum of applications,
but some aspects are more emphasized and some less in each par-
ticular application field. This book, besides introducing general prin-
ciples and methods, concentrates on applications in the field of
medical imaging, which is specific for at least two features: biomed-
ical imaging often concerns internal structures of living organisms
inaccessible to standard imaging methods, and the resulting images
are observed, evaluated, and classified mostly by nontechnically
oriented staff.

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vi Jan

The first feature means that rather specific imaging methods,
namely, tomographic modalities, had to be developed that are
entirely dependent on digital processing of measured preimage data
and that utilize rather sophisticated theoretical backgrounds stem-
ming from the advanced signal theory. Therefore, development of
new or innovated image processing approaches, as well as interpre-
tation of more complicated or unexpected results, requires a deep
understanding of the underlying theory and methods.
Excellent theoretical books on general image processing meth-
ods are available, some of them mentioned in references. In the
area of medical imaging, many books oriented toward individual
clinical branches have been published, mostly with medically inter-
preted case studies. Technical publications on modality-oriented
specialized methods are frequent, either as original journal papers
and conference proceedings or as edited books, contributed to by
numerous specialized authors and summarizing recent contribu-
tions to a particular field of medical image processing. However,
there may be a niche for books that would respect the particularities
of biomedical orientation while still providing a consistent, theo-
retically reasonably exact, and yet comprehensible explanation of
the underlying

theoretical concepts

and

principles of methods

of
image processing as applied in the broad medical field and other
application fields.
This book is intended as an attempt in this direction. It is the
author’s persuasion that a good understanding of concepts and prin-
ciples forms a necessary basis to any valid methodology and solid
application. It is relatively easy to continue studying and even
designing specialized advanced approaches with such a background;
on the other hand, it is extremely difficult to grasp a sophisticated
method without well understanding the underlying concepts. Inves-
tigating a well-defined theory from the background also makes the
study enjoyable; even this aspect was in the foundation of the con-
cept of the book.
This is a book primarily for a technically oriented audience, e.g.,
staff members from the medical environment, interdisciplinary
experts of different (not necessarily only biomedical) orientations, and
graduate and postgraduate engineering students. The purpose of the
book is to provide

insight

; this determines the way the material is
treated: the rigorous mathematical treatment —definition, lemma,
proof — has been abandoned in favor of continuous explanation, in
which most results and conclusions are consistently derived, though
the derivation is contained (and sometimes perhaps even hidden)

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Preface vii

in the text. The aim is that the reader becomes familiar with the
explained concepts and principles, and acquires the idea of not only
believing the conclusions, but also checking and interpreting every
result himself, though perhaps with informal reasoning. It is also
important that all the results would be interpreted in terms of their
“physical” meaning. This does not mean that they be related to a
concrete physical parameter, but rather that they are reasonably inter-
preted with the purpose of the applied processing in mind, e.g., in
terms of information or spectral content. The selection of the material
in the book was based on the idea of including the established back-
ground without becoming mathematically or theoretically superficial,
while possibly eliminating unnecessary details or too specialized infor-
mation that, moreover, may have a rather time-limited validity.
Though the book was primarily conceived with the engineering
community of readers in mind, it should not be unreadable to tech-
nically inclined biomedical experts. It is, of course, possible to suc-
cessfully exploit the image processing methods in clinical practice
or scientific research without becoming involved in the processing
principles. The implementation of imaging modalities must be
adapted to this standard situation by providing an environment in
which the nontechnical expert would not feel the image processing
to be a strange or even hostile element. However, the interpretation
of the image results, namely, in more involved cases, as well as the
indication of suitable image processing procedures under more com-

plex circumstances, may be supported by the user’s understanding
of the processing concepts. It is therefore a side ambition of this
book to be comprehensible enough to enable appreciation of the
principles, perhaps without derivations, even by a differently ori-
ented expert, should he be interested.
It should also be stated what the book is not intended to be.
It does not discuss the medical interpretation of the image results;
no casuistic analysis is included. Concerning the technical contents,
it is also not a theoretical in-depth monograph on a highly special-
ized theme that would not be understandable to a technically or
mathematically educated user of the imaging methods or a similarly
oriented graduate student; such specialized publications may be
found among the references. Finally, while the book may be helpful
even as a daily reference to concepts and methods, it is not a manual
on application details and does not refer to any particular program,
system, or implementation.
The content of the book has been divided into three parts.
The first part, “Images as Multidimensional Signals,” provides the

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viii Jan

introductory chapters on the basic image processing theory. The
second part, “Imaging Systems as Data Sources,” is intended as
an alternative view on the imaging modalities. While the physical
principles are limited to the extent necessary to explain the imag-
ing properties, the emphasis is put on analyzing the internal
signals and (pre)image data that are to be consequently processed.

With respect to this goal, the technological solutions and details
of the imaging systems are also omitted. The third part, “Image
Processing and Analysis,” starts with tomographic image recon-
struction, which is of fundamental importance in medical imaging.
Another topical theme of medical imaging is image fusion, includ-
ing multimodal image registration. Further, methods of image
enhancement and restoration are treated in individual chapters.
The next chapter is devoted to image analysis, including segmen-
tation, as a preparation for diagnostics. The concluding chapter,
on the image processing environment, briefly comments on hard-
ware and software exploited in medical imaging and on processing
aspects of image archiving and communication, including princi-
ples of image data compression.
With respect to the broad spectrum of potential readers, the
book was designed to be as self-contained as possible. Though back-
ground in signal theory would be advantageous, it is not necessary,
as the basic terms are briefly explained where needed. Each part
of the book is provided with a list of references, containing the
literature used as sources or recommended for further study. Cita-
tion of numerous original works, though their influence and contri-
bution to the medical imaging field are highly appreciated, was
mostly avoided as superfluous in this type of book, unless these
works served as immediate sources or examples.
The author hopes that (in spite of some ever-present oversights
and omissions) the reader will find the book’s content to be consistent
and interesting, and studying it intellectually rewarding. If the basic
knowledge contained within becomes a key to solving practical appli-
cation problems and to informed interpretation of results, or a start-
ing point to investigating more advanced approaches and methods,
the book’s intentions will have been fulfilled.

Jir˘í Jan

Brno, Czech Republic

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ix

Acknowledgments

This book is partly based on courses on basic and advanced digital
image processing methods, offered for almost 20 years to graduate
and Ph.D. students of electronics and informatics at Brno University
of Technology. A part of these courses has always been oriented toward
biomedical applications. Here I express thanks to all colleagues and
students, with whom discussions often led to a better view of indi-
vidual problems. In this respect, the comments of the book reviewer,
Dr. S.M. Krishnan, Nanyang Technological University Singapore,
have also been highly appreciated.
Most of medical images presented as illustrations or used as
material in the derived figures have been kindly provided by the coop-
erating hospitals and their staffs: the Faculty Hospital of St. Anne Brno
(Assoc. Prof. P. Krupa, M.D., Ph.D.), the Faculty Hospital Brno-Bohu-
nice (Assoc. Prof. J. Prasek, M.D., Ph.D.; Assoc. Prof. V. Chaloupka,
M.D., Ph.D., Assist. Prof. R. Gerychova, M.D.), Masaryk Memorial
Cancer Institute Brno (Karel Bolcak, M.D.), Institute of Scientific
Instruments, Academy of Sciences of the Czech Republic (Assoc. Prof.
M. Kasal, Ph.D.), and Brno University of Technology (Assoc. Prof. A.

Drastich, Ph.D., D. Janova, M.Sc.). Their courtesy is highly appreci-
ated. Recognition notices are only placed with figures that contain

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x Jan

original medical images; they are not repeated with figures where
these images serve as material to be processed or analyzed. Thanks
also belong to former doctoral students V. Jan, Ph.D., and R. Jirik,
Ph.D., who provided most of the drawn and derived-image figures.
The book utilizes as illustrations of the described methods,
among others, some results of the research conducted by the group
headed by the author. Support of the related projects by grant no.
102/02/0890 of the Grant Agency of the Czech Republic, by grants
no. CEZ MSM 262200011 and CEZ MS 0021630513 of the Ministry
of Education of the Czech Republic, and also by the research centre
grant 1M6798555601 is acknowledged.

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xi

Contents

PART I Images as Multidimensional
Signals

1

Chapter 1 Analogue (Continuous-Space)
Image Representation 3

1.1 Multidimensional Signals as Image Representation 3
1.1.1 General Notion of Multidimensional Signals 3
1.1.2 Some Important Two-Dimensional Signals 6
1.2 Two-Dimensional Fourier Transform 9
1.2.1 Forward Two-Dimensional Fourier Transform 9
1.2.2 Inverse Two-Dimensional Fourier Transform 13
1.2.3 Physical Interpretation of the Two-Dimensional
Fourier Transform 14
1.2.4 Properties of the Two-Dimensional
Fourier Transform 16
1.3 Two-Dimensional Continuous-Space Systems 19
1.3.1 The Notion of Multidimensional Systems 19
1.3.2 Linear Two-Dimensional Systems:
Original-Domain Characterization 22

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xii Jan

1.3.3 Linear Two-Dimensional Systems:
Frequency-Domain Characterization 25
1.3.4 Nonlinear Two-Dimensional
Continuous-Space Systems 26
1.3.4.1 Point Operators 27

1.3.4.2 Homomorphic Systems 29
1.4 Concept of Stochastic Images 33
1.4.1 Stochastic Fields as Generators
of Stochastic Images 34
1.4.2 Correlation and Covariance Functions 38
1.4.3 Homogeneous and Ergodic Fields 41
1.4.4 Two-Dimensional Spectra of Stochastic
Images 45
1.4.4.1 Power Spectra 45
1.4.4.2 Cross-Spectra 47
1.4.5 Transfer of Stochastic Images via
Two-Dimensional Linear Systems 49
1.4.6 Linear Estimation of Stochastic Variables 51

Chapter 2 Digital Image Representation 55

2.1 Digital Image Representation 55
2.1.1 Sampling and Digitizing Images 55
2.1.1.1 Sampling 55
2.1.1.2 Digitization 62
2.1.2 Image Interpolation from Samples 65
2.2 Discrete Two-Dimensional Operators 67
2.2.1 Discrete Linear Two-Dimensional Operators 69
2.2.1.1 Generic Operators 69
2.2.1.2 Separable Operators 70
2.2.1.3 Local Operators 71
2.2.1.4 Convolutional Operators 74
2.2.2 Nonlinear Two-Dimensional Discrete Operators 77
2.2.2.1 Point Operators 77
2.2.2.2 Homomorphic Operators 78

2.2.2.3 Order Statistics Operators 79
2.2.2.4 Neuronal Operators 81
2.3 Discrete Two-Dimensional Linear Transforms 89
2.3.1 Two-Dimensional Unitary
Transforms Generally 91

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Contents xiii

2.3.2 Two-Dimensional Discrete Fourier
and Related Transforms 94
2.3.2.1 Two-Dimensional DFT Definition 94
2.3.2.2 Physical Interpretation
of Two-Dimensional DFT 95
2.3.2.3 Relation of Two-Dimensional DFT
to Two-Dimensional Integral FT
and Its Applications in Spectral
Analysis 99
2.3.2.4 Properties of the
Two-Dimensional DFT 101
2.3.2.5 Frequency Domain Convolution 105
2.3.2.6 Two-Dimensional Cosine, Sine,
and Hartley Transforms 107
2.3.3 Two-Dimensional Hadamard–Walsh
and Haar Transforms 111
2.3.3.1 Two-Dimensional Hadamard–Walsh
Transform 111
2.3.3.2 Two-Dimensional Haar Transform 112

2.3.4 Two-Dimensional Discrete
Wavelet Transforms 116
2.3.4.1 Two-Dimensional Continuous
Wavelet Transforms 116
2.3.4.2 Two-Dimensional Dyadic
Wavelet Transforms 120
2.3.5 Two-Dimensional Discrete Karhunen–Loeve
Transform 122
2.4 Discrete Stochastic Images 125
2.4.1 Discrete Stochastic Fields as Generators
of Stochastic Images 126
2.4.2 Discrete Correlation and Covariance
Functions 127
2.4.3 Discrete Homogeneous and Ergodic
Fields 128
2.4.4 Two-Dimensional Spectra of Stochastic
Images 130
2.4.4.1 Power Spectra 130
2.4.4.2 Discrete Cross-Spectra 131
2.4.5 Transfer of Stochastic Images via
Discrete Two-Dimensional Systems 131
References for Part I 133

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xiv Jan

PART II Imaging Systems as
Data Sources

135

Chapter 3 Planar X-Ray Imaging 137

3.1 X-Ray Projection Radiography 137
3.1.1 Basic Imaging Geometry 137
3.1.2 Source of Radiation 139
3.1.3 Interaction of X-Rays with Imaged Objects 143
3.1.4 Image Detection 146
3.1.5 Postmeasurement Data Processing
in Projection Radiography 150
3.2 Subtractive Angiography 152

Chapter 4 X-Ray Computed Tomography 155

4.1 Imaging Principle and Geometry 155
4.1.1 Principle of a Slice Projection Measurement 155
4.1.2 Variants of Measurement Arrangement 158
4.2 Measuring Considerations 164
4.2.1 Technical Equipment 164
4.2.2 Attenuation Scale 165
4.3 Imaging Properties 166
4.3.1 Spatial Two-Dimensional and Three-Dimensional
Resolution and Contrast Resolution 166
4.3.2 Imaging Artifacts 167
4.4 Postmeasurement Data Processing
in Computed Tomography 172

Chapter 5 Magnetic Resonance Imaging 177

5.1 Magnetic Resonance Phenomena 178
5.1.1 Magnetization of Nuclei 178
5.1.2 Stimulated NMR Response and Free
Induction Decay 181
5.1.3 Relaxation 184
5.1.3.1 Chemical Shift and Flow Influence 187
5.2 Response Measurement and Interpretation 188
5.2.1 Saturation Recovery (SR) Techniques 189
5.2.2 Spin-Echo Techniques 191
5.2.3 Gradient-Echo Techniques 196
5.3 Basic MRI Arrangement 198

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Contents xv

5.4 Localization and Reconstruction of Image Data 201
5.4.1 Gradient Fields 201
5.4.2 Spatially Selective Excitation 203
5.4.3 RF Signal Model and General Background
for Localization 206
5.4.4 One-Dimensional Frequency Encoding:
Two-Dimensional Reconstruction
from Projections 211
5.4.5 Two-Dimensional Reconstruction
via Frequency and Phase Encoding 216
5.4.6 Three-Dimensional Reconstruction
via Frequency and Double Phase Encoding 221

5.4.7 Fast MRI 223
5.4.7.1 Multiple-Slice Imaging 224
5.4.7.2 Low Flip-Angle Excitation 224
5.4.7.3 Multiple-Echo Acquisition 225
5.4.7.4 Echo-Planar Imaging 227
5.5 Image Quality and Artifacts 231
5.5.1 Noise Properties 231
5.5.2 Image Parameters 233
5.5.3 Point-Spread Function 235
5.5.4 Resolving Power 237
5.5.5 Imaging Artifacts 237
5.6 Postmeasurement Data Processing in MRI 239

Chapter 6 Nuclear Imaging 245

6.1 Planar Gamma Imaging 247
6.1.1 Gamma Detectors and Gamma Camera 249
6.1.2 Inherent Data Processing
and Imaging Properties 254
6.1.2.1 Data Localization and System
Resolution 254
6.1.2.2 Total Response Evaluation
and Scatter Rejection 257
6.1.2.3 Data Postprocessing 258
6.2 Single-Photon Emission Tomography 258
6.2.1 Principle 258
6.2.2 Deficiencies of SPECT Principle
and Possibilities of Cure 259
6.3 Positron Emission Tomography 265
6.3.1 Principles of Measurement 265

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xvi Jan

6.3.2 Imaging Arrangements 270
6.3.3 Postprocessing of Raw Data
and Imaging Properties 274
6.3.3.1 Attenuation Correction 274
6.3.3.2 Random Coincidences 275
6.3.3.3 Scattered Coincidences 277
6.3.3.4 Dead-Time Influence 278
6.3.3.5 Resolution Issues 278
6.3.3.6 Ray Normalization 280
6.3.3.7 Comparison of PET and SPECT
Modalities 282

Chapter 7 Ultrasonography 283

7.1 Two-Dimensional Echo Imaging 285
7.1.1 Echo Measurement 285
7.1.1.1 Principle of Echo Measurement 285
7.1.1.2 Ultrasonic Transducers 287
7.1.1.3 Ultrasound Propagation
and Interaction with Tissue 293
7.1.1.4 Echo Signal Features
and Processing 296
7.1.2 B-Mode Imaging 301
7.1.2.1 Two-Dimensional Scanning Methods

and Transducers 301
7.1.2.2 Format Conversion 305
7.1.2.3 Two-Dimensional Image Properties
and Processing 307
7.1.2.4 Contrast Imaging and Harmonic
Imaging 310
7.2 Flow Imaging 313
7.2.1 Principles of Flow Measurement 313
7.2.1.1 Doppler Blood Velocity Measurement
(Narrowband Approach) 313
7.2.1.2 Cross-Correlation Blood Velocity
Measurement (Wideband Approach) 318
7.2.2 Color Flow Imaging 320
7.2.2.1 Autocorrelation-Based Doppler
Imaging 320
7.2.2.2 Movement Estimation Imaging 324
7.2.2.3 Contrast-Based Flow Imaging 324
7.2.2.4 Postprocessing of Flow Images 325

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Contents xvii

7.3 Three-Dimensional Ultrasonography 325
7.3.1 Three-Dimensional Data Acquisition 326
7.3.1.1 Two-Dimensional Scan-Based
Data Acquisition 326
7.3.1.2 Three-Dimensional Transducer
Principles 329

7.3.2 Three-Dimensional and Four-Dimensional
Data Postprocessing and Display 331
7.3.2.1 Data Block Compilation 331
7.3.2.2 Display of Three-Dimensional Data 333

Chapter 8 Other Modalities 335

8.1 Optical and Infrared Imaging 335
8.1.1 Three-Dimensional Confocal Imaging 337
8.1.2 Infrared Imaging 339
8.2 Electron Microscopy 341
8.2.1 Scattering Phenomena in the Specimen
Volume 342
8.2.2 Transmission Electron Microscopy 343
8.2.3 Scanning Electron Microscopy 346
8.2.4 Postprocessing of EM Images 349
8.3 Electrical Impedance Tomography 350
References for Part II 355

PART III Image Processing
and Analysis

361

Chapter 9 Reconstructing Tomographic Images 365

9.1 Reconstruction from Near-Ideal Projections 366
9.1.1 Representation of Images by Projections 366
9.1.2 Algebraic Methods of Reconstruction 372
9.1.2.1 Discrete Formulation of the

Reconstruction Problem 372
9.1.2.2 Iterative Solution 374
9.1.2.3 Reprojection Interpretation of the
Iteration 375
9.1.2.4 Simplified Reprojection Iteration 379
9.1.2.5 Other Iterative Reprojection
Approaches 380

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xviii Jan

9.1.3 Reconstruction via Frequency Domain 381
9.1.3.1 Projection Slice Theorem 381
9.1.3.2 Frequency-Domain Reconstruction 382
9.1.4 Reconstruction from Parallel Projections
by Filtered Back-Projection 383
9.1.4.1 Underlying Theory 383
9.1.4.2 Practical Aspects 387
9.1.5 Reconstruction from Fan Projections 391
9.1.5.1 Rebinning and Interpolation 393
9.1.5.2 Weighted Filtered Back-Projection 393
9.1.5.3 Algebraic Methods of Reconstruction 397
9.2 Reconstruction from Nonideal Projections 398
9.2.1 Reconstruction under Nonzero Attenuation 398
9.2.1.1 SPECT Type Imaging 400
9.2.1.2 PET Type Imaging 402
9.2.2 Reconstruction from Stochastic Projections 403
9.2.2.1 Stochastic Models of Projections 404

9.2.2.2 Principle of Maximum-Likelihood
Reconstruction 406
9.3 Other Approaches to Tomographic Reconstruction 409
9.3.1 Image Reconstruction in Magnetic
Resonance Imaging 409
9.3.1.1 Projection-Based Reconstruction 409
9.3.1.2 Frequency-Domain (Fourier)
Reconstruction 410
9.3.2 Image Reconstruction in Ultrasonography 413
9.3.2.1 Reflective (Response)
Ultrasonography 413
9.3.2.2 Transmission Ultrasonography 414

Chapter 10 Image Fusion 417

10.1 Ways to Consistency 419
10.1.1 Geometrical Image Transformations 422
10.1.1.1 Rigid Transformations 423
10.1.1.2 Flexible Transformations 425
10.1.1.3 Piece-Wise Transformations 431
10.1.2 Image Interpolation 433
10.1.2.1 Interpolation in the Spatial Domain 435
10.1.2.2 Spatial Interpolation via
Frequency Domain 441

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Contents xix

10.1.3 Local Similarity Criteria 443
10.1.3.1 Direct Intensity-Based
Criteria 444
10.1.3.2 Information-Based Criteria 451
10.2 Disparity Analysis 460
10.2.1 Disparity Evaluation 461
10.2.1.1 Disparity Definition and Evaluation
Approaches 461
10.2.1.2 Nonlinear Matched Filters as Sources
of Similarity Maps 464
10.2.2 Computation and Representation
of Disparity Maps 467
10.2.2.1 Organization of the Disparity
Map Computation 467
10.2.2.2 Display and Interpretation
of Disparity Maps 468
10.3 Image Registration 470
10.3.1 Global Similarity 471
10.3.1.1 Intensity-Based Global Criteria 472
10.3.1.2 Point-Based Global Criteria 474
10.3.1.3 Surface-Based Global Criteria 474
10.3.2 Transform Identification and Registration
Procedure 475
10.3.2.1 Direct Computation 476
10.3.2.2 Optimization Approaches 477
10.3.3 Registration Evaluation and Approval 479
10.4 Image Fusion 481
10.4.1 Image Subtraction and Addition 481
10.4.2 Vector-Valued Images 483
10.4.2.1 Presentation of Vector-Valued

Images 484
10.4.3 Three-Dimensional Data
from Two-Dimensional Slices 485
10.4.4 Panorama Fusion 486
10.4.5 Stereo Surface Reconstruction 486
10.4.6 Time Development Analysis 488
10.4.6.1 Time Development via Disparity
Analysis 490
10.4.6.2 Time Development via Optical
Flow 490
10.4.7 Fusion-Based Image Restoration 494

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xx Jan

Chapter 11 Image Enhancement 495

11.1 Contrast Enhancement 496
11.1.1 Piece-Wise Linear Contrast Adjustments 499
11.1.2 Nonlinear Contrast Transforms 501
11.1.3 Histogram Equalization 504
11.1.4 Pseudocoloring 508
11.2 Sharpening and Edge Enhancement 510
11.2.1 Discrete Difference Operators 511
11.2.2 Local Sharpening Operators 517
11.2.3 Sharpening via Frequency Domain 519
11.2.4 Adaptive Sharpening 523
11.3 Noise Suppression 525

11.3.1 Narrowband Noise Suppression 527
11.3.2 Wideband “Gray” Noise Suppression 528
11.3.2.1 Adaptive Wideband Noise
Smoothing 532
11.3.3 Impulse Noise Suppression 534
11.4 Geometrical Distortion Correction 538

Chapter 12 Image Restoration 539

12.1 Correction of Intensity Distortions 541
12.1.1 Global Corrections 541
12.1.2 Field Homogenization 543
12.1.2.1 Homomorphic Illumination Correction 545
12.2 Geometrical Restitution 545
12.3 Inverse Filtering 546
12.3.1 Blur Estimation 546
12.3.1.1 Analytical Derivation of PSF 547
12.3.1.2 Experimental PSF Identification 548
12.3.2 Identification of Noise Properties 552
12.3.3 Actual Inverse Filtering 554
12.3.3.1 Plain Inverse Filtering 554
12.3.3.2 Modified Inverse Filtering 555
12.4 Restoration Methods Based on Optimization 559
12.4.1 Image Restoration as Constrained
Optimization 559
12.4.2 Least Mean Square Error Restoration 561
12.4.2.1 Formalized Concept of LMS
Image Estimation 561
12.4.2.2 Classical Formulation of Wiener
Filtering for Continuous-Space Images 563

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Contents xxi

12.4.2.3 Discrete Formulation
of the Wiener Filter 572
12.4.2.4 Generalized LMS Filtering 575
12.4.3 Methods Based on Constrained Deconvolution 578
12.4.3.1 Classical Constrained Deconvolution 578
12.4.3.2 Maximum Entropy Restoration 582
12.4.4 Constrained Optimization of Resulting PSF 584
12.4.5 Bayesian Approaches 586
12.4.5.1 Maximum

a



Posteriori

Probability
Restoration 588
12.4.5.2 Maximum-Likelihood Restoration 589
12.5 Homomorphic Filtering and Deconvolution 590
12.5.1 Restoration of Speckled Images 591

Chapter 13 Image Analysis 593

13.1 Local Feature Analysis 594
13.1.1 Local Features 595
13.1.1.1 Parameters Provided
by Local Operators 595
13.1.1.2 Parameters of Local Statistics 595
13.1.1.3 Local Histogram Evaluation 596
13.1.1.4 Frequency-Domain Features 597
13.1.2 Edge Detection 598
13.1.2.1 Gradient-Based Detectors 599
13.1.2.2 Laplacian-Based Zero-Crossing
Detectors 601
13.1.2.3 Laplacian-of-Gaussian-Based
Detectors 603
13.1.2.4 Other Approaches to Edge
and Corner Detection 604
13.1.2.5 Line Detectors 605
13.1.3 Texture Analysis 607
13.1.3.1 Local Features as Texture
Descriptors 609
13.1.3.2 Co-Occurrence Matrices 609
13.1.3.3 Run-Length Matrices 610
13.1.3.4 Autocorrelation Evaluators 611
13.1.3.5 Texture Models 611
13.1.3.6 Syntactic Texture Analysis 613
13.1.3.7 Textural Parametric Images
and Textural Gradient 614

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xxii Jan

13.2 Image Segmentation 615
13.2.1 Parametric Image-Based Segmentation 615
13.2.1.1 Intensity-Based Segmentation 616
13.2.1.2 Segmentation of Vector-Valued
Parametric, Color, or Multimodal
Images 619
13.2.1.3 Texture-Based Segmentation 620
13.2.2 Region-Based Segmentation 621
13.2.2.1 Segmentation via Region Growing 621
13.2.2.2 Segmentation via Region Merging 622
13.2.2.3 Segmentation via Region Splitting
and Merging 623
13.2.2.4 Watershed-Based Segmentation 625
13.2.3 Edge-Based Segmentation 628
13.2.3.1 Borders via Modified Edge
Representation 631
13.2.3.2 Borders via Hough Transform 634
13.2.3.3 Boundary Tracking 639
13.2.3.4 Graph Searching Methods 641
13.2.4 Segmentation by Pattern Comparison 641
13.2.5 Segmentation via Flexible Contour
Optimization 642
13.2.5.1 Parametric Flexible Contours 643
13.2.5.2 Geometric Flexible Contours 646
13.2.5.3 Active Shape Contours 649
13.3 Generalized Morphological Transforms 652
13.3.1 Basic Notions 652
13.3.1.1 Image Sets and Threshold

Decomposition 652
13.3.1.2 Generalized Set Operators
and Relations 654
13.3.1.3 Distance Function 655
13.3.2 Morphological Operators 656
13.3.2.1 Erosion 658
13.3.2.2 Dilation 661
13.3.2.3 Opening and Closing 663
13.3.2.4 Fit-and-Miss Operator 665
13.3.2.5 Derived Operators 666
13.3.2.6 Geodesic Operators 668
13.3.3 Some Applications 670

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Contents xxiii

Chapter 14 Medical Image Processing Environment 675

14.1 Hardware and Software Features 676
14.1.1 Hardware Features 676
14.1.1.1 Software Features 680
14.1.1.2 Some Features of Image
Processing Software 682
14.2 Principles of Image Compression for Archiving
and Communication 685
14.2.1 Philosophy of Image Compression 685
14.2.2 Generic Still-Image Compression System 686
14.2.3 Principles of Lossless Compression 688

14.2.3.1 Predictive Coding 690
14.2.4 Principles of Lossy Compression 691
14.2.4.1 Pixel-Oriented Methods 692
14.2.4.2 Block-Oriented Methods 693
14.2.4.3 Global Compression Methods 697
14.3 Present Trends in Medical Image Processing 701
References for Part III 705

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Part I

Images as Multidimensional Signals

Part I provides the theoretical background for the rest of the book.
It introduces the concept of still images interpreted as two-dimen-
sional signals, as well as the generalization to multidimensional
interpretation of moving images and three-dimensional (spatial)
image information. Once this general notion is introduced, the sig-
nal theoretical concepts, after generalization to the two-dimensional
or multidimensional case, can be utilized for image processing and
analysis. This concept proved very successful in enabling the for-
malization (and consequently optimization) of many approaches to
image acquisition, processing, and analysis that were originally
designed as heuristic or even not feasible.
A characteristic example comes from the area of medical tomo-
graphic imaging: the intuitively suggested heuristic algorithm of
image reconstruction from projections by back-projection turned out
to be very unsatisfactory, giving only a crude approximation of the

proper image, with very disturbing artifacts. Later, relatively com-
plex theory (see Chapter 9) was developed that led to a formally
derived algorithm of

filtered

back-projection, widely used nowadays,
that is theoretically correct and provides very good images, even

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under practical limitations. Both algorithms are quite similar, with
the only difference being the filtering of each individual projection
added to the original procedure in the later method — seemingly an
elementary step, but probably impossible to discover without the
involved theory. The alternative methods of image reconstruction
from projections rely heavily on other aspects of the multidimen-
sional signal theory as well.
Part I introduces the basic image processing concepts and ter-
minology needed to understand further sections of the book. Broader
and deeper treatment of the theory can be found in the numerous
literature that is partly listed in the references to this section,
e.g., in [4], [5], [6], [18], [22], [23], [25], [26]. Other sources used but
not cited elsewhere are [1], [2], [8], [12], [14]–[17], [19], [21], [24].
In context of the theoretical principles, we shall introduce the
concepts of two-dimensional systems and operators, two-dimensional
transforms, and two-dimensional stochastic fields. The text is con-
ceived to be self-contained: the necessary concepts of the one-dimen-
sional signal theory will be briefly included, however, without detailed

derivations. A prior knowledge of the signal theory elements, though
definitely advantageous, is thus not necessary. With respect to the
purpose of the book, we shall mostly limit ourselves to the two-dimen-
sional case; the generalization to three- and four-dimensional cases is
rather straightforward and will be mentioned where necessary.
This theoretical section is subdivided into two similarly struc-
tured chapters. The first chapter deals with the theory of images in
continuous space, often briefly denoted as analogue images. Besides
being necessary as such, because some later derivations will need
this concept, the theory seems also to be more easily comprehensible,
thanks to intuitive interpretations — what is perceived by humans
is the analogue image. The second chapter deals with

discrete
images,

i.e.,



discrete

-

space (sampled) images, the values of which
are also quantized, as only these can be represented in and pro-
cessed by computers. The reader should realize that, on one hand,
there are many similarities and analogies between the worlds of
continuous and discrete images; on the other hand, discretization
changes some basic theoretical properties of the signals and opera-

tors. Therefore, the notion of a “densely enough” sampled discrete
image being equivalent to its analogue counterpart is false in prin-
ciple and often misleading, though the similarities between both
areas may occasionally be utilized with advantage; it includes the
fact that all real-world images can be represented digitally without
any loss in the information content.

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