Medical Imaging Systems

263 Pages·2018·47.056 MB·English

by  Andreas Maier, Stefan Steidl, Vincent Christlein, Joachim Hornegger

Andreas Maier · Stefan Steidl
Vincent Christlein
Joachim Hornegger (Eds.)
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An Introductory Guide
Lecture Notes in Computer Science 11111
Commenced Publication in 1973
Founding and Former Series Editors:
Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen
Editorial Board
David Hutchison
Lancaster University, Lancaster, UK
Takeo Kanade
Carnegie Mellon University, Pittsburgh, PA, USA
Josef Kittler
University of Surrey, Guildford, UK
Jon M. Kleinberg
Cornell University, Ithaca, NY, USA
Friedemann Mattern
ETH Zurich, Zurich, Switzerland
John C. Mitchell
Stanford University, Stanford, CA, USA
Moni Naor
Weizmann Institute of Science, Rehovot, Israel
C. Pandu Rangan
Indian Institute of Technology Madras, Chennai, India
Bernhard Steffen
TU Dortmund University, Dortmund, Germany
Demetri Terzopoulos
University of California, Los Angeles, CA, USA
Doug Tygar
University of California, Berkeley, CA, USA
Gerhard Weikum
Max Planck Institute for Informatics, Saarbrücken, Germany
More information about this series at http://www.springer.com/series/7412
Andreas Maier Stefan Steidl
(cid:129)
Vincent Christlein
Joachim Hornegger (Eds.)
Medical
Imaging Systems
An Introductory Guide
Editors
Andreas Maier Vincent Christlein
Lehrstuhl für Mustererkennung Lehrstuhl für Mustererkennung
Friedrich-Alexander-Universität Friedrich-Alexander-Universität
Erlangen-Nürnberg Erlangen-Nürnberg
Erlangen Erlangen
Germany Germany
StefanSteidl Joachim Hornegger
Lehrstuhl für Mustererkennung Lehrstuhl für Mustererkennung
Friedrich-Alexander-Universität Friedrich-Alexander-Universität
Erlangen-Nürnbergät Erlangen-Nürnbergät
Erlangen Erlangen
Germany Germany
ISSN 0302-9743 ISSN 1611-3349 (electronic)
Lecture Notesin Computer Science
ISBN 978-3-319-96519-2 ISBN978-3-319-96520-8 (eBook)
https://doi.org/10.1007/978-3-319-96520-8
LibraryofCongressControlNumber:2018948380
LNCSSublibrary:SL6–ImageProcessing,ComputerVision,PatternRecognition,andGraphics
©TheEditor(s)(ifapplicable)andTheAuthor(s)2018.Thisbookisanopenaccesspublication.
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Preface
ThepresentbookistheresultoffouryearsofworkthatstartedinWinter2014/15and
was finally concluded in Summer 2018. As such, numerous hours of work went into
thismanuscriptbyseveralauthors,whowereallaffiliatedwiththePatternRecognition
Lab of the Friedrich-Alexander-University Erlangen-Nuremberg. I truly appreciate the
dedication and the hard work of my colleagues that led to this final manuscript and,
althoughmanyalreadyleftthelabtotakepositionsinacademiaandindustry,theystill
supported the finalization of this book.
WhilemajorpartsofthebookwerealreadycompletedinWinter2016/17,Springer
gaveustheopportunitytoreworkthebookwithnewconceptslikethegeekboxesand
newfiguresinordertoadaptthebooktoabroaderaudience.Withthepresentconcepts,
we hope that the book is suited to early-stage undergraduate students as well as stu-
dents who already completed fundamental math classes and want to deepen their
knowledge on medical imaging. We believe, the time to improve the manuscript was
well spent and the final polish gave rise to a textbook with a coherent story line. In
particular, we break with the historical development of the described imaging devices
andpresent,e.g.,magneticresonanceimagingbeforecomputedtomography,although
theyweredevelopedinoppositeorder.Acloserlookrevealsthatthischangeoforderis
reasonable for didactical purposes: magnetic resonance imaging relies mainly on the
Fourier transform, while computed tomography requires understanding of the Fourier
slice theorem discovered by Johann Radon. These observations then also mend the
apparent historical disorder, as we celebrate Joseph Fourier’s 250th birthday this year
and celebrated the 100th birthday of the Radon transform last year.
We also tried to find many graphical explanations for many of the mathematical
operations such that the book does not require complete understanding of all mathe-
matical details. Yet, we also offer details and references to further literature in the
previously mentioned geek boxes as students in the later semesters also need to be
familiarwiththeseconcepts.Inconclusion,wehopethatwecreatedausefultextbook
thatwillbeaccessibletomanyreaders.Inordertoimprovethiseaseofaccessfurther,
we chose to publish the entire manuscript as open access book under Creative Com-
mons Attribution 4.0 International License. Thus, any information in this book can
shared, copied, adapted, or remixed even for commercial purposes as long as the
original source is appropriately referenced and a link to the license is provided.
June 2018 Andreas Maier
Contents
1 Introduction.............................................. 7
2 System Theory ........................................... 13
2.1 Signals and Systems .................................... 14
2.1.1 Signals.......................................... 14
2.1.2 Systems......................................... 15
2.2 Convolution and Correlation ............................. 17
2.2.1 Complex Numbers................................ 17
2.2.2 Convolution ..................................... 19
2.2.3 Correlation ...................................... 22
2.3 Fourier Transform ...................................... 22
2.3.1 Types of Fourier Transforms ....................... 22
2.3.2 Convolution Theorem & Properties ................. 25
2.4 Discrete System Theory ................................. 31
2.4.1 Motivation ...................................... 31
2.4.2 Sampling Theorem ............................... 32
2.4.3 Noise ........................................... 33
2.5 Examples.............................................. 34
3 Image Processing ......................................... 37
3.1 Images and Histograms.................................. 37
3.1.1 Images as Functions .............................. 37
3.1.2 Histograms of Images ............................. 38
3.2 Image Enhancement .................................... 38
3.2.1 Window and Level................................ 39
3.2.2 Gamma Correction ............................... 40
3.2.3 Histogram Equalization ........................... 40
3.3 Edge Detection......................................... 40
3.4 Image Filtering......................................... 43
3.4.1 Filtering – Basics................................. 43
3.4.2 Linear Shift-invariant Filters in Image Processing..... 44
3.4.3 Nonlinear Filters – the Median Filter ............... 47
3.5 Morphological Operators ................................ 48
3.6 Image Segmentation .................................... 52
4 Contents
4 Endoscopy................................................ 57
4.1 Minimally Invasive Surgery and Open Surgery ............. 57
4.2 Minimally Invasive Abdominal Surgery.................... 58
4.3 Assistance Systems ..................................... 61
4.4 Range Imaging in Abdominal Surgery..................... 63
4.4.1 Stereo Vision .................................... 64
4.4.2 Structured Light ................................. 65
4.4.3 Time-of-Flight (TOF)............................. 66
5 Microscopy ............................................... 69
5.1 Image Formation in a Thin Lens ......................... 70
5.2 Compound Microscope .................................. 73
5.3 Bright Field Microscopy................................. 75
5.4 Fluorescence Microscopy ................................ 78
5.5 Phase Contrast Microscopy .............................. 78
5.6 Quantitative Phase Microscopy........................... 80
5.7 Limitation of Light Microscopy........................... 83
5.8 Beyond Light Microscopy................................ 86
5.9 Light Microscopy Beyond the Diffraction Limit............. 88
6 Magnetic Resonance Imaging ............................. 91
6.1 Nuclear Magnetic Resonance (NMR)...................... 91
6.1.1 Genesis of the Resonance Effect .................... 91
6.1.2 Relaxation and Contrasts.......................... 95
6.2 Principles of Magnetic Resonance Imaging................. 100
6.2.1 Slice Selection ................................... 100
6.2.2 Spatial Encoding ................................. 101
6.2.3 k-space ......................................... 105
6.2.4 Slice-selective vs. Volume-selective 3-D Imaging ...... 105
6.3 Pulse Sequences ........................................ 106
6.3.1 Spin Echo ....................................... 107
6.3.2 Gradient Echo ................................... 107
6.4 Advanced Topics ....................................... 109
6.4.1 Parallel Imaging.................................. 109
6.4.2 Spectrally Selective Excitation ..................... 114
6.4.3 Non-contrast Angiography......................... 115
6.4.4 The BOLD Effect ................................ 117
7 X-ray Imaging ............................................ 119
7.1 Introduction ........................................... 119
7.1.1 Definition of X-rays............................... 119
7.1.2 History and Present .............................. 121
7.2 X-ray Generation....................................... 123
Contents 5
7.3 X-ray Matter Interaction ................................ 125
7.3.1 Absorption ...................................... 126
7.3.2 Photoelectric Effect............................... 129
7.3.3 Compton Scattering .............................. 129
7.3.4 Rayleigh scattering ............................... 129
7.4 X-ray Imaging ......................................... 130
7.4.1 Image Intensifiers ................................ 130
7.4.2 Flat Panel Detectors.............................. 134
7.4.3 Sources of Noise.................................. 136
7.5 X-ray Applications ..................................... 138
7.5.1 Radiography..................................... 138
7.5.2 Fluoroscopy ..................................... 141
7.5.3 Digital Subtraction Angiography ................... 143
8 Computed Tomography................................... 147
8.1 Introduction ........................................... 147
8.1.1 Motivation ...................................... 147
8.1.2 Brief History..................................... 148
8.2 Mathematical Principles................................. 149
8.2.1 Radon Transform................................. 150
8.2.2 Fourier Slice Theorem............................. 152
8.3 Image Reconstruction ................................... 155
8.3.1 Analytic Reconstruction........................... 155
8.3.2 Algebraic Reconstruction.......................... 161
8.3.3 Acquisition Geometries............................ 164
8.4 Practical Considerations................................. 167
8.4.1 Spatial Resolution................................ 168
8.4.2 Noise ........................................... 170
8.4.3 Image Artifacts .................................. 171
8.5 X-ray Attenuation with Polychromatic Attenuation ......... 176
8.5.1 Mono- vs. Polychromatic Attenuation............... 176
8.5.2 Single, Dual, and Spectral CT ..................... 179
8.5.3 Beam Hardening ................................. 180
8.6 Spectral CT ........................................... 182
8.6.1 Different Spectral CT Measurements................ 182
8.6.2 Basis Material Decomposition...................... 186
9 X-ray Phase Contrast:
Research on a Future ImagingModality............. . .... 191
9.1 Introduction ........................................... 191
9.2 Talbot-Lau Interferometer ............................... 194
9.2.1 Talbot-Lau Interferometer Setup ................... 195
9.2.2 Phase Stepping and Reconstruction................. 197
9.3 Applications ........................................... 199
9.4 Research Challenges .................................... 203
6 Contents
10 Emission Tomography .................................... 207
10.1 Introduction ........................................... 207
10.2 Physics of Emission Tomography ......................... 208
10.2.1 Photon Emission ................................. 208
10.2.2 Photon Interactions............................... 212
10.3 Acquisition Systems .................................... 214
10.3.1 SPECT ......................................... 214
10.3.2 PET............................................ 217
10.4 Reconstruction......................................... 219
10.4.1 Filtered Back-Projection .......................... 219
10.4.2 Iterative Reconstruction........................... 220
10.4.3 Quantitative Reconstructions ...................... 222
10.4.4 Practical Considerations........................... 224
10.5 Clinical Applications.................................... 227
10.5.1 Diagnostics ...................................... 227
10.5.2 Therapy......................................... 230
10.6 Hybrid Imaging ........................................ 230
10.6.1 Clinical Need .................................... 230
10.6.2 Advent und Acceptance of Hybrid Scanners.......... 231
10.6.3 Further Benefits of Hybrid Imaging................. 232
11 Ultrasound ............................................... 237
11.1 Introduction ........................................... 237
11.2 Physics of Sound Waves ................................. 238
11.2.1 Sound Waves .................................... 238
11.2.2 Sound Wave Characteristics at Boundaries .......... 239
11.2.3 Attenuation ..................................... 242
11.3 Image Acquisition for Diagnostics ........................ 243
11.3.1 Transducers ..................................... 243
11.3.2 Piezoelectric Effect ............................... 243
11.3.3 Spatial Resolution................................ 244
11.3.4 Imaging Modes .................................. 245
11.4 Safety Aspects ......................................... 247
12 Optical Coherence Tomography........................... 251
12.1 Working Principle of OCT............................... 251
12.1.1 Michelson Interferometer .......................... 253
12.1.2 Coherence Length ................................ 253
12.2 Time Domain OCT..................................... 254
12.3 Fourier Domain OCT ................................... 256
12.4 OCT Angiography...................................... 256
12.5 Applications ........................................... 257
Acronyms .................................................... 263
Author(cid:128)Index ................................................. 265