Introduction to Medical Image Analysis

185 Pages·2020·9.798 MB·English

by  Rasmus R. Paulsen, Thomas B. Moeslund

Undergraduate Topics in Computer Science
Rasmus R. Paulsen
Thomas B. Moeslund
Introduction
to Medical Image
Analysis
Undergraduate Topics in Computer
Science
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Rasmus R. Paulsen (cid:129)
Thomas B. Moeslund
Introduction to Medical
Image Analysis
123
Rasmus R. Paulsen ThomasB. Moeslund
Department for AppliedMathematics Department ofArchitecture, Design,
andComputer Science andMedia Technology
Technical University of Denmark Aalborg University
Kongens Lyngby,Denmark Aalborg, Denmark
ISSN 1863-7310 ISSN 2197-1781 (electronic)
Undergraduate Topics inComputer Science
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Preface
In recent years, there has been a tremendous progress in the use of automatic
analysisofimagesandvideos.Thefieldhasevolvedfrombeingasmallerresearch
area with applications not widely known by the public to have major impact on
everydaylives.Forexampleinself-drivingcarsorfacetrackinginmobilephones.
Thisrapidincreaseintheeverydayuseandtheaffiliatedincreaseinresearchimpact
have also benefitted the life sciences, where medical image analysis plays a major
role in modern diagnostics.
Theaimofthebookistopresentthefascinatingworldofmedicalimageanalysis
in an easy and interesting way. Compared to many standard books on image
analysis, the approach we have chosen is less mathematical and more intuitive.
SomeofthekeyalgorithmsareexemplifiedinC-code.Pleasenotethatthecodeis
neither optimal nor complete and merely serves as an additional input for com-
prehending the algorithms.
ThisbookisaresultofacollaborationbetweenDTUComputeattheTechnical
University of Denmark (DTU) and the Department of Architecture, Design and
Media Technology atAalborgUniversity, Denmark. It ispartly based on the book
“Introduction to Video and Image Processing” [5].
For Instructors
We recommend combining the more theoretical exercises found on the homepage
with practical exercises where real images are processed. The tools used for
practical image analysis is rapidly evolving. Currently, we are using MATLAB for
practicalexercisesandslowlymovingtousingPythonwithforexampleOpenCV
orscikit-image.FortimecriticalapplicationsC++usingagoodtoolkitlikefor
exampleOpenCVisstillpreferred.Forexplorativeanalysisofimages,weoftenuse
ImageJ.
v
vi Preface
Acknowledgements
We would like to thank the following for ideas, figures, and general input: Lars
Knudsen, Andreas Møgelmose, Hans Jørgen Andersen, Moritz Störring, David
Meredith, Rasmus Larsen, Michael Sass Hansen, Mikkel Stegmann, and Jens
Michael Carstensen.
Book Homepage
Updates,exercisesandothermaterialwithconnectiontothebookcanbefoundon
the book homepage: http://mediabook.compute.dtu.dk/.
We hope you will enjoy this book!
Kongens Lyngby, Denmark Rasmus R. Paulsen
Aalborg, Denmark Thomas B. Moeslund
January 2020
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 The Different Flavors of Image Processing. . . . . . . . . . . . . . . . 2
1.2 General Frameworks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Deep Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 The Chapters in This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Image Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 The Optical System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 The Lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 The Imaging Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Digital Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.1 Image Coordinate Systems . . . . . . . . . . . . . . . . . . . . . 21
2.4.2 The Region-of-Interest (ROI) . . . . . . . . . . . . . . . . . . . 22
2.4.3 Binary Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.4 Label Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.5 Multi-spectral Images . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.6 16-Bit Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Image Storage and Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1 Lossless Compression and Image Formats . . . . . . . . . . . . . . . . 28
3.2 Lossy Compression and Image Formats . . . . . . . . . . . . . . . . . . 29
3.3 DICOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Binary Image Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.1 Chain Coding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4.2 Run-Length Coding . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Point Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1 Gray-Level Mapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 The Image Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.1 Histogram Stretching . . . . . . . . . . . . . . . . . . . . . . . . . 41
vii
viii Contents
4.3 Non-Linear Gray-Level Mapping. . . . . . . . . . . . . . . . . . . . . . . 44
4.3.1 Gamma Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3.2 Logarithmic and Exponential Mapping . . . . . . . . . . . . 45
4.4 Thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4.1 Automatic Thresholding . . . . . . . . . . . . . . . . . . . . . . . 49
4.5 Image Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.5.1 Applying Image Arithmetic. . . . . . . . . . . . . . . . . . . . . 51
4.5.2 Noise Reduction Using Pixelwise Summing. . . . . . . . . 52
4.5.3 Motion Detection Using Pixelwise Differencing . . . . . . 53
4.6 Programming Point Processing Operations . . . . . . . . . . . . . . . . 53
5 Neighborhood Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1 The Median Filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1.1 Rank Filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.1 Template Matching. . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2.2 Edge Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 Correlation Versus Convolution. . . . . . . . . . . . . . . . . . . . . . . . 72
6 Morphology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.1 Level 1: Hit and Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.1.1 Hit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.1.2 Fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2 Level 2: Dilation and Erosion . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2.1 Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2.2 Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.3 Level 3: Compound Operations . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3.1 Closing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3.2 Opening. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.3.3 Combining Opening and Closing . . . . . . . . . . . . . . . . 83
6.3.4 Boundary Detection . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7 BLOB Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.1 BLOB Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.1.1 The Grass-Fire Algorithm. . . . . . . . . . . . . . . . . . . . . . 89
7.2 BLOB Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.2.1 BLOB Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2.2 BLOB Bounding Box. . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2.3 Bounding Box Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2.4 Bounding Circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2.5 Convex Hull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2.6 Compactness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Contents ix
7.2.7 Center of Mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.2.8 Perimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.2.9 Circularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.3 BLOB Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.4 Cell Classification Using BLOB Analysis. . . . . . . . . . . . . . . . . 97
7.4.1 Training Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.4.2 Feature Selection and Feature Ranges . . . . . . . . . . . . . 98
7.4.3 Evaluation of Classification. . . . . . . . . . . . . . . . . . . . . 99
8 Color Images. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.1 What Is a Color? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.2 Representation of an RGB Color Image . . . . . . . . . . . . . . . . . . 105
8.2.1 The RGB Color Space . . . . . . . . . . . . . . . . . . . . . . . . 108
8.2.2 Converting from RGB to Gray-Scale. . . . . . . . . . . . . . 109
8.2.3 The Normalized RGB Color Representation. . . . . . . . . 110
8.3 Other Color Representations . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.3.1 The HSI Color Representation . . . . . . . . . . . . . . . . . . 114
8.4 Color Thresholding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.4.1 Chroma-Keying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
8.5 Postscript on Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9 Pixel Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.1 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
9.2 Minimum Distance Classification. . . . . . . . . . . . . . . . . . . . . . . 122
9.3 Parametric Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.4 Bayesian Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.5 When to Use the Different Classifiers. . . . . . . . . . . . . . . . . . . . 129
10 Geometric Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
10.1 Affine Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
10.1.1 Translation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
10.1.2 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
10.1.3 Rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
10.1.4 Shearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
10.1.5 Combining the Transformations . . . . . . . . . . . . . . . . . 134
10.2 Backward Mapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
10.3 Profile Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
10.4 Other Geometric Transformations . . . . . . . . . . . . . . . . . . . . . . 137
10.5 Homography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
11 Image Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
11.1 Feature-Based Image Registration . . . . . . . . . . . . . . . . . . . . . . 144
11.1.1 Translation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
11.1.2 Translation + Rotation = Rigid Transformation . . . . . . 149