Fundamentals of Digital Imaging in Medicine (eBook)

Foreword 6
Preface 8
Contents 11
1 Introduction 15
1.1 What Is This Book Trying To Do? 15
1.2 Chapter Outline 16
1.2.1 Digital Images 16
1.2.2 Medical Images 17
1.2.3 The Spatial and Frequency Domains 17
1.2.4 Image Quality 17
1.2.5 Contrast Adjustment 17
1.2.6 Image Filters 18
1.2.7 Spatial Transformations 18
1.2.8 Appendices 18
1.3 Revision 19
1.4 Practical Image Processing 19
1.4.1 Images for Teaching 19
2 Digital Images 20
2.1 Introduction 20
2.2 Defining a Digital Image 21
2.3 Image Information 24
2.3.1 Pixels 24
2.3.2 Image Size, Scale, and Resolution 25
2.3.3 Pixel Information 25
2.3.3.1 Bit Depth 26
2.3.4 Ways of Representing Numbers 29
2.3.4.1 Signed and Unsigned Integers 29
2.3.4.2 Floating Point 30
2.3.5 Data Accuracy 30
2.4 Image Metadata 31
2.4.1 Metadata Content 31
2.4.2 Lookup Tables 33
2.5 Image Storage 35
2.5.1 Image File Formats 35
2.5.1.1 Bitmaps and BMP Files 35
2.5.1.2 Vector Graphics 36
2.5.1.3 JFIF (JPG) 36
2.5.1.4 GIF 36
2.5.1.5 PNG 37
2.5.1.6 TIF 37
2.5.1.7 DICOM 37
2.5.2 Image Data Compression Methods 38
2.5.2.1 JPEG 39
2.5.2.2 Packbits 41
2.5.2.3 ZIP, PKZIP 41
2.5.2.4 LZW 41
2.5.2.5 Which Method Is Best? 42
2.6 Summary 43
3 Medical Images 44
3.1 Introduction 44
3.2 The Energetics of Imaging 45
3.2.1 Radio Frequencies 46
3.2.1.1 Microwaves 46
3.2.1.2 Infrared 47
3.2.1.3 Visible Light 47
3.2.1.4 X-Rays 47
3.2.1.5 Gamma Rays 48
3.2.1.6 Energy Flow 48
3.3 Spatial and Temporal Resolution of Medical Images 49
3.4 Medical Imaging Methods 52
3.4.1 Magnetic Resonance 52
3.4.1.1 The 1H Nucleus: Water and Fat 53
3.4.1.2 Metabolites: MR Spectroscopy 55
3.4.1.3 Other Nuclei 56
3.4.2 Visible Light Imaging 56
3.4.3 X-Ray Imaging 57
3.4.3.1 Plain X-Ray 58
3.4.3.2 Computed Tomography 59
3.4.3.3 Fluoroscopy 60
3.4.4 Emission Imaging 61
3.4.5 Portal Images 64
3.4.6 Ultrasonography 65
3.5 Summary 67
4 The Spatial and Frequency Domains 68
4.1 Introduction 68
4.2 Images in the Spatial and Frequency Domains 68
4.2.1 The Spatial Domain 68
4.2.2 Common All-Garden Temporal Frequency 69
4.2.3 The Concept of Spatial Frequency 70
4.2.4 The Cosine and Hartley Transforms 76
4.3 Fourier Transforms and Fourier Spectra 77
4.3.1 1D Fourier Transforms 77
4.3.2 2D Fourier Transforms 79
4.3.3 Fourier Spectra 79
4.3.4 The Zero Frequency or `DC' Term 82
4.3.5 Fourier Spectra of More Complex Images 82
4.3.6 How Many Spatial Frequencies are Needed? 90
4.3.7 Fourier Spectra of Lines 91
4.4 The Complex Data Behind Fourier Spectra 91
4.5 Two Practical Applications of Fourier Transforms 96
4.5.1 How Does the Focal Spot of an X-Ray Tube Affect Image Resolution? 96
4.5.2 Making Diagnostic Images from Raw MRI Data 97
4.6 Summary 98
5 Image Quality 100
5.1 Introduction 100
5.2 Contrast 101
5.2.1 Simple Measures of Contrast 102
5.2.2 Contrast and Spatial Frequency 104
5.2.3 Optimizing Contrast 104
5.3 Image Noise 105
5.3.1 What Is Noise? 105
5.3.2 Quantum Mottle 106
5.3.3 Other Noises 107
5.3.3.1 Gaussian Noise 108
5.3.3.2 Speckle 109
5.3.3.3 Salt and Pepper 109
5.3.3.4 Artifacts 110
5.3.4 Signal to Noise Ratio 110
5.4 Contrast + Noise 112
5.5 Spatial Resolution 113
5.5.1 Line Pairs 113
5.5.2 The Modulation Transfer Function 114
5.5.3 The Edge, Line, and Point Spread Functions 117
5.6 Contrast + Noise + Resolution 119
5.7 Summary 119
6 Contrast Adjustment 122
6.1 Introduction 122
6.2 Human Visual Perception 122
6.3 Histograms 123
6.4 Manual Contrast Adjustment 126
6.4.1 Contrast Stretching 126
6.4.2 Window and Level 131
6.4.3 Nonlinear Mapping Functions 132
6.5 Automatic Contrast Adjustment 132
6.5.1 Normalization 132
6.5.2 Histogram Equalization 134
6.5.3 Histogram Specification 137
6.5.4 Region-Specific Contrast Adjustments 138
6.5.5 Binary Contrast Enhancement – Thresholding 139
6.5.6 Hardware Contrast 142
6.5.6.1 Gamma Adjustment 142
6.5.6.2 The DICOM Gray Scale Display Function 143
6.6 Practical Example. Adjusting the Contrast of a Magnetic Resonance Microimage 144
6.7 Summary 147
7 Image Filters 149
7.1 Introduction 149
7.2 Frequency Domain Filters 149
7.2.1 Ideal Filters 149
7.2.2 Butterworth Filters 152
7.2.3 Gaussian Filters 154
7.2.4 Band Stop Filters 156
7.2.5 Band Pass Filters 158
7.2.6 Directional Filters 162
7.3 Spatial Domain Filters 163
7.3.1 Smoothing and Blurring 163
7.3.2 Gradients and Edges 170
7.3.2.1 Roberts Cross Filter 170
7.3.2.2 Prewitt and Sobel Filters 172
7.3.2.3 Laplacian Filters 173
7.3.2.4 LoG Filters 176
7.3.3 Spatial and Frequency Domain Properties of Convolution 176
7.3.4 Convolution Versus Correlation 177
7.3.4.1 The Unsharp Mask 178
7.3.5 Median Filters 180
7.3.6 Adaptive Filters 181
7.4 Summary 183
8 Spatial Transformation 185
8.1 Introduction 185
8.2 Translation 185
8.3 Rotation 187
8.4 Interpolation 189
8.4.1 Nearest-Neighbor 189
8.4.2 Bilinear 190
8.4.3 Bicubic 190
8.5 Resizing Images 192
8.6 Summary 194
A ImageJ 196
A.1 General 196
A.1.1 Installation of ImageJ 197
A.1.2 Documentation 197
A.1.3 Plugins 198
A.2 Getting Started 198
A.3 Basic Image Operations 198
A.4 Installing Macro Plugins 198
A.5 Further Reading 199
B A Note on Precision and Accuracy 200
C Complex Numbers 201
C.1 What Is a Complex Number? 201
C.2 Manipulating Complex Numbers 201
C.3 Alternating Currents 203
C.4 MRI 204
Index 206