Medical image processing, reconstruction, and restoration: concepts and methods
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| Schriftenreihe: | Signal processing and communications
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| 490 | 1 | |a Signal processing and communications |v 25 | |
| 650 | 4 | |a Diagnostic imaging |x Digital techniques | |
| 650 | 4 | |a Image Processing, Computer-Assisted |x methods | |
| 650 | 4 | |a Diagnostic Imaging |x methods | |
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Datensatz im Suchindex
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| adam_text | 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
xii Iâ„¢
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
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 Ill
2.3.3.1 Two Dimensional Hadamard Walsh
Transform Ill
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 1 133
xiv i*n
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
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
xvi fan
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
i
Contents xvli
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
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
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
i
i
§
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 j
Filtering for Continuous Space Images.... 563 1
Contents xxl
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
s
xxii Iâ„¢
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
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
Index 711
|
| adam_txt |
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
xii Iâ„¢
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
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 Ill
2.3.3.1 Two Dimensional Hadamard Walsh
Transform Ill
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 1 133
xiv i*n
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
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
xvi fan
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
i
Contents xvli
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
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 \
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
i
i
§
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 j
Filtering for Continuous Space Images. 563 1
\
Contents xxl
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
s
xxii Iâ„¢
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
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
Index 711 |
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| spelling | Medical image processing, reconstruction, and restoration concepts and methods Jiří Jan Boca Raton, FL Taylor & Francis 2006 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Signal processing and communications 25 Diagnostic imaging Digital techniques Image Processing, Computer-Assisted methods Diagnostic Imaging methods Signal Processing, Computer-Assisted Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Bildgebendes Verfahren (DE-588)4006617-4 gnd rswk-swf Medizin (DE-588)4038243-6 gnd rswk-swf Bildgebendes Verfahren (DE-588)4006617-4 s Bildverarbeitung (DE-588)4006684-8 s Medizin (DE-588)4038243-6 s DE-604 Jan, Jiří Sonstige oth Signal processing and communications 25 (DE-604)BV019738041 25 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014969772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Medical image processing, reconstruction, and restoration concepts and methods Signal processing and communications Diagnostic imaging Digital techniques Image Processing, Computer-Assisted methods Diagnostic Imaging methods Signal Processing, Computer-Assisted Bildverarbeitung (DE-588)4006684-8 gnd Bildgebendes Verfahren (DE-588)4006617-4 gnd Medizin (DE-588)4038243-6 gnd |
| subject_GND | (DE-588)4006684-8 (DE-588)4006617-4 (DE-588)4038243-6 |
| title | Medical image processing, reconstruction, and restoration concepts and methods |
| title_auth | Medical image processing, reconstruction, and restoration concepts and methods |
| title_exact_search | Medical image processing, reconstruction, and restoration concepts and methods |
| title_exact_search_txtP | Medical image processing, reconstruction, and restoration concepts and methods |
| title_full | Medical image processing, reconstruction, and restoration concepts and methods Jiří Jan |
| title_fullStr | Medical image processing, reconstruction, and restoration concepts and methods Jiří Jan |
| title_full_unstemmed | Medical image processing, reconstruction, and restoration concepts and methods Jiří Jan |
| title_short | Medical image processing, reconstruction, and restoration |
| title_sort | medical image processing reconstruction and restoration concepts and methods |
| title_sub | concepts and methods |
| topic | Diagnostic imaging Digital techniques Image Processing, Computer-Assisted methods Diagnostic Imaging methods Signal Processing, Computer-Assisted Bildverarbeitung (DE-588)4006684-8 gnd Bildgebendes Verfahren (DE-588)4006617-4 gnd Medizin (DE-588)4038243-6 gnd |
| topic_facet | Diagnostic imaging Digital techniques Image Processing, Computer-Assisted methods Diagnostic Imaging methods Signal Processing, Computer-Assisted Bildverarbeitung Bildgebendes Verfahren Medizin |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014969772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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