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El. knyga: Biomedical Image Analysis: Statistical and Variational Methods

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(University of Louisville, Kentucky)
  • Formatas: PDF+DRM
  • Išleidimo metai: 30-Oct-2014
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781139989138
Kitos knygos pagal šią temą:
Biomedical Image Analysis: Statistical and Variational MethodsDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Išleidimo metai: 30-Oct-2014
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781139989138
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Ideal for classroom use and self-study, this book explains the implementation of the most effective modern methods in image analysis, covering segmentation, registration and visualisation, and focusing on the key theories, algorithms and applications that have emerged from recent progress in computer vision, imaging and computational biomedical science. Structured around five core building blocks - signals, systems, image formation and modality; stochastic models; computational geometry; level set methods; and tools and CAD models - it provides a solid overview of the field. Mathematical and statistical topics are presented in a straightforward manner, enabling the reader to gain a deep understanding of the subject without becoming entangled in mathematical complexities. Theory is connected to practical examples in x-ray, ultrasound, nuclear medicine, MRI and CT imaging, removing the abstract nature of the models and assisting reader understanding.

Daugiau informacijos

Ideal for classroom use and self-study, this book explains the implementation of the most effective modern methods in image analysis.
Preface xvii
Nomenclature xx
1 Overview of biomedical image analysis
1(6)
1.1 Introduction
1(1)
1.2 The scope of the book
2(2)
1.2.1 Signals and systems, image formation, and image modality
2(1)
1.2.2 Stochastic models
3(1)
1.2.3 Computational geometry
3(1)
1.2.4 Variational calculus and level-set methods
3(1)
1.2.5 Image analysis tools
4(1)
1.3 Options for class work
4(1)
1.4 Other references
4(3)
Part I Signals and systems, image formation, and image modality 7(70)
2 Overview of two-dimensional signals and systems
9(30)
2.1 Definitions
9(1)
2.2 Signal representations
10(6)
2.2.1 Special functions
11(1)
2.2.2 Fourier series
12(1)
2.2.3 Fourier transform
13(3)
2.3 Basic sampling and quantization
16(2)
2.4 Sequence Fourier series
18(5)
2.4.1 Sequence Fourier transform
21(1)
2.4.2 Relationship to the continuous Fourier transform
22(1)
2.5 Discrete Fourier transform
23(2)
2.6 The fast Fourier transform (FFT) algorithm
25(4)
2.6.1 Effect of periodic shifts
26(1)
2.6.2 Circular convolution
27(1)
2.6.3 Linear convolution
28(1)
2.7 The Z-transform
29(2)
2.8 Basic 2D digital filter design
31(2)
2.9 Anisotropic diffusion filtering
33(3)
2.10 Summary
36(1)
2.11 Exercises
36(2)
References
38(1)
3 Biomedical imaging modalities
39(38)
3.1 Introduction
39(1)
3.2 X-rays
39(4)
3.2.1 Filtration and beam hardening
41(1)
3.2.2 Simulation of X-ray transmission
41(2)
3.3 Computed tomography
43(4)
3.3.1 CT scanner generations
45(1)
3.3.2 Basic CT reconstruction algorithms
46(1)
3.3.3 Dose
47(1)
3.3.4 CT image artifacts
47(1)
3.4 Nuclear medicine
47(6)
3.4.1 Scintillation cameras
48(3)
3.4.2 Emission computed tomography
51(2)
3.5 Ultrasound
53(8)
3.5.1 Ultrasound intensity
54(1)
3.5.2 Attenuation in ultrasound
54(2)
3.5.3 Reflection in ultrasound
56(1)
3.5.4 Refraction in ultrasound
56(1)
3.5.5 Ultrasound transducers
56(1)
3.5.6 Ultrasound beams
57(1)
3.5.7 Ultrasound instrumentation
58(1)
3.5.8 Ultrasound artifacts
59(1)
3.5.9 Doppler effect
59(2)
3.6 Magnetic resonance imaging
61(10)
3.6.1 Signal induction
63(1)
3.6.2 Relaxation processes
64(1)
3.6.3 Pulse sequences
65(2)
3.6.4 Spatial encoding
67(1)
3.6.5 Tissue contrast in MRI
68(1)
3.6.6 Components of an MRI system
69(2)
3.7 Summary
71(1)
3.8 Exercises
71(1)
References
72(1)
Appendix 3.1 Parallel beam filtered back-projection algorithm
72(5)
Part II Stochastic models 77(104)
4 Random variables
79(28)
4.1 Introduction
79(1)
4.2 Statistical experiments
79(4)
4.2.1 Sample space ω
80(1)
4.2.2 Field (algebra) σF
80(1)
4.2.3 Probability measure P
80(3)
4.3 Random variables
83(13)
4.3.1 Basic concepts
83(4)
4.3.2 Properties of the CDF and the PDF of a random variable
87(1)
4.3.3 The conditional distribution
88(2)
4.3.4 Statistical expectation
90(4)
4.3.5 Functions of a random variable
94(2)
4.4 Two random variables
96(7)
4.4.1 Statistical expectation in two dimensions
99(1)
4.4.2 Functions of two random variables
100(2)
4.4.3 Two functions of two random variables
102(1)
4.5 Simulation of random variables
103(1)
4.6 Summary
104(1)
4.7 Computer laboratory
104(1)
4.8 Exercises
105(1)
References
106(1)
5 Random processes
107(24)
5.1 Definition and general concepts
107(6)
5.1.1 Description of random processes
109(1)
5.1.2 Classification of a random process
110(2)
5.1.3 Continuity of a random process
112(1)
5.1.4 The Kolmogorov consistency conditions
113(1)
5.2 Distribution functions for a random process
113(5)
5.2.1 Definitions
113(1)
5.2.2 First- and second-order probability distribution functions
114(4)
5.3 Some properties of a random process
118(8)
5.3.1 Stationarity
118(1)
5.3.2 The autocorrelation function
118(2)
5.3.3 The autocovariance function
120(1)
5.3.4 The cross-correlation function
120(1)
5.3.5 Time average
121(2)
5.3.6 The power spectrum of a random process
123(2)
5.3.7 Cross-spectral density
125(1)
5.3.8 Power spectral density of discrete-parameter random process
125(1)
5.4 Linear systems with random inputs
126(2)
5.5 Two-dimensional random processes
128(1)
5.6 Exercises
128(2)
References
130(1)
6 Basics of random fields
131(32)
6.1 Introduction
131(5)
6.2 Graphical models
136(3)
6.3 Markov system
139(1)
6.4 Hidden Markov model
140(1)
6.5 Markov random field
141(2)
6.6 Gibbs model
143(2)
6.7 Markov—Gibbs random field models
145(4)
6.7.1 Auto-models
146(1)
6.7.2 Aura-based GRF model
147(1)
6.7.3 Other models
148(1)
6.8 GRF-based image synthesis
149(4)
6.8.1 Gibbs sampler algorithm
149(1)
6.8.2 Chen algorithm
149(2)
6.8.3 Metropolis algorithm
151(2)
6.9 GRF-based image analysis
153(6)
6.9.1 Coding estimation
153(2)
6.9.2 Least square error method
155(1)
6.9.3 Analytical method for parameter identification
155(4)
6.10 Summary
159(1)
6.11 Exercises
159(2)
6.12 Computer laboratory
161(1)
References
162(1)
7 Probability density estimation by linear models
163(18)
7.1 Introduction
163(1)
7.2 Nonparametric methods
164(4)
7.2.1 Kernel-based estimators
166(1)
7.2.2 Parzen window
167(1)
7.2.3 k—NN estimator
168(1)
7.3 Parametric methods
168(4)
7.3.1 Maximum likelihood estimator (MLE)
169(1)
7.3.2 Biased versus unbiased estimator
170(1)
7.3.3 The expectation-maximization (EM) approach
171(1)
7.4 Linear combination of Gaussians model (LCG1)
172(3)
7.4.1 Modifications of the linear model (LCG2)
174(1)
7.5 Modeling the image intensity/appearance through the linear model
175(1)
7.6 Exercises
176(1)
7.7 Computer laboratory
177(2)
References
179(2)
Part III Computational geometry 181(92)
8 Basics of topology and computational geometry
183(30)
8.1 Introduction
183(1)
8.2 Shape representation
183(3)
8.2.1 What is shape?
183(1)
8.2.2 How should a shape be described?
184(1)
8.2.3 Criteria for shape representation
184(1)
8.2.4 Data representation of shape
184(2)
8.3 Topological equivalence
186(2)
8.4 Vector spaces
188(2)
8.5 Surfaces in parameter space
190(9)
8.5.1 Parametric curves
191(2)
8.5.2 Parametric surfaces
193(3)
8.5.3 Surface curvature
196(3)
8.6 Surfaces as meshes
199(5)
8.6.1 Manifolds and surfaces
199(2)
8.6.2 Barycentric coordinates
201(1)
8.6.3 Triangle local frame
202(1)
8.6.4 Surface curvature: discrete form
202(2)
8.7 Summary
204(1)
8.8 Exercises
205(2)
8.9 Computer laboratory
207(1)
References
208(5)
9 Geometric features extraction
213(60)
9.1 Introduction
213(4)
9.2 Edges and corners
217(8)
9.2.1 The Harris detector
217(2)
9.2.2 The SUSAN corner detector
219(1)
9.2.3 Harris—Laplace and Harris—affine corner detectors
219(2)
9.2.4 Blob detectors
221(2)
9.2.5 Region detectors
223(2)
9.3 Comparative evaluation of interest points
225(10)
9.3.1 Multi-scale representations
225(7)
9.3.2 Scale-space representation
232(1)
9.3.3 Scale-space and feature detection
233(1)
9.3.4 Differential singularities and feature detection
234(1)
9.4 Local descriptors
235(22)
9.4.1 Scale-invariant feature transform (SIFT)
235(3)
9.4.2 Case study: Descriptors of small-size lung nodules in chest CT
238(1)
9.4.3 Extensions to the SIFT algorithms
239(2)
9.4.4 Speeded-up robust features (SURF)
241(1)
9.4.5 Multi-resolution local binary pattern (LBP)
241(4)
9.4.6 Image stitching
245(12)
9.5 Three-dimensional local invariant feature descriptors
257(7)
9.5.1 Interest point detection
257(4)
9.5.2 3D descriptor building
261(3)
9.5.3 Descriptor matching
264(1)
9.6 Summary
264(3)
9.7 Exercises
267(1)
9.8 Computer laboratory
267(2)
References
269(4)
Part IV Variational approaches and level sets 273(22)
10 Variational approaches and level sets
275(20)
10.1 Calculus of variation and Euler equation
275(4)
10.1.1 Euler—Lagrange equation for one independent variable
276(1)
10.1.2 Euler—Lagrange equation for multiple independent variables
277(1)
10.1.3 Euler—Lagrange and the gradient descent flow
278(1)
10.2 Curve/surface evolution via classical deformable models
279(5)
10.2.1 Curves and planar differential geometry
279(1)
10.2.2 Geometry of surfaces
280(1)
10.2.3 Geodesic curvature
281(1)
10.2.4 Principal curvatures
281(1)
10.2.5 Planar curves and surface normal
281(1)
10.2.6 Curve/surface evolution as a variational problem
282(1)
10.2.7 Discretization and numerical simulation of snakes
283(1)
10.3 Level sets
284(3)
10.3.1 Implicit representation and the evolution PDE
284(2)
10.3.2 Level-set calculus
286(1)
10.4 Numerical methods for level sets
287(3)
10.4.1 Conservation law and weak solutions
287(1)
10.4.2 Entropy condition and viscosity solutions
288(1)
10.4.3 Upwind direction and discontinuous solutions
288(1)
10.4.4 The Eulerian formulation and the hyperbolic conservation law
289(1)
10.5 Numerical algorithm
290(3)
10.5.1 Need for reinitialization and the distance function
291(1)
10.5.2 Front evolution without reinitialization
292(1)
10.6 Exercises
293(1)
10.7 Computer laboratory
293(1)
References
294(1)
Part V Image analysis tools 295(163)
11 Segmentation: statistical approach
297(19)
11.1 Introduction
297(2)
11.2 Image modelling
299(7)
11.2.1 Problem formulation and image models
300(6)
11.3 Experiments and discussion
306(7)
11.3.1 Ground-truth experiments
307(1)
11.3.2 Examples of applicability to biomedical images
308(5)
11.4 Summary
313(1)
11.5 Exercises
314(1)
References
314(2)
12 Segmentation: variational approach
316(29)
12.1 Introduction
316(2)
12.2 Variational segmentation without edges
318(2)
12.2.1 The Mumford—Shah energy formulation
318(1)
12.2.2 Chan and Vese variational approach
319(1)
12.3 Image segmentation using multiple level-set functions
320(2)
12.4 Implicit shape representation
322(2)
12.4.1 Shape registration
324(1)
12.5 Shape-based segmentation
324(2)
12.6 Curve/surface modeling by level sets
326(2)
12.7 Variational model for evolution-based region statistics
328(1)
12.8 Examples and evaluation
329(5)
12.8.1 Performance on images and volumes
329(2)
12.8.2 Validation experiment on a real phantom
331(1)
12.8.3 Blood vessel extraction
332(2)
12.9 Clinical example: lung nodule segmentation
334(8)
12.9.1 Variational approach for nodule segmentation
336(1)
12.9.2 Shape alignment
337(2)
12.9.3 Level-set segmentation with shape prior
339(1)
12.9.4 Some results
339(2)
12.9.5 Extensions
341(1)
12.10 Summary
342(1)
12.11 Exercises
342(1)
12.12 Computer laboratory
342(1)
References
343(2)
13 Basics of registration
345(42)
13.1 Introduction
345(1)
13.2 Basic concepts and definitions
346(9)
13.2.1 Components of the registration transformation
349(3)
13.2.2 Choice of transformation
352(1)
13.2.3 Similarity measures
353(2)
13.3 Surface registration by the ICP algorithm
355(11)
13.3.1 Mathematical preliminaries
355(4)
13.3.2 The ICP algorithm
359(7)
13.4 Global image registration via mutual information
366(12)
13.4.1 Imaging model
369(2)
13.4.2 Basics of information theory
371(4)
13.4.3 Registration metric
375(2)
13.4.4 Mutual information registration
377(1)
13.5 Applications
378(1)
13.6 Summary
378(1)
13.7 Exercises
379(1)
13.8 Computer laboratory
380(1)
References
380(1)
Appendix 13.1 MATLAB code implementations
381(6)
14 Variational methods for shape registration
387(30)
14.1 Introduction
387(2)
14.2 Shape modeling
389(5)
14.2.1 Parametric representations
389(1)
14.2.2 Landmark-based representation
390(1)
14.2.3 Medial axes representation
391(1)
14.2.4 Implicit representation using the vector distance function
392(1)
14.2.5 Implicit representation using distance transform
392(2)
14.3 Global registration of shapes in implicit spaces
394(9)
14.3.1 Global matching of shapes
394(3)
14.3.2 VDF-based dissimilarity measure
397(1)
14.3.3 SDF-based dissimilarity measure
398(2)
14.3.4 Examples
400(3)
14.4 Local shape registration
403(10)
14.4.1 Local alignment
405(3)
14.4.2 Gradient descent flows and numerical implementation
408(5)
14.5 Summary
413(1)
References
414(3)
15 Statistical models of shape and appearance
417(41)
15.1 Introduction
417(1)
15.2 Statistical shape models
417(11)
15.2.1 Construction of statistical shape model using PCA
419(2)
15.2.2 Fitting a model to new points
421(1)
15.2.3 Statistical modeling of structures
422(2)
15.2.4 Modeling shape variations
424(4)
15.3 Statistical appearance models
428(8)
15.3.1 Image warping
428(1)
15.3.2 One-dimensional thin-plate splines
429(1)
15.3.3 N-dimensional thin-plate splines
429(2)
15.3.4 Statistical appearance model construction using PCA
431(2)
15.3.5 Combined appearance models
433(3)
15.4 Analysis of lung nodules in low-dose CT (LDCT) scans
436(5)
15.4.1 Lung nodules in low-dose CT
437(4)
15.5 Appearance-based approach for complete human jaw reconstruction
441(7)
15.5.1 Jaw prior models
444(1)
15.5.2 Model-based shape and albedo recovery
445(1)
15.5.3 Sample results
446(2)
15.6 Summary
448(1)
References
448(2)
Appendix 15.1 Pseudocodes and MATLAB realizations
450(8)
Index 458
Aly A. Farag is a Professor of Electrical and Computer Engineering, and founding Director of the Computer Vision and Image Processing Laboratory, at the University of Louisville. His research interests centre around object modelling with biomedical applications, and his more recent biomedical inventions have led to the development of improved methods for tubular object modelling, virtual colonoscopies and lung nodule detection and classification based on CT scans, real-time monitoring of vital signs from thermal imaging, and image-based reconstruction of the human jaw.
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