Medical image analysis /

Medical Image Analysis presents practical knowledge on medical image computing and analysis as written by top educators and experts.This text is a modern, practical, self-contained reference that conveys a mix of fundamental methodological concepts within different medical domains.

Bibliographic Details
Corporate Author:	ScienceDirect (Online service)
Other Authors:	Frangi, Alejandro F., Prince, Jerry, Sonka, Milan
Format:	eBook
Language:	English
Published:	London : Academic Press, [2024].
Series:	The MICCAI Society book series
Subjects:	Diagnostic imaging. Imaging systems in medicine. Diagnostic Imaging Imagerie pour le diagnostic. Imagerie médicale. Diagnostic imaging Imaging systems in medicine Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Front Cover
Medical Image Analysis
Copyright
Section editors
Contents
Editors
Contributors
Preface
Nomenclature
Acknowledgments
Part I Introductory topics
1 Medical imaging modalities
1.1 Introduction
1.2 Image quality
1.2.1 Resolution and noise
1.2.2 Comparing image appearance
1.2.3 Task-based assessment
1.3 Modalities and contrast mechanisms
1.3.1 X-ray transmission imaging
1.3.2 Molecular imaging
1.3.3 Optical imaging
1.3.4 Large wavelengths and transversal waves
1.3.5 A historical perspective on medical imaging
1.3.6 Simulating image formation
1.4 Clinical scenarios
1.4.1 Stroke
1.4.2 Oncology
1.4.3 Osteonecrosis
1.5 Exercises
References
2 Mathematical preliminaries
2.1 Introduction
2.2 Imaging: definitions, quality and similarity measures
2.3 Vector and matrix theory results
2.3.1 General concepts
2.3.2 Eigenanalysis
2.3.3 Singular value decomposition
2.3.4 Matrix exponential
2.3.4.1 Generalities
2.3.4.2 An example which gives rise to a matrix exponential
2.4 Linear processing and transformed domains
2.4.1 Linear processing. Convolution
2.4.2 Transformed domains
2.4.2.1 1D Fourier transform
2.4.2.2 2D Fourier transform
2.4.2.3 N-dimensional Fourier transform
2.5 Calculus
2.5.1 Derivatives, gradients, and Laplacians
2.5.2 Calculus of variations
2.5.3 Some specific cases
2.5.3.1 Laplace equation
2.5.3.2 Heat (or diffusion) equation
2.5.4 Leibniz rule for interchanging integrals and derivatives
2.6 Notions on shapes
2.6.1 Procrustes matching between two planar shapes
2.6.2 Mean shape
2.6.3 Procrustes analysis in higher dimensions
2.7 Exercises
References
3 Regression and classification
3.1 Introduction
Nomenclature
3.1.1 Regression as a minimization problem.
3.1.2 Regression from the statistical angle
3.2 Multidimensional linear regression
3.2.1 Direction of prediction
3.2.2 Risk minimization
3.2.2.1 Gauss-Markov theorem
3.2.3 Measures of fitting and prediction quality
3.2.4 Out-of-sample performance: cross-validation methods
3.2.5 Shrinkage methods
3.2.5.1 Dealing with multicollinearity: ridge regression
3.2.5.2 Dealing with sparsity: the LASSO
3.2.5.3 Other general regularizers
3.3 Treating non-linear problems with linear models
3.3.1 Generalized linear models: transforming y
3.3.1.1 Classification as a regression problem: logistic regression
3.3.2 Feature spaces: transforming X
3.3.2.1 Categorical variables
3.3.2.2 Linearizing non-linear regression: functional bases
3.3.3 Going further
3.4 Exercises
References
4 Estimation and inference
4.1 Introduction: what is estimation?
4.2 Sampling distributions
4.2.1 Cumulative distribution function
4.2.2 The Kolmogorov-Smirnov test
4.2.3 Histogram as probability density function estimate
4.2.4 The chi-squared test
4.3 Estimation. Data-based methods
4.3.1 Definition of estimator and criteria for design and performance measurement
4.3.2 A benchmark for unbiased estimators: the Cramer-Rao lower bound
4.3.3 Maximum likelihood estimator
4.3.4 The expectation-maximization method
4.4 A working example
4.5 Estimation. Bayesian methods
4.5.1 Definition of Bayesian estimator and design criteria
4.5.2 Design criteria for Bayesian estimators
4.5.3 Performance measurement
4.5.4 The Gaussian case
4.5.5 Conjugate distribution and conjugate priors
4.5.6 A working example
4.6 Monte Carlo methods
4.6.1 A non-stochastic use of Monte Carlo
4.7 Exercises
References
Part II Image representation and processing.
5 Image representation and 2D signal processing
5.1 Image representation
5.2 Images as 2D signals
5.2.1 Linear space-invariant systems
Properties of 2D convolution
5.2.2 Linear Circular Invariance systems
5.3 Frequency representation of 2D signals
5.3.1 Fourier transform of continuous signals
5.3.2 Discrete-space Fourier transform
5.3.3 2D discrete Fourier transform
5.3.4 Discrete cosine transform
5.4 Image sampling
5.4.1 Introduction
5.4.2 Basics on 2D sampling theory
5.4.2.1 Inexact reconstruction
5.4.3 Nyquist sampling density
5.5 Image interpolation
5.5.1 Typical interpolator kernels
5.5.1.1 Windowed sinc
5.5.1.2 Nearest neighbor interpolation
5.5.1.3 Linear interpolation
5.5.1.4 Cubic interpolation
5.6 Image quantization
5.7 Further reading
5.8 Exercises
References
6 Image filtering: enhancement and restoration
6.1 Medical imaging filtering
6.2 Point-to-point operations
6.2.1 Basic operations
6.2.2 Contrast enhancement
6.2.3 Histogram processing
Histogram equalization
Histogram specification
6.3 Spatial operations
6.3.1 Linear filtering
Smoothing filters
Highlighting borders and small details
6.3.2 Non-linear filters
Median filter
Pseudomedian filter
6.4 Operations in the transform domain
6.4.1 Linear filters in the frequency domain
6.4.2 Homomorphic processing
6.5 Model-based filtering: image restoration
6.5.1 Noise models
6.5.2 Point spread function
6.5.3 Image restoration methods
6.6 Further reading
6.7 Exercises
References
7 Multiscale and multiresolution analysis
7.1 Introduction
7.2 The image pyramid
7.3 The Gaussian scale-space
7.4 Properties of the Gaussian scale-space
7.4.1 The frequency perspective
7.4.2 The semi-group property
7.4.3 The analytical perspective.
7.4.4 The heat diffusion perspective
7.5 Scale selection
7.5.1 Blob detection
7.5.2 Edge detection
7.6 The scale-space histogram
7.7 Exercises
References
Part III Medical image segmentation
8 Statistical shape models
8.1 Introduction
8.2 Representing structures with points
8.3 Comparing shapes
8.4 Aligning two shapes
8.5 Aligning a set of shapes
8.5.1 Algorithm for aligning sets of shapes
8.5.2 Example of aligning shapes
8.6 Building shape models
8.6.1 Choosing the number of modes
8.6.2 Examples of shape models
8.6.3 Matching a model to known points
8.7 Statistical models of texture
8.8 Combined models of appearance (shape and texture)
8.9 Image search
8.10 Exhaustive search
8.10.1 Regression voting
8.11 Alternating approaches
8.11.1 Searching for each point
8.11.2 Shape model as regularizer
8.12 Constrained local models
8.12.1 Iteratively updating parameters
8.12.2 Extracting features
8.12.3 Updating parameters
8.13 3D models
8.14 Recapitulation
8.15 Exercises
References
9 Segmentation by deformable models
9.1 Introduction
9.2 Boundary evolution
9.2.1 Marker evolution
9.2.2 Level set evolution
9.3 Forces and speed functions
9.3.1 Parametric model forces
9.3.2 Geometric model speed functions
9.3.3 Non-conservative external forces
9.4 Numerical implementation
9.4.1 Parametric model implementation
9.4.2 Geometric model implementation
9.5 Other considerations
9.6 Recapitulation
9.7 Exercises
References
10 Graph cut-based segmentation
10.1 Introduction
10.2 Graph theory
10.2.1 What is a graph?
10.2.2 Flow networks, max flow, and min cut
10.3 Modeling image segmentation using Markov random fields
10.4 Energy function, image term, and regularization term
10.4.1 Image term.
10.4.2 Regularization term
10.5 Graph optimization and necessary conditions
10.5.1 Energy minimization and minimum cuts
10.5.2 Necessary conditions
10.5.3 Minimum cut graph construction
10.5.4 Limitations (and solutions)
10.6 Interactive segmentation
10.6.1 Hard constraints and user interaction
10.6.2 Example: coronary arteries in CT angiography
10.7 More than two labels
10.7.1 Move-making algorithm(s)
10.7.2 Ordered labels and convex priors
10.7.3 Optimal surfaces
10.7.4 Example: airways in CT
10.8 Recapitulation
10.9 Exercises
References
Part IV Medical image registration
11 Points and surface registration
11.1 Introduction
11.2 Points registration
11.2.1 Procrustes analysis for aligning corresponding point sets
11.2.2 Quaternion algorithm for registering two corresponding point sets
11.2.3 Iterative closest point algorithm for general points registration
11.2.4 Thin plate spline for non-rigid alignment of two corresponding point sets
11.3 Surface registration
11.3.1 Surface mesh representation
11.3.2 Surface parameterization
11.3.2.1 Conformal open surface parameterization
11.3.2.2 Area-preserving spherical parameterization
11.3.3 Surface registration strategies
11.3.3.1 SPHARM surface registration
11.3.3.2 Landmark-guided SPHARM surface registration
11.3.3.3 Landmark-guided open surface registration
11.4 Summary
11.5 Exercises
References
12 Graph matching and registration
12.1 Introduction
12.2 Graph-based image registration
12.2.1 Graphical model construction
12.2.2 Optimization
12.2.3 Application to lung registration
12.2.4 Conclusion
12.3 Exercises
References
13 Parametric volumetric registration
13.1 Introduction to volumetric registration
13.1.1 Definition and applications
13.1.2 VR as energy minimization.