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 GaussβMarkov 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 KolmogorovβSmirnov 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 CramerβRao 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
13.2 Mathematical concepts
13.2.1 Transformation
13.2.2 Transformation vs. displacement
13.2.3 Function composition
13.2.4 Computer implementation of transformations
13.2.5 Jacobian matrix and determinant
13.3 Parametric volumetric registration
13.3.1 Transformations
13.3.1.1 Affine transformations
13.3.1.2 Rotation in 3D
13.3.1.3 B-spline transformations
13.3.1.4 Radial basis functions
13.3.2 Optimization
13.3.3 Real-world approaches
13.4 Exercises
References
14 Non-parametric volumetric registration
14.1 Introduction
14.2 Mathematical concepts
14.2.1 Diffeomorphisms
14.2.1.1 Group of diffeomorphisms
14.2.1.2 Small transformations
14.2.1.3 Flow ordinary differential equation
14.2.1.4 Scaling and squaring algorithm
14.3 Optical flow and related non-parametric methods
14.3.1 Conventional optical flow approach
14.3.1.1 Preservation of intensity assumption
14.3.1.2 Smoothness assumption and formulation as energy minimization
14.3.1.3 Basic implementation
14.3.1.4 Limitations of optical flow
14.3.2 Iterative optical flow
14.3.2.1 Conceptual NVR algorithm based on optical flow
14.3.2.2 The Demons algorithm
14.3.2.3 Log-domain diffeomorphic Demons algorithm
14.4 Large deformation diffeomorphic metric mapping
14.4.1 LDDMM formulation
14.4.2 Approaches to solving the LDDMM problem
14.4.2.1 Direct minimization over the time-varying velocity field
14.4.2.2 Geodesic shooting
14.4.3 LDDMM and computational anatomy
14.4.3.1 Defining distance on the space of diffeomorphic transformations
14.4.3.2 Defining distance on the space of images
14.4.3.3 Applications to statistical analysis of images
14.5 Exercises
References
15 Image mosaicking
15.1 Introduction
15.2 Motion models
15.2.1 Image transformations
15.2.2 Affine transformation
15.2.3 Projective transformation or homography
15.2.4 Cylindrical and spherical modeling
15.3 Matching
15.3.1 Feature-based methods
15.3.2 Direct methods
15.3.3 Deep learning-based methods
15.3.4 Computing homography β image mosaicking
15.3.5 Reprojection and blending
15.4 Clinical applications
15.4.1 Panoramic X-ray in radiography
15.4.2 Whole slide mosaicking in histopathology
15.4.3 Cystoscopy in urology
15.4.4 Slit-lamp image stitching for ophthalmology
15.4.5 Fetal interventions and fetoscopy
15.4.6 General surgery view expansion
15.5 Recapitulation
15.6 Exercises
References
Part V Machine learning in medical image analysis
16 Deep learning fundamentals
16.1 Introduction
16.2 Learning as optimization
16.2.1 Multilayer perceptron
16.2.2 Activation functions
16.2.3 Loss functions
16.2.4 Weight optimization
16.2.5 Normalization in deep learning
16.2.6 Regularization in deep learning
16.3 Inductive bias, invariance, and equivariance
16.4 Recapitulation
16.5 Further reading
16.6 Exercises
References
17 Deep learning for vision and representation learning
17.1 Introduction
17.2 Convolutional neural networks
17.2.1 Convolution arithmetic
17.2.2 Forward and backward passes
17.2.3 Pooling operations
17.2.4 Dilated convolutions
17.2.5 Transposed convolutions
17.2.6 Residual (skip) connections
17.3 Deep representation learning
17.3.1 Autoencoder architecture
17.3.2 Denoising autoencoders
17.3.3 Variational autoencoders
17.3.4 Multichannel variational autoencoders
17.3.5 Contrastive learning
17.3.6 Framework, loss functions, and interpretation
17.3.7 Contrastive learning with negative samples
17.3.8 Contrastive learning without negative samples
17.4 Recapitulation
17.5 Further reading
17.6 Exercises
References
18 Deep learning medical image segmentation
18.1 Introduction
18.2 Convolution-based deep learning segmentation
18.3 Transformer-based deep learning segmentation
18.3.1 Scaled dot-product attention
18.3.2 Positional embedding
18.3.3 Vision transformers
18.4 Hybrid deep learning segmentation
18.4.1 Deep LOGISMOS
18.4.2 Machine-learned cost function
18.4.3 Just-enough interaction
18.5 Training efficiency
18.6 Explainability
18.6.1 Image attribution
18.6.2 Attention gates
18.7 Case study
18.8 Recapitulation
18.9 Further reading
18.10 Exercises
References
19 Machine learning in image registration
19.1 Introduction
19.2 Image registration with deep learning
19.3 Deep neural network architecture
19.4 Supervised image registration
19.4.1 Supervision via conventional image registration
19.4.2 Supervision via synthetic transformations
19.5 Unsupervised image registration
19.5.1 Image similarity as a loss
19.5.2 Metric learning
19.5.3 Regularization and image folding
19.5.4 Auxiliary losses
19.6 Recapitulation
19.7 Exercises
References
Part VI Advanced topics in medical image analysis
20 Motion and deformation recovery and analysis
20.1 Introduction
20.1.1 Notation: displacement, deformation, and strain
20.2 The unmet clinical need
20.3 Image-centric flow fields: Eulerian analysis
20.3.1 Motion analysis with non-rigid image registration
20.3.2 Optical flow
20.4 Object-centric, locally derived flow fields: Lagrangian analysis
20.4.1 Feature-based tracking
20.4.2 Displacement regularization
20.5 Multiframe analysis: Kalman filters, particle tracking
20.6 Advanced strategies: model-based analysis and data-driven deep learning
20.6.1 Model-based strategies: biomechanics and deformation analysis
20.6.2 Deep learning for displacement field regularization
20.6.3 Deep learning for integrated motion tracking and segmentation
20.7 Evaluation
20.8 Recapitulation
20.9 Exercises
References
21 Imaging Genetics
21.1 Introduction
21.1.1 Heritability
21.1.2 Genetic variation
21.2 Genome-wide association studies
21.2.1 Genotyping using microarray technology
21.2.2 Processing SNP data
21.2.3 Imputation
21.2.4 Univariate analysis
21.2.5 Multiple testing correction
21.2.6 Adjustments for quantitative traits
21.2.7 Statistical power
21.2.8 GWAS and imaging phenotypes
21.3 Multivariate approaches to imaging genetics
21.3.1 A sketch on classical multivariate approaches
21.3.1.1 Canonical correlation analysis
21.3.1.2 Partial least squares
21.3.1.3 Iterative numerical schemes for PLS and CCA: NIPALS
21.3.1.4 Reduced-rank regression
21.3.1.5 Parallel independent component analysis
21.3.2 Regularization in multivariate imaging-genetics
21.3.2.1 Sparsity and smoothness
21.3.2.2 Groupwise penalization
21.3.3 Stability and validation of multivariate models
21.4 Exercises
References
Part VII Large-scale databases
22 Detection and quantitative enumeration of objects from large images
22.1 Introduction
22.2 Classical image analysis methods
22.2.1 Thresholding
22.2.1.1 Global thresholding
22.2.1.2 Otsu thresholding
22.2.1.3 Local threshold
22.2.1.4 Fuzzy threshold
22.2.1.5 Hysteresis threshold
22.2.2 Filtering-based methods
22.2.2.1 Template matching
22.2.2.2 Laplacian of Gaussian filter
22.3 Learning from data
22.3.1 Classical machine learning methods
22.3.1.1 Bayesian modeling
22.3.1.2 Learning correlation filters
22.3.2 Deep learning methods
22.3.2.1 Convolutional neural networks
22.3.2.2 Encoderβdecoder architecture
22.3.2.3 CNNs for centroid prediction
22.3.2.4 CNNs for object localization
22.4 Detection and counting of mitotic cells using Bayesian modeling and classical image processing
22.4.1 Detection and segmentation of MC candidates
22.4.2 Bayesian modeling for posterior map generation
22.4.3 MC candidate detection
22.4.4 Intact MC candidate region segmentation
22.4.5 Classification of MC candidates
22.5 Detection and counting of nuclei using deep learning
22.5.1 Patch extraction and data generation
22.5.2 Convolutional neural network architecture
22.5.3 Neural network optimization
22.5.4 Post-processing and cell counting
22.6 Recapitulation
22.7 Exercises
References
23 Image retrieval in big image data
23.1 Introduction
23.2 Global image descriptors for image retrieval
23.2.1 Encoding
23.2.2 Normalization
23.3 Deep learning-based image retrieval
23.4 Efficient indexing strategies
23.4.1 Vocabulary tree
23.4.2 Hashing
23.4.2.1 Data-independent hashing
23.4.2.2 Data-dependent hashing
23.5 Exercises
References
Part VIII Evaluation in medical image analysis
24 Assessment of image computing methods
24.1 The fundamental methodological concept
24.2 Introduction
24.3 Evaluation for classification tasks
24.3.1 Evaluation for binary classification tasks
24.3.2 Evaluation for continuous prediction tasks
24.4 Learning and validation
24.5 Evaluation for segmentation tasks
24.6 Evaluation of registration tasks
24.7 Intra-rater and inter-rater comparisons
24.8 Recapitulation
24.9 Exercises
References
Index
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