Medical Image Analysis (The MICCAI Society book Series)

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
		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 – 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 Encoder–decoder 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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