http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
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.
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.
edited by Alejandro Frangi, Jerry Prince, Milan Sonka.