Statistical shape analysis with applications in R

Detalles Bibliográficos
Otros Autores:	Dryden, I. L. author (author), Mardia, K. V., author
Formato:	Libro electrónico
Idioma:	Inglés
Publicado:	Chichester, West Sussex, England : Wiley 2016.
Edición:	Second edition
Colección:	Wiley series in probability and statistics. THEi Wiley ebooks.
Materias:	Form perception.
Ver en Biblioteca Universitat Ramon Llull:	https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009849135306719

Tabla de Contenidos:

Intro
Statistical Shape Analysis
Contents
Preface
Preface to the first edition
Acknowledgements for the first edition
1 Introduction
1.1 Definition and motivation
1.2 Landmarks
1.3 The shapes package in R
1.4 Practical applications
1.4.1 Biology: Mouse vertebrae
1.4.2 Image analysis: Postcode recognition
1.4.3 Biology: Macaque skulls
1.4.4 Chemistry: Steroid molecules
1.4.5 Medicine: Schizophrenia magnetic resonance images
1.4.6 Medicine and law: Fetal alcohol spectrum disorder
1.4.7 Pharmacy: DNA molecules
1.4.8 Biology: Great ape skulls
1.4.9 Bioinformatics: Protein matching
1.4.10 Particle science: Sand grains
1.4.11 Biology: Rat skull growth
1.4.12 Biology: Sooty mangabeys
1.4.13 Physiotherapy: Human movement data
1.4.14 Genetics: Electrophoretic gels
1.4.15 Medicine: Cortical surface shape
1.4.16 Geology: Microfossils
1.4.17 Geography: Central Place Theory
1.4.18 Archaeology: Alignments of standing stones
2 Size measures and shape coordinates
2.1 History
2.2 Size
2.2.1 Configuration space
2.2.2 Centroid size
2.2.3 Other size measures
2.3 Traditional shape coordinates
2.3.1 Angles
2.3.2 Ratios of lengths
2.3.3 Penrose coefficent
2.4 Bookstein shape coordinates
2.4.1 Planar landmarks
2.4.2 Bookstein-type coordinates for 3D data
2.5 Kendall's shape coordinates
2.6 Triangle shape coordinates
2.6.1 Bookstein coordinates for triangles
2.6.2 Kendall's spherical coordinates for triangles
2.6.3 Spherical projections
2.6.4 Watson's triangle coordinates
3 Manifolds, shape and size-and-shape
3.1 Riemannian manifolds
3.2 Shape
3.2.1 Ambient and quotient space
3.2.2 Rotation
3.2.3 Coincident and collinear points
3.2.4 Removing translation
3.2.5 Pre-shape
3.2.6 Shape
3.3 Size-and-shape.
3.4 Reflection invariance
3.5 Discussion
3.5.1 Standardizations
3.5.2 Over-dimensioned case
3.5.3 Hierarchies
4 Shape space
4.1 Shape space distances
4.1.1 Procrustes distances
4.1.2 Procrustes
4.1.3 Differential geometry
4.1.4 Riemannian distance
4.1.5 Minimal geodesics in shape space
4.1.6 Planar shape
4.1.7 Curvature
4.2 Comparing shape distances
4.2.1 Relationships
4.2.2 Shape distances in R
4.2.3 Further discussion
4.3 Planar case
4.3.1 Complex arithmetic
4.3.2 Complex projective space
4.3.3 Kent's polar pre-shape coordinates
4.3.4 Triangle case
4.4 Tangent space coordinates
4.4.1 Tangent spaces
4.4.2 Procrustes tangent coordinates
4.4.3 Planar Procrustes tangent coordinates
4.4.4 Higher dimensional Procrustes tangent coordinates
4.4.5 Inverse exponential map tangent coordinates
4.4.6 Procrustes residuals
4.4.7 Other tangent coordinates
4.4.8 Tangent space coordinates in R
5 Size-and-shape space
5.1 Introduction
5.2 Root mean square deviation measures
5.3 Geometry
5.4 Tangent coordinates for size-and-shape space
5.5 Geodesics
5.6 Size-and-shape coordinates
5.6.1 Bookstein-type coordinates for size-and-shape analysis
5.6.2 Goodall-Mardia QR size-and-shape coordinates
5.7 Allometry
6 Manifold means
6.1 Intrinsic and extrinsic means
6.2 Population mean shapes
6.3 Sample mean shape
6.4 Comparing mean shapes
6.5 Calculation of mean shapes in R
6.6 Shape of the means
6.7 Means in size-and-shape space
6.7.1 Fréchet and Karcher means
6.7.2 Size-and-shape of the means
6.8 Principal geodesic mean
6.9 Riemannian barycentres
7 Procrustes analysis
7.1 Introduction
7.2 Ordinary Procrustes analysis
7.2.1 Full OPA
7.2.2 OPA in R
7.2.3 Ordinary partial Procrustes.
7.2.4 Reflection Procrustes
7.3 Generalized Procrustes analysis
7.3.1 Introduction
7.4 Generalized Procrustes algorithms for shape analysis
7.4.1 Algorithm: GPA-Shape-1
7.4.2 Algorithm: GPA-Shape-2
7.4.3 GPA in R
7.5 Generalized Procrustes algorithms for size-and-shape analysis
7.5.1 Algorithm: GPA-Size-and-Shape-1
7.5.2 Algorithm: GPA-Size-and-Shape-2
7.5.3 Partial GPA in R
7.5.4 Reflection GPA in R
7.6 Variants of generalized Procrustes analysis
7.6.1 Summary
7.6.2 Unit size partial Procrustes
7.6.3 Weighted Procrustes analysis
7.7 Shape variability: principal component analysis
7.7.1 Shape PCA
7.7.2 Kent's shape PCA
7.7.3 Shape PCA in R
7.7.4 Point distribution models
7.7.5 PCA in shape analysis and multivariate analysis
7.8 Principal component analysis for size-and-shape
7.9 Canonical variate analysis
7.10 Discriminant analysis
7.11 Independent component analysis
7.12 Bilateral symmetry
8 2D Procrustes analysis using complex arithmetic
8.1 Introduction
8.2 Shape distance and Procrustes matching
8.3 Estimation of mean shape
8.4 Planar shape analysis in R
8.5 Shape variability
9 Tangent space inference
9.1 Tangent space small variability inference for mean shapes
9.1.1 One sample Hotelling's test
9.1.2 Two independent sample Hotelling's test
9.1.3 Permutation and bootstrap tests
9.1.4 Fast permutation and bootstrap tests
9.1.5 Extensions and regularization
9.2 Inference using Procrustes statistics under isotropy
9.2.1 One sample Goodall's test and perturbation model
9.2.2 Two independent sample Goodall's test
9.2.3 Further two sample tests
9.2.4 One way analysis of variance
9.3 Size-and-shape tests
9.3.1 Tests using Procrustes size-and-shape tangent space.
9.3.2 Case-study: Size-and-shape analysis and mutation
9.4 Edge-based shape coordinates
9.5 Investigating allometry
10 Shape and size-and-shape distributions
10.1 The uniform distribution
10.2 Complex Bingham distribution
10.2.1 The density
10.2.2 Relation to the complex normal distribution
10.2.3 Relation to real Bingham distribution
10.2.4 The normalizing constant
10.2.5 Properties
10.2.6 Inference
10.2.7 Approximations and computation
10.2.8 Relationship with the Fisher-von Mises distribution
10.2.9 Simulation
10.3 Complex Watson distribution
10.3.1 The density
10.3.2 Inference
10.3.3 Large concentrations
10.4 Complex angular central Gaussian distribution
10.5 Complex Bingham quartic distribution
10.6 A rotationally symmetric shape family
10.7 Other distributions
10.8 Bayesian inference
10.9 Size-and-shape distributions
10.9.1 Rotationally symmetric size-and-shape family
10.9.2 Central complex Gaussian distribution
10.10 Size-and-shape versus shape
11 Offset normal shape distributions
11.1 Introduction
11.1.1 Equal mean case in two dimensions
11.1.2 The isotropic case in two dimensions
11.1.3 The triangle case
11.1.4 Approximations: Large and small variations
11.1.5 Exact moments
11.1.6 Isotropy
11.2 Offset normal shape distributions with general covariances
11.2.1 The complex normal case
11.2.2 General covariances: Small variations
11.3 Inference for offset normal distributions
11.3.1 General MLE
11.3.2 Isotropic case
11.3.3 Exact isotropic MLE in R
11.3.4 EM algorithm and extensions
11.4 Practical inference
11.5 Offset normal size-and-shape distributions
11.5.1 The isotropic case
11.5.2 Inference using the offset normal size-and-shape model
11.6 Distributions for higher dimensions
11.6.1 Introduction.
11.6.2 QR decomposition
11.6.3 Size-and-shape distributions
11.6.4 Multivariate approach
11.6.5 Approximations
12 Deformations for size and shape change
12.1 Deformations
12.1.1 Introduction
12.1.2 Definition and desirable properties
12.1.3 D'Arcy Thompson's transformation grids
12.2 Affine transformations
12.2.1 Exact match
12.2.2 Least squares matching: Two objects
12.2.3 Least squares matching: Multiple objects
12.2.4 The triangle case: Bookstein's hyperbolic shape space
12.3 Pairs of thin-plate splines
12.3.1 Thin-plate splines
12.3.2 Transformation grids
12.3.3 Thin-plate splines in R
12.3.4 Principal and partial warp decompositions
12.3.5 PCA with non-Euclidean metrics
12.3.6 Relative warps
12.4 Alternative approaches and history
12.4.1 Early transformation grids
12.4.2 Finite element analysis
12.4.3 Biorthogonal grids
12.5 Kriging
12.5.1 Universal kriging
12.5.2 Deformations
12.5.3 Intrinsic kriging
12.5.4 Kriging with derivative constraints
12.5.5 Smoothed matching
12.6 Diffeomorphic transformations
13 Non-parametric inference and regression
13.1 Consistency
13.2 Uniqueness of intrinsic means
13.3 Non-parametric inference
13.3.1 Central limit theorems and non-parametric tests
13.3.2 M-estimators
13.4 Principal geodesics and shape curves
13.4.1 Tangent space methods and longitudinal data
13.4.2 Growth curve models for triangle shapes
13.4.3 Geodesic model
13.4.4 Principal geodesic analysis
13.4.5 Principal nested spheres and shape spaces
13.4.6 Unrolling and unwrapping
13.4.7 Manifold splines
13.5 Statistical shape change
13.5.1 Geometric components of shape change
13.5.2 Paired shape distributions
13.6 Robustness
13.7 Incomplete data
14 Unlabelled size-and-shape and shape analysis.
14.1 The Green-Mardia model.

Statistical shape analysis with applications in R

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