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Statistical Shape Analysis
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Statistical Shape Analysis
by Kanti V. Mardia, Ian L. Dryden
Statistical Shape Analysis, 2nd Edition
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
2 Size measures and shape coordinates
2.1 History
2.2 Size
2.3 Traditional shape coordinates
2.4 Bookstein shape coordinates
2.5 Kendall’s shape coordinates
2.6 Triangle shape coordinates
3 Manifolds, shape and size-and-shape
3.1 Riemannian manifolds
3.2 Shape
3.3 Size-and-shape
3.4 Reflection invariance
3.5 Discussion
4 Shape space
4.1 Shape space distances
4.2 Comparing shape distances
4.3 Planar case
4.4 Tangent space coordinates
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
5.7 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
6.8 Principal geodesic mean
6.9 Riemannian barycentres
7 Procrustes analysis
7.1 Introduction
7.2 Ordinary Procrustes analysis
7.3 Generalized Procrustes analysis
7.4 Generalized Procrustes algorithms for shape analysis
7.5 Generalized Procrustes algorithms for size-and-shape analysis
7.6 Variants of generalized Procrustes analysis
7.7 Shape variability: principal component 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
9.2 Inference using Procrustes statistics under isotropy
9.3 Size-and-shape tests
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
10.3 Complex Watson distribution
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
10.10 Size-and-shape versus shape
11 Offset normal shape distributions
11.1 Introduction
11.2 Offset normal shape distributions with general covariances
11.3 Inference for offset normal distributions
11.4 Practical inference
11.5 Offset normal size-and-shape distributions
11.6 Distributions for higher dimensions
12 Deformations for size and shape change
12.1 Deformations
12.2 Affine transformations
12.3 Pairs of thin-plate splines
12.4 Alternative approaches and history
12.5 Kriging
12.6 Diffeomorphic transformations
13 Non-parametric inference and regression
13.1 Consistency
13.2 Uniqueness of intrinsic means
13.3 Non-parametric inference
13.4 Principal geodesics and shape curves
13.5 Statistical shape change
13.6 Robustness
13.7 Incomplete data
14 Unlabelled size-and-shape and shape analysis
14.1 The Green–Mardia model
14.2 Procrustes model
14.3 Related methods
14.4 Unlabelled points
15 Euclidean methods
15.1 Distance-based methods
15.2 Multidimensional scaling
15.3 Multidimensional scaling shape means
15.4 Euclidean distance matrix analysis for size-and-shape analysis
15.5 Log-distances and multivariate analysis
15.6 Euclidean shape tensor analysis
15.7 Distance methods versus geometrical methods
16 Curves, surfaces and volumes
16.1 Shape factors and random sets
16.2 Outline data
16.3 Semi-landmarks
16.4 Square root velocity function
16.5 Curvature and torsion
16.6 Surfaces
16.7 Curvature, ridges and solid shape
17 Shape in images
17.1 Introduction
17.2 High-level Bayesian image analysis
17.3 Prior models for objects
17.4 Warping and image averaging
18 Object data and manifolds
18.1 Object oriented data analysis
18.2 Trees
18.3 Topological data analysis
18.4 General shape spaces and generalized Procrustes methods
18.5 Other types of shape
18.6 Manifolds
18.7 Reviews
Exercises
Appendix
References
Index
WILEY SERIES IN PROBABILITY AND STATISTICS
EULA
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