Statistical Shape Analysis : With Applications in R.
- 2nd ed.
- 1 online resource (511 pages)
- Wiley Series in Probability and Statistics Series ; v.995 .
- Wiley Series in Probability and Statistics Series .
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.