Statistical shape analysis : with applications in R / Ian L. Dryden, Kanti V. Mardia.

Format:

Book

Author/Creator:

Dryden, I. L. (Ian L.), author.

Mardia, K. V., author.

Series:

Wiley series in probability and statistics.

THEi Wiley ebooks.

Wiley Series in Probability and Statistics

THEi Wiley ebooks

Standardized Title:

Statistical shape analysis

Language:

English

Subjects (All):

Form perception.

Physical Description:

1 online resource (511 p.)

Edition:

Second edition.

Place of Publication:

Chichester, West Sussex, England : Wiley, 2016.

Language Note:

English

System Details:

Access using campus network via VPN at home (THEi Users Only).

Summary:

A thoroughly revised and updated edition of this introduction to modern statistical methods for shape analysis Shape analysis is an important tool in the many disciplines where objects are compared using geometrical features. Examples include comparing brain shape in schizophrenia; investigating protein molecules in bioinformatics; and describing growth of organisms in biology. This book is a significant update of the highly-regarded Statistical Shape Analysis by the same authors. The new edition lays the foundations of landmark shape analysis, including geometrical concepts and statistical techniques, and extends to include analysis of curves, surfaces, images and other types of object data. Key definitions and concepts are discussed throughout, and the relative merits of different approaches are presented. The authors have included substantial new material on recent statistical developments and offer numerous examples throughout the text. Concepts are introduced in an accessible manner, while retaining sufficient detail for more specialist statisticians to appreciate the challenges and opportunities of this new field. Computer code has been included for instructional use, along with exercises to enable readers to implement the applications themselves in R and to follow the key ideas by hands-on analysis. * Offers a detailed yet accessible treatment of statistical methods for shape analysis * Includes numerous examples and applications from many disciplines * Provides R code for implementing the examples * Covers a wide variety of recent developments in shape analysis Shape Analysis, with Applications in R will offer a valuable introduction to this fast-moving research area for statisticians and other applied scientists working in diverse areas, including archaeology, bioinformatics, biology, chemistry, computer science, medicine, morphometics and image analysis.

Contents:

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.

Notes:

Originally published as: Statistical shape analysis, 1998

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed Aug. 1, 2016).

ISBN:

9781119072515

1119072514

9781119072508

1119072506

9781119072492

1119072492

OCLC:

946076305