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Statistical Shape Analysis, 2nd Edition

Book Description

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.

Statistical 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

 

 

 

 

 

 

 

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Table of Contents

  1. Preface
  2. Preface to the first edition
  3. Acknowledgements for the first edition
  4. 1 Introduction
    1. 1.1 Definition and motivation
    2. 1.2 Landmarks
    3. 1.3 The shapes package in R
    4. 1.4 Practical applications
  5. 2 Size measures and shape coordinates
    1. 2.1 History
    2. 2.2 Size
    3. 2.3 Traditional shape coordinates
    4. 2.4 Bookstein shape coordinates
    5. 2.5 Kendall’s shape coordinates
    6. 2.6 Triangle shape coordinates
  6. 3 Manifolds, shape and size-and-shape
    1. 3.1 Riemannian manifolds
    2. 3.2 Shape
    3. 3.3 Size-and-shape
    4. 3.4 Reflection invariance
    5. 3.5 Discussion
  7. 4 Shape space
    1. 4.1 Shape space distances
    2. 4.2 Comparing shape distances
    3. 4.3 Planar case
    4. 4.4 Tangent space coordinates
  8. 5 Size-and-shape space
    1. 5.1 Introduction
    2. 5.2 Root mean square deviation measures
    3. 5.3 Geometry
    4. 5.4 Tangent coordinates for size-and-shape space
    5. 5.5 Geodesics
    6. 5.6 Size-and-shape coordinates
    7. 5.7 Allometry
  9. 6 Manifold means
    1. 6.1 Intrinsic and extrinsic means
    2. 6.2 Population mean shapes
    3. 6.3 Sample mean shape
    4. 6.4 Comparing mean shapes
    5. 6.5 Calculation of mean shapes in R
    6. 6.6 Shape of the means
    7. 6.7 Means in size-and-shape space
    8. 6.8 Principal geodesic mean
    9. 6.9 Riemannian barycentres
  10. 7 Procrustes analysis
    1. 7.1 Introduction
    2. 7.2 Ordinary Procrustes analysis
    3. 7.3 Generalized Procrustes analysis
    4. 7.4 Generalized Procrustes algorithms for shape analysis
    5. 7.5 Generalized Procrustes algorithms for size-and-shape analysis
    6. 7.6 Variants of generalized Procrustes analysis
    7. 7.7 Shape variability: principal component analysis
    8. 7.8 Principal component analysis for size-and-shape
    9. 7.9 Canonical variate analysis
    10. 7.10 Discriminant analysis
    11. 7.11 Independent component analysis
    12. 7.12 Bilateral symmetry
  11. 8 2D Procrustes analysis using complex arithmetic
    1. 8.1 Introduction
    2. 8.2 Shape distance and Procrustes matching
    3. 8.3 Estimation of mean shape
    4. 8.4 Planar shape analysis in R
    5. 8.5 Shape variability
  12. 9 Tangent space inference
    1. 9.1 Tangent space small variability inference for mean shapes
    2. 9.2 Inference using Procrustes statistics under isotropy
    3. 9.3 Size-and-shape tests
    4. 9.4 Edge-based shape coordinates
    5. 9.5 Investigating allometry
  13. 10 Shape and size-and-shape distributions
    1. 10.1 The uniform distribution
    2. 10.2 Complex Bingham distribution
    3. 10.3 Complex Watson distribution
    4. 10.4 Complex angular central Gaussian distribution
    5. 10.5 Complex Bingham quartic distribution
    6. 10.6 A rotationally symmetric shape family
    7. 10.7 Other distributions
    8. 10.8 Bayesian inference
    9. 10.9 Size-and-shape distributions
    10. 10.10 Size-and-shape versus shape
  14. 11 Offset normal shape distributions
    1. 11.1 Introduction
    2. 11.2 Offset normal shape distributions with general covariances
    3. 11.3 Inference for offset normal distributions
    4. 11.4 Practical inference
    5. 11.5 Offset normal size-and-shape distributions
    6. 11.6 Distributions for higher dimensions
  15. 12 Deformations for size and shape change
    1. 12.1 Deformations
    2. 12.2 Affine transformations
    3. 12.3 Pairs of thin-plate splines
    4. 12.4 Alternative approaches and history
    5. 12.5 Kriging
    6. 12.6 Diffeomorphic transformations
  16. 13 Non-parametric inference and regression
    1. 13.1 Consistency
    2. 13.2 Uniqueness of intrinsic means
    3. 13.3 Non-parametric inference
    4. 13.4 Principal geodesics and shape curves
    5. 13.5 Statistical shape change
    6. 13.6 Robustness
    7. 13.7 Incomplete data
  17. 14 Unlabelled size-and-shape and shape analysis
    1. 14.1 The Green–Mardia model
    2. 14.2 Procrustes model
    3. 14.3 Related methods
    4. 14.4 Unlabelled points
  18. 15 Euclidean methods
    1. 15.1 Distance-based methods
    2. 15.2 Multidimensional scaling
    3. 15.3 Multidimensional scaling shape means
    4. 15.4 Euclidean distance matrix analysis for size-and-shape analysis
    5. 15.5 Log-distances and multivariate analysis
    6. 15.6 Euclidean shape tensor analysis
    7. 15.7 Distance methods versus geometrical methods
  19. 16 Curves, surfaces and volumes
    1. 16.1 Shape factors and random sets
    2. 16.2 Outline data
    3. 16.3 Semi-landmarks
    4. 16.4 Square root velocity function
    5. 16.5 Curvature and torsion
    6. 16.6 Surfaces
    7. 16.7 Curvature, ridges and solid shape
  20. 17 Shape in images
    1. 17.1 Introduction
    2. 17.2 High-level Bayesian image analysis
    3. 17.3 Prior models for objects
    4. 17.4 Warping and image averaging
  21. 18 Object data and manifolds
    1. 18.1 Object oriented data analysis
    2. 18.2 Trees
    3. 18.3 Topological data analysis
    4. 18.4 General shape spaces and generalized Procrustes methods
    5. 18.5 Other types of shape
    6. 18.6 Manifolds
    7. 18.7 Reviews
  22. Exercises
  23. Appendix
  24. References
  25. Index
  26. WILEY SERIES IN PROBABILITY AND STATISTICS
  27. EULA