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
.
Table of contents
- Preface
- Preface to the first edition
- Acknowledgements for the first edition
- 1 Introduction
- 2 Size measures and shape coordinates
- 3 Manifolds, shape and size-and-shape
- 4 Shape space
- 5 Size-and-shape space
- 6 Manifold means
-
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
- 9 Tangent space inference
-
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
- 12 Deformations for size and shape change
- 13 Non-parametric inference and regression
- 14 Unlabelled size-and-shape and shape analysis
- 15 Euclidean methods
- 16 Curves, surfaces and volumes
- 17 Shape in images
- 18 Object data and manifolds
- Exercises
- Appendix
- References
- Index
- WILEY SERIES IN PROBABILITY AND STATISTICS
- EULA
Product information
- Title: Statistical Shape Analysis, 2nd Edition
- Author(s):
- Release date: September 2016
- Publisher(s): Wiley
- ISBN: 9780470699621
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