Statistical Shape Analysis: With Applications in R

Front Cover
John Wiley & Sons, Jun 28, 2016 - Mathematics - 496 pages

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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Contents

1 Introduction
1
2 Size measures and shape coordinates
31
3 Manifolds shape and sizeandshape
59
4 Shape space
69
5 Sizeandshape space
99
6 Manifold means
111
7 Procrustes analysis
125
8 2D Procrustes analysis using complex arithmetic
175
14 Unlabelled sizeandshape and shape analysis
341
15 Euclidean methods
353
16 Curves surfaces and volumes
363
17 Shape in images
377
18 Object data and manifolds
391
Exercises
399
Appendix
403
References
407

9 Tangent space inference
185
10 Shape and sizeandshape distributions
217
11 Offset normal shape distributions
239
12 Deformations for size and shape change
269
13 Nonparametric inference and regression
317
Index
449
WILEY SERIES IN PROBABILITY AND STATISTICS
455
Supplemental Images
467
EULA
483
Copyright

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About the author (2016)

Ian Dryden, University of Nottingham, UK

Kanti Mardia, University of Leeds and University of Oxford, UK

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