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The Statistical Theory of Shape

  • Christopher G. Small

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Christopher G. Small
    Pages 1-28
  3. Christopher G. Small
    Pages 29-67
  4. Christopher G. Small
    Pages 69-116
  5. Christopher G. Small
    Pages 117-148
  6. Christopher G. Small
    Pages 149-172
  7. Christopher G. Small
    Pages 173-200
  8. Back Matter
    Pages 201-227

About this book

Introduction

In general terms, the shape of an object, data set, or image can be de­ fined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measure­ ment error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statis­ tical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathe­ matical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature.

Keywords

Maxima Probability theory Transformation Variance calculus differential geometry geometry linear optimization manifold statistics

Authors and affiliations

  • Christopher G. Small
    • 1
  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4032-7
  • Copyright Information Springer-Verlag New York 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8473-4
  • Online ISBN 978-1-4612-4032-7
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site
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