Shapes and Diffeomorphisms

  • Laurent Younes

Part of the Applied Mathematical Sciences book series (AMS, volume 171)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Laurent Younes
    Pages 1-42
  3. Laurent Younes
    Pages 43-57
  4. Laurent Younes
    Pages 59-63
  5. Laurent Younes
    Pages 65-103
  6. Laurent Younes
    Pages 105-113
  7. Laurent Younes
    Pages 115-148
  8. Laurent Younes
    Pages 149-160
  9. Laurent Younes
    Pages 177-202
  10. Laurent Younes
    Pages 203-247
  11. Laurent Younes
    Pages 249-301
  12. Laurent Younes
    Pages 303-329
  13. Laurent Younes
    Pages 331-345
  14. Back Matter
    Pages 347-434

About this book

Introduction

Shapes are complex objects, which are difficult to apprehend as mathematical entities, in ways that can also be amenable to computerized analysis and interpretation. This volume provides the background that is required for this purpose, including different approaches that can be used to model shapes, and algorithms that are available to analyze them. It explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms. The book is, as far as possible, self-contained, with an appendix that describes a series of classical topics in mathematics (Hilbert spaces, differential equations, Riemannian manifolds) and sections that represent the state of the art in the analysis of shapes and their deformations.

A direct application of what is presented in the book is a branch of the computerized analysis of medical images, called computational anatomy.

Keywords

Curves and Surfaces Groups of Diffeomorphisms Riemannian Geometry Shape Analysis algorithms diffeomorphism differential geometry manifold optimization

Authors and affiliations

  • Laurent Younes
    • 1
  1. 1.Ctr. Imaging ScienceJohn Hopkins UniversityBaltimoreUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-12055-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-12054-1
  • Online ISBN 978-3-642-12055-8
  • Series Print ISSN 0066-5452
  • About this book
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