Applied Mathematical Sciences

Shapes and Diffeomorphisms

Authors: Younes, Laurent

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  • Suitable for an advanced undergraduate course in the differential geometry of curves and surfaces, featuring applications that are rarely treated in standard texts
  • Provides a graduate-level theoretical background in shape analysis and connects it with algorithms and statistical methods
  • Offers a unique presentation of diffeomorphic registration methods, which has no equivalent in the current literature
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  • ISBN 978-3-662-58496-5
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Hardcover 83,19 €
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  • ISBN 978-3-662-58495-8
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About this Textbook


This book covers mathematical foundations and methods for the computerized analysis of shapes, providing the requisite background in geometry and functional analysis and introducing various algorithms and approaches to shape modeling, with a special focus on the interesting connections between shapes and their transformations by diffeomorphisms. A direct application is to computational anatomy, for which techniques such as large‒deformation diffeomorphic metric mapping and metamorphosis, among others, are presented. The appendices detail a series of classical topics (Hilbert spaces, differential equations, Riemannian manifolds, optimal control).

The intended audience is applied mathematicians and mathematically inclined engineers interested in the topic of shape analysis and its possible applications in computer vision or medical imaging. The first part can be used for an advanced undergraduate course on differential geometry with a focus on applications while the later chapters are suitable for a graduate course on shape analysis through the action of diffeomorphisms.

Several significant additions appear in the 2nd edition, most notably a new chapter on shape datasets, and a discussion of optimal control theory in an infinite-dimensional framework, which is then used to enrich the presentation of diffeomorphic matching.

 

About the authors

A former student of the Ecole Normale Supérieure in Paris, Laurent Younes received his Ph.D. from the University Paris Sud in 1989. Now a professor in the Department of Applied Mathematics and Statistics at Johns Hopkins University (which he joined in 2003), he was a junior, then senior researcher at CNRS in France from 1991 to 2003. His research is in stochastic modeling for imaging and biology, shape analysis and computational anatomy. He is a core faculty member of the Center for Imaging Science and of the Institute for Computational Medicine at JHU.



Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook 67,82 €
price for Spain (gross)
  • ISBN 978-3-662-58496-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 83,19 €
price for Spain (gross)
  • ISBN 978-3-662-58495-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Shapes and Diffeomorphisms
Authors
Series Title
Applied Mathematical Sciences
Series Volume
171
Copyright
2019
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag GmbH Germany, part of Springer Nature
eBook ISBN
978-3-662-58496-5
DOI
10.1007/978-3-662-58496-5
Hardcover ISBN
978-3-662-58495-8
Series ISSN
0066-5452
Edition Number
2
Number of Pages
XXIII, 558
Number of Illustrations
33 b/w illustrations, 14 illustrations in colour
Topics