© 2019

Shapes and Diffeomorphisms

  • 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


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

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Laurent Younes
    Pages 1-55
  3. Laurent Younes
    Pages 57-72
  4. Laurent Younes
    Pages 73-100
  5. Laurent Younes
    Pages 101-130
  6. Laurent Younes
    Pages 131-167
  7. Laurent Younes
    Pages 169-181
  8. Laurent Younes
    Pages 205-241
  9. Laurent Younes
    Pages 243-289
  10. Laurent Younes
    Pages 291-346
  11. Laurent Younes
    Pages 347-372
  12. Laurent Younes
    Pages 373-404
  13. Laurent Younes
    Pages 405-421
  14. Back Matter
    Pages 423-558

About this book


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. 


68T10, 53-01, 68-02, 37C10, 37E30, 53A04, 53A05, 68U05, 92C55 curves and surfaces groups of diffeomorphisms Riemannian geometry shape analysis shape spaces differential geometry optimization optimal control computational anatomy large deformation diffeomorphic metric mapping (LDDMM) statistics on manifolds

Authors and affiliations

  1. 1.Center for Imaging ScienceJohns Hopkins UniversityBaltimoreUSA

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.

Bibliographic information