Shapes and Diffeomorphisms

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.

• Preface to the 2nd Edition.- Preface to the 1st Edition.- Parametrized Plane Curves.- Medial Axis.- Local Properties of Surfaces.- Computations on Triangulated Surfaces- Evolving Curves and Surfaces.- Deformable templates.- Ordinary Differential Equations and Groups of Diffeomorphisms.- Building Admissible Spaces.- Deformable Objects and Matching Functionals.- Diffeomorphic Matching.- Distances and Group Actions.- Metamorphosis.- Analyzing Shape Datasets.- Appendices: Elements from Functional Analysis.- Elements from Differential Geometry.- Ordinary Differential Equations.- Introduction to Optimization and Optimal Control Theory. - Principal Component Analysis.- Dynamic Programming.- References.- Index.

“The book is an in-depth, modern, clear exposition of the advanced theory of shapes and diffeomorphisms … . This makes the book accessible to a large audience, including graduate and postgraduate students. Moreover the book is extremely well written and very pleasant to read. … I strongly recommend this excellent book to every researcher or graduate student in the field of shapes and geometric analysis. Naturally, it will also be of interest to many Mathematicians … .” (Diaraf Seck, SIAM Review, Vol. 64 (1), March, 2022)