• Parametrized Plane Curves.- Medial Axis.- Moment-Based Representation.- Local Properties of Surfaces.- Isocontours and Isosurfaces.- 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.

From the reviews: "The book under review deals with the fascinating subject of shapes. ... This is a book on applied mathematics which provides a description of the wide range of methods that have been invented to represent, detect, or compare shapes ... together with the necessary mathematical background that they require. The book could also be of interest to an engineering- or computer-science-oriented reader, as it gives in several places concrete algorithms and applicable methods, including experimental illustrations." (Luca Granieri, Mathematical Reviews, Issue 2011 h) "This book is an attempt at providing a description of a large range of methods used to represent, detect and compare shapes ... together with the mathematical background that they require. ... This book on applied mathematics is of interest to engineers and computer scientists having direct applications in the computerized analysis of medical images. This theory will as well lead to other interesting applications in the future." (Corina Mohorianu, Zentralblatt MATH, Vol. 1205, 2011)