Shapes and Diffeomorphisms

• Main Author: Younes, Laurent. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Applied Mathematical Sciences, 171
• Subjects: Mathematics.; Global analysis.; Visualization.; Global differential geometry.; Differential Geometry.; Global Analysis and Analysis on Manifolds.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-12055-8

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...

Table of Contents:

• Introduction
• 1. Parametrized Plane Curves
• 2. Medial Axis
• 3. Moment-Based Representation
• 4. Local Properties of Surfaces
• 5. Isocontours and Isosurfaces
• 6. Evolving Curves and Surfaces
• 7. Deformable templates
• 8. Ordinary Differential Equations and Groups of Diffeomorphisms
• 9. Building Admissible Spaces
• 10. Deformable Objects and Matching Functionals
• 11. Diffeomorphic Matching
• 12. Distances and Group Actions
• 13. Metamorphosis
• A. Elements from Hilbert Space Theory
• B. Elements from Differential Geometry
• C. Ordinary Differential Equations
• D. Optimization Algorithms
• E. Principal Component Analysis
• F. Dynamic Programming
• References
• Index.