Level Set Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science available in Hardcover
- Pub. Date:
- Cambridge University Press
This book is an introduction to level set methods, which are powerful numerical techniques for analysing and computing interface motion in a host of settings. They rely on a fundamental shift in how one views moving boundaries; rethinking the natural geometric Lagrangian perspective and exchanging it for an Eulerian, initial value partial differential equation perspective. The resulting numerical techniques can be used to track three-dimensional complex fronts that can develop sharp corners and change topology as they evolve. A large collection of applications is provided in the text, including examples from physics, chemistry, fluid mechanics, combustion, image processing, material science, fabrication of microelectronic components, computer vision and control theory. This book will be a useful resource for mathematicians, applied scientists, practising engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces.
Table of ContentsPart I. The Theory of Moving Interfaces: 1. Theory of front evolution; 2. Level set formulation; Part II. Algorithms, Analysis, and Implementations of Level Set Methods: 3. Traditional techniques for tracking interfaces; 4. Hyperbolic conservation laws; 5. Approximating the level set equation; 6. Viscosity solutions and Hamilton-Jacobi equations; 7. A hierarchy of fast level set methods; 8. A fast marching level set method; 9. Extensions to the basic method; Part III. Applications: 10. Geometry: curve/surface shrinkage and self-similar surfaces; 11. Grid generation; 12. Image enhancement and noise removal; 13. Minimal surfaces and surfaces of prescribed curvature; 14. Combustion, crystal growth, and two-fluid flow; 15. Computer vision: shape detection and recognition; 16. Applications of the fast marching level set method; 17. Etching and deposition in microchip fabrication; 18. New areas.