Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science ... Computational Mathematics, Series Number 3)
Cambridge University Press
Edition: 2, 8/12/1999
EAN 9780521645577, ISBN10: 0521645573
Paperback, 404 pages, 22.9 x 15.5 x 2 cm
Language: English
This new edition of Professor Sethian's successful text provides an introduction to level set methods and fast marching methods, which are powerful numerical techniques for analyzing 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. For this edition, the collection of applications provided in the text has been expanded, including examples from physics, chemistry, fluid mechanics, combustion, image processing, material science, fabrication of microelectronic components, computer vision, computer-aided design, and optimal 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.
Introduction
1. Formulations of interface propagation
Part I. Theory and Algorithms
2. Theory of curve and surface evolution
3. Hamilton–Jacobi equations and associated theory
4. Numerical approximations
first attempt
5. Numerical schemes for hyperbolic conservation laws
6. Algorithms for the initial and boundary value formulations
7. Efficient schemes
adaptivity
8. Triangulated versions of level set and fast marching method
extensions and variations
9. Tests of basic methods
Part II. Applications
10. Geometry
11. Grid generation
12 Image denoising
13. Computer vision
shape detection and recognition
14. Fluid mechanics and materials sciences
adding physics
15. Computational geometry and computer-aided-design
16. First arrivals, optimizations, and control
17. Applications to semi-conductor manufacturing
18. Comments, conclusions, future directions
References
Index.