• Corpus ID: 122661119

Level set methods : evolving interfaces in geometry, fluid mechanics, computer vision, and materials science

@inproceedings{Sethian1996LevelSM,
  title={Level set methods : evolving interfaces in geometry, fluid mechanics, computer vision, and materials science},
  author={James A. Sethian},
  year={1996}
}
Part 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… 

Theory, algorithms, and applications of level set methods for propagating interfaces

TLDR
This work describes a hierarchy of fast methods, including an extremely fast marching level set scheme for monotonically advancing fronts, based on a stationary formulation of the problem, and demonstrates the technique applied to a series of examples from geometry, material science and computer vision.

Another Look at Velocity Extensions in the Level Set Method

  • D. Chopp
  • Computer Science
    SIAM J. Sci. Comput.
  • 2009
TLDR
This paper looks more closely at the characteristics near the interface, and presents a modified velocity extension method, also based on the fast marching method, which handles the characteristcs more accurately and will lead to some interesting new possibilities for thefast marching method.

The marker level set method: applications to simulation of liquids

TLDR
A new method for advection of interfaces by an external velocity field with improved performance in the problematic areas of the classic level set method is introduced, and a new MLS-based level set reinitialization procedure is introduced which gives improved performance over classical reinitialized procedures used in the context of thelevel set method alone.

Isosurfaces and Level-Sets

  • R. Whitaker
  • Computer Science
    The Visualization Handbook
  • 2005

Level set and fast marching methods in image processing and computer vision

  • R. MalladiJ. Sethian
  • Computer Science
    Proceedings of 3rd IEEE International Conference on Image Processing
  • 1996
TLDR
The application of fast marching methods to solve static Hamilton-Jacobi equations which arise in aspects of computer vision, including image denoising and enhancement schemes based on curvature-controlled diffusion with automatic stopping and hierarchical scales is shown.

The Hamilton-Jacobi skeleton

TLDR
A new algorithm for simulating the eikonal equation is introduced, which offers a number of computational and conceptual advantages over the earlier methods when it comes to shock tracking and a very efficient algorithm for shock detection.

A Domain Decomposition Parallelization of the Fast Marching Method

Abstract : Evolving interfaces play an important role in a multitude of different areas, ranging from fluid mechanics, combustion, and grid generation to material sciences, semiconductor
...

References

Level set methods: evolving interfaces in geometry, fluid mechanics, computer vision, and materials science

  • Level Set Methods and Fast Marching Methods Level Set Methods and Fast Marching Methods Evolving Interfaces. 1999 first published 1996 as Level Set Methods xviii + 420 pp., ISBN paperback METHODS: EVOLVING INTERFACES IN COMPUTATIONAL GEOMETRY FLUID MECHANICS, COMPUTER VISION, AND MATERIALS SCIENCE,