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Image Registration Computer Vision Computat. Anatomy Point Clouds Surface Denoising Image Segmentation Medical Imaging Image Processing Compressible Fluids Incompressible Fluids Level Set Methods Vortex Sheets

LEVEL SET METHODS

    Level Set Methods, introduced by Stanley Osher and James Sethian, are powerful techniques for analyzing and computing moving fronts in a variety of different settings. Level Sets are used in image processing, computer vision, computational fluid dynamics, material science, and many other fields. For a good introduction to Level Set Methods, one may read "Level Set Methods and Dynamic Implicit Surfaces" by Stanley Osher and Ronald Fedkiw.
    There is a variety of methods that numerically approximate level set equations. A few 2D movies below illustrate that third generation methods, HJ ENO and HJ WENO, give much more accurate approximations than first generation schemes, such as Lax-Friedrichs, do.

 

MOVIES

Advection - Motion in an externally generated velocity field

Methods \ Motion Translation Rotation Rigid Body Rotation
Lax-Friedrichs view view view
LLLxF view view view
Upwind view view view
HJ ENO(3) - RK3 view view view
HJ WENO(5) - RK3view view view

Propagation - Motion in the normal direction

HJ WENO(5) - RK3
with Godunov solver
view view  

Motion by mean curvature

Second order view view

 

Combination

  view view

 

 

Motion by mean curvature in 3D

 

 

 

horizontal rule

Igor Yanovsky