Level Sets

We propose to use level-set based implicit models to represent surface shape. Osher & Sethian
A curve can be thought of as a level set of some discretely sampled 2D function.
showed how deformation could be modeled on discrete grids using level sets. Level-set models possess several advantages over conventional parametric models. The models are topologically flexible, and can split and rejoin as necessary in the course of deformation without the need for re-parametrization. The model can be thought of as the level set of a surface, for instance a lake shore as depicted here. Changing the surface moves the boundary of the model, as changing the terrain would move the boundary of the lake shown here. The evolution of the level-set function is independent of translation, rotation, and arbitrary decisions regarding parametrization. The resulting shapes are solely dependent on the resolution of the voxels used to represent the function, and not on some basis function. Finally, multi-scale solutions are possible, allowing the model to start on a coarse
The model can also be thought of as the level set of a surface, i.e. a lake shore.
grid and progress on finer grids until a solution is reached. This not only reduces computation time, but also controls the relative importance of different sized structures in the model. One of several examples of level sets in computer graphics is morphing from one shape to another.

For a more in-depth explanation of level sets see Dr. J. A. Sethian's informative page on the subject. Further information is also available from the UCLA Computational and Applied Mathematics group.







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