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Level Sets

First up are level sets, which, in general, iteratively deform an implicit surface according to a partial different equation of the surface properties, usually involving curvature.

We looked at a particular level set method, which generalizes Perona+Malik's anisotropic image diffusion by working in the space of surface normals. This work was presented at last year's Vis conference by Tolga Tasdizen. The curvature property that matters here is total curvature, the Frobenious norm of the geometry tensor.

We have adopted direct volume rendering as a level set visualization tool:

• Both methods share an implicit surface representation and an underlying grid.
• You usually have to periodically inspect the iterative steps of the solution. Volume rendering can do this directly, without any intermediate surface extraction or pre-processing.
• And now, we know how to use volume rendering to inspect the same curvature quantities that are used to drive the level set PDE.