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Isosurfaced Uncertainty

Here is the second of the three applications of curvature-based transfer functions. I should say that this one is probably the most experimental in nature.

Let's consider these two kinds of boundaries.

Here are two flat regions, with parallel isocontours. If we place water here, it will flow down in a straight path, viewed from above. But here, the high part is not level, the isocontours aren't really parallel. and water flows in a curved path, when viewed from above.

I think we can also say that the individual iso-contours here are a poor model of the real boundary between the two regions, which is something like this.

What we have here is called "flow-line curvature": a property unique to implicit surfaces, which measures how much the surface normal tilts as you move off of, or further into the surface. We measure flow-line curvature with the same framework described before, see the paper for details.

We propose that flow-line curvature can be a qualitative tool for visualizing the uncertainty of surface models generated by isosurface extraction, in the following sense.

• The physical shape of a boundary between two materials is a fixed and intrinsic property of the object being sampled in a dataset.
• If you have locations on an isosurface, where small changes in the isovalue, result in large changes in the surface orientation, that location of that isosurface is probably a poor indicator of the underlying material boundary.
• So perhaps if you colormap flow-line curvature onto isosurfaces, you can get a sense of where the isosurface is not to be trusted as a model of the material surface.