Carlos Scheidegger, John Schreiner, Brian Duffy, Hamish Carr, Claudio Silva. IEEE TVCG, 14(6):1659-1666, 2008. (Vis 2008)
Recent results have shown a link between geometric properties of isosurfaces and statistical properties of the underlying sampled data. However, this has two defects: not all of the properties described converge to the same solution, and the statistics computed are not always invariant under isosurface-preserving transformations. We apply Federer’s Coarea Formula from geometric measure theory to explain these discrepancies. We describe an improved substitute for histograms based on weighting with the inverse gradient magnitude, develop a statistical model that is invariant under isosurface-preserving transformations, and argue that this provides a consistent method for algorithm evaluation across multiple datasets based on histogram equalization. We use our corrected formulation to reevaluate recent results on average isosurface complexity, and show evidence that noise is one cause of the discrepancy between the expected figure and the observed one.
Get the paper in PDF format (7MB).
We are publishing the set of volumes we collected to compute the histograms and isosurface statistics. Note that this is a fairly large dataset (~1GB). The files are in NRRD format. We have tried to give attribution to the people who originally made the data available in the NRRD header, as a comment. We couldn’t find the authors for a few of those files, so if you see your file here and it is incorrectly attributed, do not hesitate to let me know.