Authors
Miriah Meyer
Carlos E. Scheidegger
John M. Schreiner
Brian Duffy
Hamish Carr
Cláudio T. Silva
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2008.160
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Running Time: 23 min
Abstract
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.
Citation
Miriah Meyer, Carlos E. Scheidegger, John M. Schreiner, Brian Duffy, Hamish Carr, Cláudio T. Silva, “Revisiting Histograms and Isosurface Statistics,” IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 6, pp. 1659-1666, Nov/Dec, 2008