Revisiting Histograms and Isosurface Statistics

Authors:
Carlos E. Scheidegger;John M. Schreiner;Brian Duffy;Hamish Carr;Cláudio T. Silva
Affiliations:
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT;Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT;School of Computer Science and Informatics, University College Dublin, Ireland;School of Computer Science and Informatics, University College Dublin, Ireland;Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT
Venue:
IEEE Transactions on Visualization and Computer Graphics
Year:
2008

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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 Federerâs 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.