Revisiting histograms and isosurface statistics

Carlos E. Scheidegger, John M. Schreiner, Brian Duffy, Hamish Carr, Cláudio T. Silva

Research output: Contribution to journalArticlepeer-review


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-preservlng 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.

Original languageEnglish (US)
Article number4658188
Pages (from-to)1659-1666
Number of pages8
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number6
StatePublished - Nov 2008


  • Coarea formula
  • Histograms
  • Isosurfaces

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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