Integrating Isosurface Statistics and Histograms

Integrating Isosurface Statistics and Histograms

Abstract

Many data sets are sampled on regular lattices in two, three or more dimensions, and recent work has shown that statistical properties of these data sets must take into account the continuity of the underlying physical phenomena. However, the effects of quantization on the statistics have not yet been accounted for. This paper therefore reconciles the previous papers to the underlying mathematical theory, develops a mathematical model of quantized statistics of continuous functions, and proves convergence of geometric approximations to continuous statistics for regular sampling lattices. In addition, the computational cost of various approaches is considered, and recommendations made about when to use each type of statistic.

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Authors
  • Duffy, Brian
  • Carr, Hamish
  • Möller, Torsten
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Supplemental Material
Shortfacts
Category
Journal Paper
Divisions
Visualization and Data Analysis
Journal or Publication Title
IEEE Transactions on Visualization and Computer Graphics
ISSN
1077-2626
Page Range
xxx-xxx
Number
x
Volume
19
Date
2013
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