DocumentCode :
963847
Title :
Revisiting Histograms and Isosurface Statistics
Author :
Scheidegger, Carlos E. ; Schreiner, J.M. ; Duffy, Brian ; Carr, Harriet ; Silva, Claudio T.
Author_Institution :
Inst. of Sci. Comput. & Imaging, Utah Univ., Salt Lake City, UT
Volume :
14
Issue :
6
fYear :
2008
Firstpage :
1659
Lastpage :
1666
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.
Keywords :
data visualisation; statistical analysis; Federer Coarea Formula; histogram equalization; isosurface statistics; isosurface-preserving transformations; statistical model; Brightness; Convergence; Data visualization; Frequency; Higher order statistics; Histograms; Humans; Isosurfaces; Kernel; Noise figure; Coarea Formula; Histograms; Index Terms— Isosurfaces;
fLanguage :
English
Journal_Title :
Visualization and Computer Graphics, IEEE Transactions on
Publisher :
ieee
ISSN :
1077-2626
Type :
jour
DOI :
10.1109/TVCG.2008.160
Filename :
4658188
Link To Document :
بازگشت