Paper Info
Title
On the Fractal Dimension of Isosurfaces
Abstract
A (3D) scalar grid is a regular n1 x n2 x n3 grid of vertices where each vertex v is associated with some scalar value sv. Applying trilinear interpolation, the scalar grid determines a scalar function g where g(v) = sv for each grid vertex v. An isosurface with isovalue σ is a triangular mesh which approximates the level set g(-1)(σ). The fractal dimension of an isosurface represents the growth ;in the isosurface as the number of grid cubes increases. We define and discuss the fractal isosurface dimension. Plotting the fractal ;dimension as a function of the isovalues in a data set provides information about the isosurfaces determined by the data set. We present statistics on the average fractal dimension of 60 publicly available benchmark data sets. We also show the fractal dimension is highly correlated with topological noise in the benchmark data sets, measuring the topological noise by the number of connected components in the isosurface. Lastly, we present a formula predicting the fractal dimension as a function of noise and validate the formula with experimental results.
Year
DOI
Venue
2010
10.1109/TVCG.2010.182
Visualization and Computer Graphics, IEEE Transactions
Keywords
Field
DocType
fractals,interpolation,mesh generation,solid modelling,statistical analysis,3D scalar grid,data set,fractal dimension plotting,fractal isosurface dimension,grid cube,grid vertex,isovalue,scalar function,statistics,topological noise,triangular mesh,trilinear interpolation,Isosurfaces,fractal dimension,scalar data
Effective dimension,Topology,Minkowski–Bouligand dimension,Fractal dimension,Mathematical analysis,Fractal,Level set,Isosurface,Theoretical computer science,Correlation dimension,Trilinear interpolation,Mathematics
Journal
Volume
Issue
ISSN
16
6
1077-2626
Citations 
PageRank 
References 
13
0.69
17
Authors
2
Name
Order
Citations
PageRank
Marc Khoury1462.95
Rephael Wenger244143.54