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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(More)
The contour tree, an abstraction of a scalar field that encodes the nesting relationships of isosurfaces, can be used to accelerate isosurface extraction, to identify important isovalues for volume-rendering transfer functions, and to guide exploratory visualization through a flexible isosurface interface. Many real-world data sets produce unmanageably(More)
Topology provides a foundation for the development of mathematically sound tools for processing and exploration of scalar fields. Existing topology-based methods can be used to identify interesting features in volumetric data sets, to find seed sets for accelerated isosurface extraction, or to treat individual connected components as distinct entities for(More)
In this paper, we show that histograms represent spatial function distributions with a nearest neighbour interpolation. We confirm that this results in systematic underrepresentation of transitional features of the data, and provide new insight why this occurs. We further show that isosurface statistics, which use higher quality interpolation, give better(More)
We propose a novel method to improve the quality of multi-resolution visualizations. We reduce aliasing artifacts by approximating the data distribution with a Gaussian basis function at each level of detail for more accurate rendering at coarser levels of detail. We then show an efficient implementation of our novel Gaussian based approximation scheme and(More)
Isosurfaces, one of the most fundamental volumetric visualization tools, are commonly rendered using the well-known Marching Cubes cases that approximate contours of trilinearly-interpolated scalar fields. While a complete set of cases has recently been published by Nielson, the formal proof that these cases are the only ones possible and that they are(More)