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<p><b>Abstract</b>—One of the most effective techniques for developing efficient isosurfacing algorithms is the reduction of visits to nonisosurface cells. Recent algorithms have drastically reduced the unnecessary cost of visiting nonisosurface cells. The experimental results show almost optimal performance in their isosurfacing processes. However, most of them have a bottleneck in that they require more than <tmath>$O(n)$</tmath> computation time for their preprocessing, where <tmath>$n$</tmath> denotes the total number of cells. In this paper, we propose an efficient isosurfacing technique, which can be applied to unstructured as well as structured volumes and which does not require more than <tmath>$O(n)$</tmath> computation time for its preprocessing. A preprocessing step generates an extrema skeleton, which consists of cells and connects all extremum points, by the volume thinning algorithm. All disjoint parts of every isosurface intersect at least one cell in the extrema skeleton. Our implementation generates isosurfaces by searching for isosurface cells in the extrema skeleton and then recursively visiting their adjacent isosurface cells, while it skips most of the nonisosurface cells. The computation time of the preprocessing is estimated as <tmath>$O(n)$</tmath>. The computation time of the isosurfacing process is estimated as <tmath>$O(n^{1/3} m + k)$</tmath>, where <tmath>$k$</tmath> denotes the number of isosurface cells and <tmath>$m$</tmath> denotes the number of extremum points since the number of cells in an extrema skeleton is estimated as <tmath>$O(n^{1/3} m)$</tmath>.</p>
Isosurface, extremum points, volume thinning, extrema skeleton, lattice classification.

K. Koyamada, Y. Yamaguchi and T. Itoh, "Fast Isosurface Generation Using the Volume Thinning Algorithm," in IEEE Transactions on Visualization & Computer Graphics, vol. 7, no. , pp. 32-46, 2001.
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