Unbiased Sampling and Meshing of Isosurfaces

Yan, Dongming; Wallner, Johannes; Wonka, Peter

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Article

Authors

Yan, Dongming

Wallner, Johannes
Wonka, Peter

KAUST Department

Visual Computing Center (VCC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program

Date

2014-05-07

Online Publication Date

2014-05-07

Print Publication Date

2014-11-01

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http://hdl.handle.net/10754/563841

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Abstract

In this paper, we present a new technique to generate unbiased samples on isosurfaces. An isosurface, F(x,y,z) = c , of a function, F , is implicitly defined by trilinear interpolation of background grid points. The key idea of our approach is that of treating the isosurface within a grid cell as a graph (height) function in one of the three coordinate axis directions, restricted to where the slope is not too high, and integrating / sampling from each of these three. We use this unbiased sampling algorithm for applications in Monte Carlo integration, Poisson-disk sampling, and isosurface meshing.

Citation

Yan D-M, Wallner J, Wonka P (2014) Unbiased Sampling and Meshing of Isosurfaces. IEEE Transactions on Visualization and Computer Graphics 20: 1579–1589. Available: http://dx.doi.org/10.1109/TVCG.2014.2322357.

Sponsors

The authors thank the anonymous reviewers for their valuable comments and suggestions. They are grateful to Takashi Michikawa and Hiromasa Suzuki for providing them an implementation of marching cubes, the authors of "afront" [5] for making it publicly available, Miriah Meyer for sharing data with them, and Jianwei Guo for helping on the DDA [36] software. This work was supported by the KAUST Visual Computing Center, the National Natural Science Foundation of China (no. 61372168, 61331018, 61271431, and 61272327), and the U.S. National Science Foundation.