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Verifiable Visualization for Isosurface Extraction
November/December 2009 (vol. 15 no. 6)
pp. 1227-1234
Tiago Etiene, University of Utah
Carlos Scheidegger, University of Utah
Luis Gustavo Nonato, Universidade de São Paulo
Robert Mike Kirby, University of Utah
Cláudio Silva, University of Utah
Visual representations of isosurfaces are ubiquitous in the scientific and engineering literature. In this paper, we present techniques to assess the behavior of isosurface extraction codes. Where applicable, these techniques allow us to distinguish whether anomalies in isosurface features can be attributed to the underlying physical process or to artifacts from the extraction process. Such scientific scrutiny is at the heart of verifiable visualization – subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. More concretely, we derive formulas for the expected order of accuracy (or convergence rate) of several isosurface features, and compare them to experimentally observed results in the selected codes. This technique is practical: in two cases, it exposed actual problems in implementations. We provide the reader with the range of responses they can expect to encounter with isosurface techniques, both under “normal operating conditions” and also under adverse conditions. Armed with this information – the results of the verification process – practitioners can judiciously select the isosurface extraction technique appropriate for their problem of interest, and have confidence in its behavior.

[1] I. Babuska and J. Oden, Verification and validation in computational engineering and science: basic concepts. Computer Methods in Applied Mechanics and Engineering, 193 (36-38): 4057–4066, 2004.
[2] P. Bhaniramka, R. Wenger, and R. Crawfis, Isosurface construction in any dimension using convex hulls. IEEE TVCG, 10 (2): 130–141, 2004.
[3] H. Carr, T. Moller, and J. Snoeyink, Artifacts caused by simplicial subdivision. IEEE TVCG, 12 (2): 231–242, 2006.
[4] P. Cignoni, C. Rocchini, and R. Scopigno, Metro: measuring error on simplified surfaces. Computer Graphics Forum, 17 (2): 167–174, 1998.
[5] T. K. Dey and J. A. Levine, Delaunay meshing of isosurfaces. In SMI '07: Proceedings of the IEEE International Conference on Shape Modeling and Applications 2007, pages 241–250. IEEE Computer Society, 2007.
[6] C. A. Dietrich, C. Scheidegger, J. Schreiner, J. L. D. Comba, L. P. Nedel, and C. Silva, Edge transformations for improving mesh quality of marching cubes. IEEE TVCG, 15 (1): 150–159, 2008.
[7] S. Gibson, Using distance maps for accurate surface representation in sampled volumes. In IEEE Vol. Vis., pages 23–30, 1998.
[8] A. Globus and S. Uselton, Evaluation of visualization software. SIGGRAPH Comp. Graph., 29 (2): 41–44, 1995.
[9] K. Hildebrandt, K. Polthier, and M. Wardetzky, On the convergence of metric and geometric properties of polyhedral surfaces. Geometriae Dediacata, (123):89–112, 2006.
[10] C. R. Johnson and A. R. Sanderson, A next step: Visualizing errors and uncertainty. IEEE CG&A, 23 (5): 6–10, 2003.
[11] T. Ju, F. Losasso, S. Schaefer, and J. Warren, Dual contouring of hermite data. In SIGGRAPH'02, pages 339–346. ACM, 2002.
[12] R. Kirby and C. Silva, The need for verifiable visualization. IEEE Computer Graphics and Applications, 28 (5): 78–83, 2008.
[13] L. Kobbelt, M. Botsch, U. Schwanecke, and H.-P. Seidel, Feature sensitive surface extraction from volume data. In SIGGRAPH '01, pages 57–66. ACM, 2001.
[14] T. Lewiner, H. Lopes, A. W. Vieira, and G. Tavares, Efficient implementation of marching cubes cases with topological guarantees. Journal of Graphics Tools, 8 (2): 1–15, 2003.
[15] W. Lorensen and H. Cline, Marching cubes: A high resolution 3d surface construction algorithm. SIGGRAPH Comp. Graph., 21:163–169, 1987.
[16] S. R. Marschner and R. J. Lobb, An evaluation of reconstruction filters for volume rendering. In IEEE Visualization '94, pages 100–107, 1994.
[17] D. Meek and D. Walton, On surface normal and gaussian curvature approximation given data sampled from a smooth surface, Computer-Aided Geometric Design, 17:521–543, 2000.
[18] P. Ning and J. Bloomenthal, An evaluation of implicit surface tilers. IEEE Computer Graphics and Applications, 13 (6): 33–41, 1993.
[19] J. Patera and V. Skala, A comparison of fundamental methods for iso surface extraction. Machine Graphics & Vision International Journal, 13 (4): 329–343, 2004.
[20] A. Pommert, U. Tiede, and K. Höhne On the accuracy of isosurfaces in tomographic volume visualization. In MICCAI'02, pages 623–630, London, UK, 2002. Springer-Verlag.
[21] S. Raman, and R. Wenger, Quality isosurface mesh generation using an extended marching cubes lookup table. Computer Graphics Forum, 27 (3): 791–798, 2008.
[22] C. J. Roy, Review of code and solution verification procedures for computational simulation. J. Comput Phys., 205 (1): 131–156, 2005.
[23] J. Schreiner, C. Scheidegger, and C. Silva, High-quality extraction of isosurfaces from regular and irregular grids. IEEE TVCG, 12(5):1205– 1212, 2006.
[24] P. Sutton, C. Hansen, H.-W. Shen, and D. Schikore, A case study of isosurface extraction algorithm performance. In Data Visualization 2000, pages 259–268. Springer, 2000.
[25] G. Taubin, F. Cukierman, S. Sullivan, J. Ponce, and D. Kriegman, Parameterized families of polynomials for bounded algebraic curve and surface fitting. IEEE PAMI, 16(3):287–303, Mar 1994.
[26] M. Tory and T. Moeller, Human factors in visualization research. IEEE TVCG, 10 (1): 72–84, 2004.
[27] G. Xu, Convergence analysis of a discretization scheme for gaussian curvature over triangular surfaces. Comput. Aided Geom. Des., 23(2):193– 207, 2006.
[28] Z. Xu, G. Xu, and J.-G. Sun, Convergence analysis of discrete differential geometry operators over surfaces. In Mathematics of Surfaces XI, volume 3604 of LNCS, pages 448–457. Springer, 2005.
[29] L. Zhou and A. Pang, Metrics and visualization tools for surface mesh comparison. In Proc. SPIE - Visual Data Exploration and Analysis VIII, volume 4302, pages 99–110, 2001.

Index Terms:
Verification, V&V, Isosurface Extraction, Marching Cubes
Citation:
Tiago Etiene, Carlos Scheidegger, Luis Gustavo Nonato, Robert Mike Kirby, Cláudio Silva, "Verifiable Visualization for Isosurface Extraction," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 6, pp. 1227-1234, Nov.-Dec. 2009, doi:10.1109/TVCG.2009.194
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