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Interpolation-Based Extraction of Representative Isosurfaces

  • Oliver FernandesEmail author
  • Steffen Frey
  • Thomas Ertl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10072)

Abstract

We propose a novel technique for the automatic, similarity-based selection of representative surfaces. While our technique can be applied to any set of manifolds, we particularly focus on isosurfaces from volume data. We select representatives from sets of surfaces stemming from varying isovalues or time-dependent data. For selection, our approach interpolates between surfaces using a minimum cost flow solver, and determines whether the interpolate adequately represents the actual surface in-between. For this, we employ the Hausdorff distance as an intuitive measure of the similarity of two components. In contrast to popular contour tree-based approaches which are limited to changes in topology, our approach also accounts for geometric deviations. For interactive visualization, we employ a combination of surface renderings and a graph view that depicts the selected surfaces and their relation. We finally demonstrate the applicability and utility of our approach by means of several data sets from different areas.

Keywords

Point Cloud Hausdorff Distance Bucky Ball Minimum Cost Flow Marching Cube 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was primarily funded by Deutsche Forschungsgemeinschaft (DFG) under grant SPP 1648 (ExaScaleFSA).

References

  1. 1.
    Lorensen, W., Cline, H.: Marching cubes: a high resolution 3D surface construction algorithm. Comput. Graph. 21, 163–169 (1987)CrossRefGoogle Scholar
  2. 2.
    Dey, T., Levine, J.: Delaunay meshing of isosurfaces. Shape Model. Appl. 2007, 241–250 (2007)Google Scholar
  3. 3.
    Schreiner, J., Scheidegger, C., Silva, C.: High-quality extraction of isosurfaces from regular and irregular grids. TVCG 12, 1205–1212 (2006)Google Scholar
  4. 4.
    Scheidegger, C.E., Fleishman, S., Silva, C.T.: Triangulating point set surfaces with bounded error. In: EG symposium on Geometry processing (2005)Google Scholar
  5. 5.
    Bommes, D., Lévy, B., Pietroni, N., Puppo, E., Silva, C., Tarini, M., Zorin, D.: Quad meshing. In: Eurographics, The Eurographics Association, pp. 159–182 (2012)Google Scholar
  6. 6.
    Theisel, H.: Exact isosurfaces for marching cubes. Comput. Graph. Forum 21, 19–32 (2002)CrossRefzbMATHGoogle Scholar
  7. 7.
    Remacle, J.F., Henrotte, F., Baudouin, T., Geuzaine, C., Béchet, E., Mouton, T., Marchandise, E.: A frontal Delaunay quad mesh generator. In: 20th Meshing Roundtable, pp. 455–472 (2012)Google Scholar
  8. 8.
    Wiley, D.F., Childs, H.R., Gregorski, B.F., Hamann, B., Joy, K.I.: Contouring curved quadratic elements. In: VisSym, p. 1 (2003)Google Scholar
  9. 9.
    Pagot, C.A., Vollrath, J., Sadlo, F., Weiskopf, D., Ertl, T., Comba, J.: Interactive isocontouring of high-order surfaces. In: Scientific Visualization (2011)Google Scholar
  10. 10.
    Shirazian, P., Wyvill, B., Duprat, J.L.: Polygonization of implicit surfaces on multi-core architectures with SIMD instructions. In: EGPGV, pp. 89–98 (2012)Google Scholar
  11. 11.
    Knoll, A., Hijazi, Y., Kensler, A., Schott, M., Hansen, C.D., Hagen, H.: Fast ray tracing of arbitrary implicit surfaces. CGF 28, 26–40 (2009)Google Scholar
  12. 12.
    Biasotti, S., De Floriani, L., Falcidieno, B., Frosini, P., Giorgi, D., Landi, C., Papaleo, L., Spagnuolo, M.: Describing shapes by geometrical-topological properties of real functions. ACM Comput. Surv. 40, 12:1–12:87 (2008)CrossRefGoogle Scholar
  13. 13.
    Carr, H., Snoeyink, J., van de Panne, M.: Flexible isosurfaces: simplifying and displaying scalar topology using the contour tree. CGTA 43, 42–58 (2010)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Khoury, M., Wenger, R.: On the fractal dimension of isosurfaces. IEEE Trans. Vis. Comput. Graph. 16, 1198–1205 (2010)CrossRefGoogle Scholar
  15. 15.
    Tenginakai, S., Lee, J., Machiraju, R.: Salient iso-surface detection with model-independent statistical signatures. In: IEEE Visualization (2001)Google Scholar
  16. 16.
    Tang, M., Lee, M., Kim, Y.J.: Interactive Hausdorff distance computation for general polygonal models. ACM Trans. Graph. 28, 74:1–74:9 (2009)CrossRefGoogle Scholar
  17. 17.
    Bruckner, S., Möller, T.: Isosurface similarity maps. Comput. Graph. Forum 29, 773–782 (2010). EuroVis 2010 best paper awardCrossRefGoogle Scholar
  18. 18.
    Wei, T.H., Lee, T.Y., Shen, H.W.: Evaluating isosurfaces with level-set-based information maps. Comput. Graph. Forum 32, 1–10 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.VISUS Visualization Research InstituteUniversity of StuttgartStuttgartGermany

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