The Visual Computer

, Volume 32, Issue 4, pp 465–478 | Cite as

Visual inspection of multivariate volume data based on multi-class noise sampling

  • Zhiyu Ding
  • Ziang Ding
  • Weifeng Chen
  • Haidong Chen
  • Yubo Tao
  • Xin Li
  • Wei Chen
Original Article


Visualizing multivariate volume data is useful when the user wants to inspect the correlational distributions of multiple variables in a spatial field. Existing solutions commonly rely on color blending or weaving techniques to show multiple variables on a sampling point, probably causing heavy visual confusion. This paper presents an alternative solution that employs a multi-class sampling technique to generate spatially separated sampling points for multiple variables and illustrates the sampling points of each variable individually. We combine this new sampling scheme with the conventional direct volume rendering mode, iso-surface mode, and the cutting plane mode to support interactive inspection of volumetric distributions of multiple variables. The effectiveness of our approach is demonstrated with the IEEE VIS Contest 2004 Hurricane dataset and a 3D nuclear fusion simulation dataset.


Multivariate volume Volume visualization Blue noise Sampling 



The authors would like to thank the anonymous reviewers for their valuable comments. This work was partially supported by the National High Technology Research and Development Program of China (2012AA12090), Major Program of National Natural Science Foundation of China (61232012), National Natural Science Foundation of China (61422211), National Natural Science Foundation of China (61303134), the Fundamental Research Funds for the Central Universities (2013QNA5010).


  1. 1.
    Johnson, C.: Top scientific visualization research problems. IEEE Comput. Graph. Appl. 24(4), 13–17 (2004)CrossRefGoogle Scholar
  2. 2.
    Woodring, J., Shen, H.-W.: Multi-variate, time varying, and comparative visualization with contextual cues. IEEE Trans. Vis. Comput. Graph. 12(5), 909–916 (2006)CrossRefGoogle Scholar
  3. 3.
    Urness, T., Interrante, V., Marusic, I., Longmire, E., Ganapathisubramani, B.: Effectively visualizing multi-valued flow data using color and texture. In: Proceedings of the 14th IEEE Visualization 2003 (VIS’03), p. 16. IEEE Computer Society Seattle, WA (2003)Google Scholar
  4. 4.
    Fang, M., Lu, J., Peng, Q.: Volumetric data modeling and analysis based on seven-directional box spline. Sci. China Inf. Sci. 57(6), 1–14 (2014)CrossRefzbMATHGoogle Scholar
  5. 5.
    Strengert, M., Klein, T., Botchen, R., Stegmaier, S., Chen, M., Ertl, T.: Spectral volume rendering using gpu-based raycasting. Vis. Comput. 22(8), 550–561 (2006)CrossRefGoogle Scholar
  6. 6.
    Max, N.: Optical models for direct volume rendering. IEEE Trans. Vis. Comput. Graph. 1(2), 99–108 (1995)CrossRefGoogle Scholar
  7. 7.
    Chuang, J., Weiskopf, D., Moller, T.: Hue-preserving color blending. IEEE Trans. Vis. Comput. Graph. 15(6), 1275–1282 (2009)CrossRefGoogle Scholar
  8. 8.
    Kuhne, L., Giesen, J., Zhang, Z., Ha, S., Mueller, K.: A data-driven approach to hue-preserving color-blending. IEEE Trans. Vis. Comput. Graph. 18(12), 2122–2129 (2012)CrossRefGoogle Scholar
  9. 9.
    Khlebnikov, R., Kainz, B., Steinberger, M., Schmalstieg, D.: Noise-based volume rendering for the visualization of multivariate volumetric data. IEEE Trans. Vis. Comput. Graph. 19(12), 2926–2935 (2013)CrossRefGoogle Scholar
  10. 10.
    Khlebnikov, R., Kainz, B., Steinberger, M., Streit, M., Schmalstieg, D.: Procedural texture synthesis for zoom-independent visualization of multivariate data. Comp. Graph. Forum 31(3pt4), 1355–1364 (2012). doi: 10.1111/j.1467-8659.2012.03127.x
  11. 11.
    Tufte, E.R.: Envisioning information. Optom. Vis. Sci. 68(4), 322–324 (1991)CrossRefGoogle Scholar
  12. 12.
    Biswas, A., Dutta, S., Shen, H.-W., Woodring, J.: An information-aware framework for exploring multivariate data sets. IEEE Trans. Vis. Comput. Graph. 19(12), 2683–2692 (2013)CrossRefGoogle Scholar
  13. 13.
    Guo, H., Xiao, H., Yuan, X.: Multi-dimensional transfer function design based on flexible dimension projection embedded in parallel coordinates. In: Pacific Visualization Symposium (PacificVis), 2011 IEEE, pp. 19–26. IEEE, Hong Kong (2011)Google Scholar
  14. 14.
    Guo, H., Xiao, H., Yuan, X., et al.: Scalable multivariate volume visualization and analysis based on dimension projection and parallel coordinates. IEEE Trans. Vis. Comput. Graph. 18(9), 1397–1410 (2012)CrossRefGoogle Scholar
  15. 15.
    Cai, W., Sakas, G.: Data intermixing and multi-volume rendering. Comp. Graph. Forum 18(3), 359–368 (1999). doi: 10.1111/1467-8659.00356
  16. 16.
    Akiba, H., Ma, K.-L., Chen, J.H., Hawkes, E.R.: Visualizing multivariate volume data from turbulent combustion simulations. Comput. Sci. Eng. 9(2), 76–83 (2007)CrossRefGoogle Scholar
  17. 17.
    Akiba, H., Ma, K.-L.: A tri-space visualization interface for analyzing time-varying multivariate volume data. In: Proceedings of the 9th Joint Eurographics/IEEE VGTC Conference on Visualization. EUROVIS’07, pp. 115–122. Eurographics Association, Aire-la-Ville, Switzerland (2007)Google Scholar
  18. 18.
    Sauber, N., Theisel, H., Seidel, H.-P.: Multifield-graphs: an approach to visualizing correlations in multifield scalar data. IEEE Trans. Vis. Comput. Graph. 12(5), 917–924 (2006)CrossRefGoogle Scholar
  19. 19.
    Crawfis, R.: Multivariate volume rendering. In: Tech. rep.. Lawrence Livermore National Lab., CA (1996)Google Scholar
  20. 20.
    Djurcilov, S., Kim, K., Lermusiaux, P., Pang, A.: Visualizing scalar volumetric data with uncertainty. Comput. Graph. 26(2), 239–248 (2002)CrossRefGoogle Scholar
  21. 21.
    Hagh-Shenas, H., Kim, S., Interrante, V., Healey, C.: Weaving versus blending: a quantitative assessment of the information carrying capacities of two alternative methods for conveying multivariate data with color. IEEE Trans. Vis. Comput. Graph. 13(6), 1270–1277 (2007)CrossRefGoogle Scholar
  22. 22.
    Fuchs, R., Hauser, H.: Visualization of multi-variate scientific data. Comp. Graph. Forum 28(6), 1670–1690 (2009). doi: 10.1111/j.1467-8659.2009.01429.x
  23. 23.
    Kehrer, J., Hauser, H.: Visualization and visual analysis of multifaceted scientific data: a survey. IEEE Trans. Vis. Comput. Graph. 19(3), 495–513 (2013)CrossRefGoogle Scholar
  24. 24.
    Yellott, J.I.: Spectral consequences of photoreceptor sampling in the rhesus retina. Science 221(4608), 382–385 (1983)CrossRefGoogle Scholar
  25. 25.
    Cook, R.L.: Stochastic sampling in computer graphics. ACM Trans. Graph. 5(1), 51–72 (1986)CrossRefGoogle Scholar
  26. 26.
    Cohen, M.F., Shade, J., Hiller, S., Deussen, O.: Wang tiles for image and texture generation. ACM Trans. Graph. 22(3), 287–294 (2003). doi: 10.1145/882262.882265
  27. 27.
    Lagae, A., Dutré, P.: A procedural object distribution function. ACM Trans. Graph. 24(4), 1442–1461 (2005)CrossRefGoogle Scholar
  28. 28.
    Balzer, M., Schlömer, T., Deussen, O.: Capacity-constrained point distributions: a variant of Lloyd’s method. ACM Trans. Graph. 28(3), 86:1–86:8 (2009). doi: 10.1145/1531326.1531392
  29. 29.
    Wei, L.-Y.: Multi-class blue noise sampling, ACM Trans. Graph 29(4) (2010)Google Scholar
  30. 30.
    Wu, Y.-C., Tsai, Y.-T., Lin, W.-C., Li, W.-H.: Generating pointillism paintings based on seurat’s color composition. Comp. Graph. Forum 32(4), 153–162 (2013). doi: 10.1111/cgf.12161
  31. 31.
    Yuan, X., Guo, P., Xiao, H., Zhou, H., Qu, H.: Scattering points in parallel coordinates. IEEE Trans. Vis. Comput. Graph. 15(6), 1001–1008 (2009)CrossRefGoogle Scholar
  32. 32.
    Janicke, H., Bottinger, M., Scheuermann, G.: Brushing of attribute clouds for the visualization of multivariate data. IEEE Trans. Vis. Comput. Graph. 14(6), 1459–1466 (2008)CrossRefGoogle Scholar
  33. 33.
    Tzeng, F.-Y., Lum, E.B., Ma, K.-L.: An intelligent system approach to higher-dimensional classification of volume data. IEEE Trans. Vis. Comput. Graph. 11(3), 273–284 (2005)CrossRefGoogle Scholar
  34. 34.
    Theisel, H., Sahner, J., Weinkauf, T., Hege, H.-C., Seidel, H.-P.: Extraction of parallel vector surfaces in 3d time-dependent fields and application to vortex core line tracking. In: Visualization, 2005. VIS 05. IEEE, pp. 631–638. IEEE, Minneapolis, MN (2005)Google Scholar
  35. 35.
    Barakat, S., Andrysco, N., Tricoche, X.: Fast extraction of high-quality crease surfaces for visual analysis. Comp. Graph. Forum 30(3), 961–970 (2011). doi: 10.1111/j.1467-8659.2011.01945.x

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Zhiyu Ding
    • 1
  • Ziang Ding
    • 2
  • Weifeng Chen
    • 3
  • Haidong Chen
    • 1
  • Yubo Tao
    • 1
  • Xin Li
    • 4
  • Wei Chen
    • 1
  1. 1.State Key Lab of CAD&CGZhejiang UniversityHangzhouChina
  2. 2.Department of Computer SciencePurdue UniversityWest LafayetteUSA
  3. 3.Zhejiang University of Finance and EconomicsHangzhouChina
  4. 4.China University of PetroleumBeijingChina

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