Advertisement

Fractal Map: Fractal-Based 2D Expansion Method for Multi-scale High-Dimensional Data Visualization

  • Takanori Fujiwara
  • Ryo Matsushita
  • Masaki Iwamaru
  • Manabu Tange
  • Satoshi Someya
  • Koji Okamoto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6453)

Abstract

Visualization of high-dimensional data is difficult to realize and manipulate with 2D display. For example, visualizing time-varying volume data (4D) with volume rendering and animation has spatial and temporal shielding, and data of 5 or more dimensions cannot be visualized on 2D display with existing methods. In this paper, we propose a method that expands high-dimensional data onto a 2D image plane. The proposed method uses the self-similarity of the fractal shape and achieves multi-scale high-dimensional data visualization on 2D display. With this method, we can visualize the entire domain of high-dimensional data without occlusions. Also, one-to-one correspondence in the elements of high-dimensional data and its 2D expansion enables us to manipulate high-dimensional data with 2D expanded result as an interface.

Keywords

Volume Data Volume Rendering Visualization Method Mapping Rule Information Visualization 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Teyseyre, A.R., Campo, M.R.: An overview of 3d software visualization. IEEE Transactions on Visualization and Computer Graphics 15, 87–105 (2009)CrossRefGoogle Scholar
  2. 2.
    Levoy, M.: Display of surfaces from volume data. IEEE Computer Graphics and Applications 8, 29–37 (1988)CrossRefGoogle Scholar
  3. 3.
    Drebin, R., Carpenter, L., Hanrahan, P.: Volume rendering. ACM SIGGRAPH Computer Graphics 22, 74 (1988)CrossRefGoogle Scholar
  4. 4.
    Sabella, P.: A rendering algorithm for visualizing 3D scalar fields. In: Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, p. 58. ACM, New York (1988)Google Scholar
  5. 5.
    Upson, C., Keeler, M.: V-buffer: visible volume rendering. In: Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, p. 64. ACM, New York (1988)Google Scholar
  6. 6.
    Kaufman, A., Mueller, K.: Overview of volume rendering. In: The Visualization Handbook, pp. 127–174 (2005)Google Scholar
  7. 7.
    Johnson, B., Shneiderman, B.: Tree-maps: a space-filling approach to the visualization of hierarchical information structures. In: Proceedings of the 2nd Conference on Visualization 1991, VIS 1991, pp. 284–291. IEEE Computer Society Press, Los Alamitos (1991)Google Scholar
  8. 8.
    Itoh, T., Yamaguchi, Y., Ikehata, Y., Kajinaga, Y.: Hierarchical data visualization using a fast rectangle-packing algorithm. IEEE Transactions on Visualization and Computer Graphics, 302–313 (2004)Google Scholar
  9. 9.
    Koike, H.: Fractal views: a fractal-based method for controlling information display. ACM Trans. Inf. Syst. 13, 305–323 (1995)CrossRefGoogle Scholar
  10. 10.
    Tory, M., Moller, T., Atkins, M., Kirkpatrick, A.: Combining 2D and 3D views for orientation and relative position tasks. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 73–80. ACM, New York (2004)Google Scholar
  11. 11.
    Piringer, H., Kosara, R., Hauser, H.: Interactive focus+context visualization with linked 2d/3d scatterplots. In: International Conference on Coordinated and Multiple Views in Exploratory Visualization, pp. 49–60 (2004)Google Scholar
  12. 12.
    Yang, J., Hubball, D., Ward, M.O., Rundensteiner, E.A., Ribarsky, W.: Value and relation display: Interactive visual exploration of large data sets with hundreds of dimensions. IEEE Transactions on Visualization and Computer Graphics 13, 494–507 (2007)CrossRefGoogle Scholar
  13. 13.
    Keim, D.: Designing pixel-oriented visualization techniques: theory and applications. IEEE Transactions on Visualization and Computer Graphics 6, 59–78 (2000)CrossRefGoogle Scholar
  14. 14.
    Bentley, C., Ward, M.: Animating multidimensional scaling to visualize N-dimensional data sets. In: Proceedings of the 1996 IEEE Symposium on Information Visualization (INFOVIS 1996), p. 72. IEEE Computer Society, Los Alamitos (1996)Google Scholar
  15. 15.
    Wattenberg, M.: A note on space-filling visualizations and space-filling curves (2005)Google Scholar
  16. 16.
    Iwamaru, M., Okamoto, K.: Multiresolutional volume expansion and visualization with fractal diagram. Journal of the Visualization Society of Japan 28, 75–78 (2008)CrossRefGoogle Scholar
  17. 17.
    Tsubokura, M., Kobayashi, T., Nakashima, T., Nouzawa, T., Nakamura, T., Zhang, H., Onishi, K., Oshima, N.: Computational visualization of unsteady flow around vehicles using high performance computing. Computers & Fluids 38, 981–990 (2009)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Takanori Fujiwara
    • 1
  • Ryo Matsushita
    • 1
  • Masaki Iwamaru
    • 2
  • Manabu Tange
    • 3
  • Satoshi Someya
    • 1
  • Koji Okamoto
    • 1
  1. 1.The Graduate School of Frontier SciencesThe University of TokyoJapan
  2. 2.SGI Japan, Ltd.Japan
  3. 3.Department of Technical EngineeringShibaura Institute of TechnologyJapan

Personalised recommendations