VISUALIZATION OF UNCERTAIN CONTOUR TREES

Martin Kraus

Abstract

Contour trees can represent the topology of large volume data sets in a relatively compact, discrete data structure. However, the resulting trees often contain many thousands of nodes; thus, many graph drawing techniques fail to produce satisfactory results. Therefore, several visualization methods were proposed recently for the visualization of contour trees. Unfortunately, none of these techniques is able to handle uncertain contour trees although any uncertainty of the volume data inevitably results in partially uncertain contour trees. In this work, we visualize uncertain contour trees by combining the contour trees of two morphologically filtered versions of a volume data set, which represent the range of uncertainty. These two contour trees are combined and visualized within a single image such that a range of potential contour trees is represented by the resulting visualization. Thus, potentially erroneous topological structures are visually distinguished from more certain structures. Moreover, topological structures can be revealed that are otherwise obscured by data errors. We present and discuss results obtained with a prototypical implementation using well-known volume data sets.

References

  1. Bajaj, C. L., Pascucci, V., and Schikore, D. R. (1997). The contour spectrum. In Proceedings of the conference on Visualization 7897, pages 167-ff.
  2. Bartz, D. (2005). Volren and volvis homepage. URL: http://www.volvis.org/; last accessed November 18, 2009.
  3. Byron, L. and Wattenberg, M. (2008). Stacked graphs - geometry & aesthetics. Visualization and Computer Graphics, IEEE Transactions on, 14(6):1245-1252.
  4. Carr, H., Snoeyink, J., and van de Panne, M. (2004). Simplifying flexible isosurfaces using local geometric measures. In Proceedings of the conference on Visualization 7804, pages 497-504.
  5. Delugach, H. and de Moor, A. (2005). Difference graphs. In Common Semantics for Sharing Knowledge: Contributions to ICCS 2005. kassel university press.
  6. Freeman, S. and Morse, S. P. (1967). On searching a contour map for a given terrain elevation profile. Journal of the Franklin Institute, 284(1):1-25.
  7. Fry, B. J. (2004). Computational Information Design. PhD thesis. Supervisor: John Maeda.
  8. Griethe, H. and Schumann, H. (2006). The visualization of uncertain data: Methods and problems. In Proceedings of SimVis06, pages 143-156.
  9. Havre, S., Hetzler, E., Whitney, P., and Nowell, L. (2002). Themeriver: Visualizing thematic changes in large document collections. Visualization and Computer Graphics, IEEE Transactions on, 8(1):9-20.
  10. Johnson, C. R. and Sanderson, A. R. (2003). A next step: Visualizing errors and uncertainty. IEEE Computer Graphics and Applications, 23(5):6-10.
  11. Kardos, J., Moore, A., , and Benwell, G. (2006). Expressing attribute uncertainty in spatial data using blinking regions. In Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resssources and Environmental Sciences.
  12. Klemelä, J. (2004). Visualization of multivariate density estimates with level set trees. Journal of Computational and Graphical Statistics, 13(3):599-620.
  13. Kraus, M. (2010). Visualizing contour trees within histograms. In Proceedings of Computer Graphics and Imaging (CGIM 2010). Accepted for publication.
  14. Levoy, M. (2001). The stanford volume data archive. URL: http://graphics.stanford.edu/data/voldata/; last accessed November 18, 2009.
  15. Pascucci, V. and Cole-McLaughlin, K. (2002). Efficient computation of the topology of level sets. In Proceedings of the conference on Visualization 7802, pages 187-194.
  16. Pascucci, V., Cole-McLaughlin, K., and Scorzelli, G. (2004). Multi-resolution computation and presentation of contour trees. In Proceedings IASTED Conference Visualization, Imaging, and Image Processing, pages 452-290.
  17. Phan, D., Xiao, L., Yeh, R., Hanrahan, P., and Winograd, T. (2005). Flow map layout. In Proceedings of the 2005 IEEE Symposium on Information Visualization, page 29.
  18. Riehmann, P., Hanfler, M., and Froehlich, B. (2005). Interactive Sankey diagrams. In Proceedings of 2005 IEEE Symposium on Information Visualization, page 31.
  19. Rosvall, M. and Bergstrom, C. T. (2008). ping change in large networks. http://arxiv.org/abs/0812.1242v1; last November 18, 2009. MapURL: accessed
  20. Shinagawa, Y., Kunii, T., and Kergosien, Y. (1991). Surface coding based on morse theory. IEEE Computer Graphics and Applications, 11(5):66-78.
  21. Sternberg, S. (1986). Grayscale morphology. Computer Vision, Graphics, and Image Processing, 35(3):333- 355.
  22. Takahashi, S., Takeshima, Y., and Fujishiro, I. (2004a). Topological volume skeletonization and its application to transfer function design. Graph. Models, 66(1):24-49.
  23. Takahashi, S., Takeshima, Y., Nielson, G. M., and Fujishiro, I. (2004b). Topological volume skeletonization using adaptive tetrahedralization. Geometric Modeling and Processing, 2004. Proceedings, pages 227-236.
  24. Weber, G., Bremer, P.-T., and Pascucci, V. (2007a). Topological landscapes: A terrain metaphor for scientific data. Visualization and Computer Graphics, IEEE Transactions on, 13(6):1416-1423.
  25. Weber, G. H., Dillard, S. E., Carr, H., Pascucci, V., and Hamann, B. (2007b). Topology-controlled volume rendering. Visualization and Computer Graphics, IEEE Transactions on, 13(2):330-341.
Download


Paper Citation


in Harvard Style

Kraus M. (2010). VISUALIZATION OF UNCERTAIN CONTOUR TREES . In Proceedings of the International Conference on Imaging Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: IVAPP, (VISIGRAPP 2010) ISBN 978-989-674-027-6, pages 132-139. DOI: 10.5220/0002817201320139


in Bibtex Style

@conference{ivapp10,
author={Martin Kraus},
title={VISUALIZATION OF UNCERTAIN CONTOUR TREES},
booktitle={Proceedings of the International Conference on Imaging Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: IVAPP, (VISIGRAPP 2010)},
year={2010},
pages={132-139},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002817201320139},
isbn={978-989-674-027-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Imaging Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: IVAPP, (VISIGRAPP 2010)
TI - VISUALIZATION OF UNCERTAIN CONTOUR TREES
SN - 978-989-674-027-6
AU - Kraus M.
PY - 2010
SP - 132
EP - 139
DO - 10.5220/0002817201320139