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Issue No.06 - November/December (2009 vol.15)
pp: 1473-1480
Ross Maciejewski , Purdue University
Insoo Woo , Purdue University
Wei Chen , Zhejiang University
David Ebert , Purdue University
ABSTRACT
The use of multi-dimensional transfer functions for direct volume rendering has been shown to be an effective means of extracting materials and their boundaries for both scalar and multivariate data. The most common multi-dimensional transfer function consists of a two-dimensional (2D) histogram with axes representing a subset of the feature space (e.g., value vs. value gradient magnitude), with each entry in the 2D histogram being the number of voxels at a given feature space pair. Users then assign color and opacity to the voxel distributions within the given feature space through the use of interactive widgets (e.g., box, circular, triangular selection). Unfortunately, such tools lead users through a trial-and-error approach as they assess which data values within the feature space map to a given area of interest within the volumetric space. In this work, we propose the addition of non-parametric clustering within the transfer function feature space in order to extract patterns and guide transfer function generation. We apply a non-parametric kernel density estimation to group voxels of similar features within the 2D histogram. These groups are then binned and colored based on their estimated density, and the user may interactively grow and shrink the binned regions to explore feature boundaries and extract regions of interest. We also extend this scheme to temporal volumetric data in which time steps of 2D histograms are composited into a histogram volume. A three-dimensional (3D) density estimation is then applied, and users can explore regions within the feature space across time without adjusting the transfer function at each time step. Our work enables users to effectively explore the structures found within a feature space of the volume and provide a context in which the user can understand how these structures relate to their volumetric data. We provide tools for enhanced exploration and manipulation of the transfer function, and we show that the initial transfer function generation serves as a reasonable base for volumetric rendering, reducing the trial-and-error overhead typically found in transfer function design.
INDEX TERMS
Volume rendering, kernel density estimation, transfer function design, temporal volume rendering
CITATION
Ross Maciejewski, Insoo Woo, Wei Chen, David Ebert, "Structuring Feature Space: A Non-Parametric Method for Volumetric Transfer Function Generation", IEEE Transactions on Visualization & Computer Graphics, vol.15, no. 6, pp. 1473-1480, November/December 2009, doi:10.1109/TVCG.2009.185
REFERENCES
[1] H. Akiba and K.-L. Ma, A tri-space visualization interface for analyzing time-varying multivariate volume data. In Proceedings of Eurographics/IEEE VGTC Symposium on Visualization, pages 115–122, May 2007.
[2] H. Akiba, K.-L. Ma, J. H. Chen, and E. R. Hawkes, Visualizing multivariate volume data from turbulent combustion simulations. Computing in Science and Engineering, 9 (2): 76–83, 2007.
[3] S. Bachthaler and D. Weiskopf, Continuous scatterplots. IEEE Transactions on Visualization and Computer Graphics, 14 (6): 1428–1435, 2008.
[4] C. A. Brewer, Designing better Maps: A Guide for GIS users. ESRI Press, 2005.
[5] C. Correa and K.-L. Ma, Size-based transfer functions: A new volume exploration technique. IEEE Transactions on Visualization and Computer Graphics, 14 (6): 1380–1387, October 2008.
[6] C. Correa and K.-L. Ma, Visibility-driven transfer functions. In Proceedings IEEE-VGTC Pacific Visualization Symposium, Beijing, China, April 2009.
[7] S. Fang, T. Biddlecome, and M. Tuceryan, Image-based transfer function design for data exploration in volume visualization. In Proceedings of the IEEE Conference on Visualization, pages 319–326, 1998.
[8] G. Kindlmann and J. W. Durkin, Semi-automatic generation of transfer functions for direct volume rendering. In Proceedings of the IEEE Symposium on Volume Visualization, pages 79–86, 1998.
[9] G. Kindlmann, R. Whitaker, T. Tasdizen, and T. Moller, Curvature-based transfer functions for direct volume rendering: Methods and applications. In Proceedings of the IEEE Conference on Visualization, pages 513–520, 2003.
[10] J. Kniss, G. Kindlmann, and C. Hansen, Interactive volume rendering using multi-dimensional transfer functions and direct manipulation widgets. In Proceedings of the IEEE Conference on Visualization, pages 255–262, 2001.
[11] J. M. Kniss, R. V. Uitert, A. Stephens, G. S. Li, T. Tasdizen, and C. Hansen, Statistically quantitative volume visualization. In Proceedings of the IEEE Conference on Visualization, pages 287–294, 2005.
[12] M. Levoy, Display of surfaces from volume data. IEEE Computer Graphics & Applications, 8 (3): 29–37, 1988.
[13] C. L. P. Ljung and A. Ynnerman, Local histograms for design of transfer functions in direct volume rendering. IEEE Transactions on Visualization and Computer Graphics, 12 (6): 1570–1579, 2006.
[14] C. Lundström, A. Ynnerman, P. Ljung, A. Persson, and H. Knutsson, The alpha-histogram: Using spatial coherence to enhance histograms and transfer function design. In Proceedings Eurographics/IEEE-VGTC Symposium on Visualization 2006, May 2006.
[15] C. Muelder and K.-L. Ma, Interactive feature extraction and tracking by utilizing region coherency. In Proceedings of IEEE Pacific Visualization Symposium, April 2009.
[16] S. Potts and T. Moller, Transfer functions on a logarithmic scale for volume rendering. In Proceedings of Graphics Interface, pages 57–63, 2004.
[17] C. Rezk-Salama, M. Keller, and P. Kohlmann, High-level user interfaces for transfer function design with semantics. IEEE Transactions on Visualization and Computer Graphics, 12 (5): 1021–1028, 2006.
[18] S. Roettger, M. Bauer, and M. Stamminger, Spatialized transfer functions. In Proceedings Eurographics/IEEE-VGTC Symposium on Visualization 2005, 2005.
[19] T. Ropinski, J.-S. Prani, F. Steinicke, and K. H. Hinrichs, Stroke-based transfer function design. In IEEE/EG International Symposium on Volume and Point-Based Graphics, pages 41–48, 2008.
[20] A. Shamir, Feature-space analysis of unstructured meshes. In Proceedings of the IEEE Conference on Visualization, pages 185–192, 2003.
[21] B. W. Silverman, Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC, 1986.
[22] N. Svakhine and D. S. Ebert, Interactive volume illustration and feature halos. In Proceedings IEEE-VGTC Pacific Visualization Symposium, October 2003.
[23] N. A. Svakhine, Y. Jang, D. S. Ebert, and K. P. Gaither, Illustration and photography inspired visualization of flows and volumes. In Proceedings of the IEEE Conference on Visualization, pages 687–694, 2005.
[24] I. Takanashi, E. B. Lum, K.-L. Ma, and S. Muraki, ISpace: Interactive volume data classification techniques using independent component analysis. In Proceedings of Pacific Graphics, pages 366–374, 2002.
[25] F.-Y. Tzeng, E. B. Lum, and K.-L. Ma, A novel interface for higher-dimensional classification of volume data. In Proceedings of the IEEE Conference on Visualization, pages 505–512, 2003.
[26] M. P. Wand, Kernel Smoothing. Chapman & Hall/CRC, 1995.
[27] G. H. Weber, S. E. Dillard, H. Carr, V. Pascucci, and B. Hamann, Topology-controlled volume rendering. IEEE Transactions on Visualization and Computer Graphics, 13 (2): 330–341, 2007.
[28] E. W. Weisstein, "The Cayley Cubic." From MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.comGreensIdentities.html.
[29] Y. Wu and H. Qu, Interactive transfer function design based on editing direct volume rendered images. IEEE Transactions on Visualization and Computer Graphics, 13 (5): 1027–1040, 2007.
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