This Article 
 Bibliographic References 
 Add to: 
IStar: A Raster Representation for Scalable Image and Volume Data
November/December 2007 (vol. 13 no. 6)
pp. 1424-1431
Topology has been an important tool for analyzing scalar data and flow fields in visualization. In this work, we analyze the topology of multivariate image and volume data sets with discontinuities in order to create an efficient, raster-based representation we call IStar. Specifically, the topology information is used to create a dual structure that contains nodes and connectivity information for every segmentable region in the original data set. This graph structure, along with a sampled representation of the segmented data set, is embedded into a standard raster image which can then be substantially downsampled and compressed. During rendering, the raster image is upsampled and the dual graph is used to reconstruct the original function. Unlike traditional raster approaches, our representation can preserve sharp discontinuities at any level of magnification, much like scalable vector graphics. However, because our representation is raster-based, it is well suited to the real-time rendering pipeline. We demonstrate this by reconstructing our data sets on graphics hardware at real-time rates.

[1] K. S. Bonnell, M. A. Duchaineau, D. Schikore, B. Hamann, and K. I. Joy, Material interface reconstruction. IEEE Transactions on Visualization and Computer Graphics(TVCG), 9 (4): 500–511, 2003.
[2] T. Dey, H. Edelsbrunner, and S. Guha, Computational topology. Advances in Discrete and Computational Geometry (Contemporary mathematics 223), American Mathematical Society, pages 109–143, 1999.
[3] I. Fary, On straight line representation of planar graphs. Acta Univ. Szeged. Sect. Sci. Math., 11: 229–233, 1948.
[4] L. Grady, Multilabel random walker image segmentation using prior models. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR '05), volume 1, pages 763–770, 2005.
[5] A. Gyulassy, V. Natarajan, V. Pascucci, P.-T. Bremer, and B. Hamann, Topology-based simplification for feature extraction from 3d scalar fields. In IEEE Visualization 2005, pages 275–280, 2005.
[6] J. Hart, Computational topology for shape modeling. Shape Modeling International '99, pages 36–45, 1999.
[7] A. Hatcher, Algebraic Topology. University Press, Cambridge, 2002.
[8] J. Helman and L. Hesselink, Representation and display of vector field topology in fluid flow data sets. IEEE Computer, pages 27–36, Aug. 1989.
[9] J. Kniss and R. Hanson, Images and dual dataspaces. Technical report, University of Utah, 2006.
[10] J. Kniss, R. V. Uitert, A. Stephens, G. Li, T. Tasdizen, and C. Hansen, Statictically quantitative volume visualization. In IEEE Visualization 2005, pages 287–294, 2005.
[11] T. Kolda, R. Lewis, and V. Torczon, Optimization by direct search: New perspectives on some classical and modern methods. SIAM Review, 45 (3): 385–482, 2004.
[12] T. Kong, A. Roscoe, and A. Rosenfeld, Concepts of digital topology. Topology and its Applications, 46: 219–262, 1992.
[13] T. Kong and A. Rosenfeld, Digital topology: Introduction and survey. Computer Vision, Graphics, and Image Proc., 48 (3): 357–393, Dec. 1989.
[14] D. Laidlaw, Geometric Model Extraction from Magnetic Resonance Volume Data. PhD thesis, California Institute of Tech nology, 1995.
[15] C. Loop and J. Blinn, Resolution independent curve rendering using programmable graphics hardware. ACM Transactions on Graphics, 24 (3): 1000–1009, 2005.
[16] J. Loviscach and H. Bremen, Efficient magnification of bilevel textures. In ACM SIGGRAPH 2005 Conference Abstracts and Applications, 2005.
[17] J. Matas, R. Marik, and J. Kittler, The color adjacency graph representation of multi-coloured objects. Technical Report VSSP-TR-1/95, University of Surrey, 1995.
[18] J. Munkres, Topology. Prentice-Hall, Englewood Cliffs, NJ, 1975.
[19] J. B. Orlin, A. S. Schulz, and S. Sengupta, ɛ-optimization schemes and L-bit precision: alternative perspectives in combinatorial optimization. In ACM Symposium on Theory of Computing, pages 565–572, 2000.
[20] V. Pascucci, Topology Diagram of Scalar Fields in Scientific Visualization, chapter Chapter 8 in Topological Data Structures for Surfaces. 2004.
[21] N. Ray, X. Cavin, and B. Levy, Vector texture maps on the gpu. Technical Report ALICE-TR-05-003, 2005.
[22] G. Scheuermann and X. Tricoche, Visualization Handbook, chapter Topological Methods in Flow Visualization, pages 341–356. Elsevier, 2004.
[23] P. Sen, Silhouette maps for improved texture magnification. In Proceedings of Graphics Hardware, pages 65–73, 2004.
[24] P. Sen, M. Cammarano, and P. Hanrahan, Shadow silhouette maps. ACM Transactions on Graphics, 22 (3): 521–526, 2003.
[25] A. Systems, Postscript Language Reference Manual. 1985.
[26] T. Tasdizen, S. Awate, R. Whitaker, and N. Foster, Mri tissue classification with neighborhood statistics: A nonparametric, entropy-minimizing approach. In Proceedings of (MICCAI), volume 2, pages 517–525, 2005.
[27] J. Tumblin and P. Choudhury, Bixels: Picture samples with sharp embedded boundaries. In Proceedings of the Eurographics Symposium on Rendering, pages 186–196, 2004.
[28] R. Whitaker, D. Breen, K. Museth, and N. Soni, A framework for level set segmentation of volume datasets. In Proceedings of ACM Workshop on Volume Graphics, pages 159–168, June 2001.

Index Terms:
Topology, Compression, Image Representation, Multi-field Visualization
Joe Kniss, Warren Hunt, Kristin Potter, Pradeep Sen, "IStar: A Raster Representation for Scalable Image and Volume Data," IEEE Transactions on Visualization and Computer Graphics, vol. 13, no. 6, pp. 1424-1431, Nov.-Dec. 2007, doi:10.1109/TVCG.2007.70572
Usage of this product signifies your acceptance of the Terms of Use.