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Simplifying Flexible Isosurfaces Using Local Geometric Measures

Published: 10 October 2004 Publication History

Abstract

The contour tree, an abstraction of a scalar field that encodes the nesting relationships of isosurfaces, can be used to accelerate isosurface extraction, to identify important isovalues for volume-rendering transfer functions, and to guide exploratory visualization through a flexible isosurface interface. Many real-world data sets produce unmanageably large contour trees which require meaningful simplification. We define local geometric measures for individual contours, such as surface area and contained volume, and provide an algorithm to compute these measures in a contour tree. We then use these geometric measures to simplify the contour trees, suppressing minor topological features of the data. We combine this with a flexible isosurface interface to allow users to explore individual contours of a dataset interactively.

References

[1]
BAJAJ, C. L., PASCUCCI, V., AND SCHIKORE, D. R. 1997. The Contour Spectrum. In Proceedings of IEEE Visualization 1997, 167-173.
[2]
BENTLEY, J. L. 1979. Decomposable searching problems. Inform. Process. Lett. 8, 244-251.
[3]
BREMER, P.-T., EDELSBRUNNER, H., HAMANN, B., AND PASCUCCI, V. 2003. A Multi-resolution Data Structure for Two-dimensional Morse-Smale Functions. In Proceedings of IEEE Visualization 2003, 139-146.
[4]
BRODLIE, K., AND WOOD, J. 2001. Recent advances in volume visualization. Computer Graphics Forum 20, 2 (June), 125-148.
[5]
CARR, H., AND SNOEYINK, J. 2003. Path Seeds and Flexible Isosurfaces: Using Topology for Exploratory Visualization. In Proceedings of Eurographics Visualization Symposium 2003, 49-58, 285.
[6]
CARR, H., MÖLLER, T., AND SNOEYINK, J. 2001. Simplicial Subdivisions and Sampling Artifacts. In Proceedings of IEEE Visualization 2001, 99-106.
[7]
CARR, H., SNOEYINK, J., AND AXEN, U. 2003. Computing Contour Trees in All Dimensions. Computational Geometry: Theory and Applications 24, 2, 75-94.
[8]
CARR, H. 2004. Topological Manipulation of Isosurfaces. PhD thesis, University of British Columbia, Vancouver, BC, Canada.
[9]
CHIANG, Y.-J., AND LU, X. 2003. Progressive Simplification of Tetrahedral Meshes Preserving All Isosurface Topologies. Computer Graphics Forum 22, 3, to appear.
[10]
CHIANG, Y.-J., LENZ, T., LU, X., AND ROTE, G. 2002. Simple and Output-Sensitive Construction of Contour Trees Using Monotone Paths. Tech. Rep. ECGTR-244300-01, Institut für Informatik, Freie Universtät Berlin.
[11]
EDELSBRUNNER, H., AND MÜCKE, E. P. 1990. Simulation of Simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics 9, 1, 66-104.
[12]
EDELSBRUNNER, H., LETSCHER, D., AND ZOMORODIAN, A. 2002. Topological persistence and simplification. Discrete Comput. Geom. 28, 511-533.
[13]
EDELSBRUNNER, H., HARER, J., AND ZOMORODIAN, A. 2003. Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds. Discrete Comput. Geom. 30, 87-107.
[14]
HILAGA, M., SHINAGAWA, Y., KOHMURA, T., AND KUNII, T. L. 2001. Topology matching for fully automatic similarity estimation of 3d shapes. In SIGGRAPH 2001, 203-212.
[15]
KETTNER, L., ROSSIGNAC, J., AND SNOEYINK, J. 2001. The Safari Interface for Visualizing Time-Dependent Volume Data Using Iso-surfaces and Contour Spectra. Computational Geometry: Theory and Applications 25, 1-2, 97-116.
[16]
LORENSON, W. E., AND CLINE, H. E. 1987. Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics 21, 4, 163-169.
[17]
MATSUMOTO, Y. 2002. An Introduction to Morse Theory. AMS.
[18]
MILNOR, J. 1963. Morse Theory. Princeton University Press, Princeton, NJ.
[19]
MONTANI, C., SCATENI, R., AND SCOPIGNO, R. 1994. A modified look-up table for implicit disambiguation of Marching Cubes. Visual Computer 10, 353-355.
[20]
PASCUCCI, V., AND COLE-MCLAUGHLIN, K. 2002. Efficient Computation of the Topology of Level Sets. In Proceedings of IEEE Visualization 2002, 187-194.
[21]
PASCUCCI, V. 2001. On the Topology of the Level Sets of a Scalar Field. In Abstracts of the 13th Canadian Conference on Computational Geometry, 141-144.
[22]
REEB, G. 1946. Sur les points singuliers d'une forme de Pfaff complètement intégrable ou d'une fonction numérique. Comptes Rendus de l'Acadèmie des Sciences de Paris 222, 847-849.
[23]
TAKAHASHI, S., FUJISHIRO, I., AND TAKESHIMA, Y. 2004. Topological volume skeletonization and its application to transfer function design. Graphical Models 66, 1, 24-49.
[24]
TAKAHASHI, S., NIELSON, G. M., TAKESHIMA, Y., AND FUJISHIRO, I. 2004. Topological Volume Skeletonization Using Adaptive Tetrahedralization. In Geometric Modelling and Processing 2004.
[25]
TARASOV, S. P., AND VYALYI, M. N. 1998. Construction of Contour Trees in 3D in O(nlogn) steps. In Proceedings of the 14th ACM Symposium on Computational Geometry, 68-75.
[26]
VAN KREVELD, M., VAN OOSTRUM, R., BAJAJ, C. L., PASCUCCI, V., AND SCHIKORE, D. R. 1997. Contour Trees and Small Seed Sets for Isosurface Traversal. In Proceedings of the 13th ACM Symposium on Computational Geometry, 212-220.

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    cover image ACM Conferences
    VIS '04: Proceedings of the conference on Visualization '04
    October 2004
    667 pages
    ISBN:0780387880

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    IEEE Computer Society

    United States

    Publication History

    Published: 10 October 2004

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    Author Tags

    1. Isosurfaces
    2. contour trees
    3. topological simplification

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    • (2016)Towards visual mega-analysis of voxel-based measurement in brain cohortsProceedings of the Eurographics / IEEE VGTC Conference on Visualization: Short Papers10.5555/3058878.3058890(55-59)Online publication date: 6-Jun-2016
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