Abstract
We present a new downsampling method for structured volume grids, which preserves much more of the topology of a scalar field than existing downsampling methods by preferably selecting scalar values of critical points. In particular, many critical points can be preserved which are lost by traditional downsampling methods. Our method is named “topology-guided downsampling” as topology-preserving downsampling is impossible in general. However, we show that even an approximate preservation of topology is highly desirable if isosurfaces are extracted from the downsampled volume grid, e.g. for interactive previewing, because many topological features of the isosurfaces, e.g. the number of components, tunnels, and holes, are preserved. We illustrate the benefits of our method with examples from medical and technical applications of volume visualization.
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References
Bajaj, C.L., Pascucci, V.: Visualization of Scalar Topology for Structural Enhancement. In: Proc. IEEE Visualization ‘88 (1998) 51–58
Bajaj, C.L., Schikore, D.R.: Topology Preserving Data Simplification with Error Bounds. Computers & Graphics 22 (1998) 3–12
Carr, H., Snoeyink, J., Axen, U.: Computing Contour Trees in All Dimensions. In: Proc. of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (2000) 918–926
Danskin, J., Hanrahan, P.: Fast Algorithms for Volume Ray Tracing. In: Proc. 1992 Workshop on Volume Visualization (1992) 91–98
Fujishiro, I., Azuma, T., Takeshima, Y.: Automating Transfer Function Design for Comprehensible Volume Rendering Based on 3D Field Topology Analysis. In: Proc. IEEE Visualization ‘89 (1999) 467–470
Gerstner, T., Pajarola, R.: Topology Preserving and Controlled Topology Simplifying Multiresolution Isosurface Extraction. In: Proc. IEEE Visualization ‘00 (2000) 259–266
He, T., Hong, L., Varshney, A., Wang, S.: Controlled Topology Simplification. IEEE Transactions on Visualization and Computer Graphics 2 (1996) 171–183
Laur, D., Hanrahan, P.: Hierarchical Splatting: A Progressive Refinement Algorithm for Volume Rendering. Computer Graphics (Proc. SIGGRAPH ‘81) 25 (1991) 258–288
Levoy, M., Whitaker, R.: Gaze-Directed Volume Rendering. Computer Graphics 24 (1990) 217–223
Milnor, J.: Morse Theory. Princeton University Press (1963)
Ohlberger, M., Rumpf, M.: Hierarchical and Adaptive Visualization on Nested Grids. Computing 59 (1997) 269–285
Resk-Salama, C., Engel, K., Bauer, M., Greiner, G., Ertl, T.: Interactive Volume Rendering on Standard PC Graphics Hardware Using Multi-Textures and MultiStage-Rasterization. In: Proc. 2000 SIGGRAPH/EUROGRAPHICS Workshop on Graphics Hardware (2000) 109–118
Shekhar, R., Fayyad, E., Yagel, R., Cornhill, J.F.: Octree-Based Decimation of Marching Cubes Surfaces. In: Proc. IEEE Visualization ‘86 (1996) 335–342
Westermann, R., Kobbelt, L., Ertl, T.: Real-time Exploration of Regular Volume Data by Adaptive Reconstruction of Isosurfaces. The Visual Computer 15 (1999) 100–111
Williams, L.: Pyramidal Parametrics. Computer Graphics (Proc. SIGGRAPH ‘83) 17 (1983) 1–11
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Kraus, M., Ertl, T. (2001). Topology-Guided Downsampling. In: Mueller, K., Kaufman, A.E. (eds) Volume Graphics 2001. Eurographics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6756-4_15
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DOI: https://doi.org/10.1007/978-3-7091-6756-4_15
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83737-5
Online ISBN: 978-3-7091-6756-4
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