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| Attila Gyulassy, Vijay Natarajan, Valerio Pascucci, Peer-Timo Bremer, Bernd Hamann, "A Topological Approach to Simplification of Three-Dimensional Scalar Functions," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 4, pp. 474-484, July/August, 2006. | |||
| BibTex | x | ||
| @article{ 10.1109/TVCG.2006.57, author = {Attila Gyulassy and Vijay Natarajan and Valerio Pascucci and Peer-Timo Bremer and Bernd Hamann}, title = {A Topological Approach to Simplification of Three-Dimensional Scalar Functions}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {12}, number = {4}, issn = {1077-2626}, year = {2006}, pages = {474-484}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2006.57}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Visualization and Computer Graphics TI - A Topological Approach to Simplification of Three-Dimensional Scalar Functions IS - 4 SN - 1077-2626 SP474 EP484 EPD - 474-484 A1 - Attila Gyulassy, A1 - Vijay Natarajan, A1 - Valerio Pascucci, A1 - Peer-Timo Bremer, A1 - Bernd Hamann, PY - 2006 KW - Morse theory KW - Morse-Smale complexes KW - computational topology KW - computational geometry KW - simplification KW - multiresolution KW - feature detection KW - volumetric data. VL - 12 JA - IEEE Transactions on Visualization and Computer Graphics ER - | |||
Abstract—This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a function's associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features while removing small features and noise.
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