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Attila Gyulassy, Vijay Natarajan, Valerio Pascucci, PeerTimo Bremer, Bernd Hamann, "A Topological Approach to Simplification of ThreeDimensional Scalar Functions," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 4, pp. 474484, July/August, 2006.  
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@article{ 10.1109/TVCG.2006.57, author = {Attila Gyulassy and Vijay Natarajan and Valerio Pascucci and PeerTimo Bremer and Bernd Hamann}, title = {A Topological Approach to Simplification of ThreeDimensional Scalar Functions}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {12}, number = {4}, issn = {10772626}, year = {2006}, pages = {474484}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2006.57}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  A Topological Approach to Simplification of ThreeDimensional Scalar Functions IS  4 SN  10772626 SP474 EP484 EPD  474484 A1  Attila Gyulassy, A1  Vijay Natarajan, A1  Valerio Pascucci, A1  PeerTimo Bremer, A1  Bernd Hamann, PY  2006 KW  Morse theory KW  MorseSmale 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 MorseSmale 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 MorseSmale 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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