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Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees
November/December 2009 (vol. 15 no. 6)
pp. 1177-1184
ASCII Text
x 
 
J. Tierny, A. Gyulassy, E. Simon, V. Pascucci, "Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 6, pp. 1177-1184, November/December, 2009.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2009.163,
author = {J. Tierny and A. Gyulassy and E. Simon and V. Pascucci},
title = {Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {15},
number = {6},
issn = {1077-2626},
year = {2009},
pages = {1177-1184},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2009.163},
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 - Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees
IS - 6
SN - 1077-2626
SP1177
EP1184
EPD - 1177-1184
A1 - J. Tierny,
A1 - A. Gyulassy,
A1 - E. Simon,
A1 - V. Pascucci,
PY - 2009
KW - Surgery
KW - Tree graphs
KW - Data visualization
KW - Isosurfaces
KW - Data mining
KW - Topology
KW - Algorithm design and analysis
KW - Stress
KW - Scalability
KW - Level set
KW - topological simplification
KW - Reeb graph
KW - scalar field topology
KW - isosurfaces
VL - 15
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
J. Tierny, Sci. Comput. & Imaging Inst., Univ. of Utah, Salt Lake City, UT, USA
A. Gyulassy, Sci. Comput. & Imaging Inst., Univ. of Utah, Salt Lake City, UT, USA
E. Simon, Dassault Syst., UT, USA
V. Pascucci, Sci. Comput. & Imaging Inst., Univ. of Utah, Salt Lake City, UT, USA
This paper introduces an efficient algorithm for computing the Reeb graph of a scalar function f defined on a volumetric mesh M in Ropf3. We introduce a procedure called "loop surgery" that transforms M into a mesh M' by a sequence of cuts and guarantees the Reeb graph of f(M') to be loop free. Therefore, loop surgery reduces Reeb graph computation to the simpler problem of computing a contour tree, for which well-known algorithms exist that are theoretically efficient (O(n log n)) and fast in practice. Inverse cuts reconstruct the loops removed at the beginning. The time complexity of our algorithm is that of a contour tree computation plus a loop surgery overhead, which depends on the number of handles of the mesh. Our systematic experiments confirm that for real-life data, this overhead is comparable to the computation of the contour tree, demonstrating virtually linear scalability on meshes ranging from 70 thousand to 3.5 million tetrahedra. Performance numbers show that our algorithm, although restricted to volumetric data, has an average speedup factor of 6,500 over the previous fastest techniques, handling larger and more complex data-sets. We demonstrate the verstility of our approach by extending fast topologically clean isosurface extraction to non simply-connected domains. We apply this technique in the context of pressure analysis for mechanical design. In this case, our technique produces results in matter of seconds even for the largest meshes. For the same models, previous Reeb graph techniques do not produce a result.

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Index Terms:
Surgery,Tree graphs,Data visualization,Isosurfaces,Data mining,Topology,Algorithm design and analysis,Stress,Scalability,Level set,topological simplification,Reeb graph,scalar field topology,isosurfaces
Citation:
J. Tierny, A. Gyulassy, E. Simon, V. Pascucci, "Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 6, pp. 1177-1184, Nov.-Dec. 2009, doi:10.1109/TVCG.2009.163
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