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Efficient Morse Decompositions of Vector Fields
July/August 2008 (vol. 14 no. 4)
pp. 848-862
ASCII Text
x 
 
Guoning Chen, Konstantin Mischaikow, Robert S. Laramee, Eugene Zhang, "Efficient Morse Decompositions of Vector Fields," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 4, pp. 848-862, July/August, 2008.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2008.33,
author = {Guoning Chen and Konstantin Mischaikow and Robert S. Laramee and Eugene Zhang},
title = {Efficient Morse Decompositions of Vector Fields},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {14},
number = {4},
issn = {1077-2626},
year = {2008},
pages = {848-862},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2008.33},
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 - Efficient Morse Decompositions of Vector Fields
IS - 4
SN - 1077-2626
SP848
EP862
EPD - 848-862
A1 - Guoning Chen,
A1 - Konstantin Mischaikow,
A1 - Robert S. Laramee,
A1 - Eugene Zhang,
PY - 2008
KW - Flow analysis
KW - Visualization
VL - 14
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories which are sensitive to noise and errors introduced by simulation and interpolation. This makes such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG). While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCG's, while fast, are overly conservative and usually results in MCG's that are too coarse to be useful. To address this issue, we present a new technique for performing Morse decomposition based on the concept of tau-maps, which typically provides finer MCG's than existing techniques. Furthermore, the choice of tau provides a natural tradeoff between the fineness of the MCG's and the computational costs. We provide efficient implementations of Morse decomposition based on tau-maps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles. Furthermore, we propose the use of spatial tau-maps in addition to the original temporal tau-maps.

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Index Terms:
Flow analysis, Visualization
Citation:
Guoning Chen, Konstantin Mischaikow, Robert S. Laramee, Eugene Zhang, "Efficient Morse Decompositions of Vector Fields," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 4, pp. 848-862, July-Aug. 2008, doi:10.1109/TVCG.2008.33
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