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H. Doraiswamy, V. Natarajan, "Computing Reeb Graphs as a Union of Contour Trees," IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 2, pp. 249262, Feb., 2013.  
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@article{ 10.1109/TVCG.2012.115, author = {H. Doraiswamy and V. Natarajan}, title = {Computing Reeb Graphs as a Union of Contour Trees}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {19}, number = {2}, issn = {10772626}, year = {2013}, pages = {249262}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.115}, 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  Computing Reeb Graphs as a Union of Contour Trees IS  2 SN  10772626 SP249 EP262 EPD  249262 A1  H. Doraiswamy, A1  V. Natarajan, PY  2013 KW  trees (mathematics) KW  data handling KW  piecewise linear techniques KW  set theory KW  large data handling KW  contour tree union KW  scalar function KW  topology evolution KW  level set KW  piecewiselinear function KW  nonmanifold KW  efficient contour tree algorithm KW  loopfree Reeb graph KW  join tree KW  unionfind operation KW  generic algorithm KW  Level set KW  Vegetation KW  Memory management KW  Topology KW  Manifolds KW  Algorithm design and analysis KW  Complexity theory KW  outofcore algorithm KW  Computational topology KW  scalar functions KW  Reeb graphs KW  level set topology VL  19 JA  IEEE Transactions on Visualization and Computer Graphics ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.115
The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewiselinear (PL) function defined over manifolds and nonmanifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loopfree Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of unionfind operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.
Index Terms:
trees (mathematics),data handling,piecewise linear techniques,set theory,large data handling,contour tree union,scalar function,topology evolution,level set,piecewiselinear function,nonmanifold,efficient contour tree algorithm,loopfree Reeb graph,join tree,unionfind operation,generic algorithm,Level set,Vegetation,Memory management,Topology,Manifolds,Algorithm design and analysis,Complexity theory,outofcore algorithm,Computational topology,scalar functions,Reeb graphs,level set topology
Citation:
H. Doraiswamy, V. Natarajan, "Computing Reeb Graphs as a Union of Contour Trees," IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 2, pp. 249262, Feb. 2013, doi:10.1109/TVCG.2012.115
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