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Suresh K. Lodha, Nikolai M. Faaland, Jose C. Renteria, "Topology Preserving TopDown Compression of 2D Vector Fields Using Bintree and Triangular Quadtrees," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 4, pp. 433442, OctoberDecember, 2003.  
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@article{ 10.1109/TVCG.2003.1260738, author = {Suresh K. Lodha and Nikolai M. Faaland and Jose C. Renteria}, title = {Topology Preserving TopDown Compression of 2D Vector Fields Using Bintree and Triangular Quadtrees}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {9}, number = {4}, issn = {10772626}, year = {2003}, pages = {433442}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2003.1260738}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Topology Preserving TopDown Compression of 2D Vector Fields Using Bintree and Triangular Quadtrees IS  4 SN  10772626 SP433 EP442 EPD  433442 A1  Suresh K. Lodha, A1  Nikolai M. Faaland, A1  Jose C. Renteria, PY  2003 KW  Vector fields KW  compression KW  topology KW  topdown KW  bintree KW  quadtree KW  hierarchical algorithm. VL  9 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—We present a hierarchical topdown refinement algorithm for compressing 2D vector fields that preserves topology. Our approach is to reconstruct the data set using adaptive refinement that considers topology. The algorithms start with little data and subdivide regions that are most likely to reconstruct the original topology of the given data set. We use two different refinement techniques. The first technique uses bintree subdivision and linear interpolation. The second algorithm is driven by triangular quadtree subdivision with Coons patch quadratic interpolation. We employ local error metrics to measure the quality of compression and as a global metric we compute Earth Mover's Distance (EMD) to measure the deviation from the original topology. Experiments with both analytic and simulated data sets are presented. Results indicate that one can obtain significant compression with low errors without losing topological information. Advantages and disadvantages of different topology preserving compression algorithms are also discussed in the paper.
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