Combinatorial Vector Field Topology
Analysis and comparison of vector fields can be done via a segmentation of the flow field into regions of similar behavior and a subsequent extraction of the topological skeleton. Our goals are a numerically stable computation of the topological skeleton including the extraction and classification of all closed streamlines, and a simple but consistent simplification of the topological skeleton to allow for a multi-scale vector field analysis. To achieve these goals we are investigating the applicability of a combinatorial approach to vector field topology.
Publications
2012
2011
2010
2012 |
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Jan Reininghaus, David Günther, Ingrid Hotz, Tino Weinkauf, Hans Peter Seidel | Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices | 2012arXiv |
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arXiv |
Jan Reininghaus | Computational discrete Morse theory | Doctoral thesis, Otto-von-Guericke-Universität Magdeburg, 2012 |
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Jan Reininghaus, Jens Kasten, Tino Weinkauf, Ingrid Hotz | Efficient Computation of Combinatorial Feature Flow Fields | Transactions on Visualization and Computer Graphics, 18(9), pp. 1563-1573, 2012 |
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2011 |
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Jan Reininghaus, N. Kotava, David Günther, Jens Kasten, Hans Hagen, Ingrid Hotz | A Scale Space Based Persistence Measure for Critical Points in 2D Scalar Fields | Visualization and Computer Graphics, IEEE Transactions on, 17(12), pp. 2045-2052, 2011 |
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Jan Reininghaus, Ingrid Hotz | Combinatorial 2D Vector Field Topology Extraction and Simplification | Topological Methods in Data Analysis and Visualization, pp. 103-114, Valerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny (Eds.), Springer, 2011, ISBN: 978-3-642-15013-5 |
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Jan Reininghaus, Jens Kasten, Tino Weinkauf, Ingrid Hotz | Combinatorial Feature Flow Fields: Tracking Critical Points in Discrete Scalar Fields | ZIB-Report 11-02 |
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Jan Reininghaus, Christian Löwen, Ingrid Hotz | Fast Combinatorial Vector Field Topology | IEEE Trans. Computer Graphics and Visualization, 17(10), pp. 1433-1443, 2011 |
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2010 |
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Jan Reininghaus, David Günther, Ingrid Hotz, Steffen Prohaska, Hans-Christian Hege | TADD: A Computational Framework for Data Analysis Using Discrete Morse Theory | Mathematical Software - ICMS 2010, pp. 198-208, Vol.6327, Lecture Notes in Computer Science, 2010 |
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