TY - GEN A1 - Reininghaus, Jan A1 - Kasten, Jens A1 - Weinkauf, Tino A1 - Hotz, Ingrid T1 - Combinatorial Feature Flow Fields: Tracking Critical Points in Discrete Scalar Fields N2 - We propose a combinatorial algorithm to track critical points of 2D time-dependent scalar fields. Existing tracking algorithms such as Feature Flow Fields apply numerical schemes utilizing derivatives of the data, which makes them prone to noise and involve a large number of computational parameters. In contrast, our method is robust against noise since it does not require derivatives, interpolation, and numerical integration. Furthermore, we propose an importance measure that combines the spatial persistence of a critical point with its temporal evolution. This leads to a time-aware feature hierarchy, which allows us to discriminate important from spurious features. Our method requires only a single, easy-to-tune computational parameter and is naturally formulated in an out-of-core fashion, which enables the analysis of large data sets. We apply our method to a number of data sets and compare it to the stabilized continuous Feature Flow Field tracking algorithm. T3 - ZIB-Report - 11-02 KW - data analysis KW - feature detection KW - time-varying data KW - topology-based techniques Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12151 ER - TY - THES A1 - Reininghaus, Jan T1 - Computational discrete Morse theory Y1 - 2012 ER - TY - JOUR A1 - Reininghaus, Jan A1 - Kotava, N. A1 - Günther, David A1 - Kasten, Jens A1 - Hagen, Hans A1 - Hotz, Ingrid T1 - A Scale Space Based Persistence Measure for Critical Points in 2D Scalar Fields JF - Visualization and Computer Graphics, IEEE Transactions on Y1 - 2011 U6 - https://doi.org/10.1109/TVCG.2011.159 VL - 17 IS - 12 SP - 2045 EP - 2052 ER - TY - CHAP A1 - Reininghaus, Jan A1 - Günther, David A1 - Hotz, Ingrid A1 - Prohaska, Steffen A1 - Hege, Hans-Christian T1 - TADD: A Computational Framework for Data Analysis Using Discrete Morse Theory T2 - Mathematical Software - ICMS 2010 Y1 - 2010 U6 - https://doi.org/10.1007/978-3-642-15582-6_35 VL - 6327 SP - 198 EP - 208 PB - Springer ER - TY - GEN A1 - Reininghaus, Jan A1 - Hotz, Ingrid ED - Pascucci, Valerio ED - Tricoche, Xavier ED - Hagen, Hans ED - Tierny, Julien T1 - Combinatorial 2D Vector Field Topology Extraction and Simplification T2 - Topological Methods in Data Analysis and Visualization Y1 - 2011 SN - 978-3-642-15013-5 U6 - https://doi.org/10.1007/978-3-642-15014-2_9 SP - 103 EP - 114 PB - Springer ER - TY - JOUR A1 - Reininghaus, Jan A1 - Löwen, Christian A1 - Hotz, Ingrid T1 - Fast Combinatorial Vector Field Topology JF - IEEE Trans. Computer Graphics and Visualization Y1 - 2011 VL - 17 IS - 10 SP - 1433 EP - 1443 ER - TY - JOUR A1 - Reininghaus, Jan A1 - Kasten, Jens A1 - Weinkauf, Tino A1 - Hotz, Ingrid T1 - Efficient Computation of Combinatorial Feature Flow Fields JF - Transactions on Visualization and Computer Graphics Y1 - 2012 U6 - https://doi.org/10.1109/TVCG.2011.269 VL - 18 IS - 9 SP - 1563 EP - 1573 ER - TY - GEN A1 - Reininghaus, Jan A1 - Günther, David A1 - Hotz, Ingrid A1 - Weinkauf, Tino A1 - Seidel, Hans Peter T1 - Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices Y1 - 2012 UR - http://arxiv.org/abs/1208.6523 ER -