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 - Kasten, Jens A1 - Reininghaus, Jan A1 - Hotz, Ingrid A1 - Hege, Hans-Christian T1 - Two-Dimensional Time-Dependent Vortex Regions Based on the Acceleration Magnitude JF - IEEE Transactions on Visualization and Computer Graphics Y1 - 2011 VL - 17 IS - 12 SP - 2080 EP - 2087target 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 - JOUR A1 - Günther, David A1 - Reininghaus, Jan A1 - Wagner, Hubert A1 - Hotz, Ingrid T1 - Memory-Efficient Computation of Persistent Homology for 3D Images using Discrete Morse Theory JF - Proc. Sibgrapi – Conference on Graphics, Patterns and Images Y1 - 2011 PB - Kluwer Academic Publishers ER - TY - CHAP A1 - Boyer, Edmond A1 - Bronstein, Alexander A1 - Bronstein, Michael A1 - Bustos, Benjamin A1 - Darom, Tal A1 - Horaud, Radu A1 - Hotz, Ingrid A1 - Keller, Yosi A1 - Keustermans, Johannes A1 - Kovnatsky, Artiom A1 - Litman, Roee A1 - Reininghaus, Jan A1 - Sipiran, Ivan A1 - Smeets, Dirk A1 - Suetens, Paul A1 - Vandermeulen, Dirk A1 - Zaharescu, Andrei A1 - Zobel, Valentin T1 - SHREC 2011: robust feature detection and description benchmark T2 - Proc. Eurographics 2011 Workshop on 3D Object Retrieval (3DOR’11) Y1 - 2011 U6 - https://doi.org/10.2312/3DOR/3DOR11/079-088 target SP - 71 EP - 78 PB - Eurographics Association 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 - Zobel, Valentin A1 - Reininghaus, Jan A1 - Hotz, Ingrid T1 - Visualization of Two-Dimensional Symmetric Tensor Fields Using the Heat Kernel Signature T2 - Topological Methods in Data Analysis and Visualization III Y1 - 2013 SP - 249 EP - 262 CY - Davis, CA, USA 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 - Kasten, Jens A1 - Reininghaus, Jan A1 - Hotz, Ingrid A1 - Hege, Hans-Christian A1 - Noack, Bernd A1 - Daviller, Guillaume A1 - Morzyński, Marek T1 - Acceleration feature points of unsteady shear flows JF - Archives of Mechanics N2 - A framework is proposed for extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance. The minima of the acceleration magnitude, i.e. a superset of the acceleration zeros, are extracted and discriminated into vortices and saddle points --- based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These features are tracked in time with a robust algorithm for tracking features. Thus a space-time hierarchy of the minima is built and vortex merging events are detected. The acceleration feature extraction strategy is applied to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of pressure field and minima of λ2. Y1 - 2016 VL - 68 IS - 1 SP - 55 EP - 80 ER - TY - GEN A1 - Kasten, Jens A1 - Reininghaus, Jan A1 - Hotz, Ingrid A1 - Hege, Hans-Christian A1 - Noack, Bernd A1 - Daviller, Guillaume A1 - Morzyński, Marek T1 - Acceleration feature points of unsteady shear flows N2 - A framework is proposed for extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance. The minima of the acceleration magnitude, i.e. a superset of the acceleration zeros, are extracted and discriminated into vortices and saddle points --- based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These features are tracked in time with a robust algorithm for tracking features. Thus a space-time hierarchy of the minima is built and vortex merging events are detected. The acceleration feature extraction strategy is applied to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of pressure field and minima of λ2. T3 - ZIB-Report - 15-65 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58397 SN - 1438-0064 ER - TY - GEN A1 - Günther, David A1 - Reininghaus, Jan A1 - Prohaska, Steffen A1 - Weinkauf, Tino A1 - Hege, Hans-Christian ED - Peikert, Ronny ED - Hauser, Helwig ED - Carr, Hamish T1 - Efficient Computation of a Hierarchy of Discrete 3D Gradient Vector Fields T2 - Topological Methods in Data Analysis and Visualization II Y1 - 2012 U6 - https://doi.org/10.1007/978-3-642-23175-9_2 SP - 15 EP - 29 PB - Springer ER - TY - JOUR A1 - Zobel, Valentin A1 - Reininghaus, Jan A1 - Hotz, Ingrid T1 - Generalized Heat Kernel Signature JF - Journal of WSCG, International Conference on Computer Graphics, Visualization and Computer Vision Y1 - 2011 SP - 93 EP - 100target ER - TY - GEN A1 - Kasten, Jens A1 - Reininghaus, Jan A1 - Oberleithner, Kilian A1 - Hotz, Ingrid A1 - Noack, Bernd A1 - Hege, Hans-Christian T1 - Flow over a Cavity – Evolution of the Vortex Skeleton Y1 - 2010 PB - Visualization at 28th Annual Gallery of Fluid Motion exhibit, held at the 63th Annual Meeting of the American Physical Society, Division of Fluid Dynamics (Long Beach, CA, USA, November 21-23, 2010). 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 - Günther, David A1 - Reininghaus, Jan A1 - Wagner, Hubert A1 - Hotz, Ingrid T1 - Efficient Computation of 3D Morse-Smale Complexes and Persistent Homology using Discrete Morse Theory JF - The Visual Computer Y1 - 2012 U6 - https://doi.org/10.1007/s00371-012-0726-8 VL - 28 IS - 10 SP - 959 EP - 969 ER - TY - GEN A1 - Reininghaus, Jan A1 - Hotz, Ingrid ED - Peikert, Ronald ED - Carr, Hamish ED - Hauser, Helwig T1 - Computational Discrete Morse Theory for Divergence-Free 2D Vector Fields T2 - Topological Methods in Data Analysis and Visualization. Theory, Algorithms, and Applications. (TopoInVis 2011) Y1 - 2012 SP - 3 EP - 14 PB - Springer 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 - TY - GEN A1 - Kratz, Andrea A1 - Reininghaus, Jan A1 - Hadwiger, Markus A1 - Hotz, Ingrid T1 - Adaptive Screen-Space Sampling for Volume Ray-Casting N2 - This work is concerned with adaptive screen-space sampling for volume ray-casting. The goal is to reduce the number of rays being cast into the scene and, thus, the overall number of sampling points. We guarantee reliable images through explicit error control using an error estimator that is founded in the field of finite element methods (FEM). FEM theory further provides a well-founded theory to prove the efficiency of the presented algorithm via convergence analysis. We, therefore, compare the convergence behavior of our method against uniform subdivisions and a refinement scheme that was presented in the context of CPU volume ray-casting. Minimizing the number of sampling points is of interest for rendering large datasets where each evaluation might need an expensive decompression. Furthermore, with increasing screen resolutions high-resolution images are created more efficiently with our method. T3 - ZIB-Report - 11-04 Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12446 ER -