@article{KastenReininghausHotzetal.2016, author = {Kasten, Jens and Reininghaus, Jan and Hotz, Ingrid and Hege, Hans-Christian and Noack, Bernd and Daviller, Guillaume and Morzyński, Marek}, title = {Acceleration feature points of unsteady shear flows}, series = {Archives of Mechanics}, volume = {68}, journal = {Archives of Mechanics}, number = {1}, pages = {55 -- 80}, year = {2016}, abstract = {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.}, language = {en} } @misc{KastenReininghausHotzetal., author = {Kasten, Jens and Reininghaus, Jan and Hotz, Ingrid and Hege, Hans-Christian and Noack, Bernd and Daviller, Guillaume and Morzyński, Marek}, title = {Acceleration feature points of unsteady shear flows}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58397}, abstract = {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.}, language = {en} } @misc{ZobelReininghausHotz2013, author = {Zobel, Valentin and Reininghaus, Jan and Hotz, Ingrid}, title = {Visualization of Two-Dimensional Symmetric Tensor Fields Using the Heat Kernel Signature}, series = {Topological Methods in Data Analysis and Visualization III}, journal = {Topological Methods in Data Analysis and Visualization III}, address = {Davis, CA, USA}, pages = {249 -- 262}, year = {2013}, language = {en} } @phdthesis{Reininghaus2012, author = {Reininghaus, Jan}, title = {Computational discrete Morse theory}, year = {2012}, language = {en} } @misc{GuentherReininghausProhaskaetal.2012, author = {G{\"u}nther, David and Reininghaus, Jan and Prohaska, Steffen and Weinkauf, Tino and Hege, Hans-Christian}, title = {Efficient Computation of a Hierarchy of Discrete 3D Gradient Vector Fields}, series = {Topological Methods in Data Analysis and Visualization II}, journal = {Topological Methods in Data Analysis and Visualization II}, editor = {Peikert, Ronny and Hauser, Helwig and Carr, Hamish}, publisher = {Springer}, doi = {10.1007/978-3-642-23175-9_2}, pages = {15 -- 29}, year = {2012}, language = {en} } @article{GuentherReininghausWagneretal.2012, author = {G{\"u}nther, David and Reininghaus, Jan and Wagner, Hubert and Hotz, Ingrid}, title = {Efficient Computation of 3D Morse-Smale Complexes and Persistent Homology using Discrete Morse Theory}, series = {The Visual Computer}, volume = {28}, journal = {The Visual Computer}, number = {10}, doi = {10.1007/s00371-012-0726-8}, pages = {959 -- 969}, year = {2012}, language = {en} } @misc{ReininghausHotz2012, author = {Reininghaus, Jan and Hotz, Ingrid}, title = {Computational Discrete Morse Theory for Divergence-Free 2D Vector Fields}, series = {Topological Methods in Data Analysis and Visualization. Theory, Algorithms, and Applications. (TopoInVis 2011)}, journal = {Topological Methods in Data Analysis and Visualization. Theory, Algorithms, and Applications. (TopoInVis 2011)}, editor = {Peikert, Ronald and Carr, Hamish and Hauser, Helwig}, publisher = {Springer}, pages = {3 -- 14}, year = {2012}, language = {en} } @article{ReininghausKastenWeinkaufetal.2012, author = {Reininghaus, Jan and Kasten, Jens and Weinkauf, Tino and Hotz, Ingrid}, title = {Efficient Computation of Combinatorial Feature Flow Fields}, series = {Transactions on Visualization and Computer Graphics}, volume = {18}, journal = {Transactions on Visualization and Computer Graphics}, number = {9}, doi = {10.1109/TVCG.2011.269}, pages = {1563 -- 1573}, year = {2012}, language = {en} } @misc{ReininghausGuentherHotzetal.2012, author = {Reininghaus, Jan and G{\"u}nther, David and Hotz, Ingrid and Weinkauf, Tino and Seidel, Hans Peter}, title = {Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices}, year = {2012}, language = {en} } @misc{ReininghausKastenWeinkaufetal., author = {Reininghaus, Jan and Kasten, Jens and Weinkauf, Tino and Hotz, Ingrid}, title = {Combinatorial Feature Flow Fields: Tracking Critical Points in Discrete Scalar Fields}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12151}, number = {11-02}, abstract = {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.}, language = {en} }