@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} } @phdthesis{Reininghaus2012, author = {Reininghaus, Jan}, title = {Computational discrete Morse theory}, year = {2012}, language = {en} } @article{KastenReininghausHotzetal.2011, author = {Kasten, Jens and Reininghaus, Jan and Hotz, Ingrid and Hege, Hans-Christian}, title = {Two-Dimensional Time-Dependent Vortex Regions Based on the Acceleration Magnitude}, series = {IEEE Transactions on Visualization and Computer Graphics}, volume = {17}, journal = {IEEE Transactions on Visualization and Computer Graphics}, number = {12}, pages = {2080 -- 2087target}, year = {2011}, language = {en} } @article{ReininghausKotavaGuentheretal.2011, author = {Reininghaus, Jan and Kotava, N. and G{\"u}nther, David and Kasten, Jens and Hagen, Hans and Hotz, Ingrid}, title = {A Scale Space Based Persistence Measure for Critical Points in 2D Scalar Fields}, series = {Visualization and Computer Graphics, IEEE Transactions on}, volume = {17}, journal = {Visualization and Computer Graphics, IEEE Transactions on}, number = {12}, doi = {10.1109/TVCG.2011.159}, pages = {2045 -- 2052}, year = {2011}, language = {en} } @article{GuentherReininghausWagneretal.2011, author = {G{\"u}nther, David and Reininghaus, Jan and Wagner, Hubert and Hotz, Ingrid}, title = {Memory-Efficient Computation of Persistent Homology for 3D Images using Discrete Morse Theory}, series = {Proc. Sibgrapi - Conference on Graphics, Patterns and Images}, journal = {Proc. Sibgrapi - Conference on Graphics, Patterns and Images}, publisher = {Kluwer Academic Publishers}, year = {2011}, language = {en} } @inproceedings{BoyerBronsteinBronsteinetal.2011, author = {Boyer, Edmond and Bronstein, Alexander and Bronstein, Michael and Bustos, Benjamin and Darom, Tal and Horaud, Radu and Hotz, Ingrid and Keller, Yosi and Keustermans, Johannes and Kovnatsky, Artiom and Litman, Roee and Reininghaus, Jan and Sipiran, Ivan and Smeets, Dirk and Suetens, Paul and Vandermeulen, Dirk and Zaharescu, Andrei and Zobel, Valentin}, title = {SHREC 2011: robust feature detection and description benchmark}, series = {Proc. Eurographics 2011 Workshop on 3D Object Retrieval (3DOR'11)}, booktitle = {Proc. Eurographics 2011 Workshop on 3D Object Retrieval (3DOR'11)}, publisher = {Eurographics Association}, doi = {10.2312/3DOR/3DOR11/079-088 target}, pages = {71 -- 78}, year = {2011}, language = {en} } @inproceedings{ReininghausGuentherHotzetal.2010, author = {Reininghaus, Jan and G{\"u}nther, David and Hotz, Ingrid and Prohaska, Steffen and Hege, Hans-Christian}, title = {TADD: A Computational Framework for Data Analysis Using Discrete Morse Theory}, series = {Mathematical Software - ICMS 2010}, volume = {6327}, booktitle = {Mathematical Software - ICMS 2010}, publisher = {Springer}, doi = {10.1007/978-3-642-15582-6_35}, pages = {198 -- 208}, year = {2010}, 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} } @misc{ReininghausHotz2011, author = {Reininghaus, Jan and Hotz, Ingrid}, title = {Combinatorial 2D Vector Field Topology Extraction and Simplification}, series = {Topological Methods in Data Analysis and Visualization}, journal = {Topological Methods in Data Analysis and Visualization}, editor = {Pascucci, Valerio and Tricoche, Xavier and Hagen, Hans and Tierny, Julien}, publisher = {Springer}, isbn = {978-3-642-15013-5}, doi = {10.1007/978-3-642-15014-2_9}, pages = {103 -- 114}, year = {2011}, language = {en} } @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{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{ZobelReininghausHotz2011, author = {Zobel, Valentin and Reininghaus, Jan and Hotz, Ingrid}, title = {Generalized Heat Kernel Signature}, series = {Journal of WSCG, International Conference on Computer Graphics, Visualization and Computer Vision}, journal = {Journal of WSCG, International Conference on Computer Graphics, Visualization and Computer Vision}, pages = {93 -- 100target}, year = {2011}, language = {en} } @misc{KastenReininghausOberleithneretal.2010, author = {Kasten, Jens and Reininghaus, Jan and Oberleithner, Kilian and Hotz, Ingrid and Noack, Bernd and Hege, Hans-Christian}, title = {Flow over a Cavity - Evolution of the Vortex Skeleton}, publisher = {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).}, year = {2010}, language = {en} } @article{ReininghausLoewenHotz2011, author = {Reininghaus, Jan and L{\"o}wen, Christian and Hotz, Ingrid}, title = {Fast Combinatorial Vector Field Topology}, series = {IEEE Trans. Computer Graphics and Visualization}, volume = {17}, journal = {IEEE Trans. Computer Graphics and Visualization}, number = {10}, pages = {1433 -- 1443}, year = {2011}, 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{KratzReininghausHadwigeretal.2011, author = {Kratz, Andrea and Reininghaus, Jan and Hadwiger, Markus and Hotz, Ingrid}, title = {Adaptive Screen-Space Sampling for Volume Ray-Casting}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12446}, number = {11-04}, year = {2011}, abstract = {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.}, language = {en} }