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  • 1.
    Auer, Cornelia
    et al.
    Zuse Institut Berlin, Germany.
    Hotz, Ingrid
    Zuse Institut Berlin, Germany.
    Complete Tensor Field Topology on 2D Triangulated Manifolds embedded in 3D2011In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 30, no 3, p. 831-840Article in journal (Refereed)
    Abstract [en]

    This paper is concerned with the extraction of the surface topology of tensor fields on 2D triangulated manifoldsembedded in 3D. In scientific visualization topology is a meaningful instrument to get a hold on the structure of agiven dataset. Due to the discontinuity of tensor fields on a piecewise planar domain, standard topology extractionmethods result in an incomplete topological skeleton. In particular with regard to the high computational costs ofthe extraction this is not satisfactory. This paper provides a method for topology extraction of tensor fields thatleads to complete results. The core idea is to include the locations of discontinuity into the topological analysis.For this purpose the model of continuous transition bridges is introduced, which allows to capture the entiretopology on the discontinuous field. The proposed method is applied to piecewise linear three-dimensional tensorfields defined on the vertices of the triangulation and for piecewise constant two or three-dimensional tensor fieldsgiven per triangle, e.g. rate of strain tensors of piecewise linear flow fields.

  • 2.
    Auer, Cornelia
    et al.
    Zuse Institute Berlin, Berlin, Germany.
    Nair, Jaya
    IIIT – Bangalore, Electronics City, Hosur Road, Bangalore, India.
    Zobel, Valentin
    Zuse Institue Berlin, Berlin, Germany.
    Hotz, Ingrid
    Zuse Institue Berlin, Berlin, Germany.
    2D Tensor Field Segmentation2011In: Dagstuhl Follow-Ups, E-ISSN 1868-8977, Vol. 2, p. 17-35Article in journal (Refereed)
    Abstract [en]

    We present a topology-based segmentation as means for visualizing 2D symmetric tensor fields. The segmentation uses directional as well as eigenvalue characteristics of the underlying field to delineate cells of similar (or dissimilar) behavior in the tensor field. A special feature of the resulting cells is that their shape expresses the tensor behavior inside the cells and thus also can be considered as a kind of glyph representation. This allows a qualitative comprehension of important structures of the field. The resulting higher-level abstraction of the field provides valuable analysis. The extraction of the integral topological skeleton using both major and minor eigenvector fields serves as a structural pre-segmentation and renders all directional structures in the field. The resulting curvilinear cells are bounded by tensorlines and already delineate regions of equivalent eigenvector behavior. This pre-segmentation is further adaptively refined to achieve a segmentation reflecting regions of similar eigenvalue and eigenvector characteristics. Cell refinement involves both subdivision and merging of cells achieving a predetermined resolution, accuracy and uniformity of the segmentation. The buildingblocks of the approach can be intuitively customized to meet the demands or different applications. Application to tensor fields from numerical stress simulations demonstrates the effectiveness of our method.

  • 3.
    Boyer, E
    et al.
    Grenoble, France.
    Bronstein, A.M.
    Tel Aviv University, Israel.
    Bronstein, M.M.
    Università della Svizzera Italiana, Lugano, Switzerland.
    Bustos, B
    University of Chile.
    Darom, T
    Bar-Ilan University, Ramat-Gan, Israel.
    Horaud, R
    Grenoble, France.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Kelle, Y
    Bar-Ilan University, Ramat-Gan, Israel.
    Keustermans, J
    K.U. Leuven, Belgium.
    Kovnatsky, A
    Israel Institute of Technology, Haifa, Israel.
    Litman, R
    Tel Aviv University, Israel.
    Reininghaus, Jan
    Zuse Institue Berlin.
    Sipiran, I
    University of Chile.
    Smeets, D
    K.U. Leuven, Belgium.
    Suetens, P
    K.U. Leuven, Belgium.
    Vandermeulen, D
    K.U. Leuven, Belgium.
    Zaharescu, A
    Waterloo, Canada.
    Zobel, Valentin
    Zuse Institut Berlin, Germany.
    SHREC 2011: Robust Feature Detection and Description Benchmark2011Conference paper (Refereed)
    Abstract [en]

    Feature-based approaches have recently become very popular in computer vision and image analysis applications, and are becoming a promising direction in shape retrieval. SHREC’11 robust feature detection and description benchmark simulates the feature detection and description stages of feature-based shape retrieval algorithms. The benchmark tests the performance of shape feature detectors and descriptors under a wide variety of transformations. The benchmark allows evaluating how algorithms cope with certain classes of transformations and strength of the transformations that can be dealt with. The present paper is a report of the SHREC’11 robust feature detection and description benchmark results.

  • 4.
    Bremer, Peer-Timo
    et al.
    California, Usa.
    Hotz, IngridBerlin, Germany.Pascucci, ValerioUtah, Usa.Peikert, RonaldZurich, Switzerland.
    Topological Methods in Data Analysis and Visualization III: Theory, Algorithms, and Applications2014Collection (editor) (Refereed)
  • 5.
    Bujack, Roxana
    et al.
    Leipzig University, Leipzig, Germany.
    Hotz, Ingrid
    German Aerospace Center, Braunschweig, Germany..
    Scheuermann, Gerik
    Leipzig University, Leipzig, Germany.
    Hitzer, E.
    Christian University, Tokyo, Japan.
    Moment Invariants for 2D Flow Fields via Normalization in Detail2014Conference paper (Refereed)
    Abstract [en]

    The analysis of 2D flow data is often guided by the search for characteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a human observer, with the goal of finding similar structures in the same or other datasets. The major challenges related to this task are to specify the notion of similarity and define respective pattern descriptors. While the descriptors should be invariant to certain transformations, such as rotation and scaling, they should provide a similarity measure with respect to other transformations, such as deformations. In this paper, we propose to use moment invariants as pattern descriptors for flow fields. Moment invariants are one of the most popular techniques for the description of objects in the field of image recognition. They have recently also been applied to identify 2D vector patterns limited to the directional properties of flow fields. Moreover, we discuss which transformations should be considered for the application to flow analysis. In contrast to previous work, we follow the intuitive approach of moment normalization, which results in a complete and independent set of translation, rotation, and scaling invariant flow field descriptors. They also allow to distinguish flow features with different velocity profiles. We apply the moment invariants in a pattern recognition algorithm to a real world dataset and show that the theoretical results can be extended to discrete functions in a robust way.

  • 6.
    Bujack, Roxana
    et al.
    Leipzig University, Leipzig, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    Scheuermann, Gerik
    Leipzig University, Leipzig, Germany.
    Hitzer, Eckhard
    International Christian University, Tokyo, Japan.
    Moment Invariants for 2D Flow Fields Using Normalization in Detail2015In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 21, no 8, p. 916-929Article in journal (Refereed)
    Abstract [en]

    The analysis of 2D flow data is often guided by the search for characteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a human observer, with the goal of finding similar structures in the same or other datasets. The major challenges related to this task are to specify the notion of similarity and define respective pattern descriptors. While the descriptors should be invariant to certain transformations, such as rotation and scaling, they should provide a similarity measure with respect to other transformations, such as deformations. In this paper, we propose to use moment invariants as pattern descriptors for flow fields. Moment invariants are one of the most popular techniques for the description of objects in the field of image recognition. They have recently also been applied to identify 2D vector patterns limited to the directional properties of flow fields. Moreover, we discuss which transformations should be considered for the application to flow analysis. In contrast to previous work, we follow the intuitive approach of moment normalization, which results in a complete and independent set of translation, rotation, and scaling invariant flow field descriptors. They also allow to distinguish flow features with different velocity profiles. We apply the moment invariants in a pattern recognition algorithm to a real world dataset and show that the theoretical results can be extended to discrete functions in a robust way.

  • 7.
    Bujack, Roxana
    et al.
    Leipzig University,Germany.
    Kasten, Jens
    Leipzig University,Germany.
    Ingrid, Ingrid
    German Aerospace, Center, Germany.
    Scheuermann, Gerik
    Leipzig University,Germany.
    Hitzer, Eckhard
    International Christian ,University, Japan.
    Moment Invariants for 3D Flow Fields Using Normalization2015Conference paper (Refereed)
    Abstract [en]

    We generalize the framework of moments and introduce a definition of invariants for three-dimensional vector fields. To do so, we use the method of moment normalization that has been shown to be useful in the two dimensions. Using invariant moments, we show how to search for patterns in these fields independent from their position, orientation and scale. From the first order vector moment tensor, we construct a complete and independent set of descriptors. We test the invariants in queries on synthetic and real world flow fields.

  • 8.
    Dwyer, Tim
    et al.
    Monash University, Australia.
    Elmqvist, Niklas
    University of Maryland, MD 20742 USA.
    Fisher, Brian
    Simon Fraser University, Canada.
    Franconeri, Steve
    Northwestern University, IL 60208 USA.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Mike Kirby, Robert M.
    University of Utah, UT 84112 USA.
    Liu, Shixia
    Tsinghua University, Peoples R China.
    Schreck, Tobias
    Graz University of Technology, Austria.
    Yuan, Xiaoru
    Peking University, Peoples R China.
    Message from the VIS Paper Chairs and Guest Editors Preface2018In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 24, no 1, p. XI-XVArticle in journal (Other academic)
  • 9.
    Englund, Rickard
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Lundin Palmerius, Karljohan
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Ynnerman, Anders
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Touching Data: Enhancing Visual Exploration of Flow Data with Haptics2018In: Computing in science & engineering (Print), ISSN 1521-9615, E-ISSN 1558-366X, Vol. 20, no 3, p. 89-100Article in journal (Other academic)
    Abstract [en]

    n/a

  • 10.
    Englund, Rickard
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Ropinski, Timo
    Visual Computing Group, Ulm University, Germany.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Coherence Maps for Blood Flow Exploration2016In: VCBM 16: Eurographics Workshop on Visual Computing for Biology and Medicine, Eurographics - European Association for Computer Graphics, 2016, p. 79-88Conference paper (Refereed)
    Abstract [en]

    Blood flow data from direct measurements (4D flow MRI) or numerical simulations opens new possibilities for the understanding of the development of cardiac diseases. However, before this new data can be used in clinical studies or for diagnosis, it is important to develop a notion of the characteristics of typical flow structures. To support this process we developed a novel blood flow clustering and exploration method. The method builds on the concept of coherent flow structures. Coherence maps for cross-sectional slices are defined to show the overall degree of coherence of the flow. In coherent regions the method summarizes the dominant blood flow using a small number of pathline representatives. In contrast to other clustering approaches the clustering is restricted to coherent regions and pathlines with low coherence values, which are not suitable for clustering and thus are not forced into clusters. The coherence map is based on the Finite-time Lyapunov Exponent (FTLE). It is created on selected planes in the inflow respective outflow area of a region of interest. The FTLE value measures the rate of separation of pathlines originating from this plane. Different to previous work using FTLE we do not focus on separating extremal lines but on local minima and regions of low FTLE intensities to extract coherent flow. The coherence map and the extracted clusters serve as basis for the flow exploration. The extracted clusters can be selected and inspected individually. Their flow rate and coherence provide a measure for their significance. Switching off clusters reduces the amount of occlusion and reveals the remaining part of the flow. The non-coherent regions can also be explored by interactive manual pathline seeding in the coherence map.

  • 11.
    Falk, Martin
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Ljung, Patric
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Treanor, Darren
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Leeds Teaching Hospitals NHS Trust, United Kingdom.
    Ynnerman, Anders
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Lundström, Claes
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV). Sectra AB.
    Transfer Function Design Toolbox for Full-Color Volume Datasets2017In: 2017 IEEE PACIFIC VISUALIZATION SYMPOSIUM (PACIFICVIS), IEEE, IEEE, 2017, p. 171-179Conference paper (Refereed)
    Abstract [en]

    In this paper, we tackle the challenge of effective Transfer Function (TF) design for Direct Volume Rendering (DVR) of full-color datasets. We propose a novel TF design toolbox based on color similarity which is used to adjust opacity as well as replacing colors. We show that both CIE L*u*v* chromaticity and the chroma component of YCbCr are equally suited as underlying color space for the TF widgets. In order to maximize the area utilized in the TF editor, we renormalize the color space based on the histogram of the dataset. Thereby, colors representing a higher share of the dataset are depicted more prominently, thus providing a higher sensitivity for fine-tuning TF widgets. The applicability of our TF design toolbox is demonstrated by volume ray casting challenging full-color volume data including the visible male cryosection dataset and examples from 3D histology.

  • 12.
    Feng, Louis
    et al.
    University of California, Davis.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Hamann, Bernd
    University of California, Davis, USA.
    Joy, Ken
    University of California, Davis, USA.
    Anisotropic Noise Samples2008In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 14, no 2, p. 342-354Article in journal (Refereed)
    Abstract [en]

    We present a practical approach to generate stochastic anisotropic samples with Poisson-disk characteristic over a two-dimensional domain. In contrast to isotropic samples, we understand anisotropic samples as non-overlapping ellipses whose size and density match a given anisotropic metric. Anisotropic noise samples are useful for many visualization and graphics applications. The spot samples can be used as input for texture generation, e.g., line integral convolution (LIC), but can also be used directly for visualization. The definition of the spot samples using a metric tensor makes them especially suitable for the visualization of tensor fields that can be translated into a metric. Our work combines ideas from sampling theory and mesh generation. To generate these samples with the desired properties we construct a first set of non-overlapping ellipses whose distribution closely matches the underlying metric. This set of samples is used as input for a generalized anisotropic Lloyd relaxation to distribute noise samples more evenly. Instead of computing the Voronoi tessellation explicitly, we introduce a discrete approach which combines the Voronoi cell and centroid computation in one step. Our method supports automatic packing of the elliptical samples, resulting in textures similar to those generated by anisotropic reaction-diffusion methods. We use Fourier analysis tools for quality measurement of uniformly distributed samples. The resulting samples have nice sampling properties, for example, they satisfy a blue noise property where low frequencies in the power spectrum are reduced to a minimum.

  • 13.
    Feng, Louis
    et al.
    University of California, Davis.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Hamann, Bernd
    University of California, Davis, USA.
    Joy, Ken
    University of California, Davis, USA.
    Dense Glyph Sampling for Visualization2008In: Visualization and Processing of Tensor Fields: Advances and Perspectives / [ed] David Laidlaw, Joachim Weickert, Springer, 2008, p. 177-193Chapter in book (Refereed)
    Abstract [en]

    We present a simple and efficient approach to generate a dense set of anisotropic, spatially varying glyphs over a two-dimensional domain. Such glyph samples are useful for many visualization and graphics applications. The glyphs are embedded in a set of nonoverlapping ellipses whose size and density match a given anisotropic metric. An additional parameter controls the arrangement of the ellipses on lines, which can be favorable for some applications, for example, vector fields and distracting for others. To generate samples with the desired properties, we combine ideas from sampling theory and mesh generation. We start with constructing a first set of nonoverlapping ellipses whose distribution closely matches the underlying metric. This set of samples is used as input for a generalized anisotropic Lloyd relaxation to distribute samples more evenly.

  • 14.
    Gustafsson, Torsten
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Engelke, Wito
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Englund, Rickard
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Concepts of Hybrid Data Rendering2017In: Proceedings of SIGRAD 2017, August 17-18, 2017 Norrköping, Sweden / [ed] Ingrid Hotz and Martin Falk, Linköping: Linköping University Electronic Press, 2017, Vol. 143, p. 32-39Conference paper (Refereed)
    Abstract [en]

    We present a concept for interactive rendering of multiple data sets of varying type, including geometry and volumetric data, in one scene with correct transparency. Typical visualization applications involve multiple data fields from various sources. A thorough understanding of such data often requires combined rendering of theses fields. The choice of the visualization concepts, and thus the rendering techniques, depends on the context and type of the individual fields. Efficiently combining different techniques in one scene, however, is not always a straightforward task. We tackle this problem by using an A-buffer based approach to gather color and transparency information from different sources, combine them and generate the final output image. Thereby we put special emphasis on efficiency and low memory consumption to allow a smooth exploration of the data. Therefore, we compare different A-buffer implementations with respect to memory consumption and memory access pattern. Additionally we introduce an early-fragment-discarding heuristic using inter-frame information to speed up the rendering..

  • 15.
    Günther, David
    et al.
    Saarbrücken, Germany.
    Reininghaus, Jan
    Zuse Institute Berlin, Germany.
    Wagner, Huber
    Lojasiewicza 6, Krakow, Poland .
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    Efficient Computation of 3D Morse-Smale Complexes and Persistent Homology using Discrete Morse Theory2012In: The Visual Computer, ISSN 0178-2789, E-ISSN 1432-2315, Vol. 28, no 10, p. 959-969Article in journal (Refereed)
    Abstract [en]

    We propose an efficient algorithm that computes the Morse–Smale complex for 3D gray-scale images. This complex allows for an efficient computation of persistent homology since it is, in general, much smaller than the input data but still contains all necessary information. Our method improves a recently proposed algorithm to extract the Morse–Smale complex in terms of memory consumption and running time. It also allows for a parallel computation of the complex. The computational complexity of the Morse–Smale complex extraction solely depends on the topological complexity of the input data. The persistence is then computed using the Morse–Smale complex by applying an existing algorithm with a good practical running time. We demonstrate that our method allows for the computation of persistent homology for large data on commodity hardware.

  • 16.
    Günther, David
    et al.
    Zuse Institute Berlin.
    Reininghaus, Jan
    Zuse Institue Berlin.
    Wagner, J
    Jagiellonian University,Krakow, Poland.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Memory-Efficient Computation of Persistent Homology for 3D Images using Discrete Morse Theory2011Conference paper (Refereed)
    Abstract [en]

    We propose a memory-efficient method that computes persistent homology for 3D gray-scale images. The basic idea is to compute the persistence of the induced Morse-Smale complex. Since in practice this complex is much smaller than the input data, significantly less memory is required for the subsequent computations. We propose a novel algorithm that efficiently extracts the Morse-Smale complex based on algorithms from discrete Morse theory. The proposed algorithm is thereby optimal with a computational complexity of O(n2). The persistence is then computed using the Morse-Smale complex by applying an existing algorithm with a good practical running time. We demonstrate that our method allows for the computation of persistent homology for large data on commodity hardware.

  • 17.
    Hagen, Hans
    et al.
    University of Kaiserslautern.
    Hotz, Ingrid
    University of Kaiserslautern.
    Variational modeling methods for Visualization2004In: Visualization Handbook / [ed] Charles D. Hansen and Chris R. Johnson, Springer, 2004, p. 381-392Chapter in book (Refereed)
    Abstract [en]

    Publisher Summary Variational modeling techniques are powerful tools for free-form modeling in CAD/CAM applications. Some of the basic principles are carrying over to scientific visualization. Others have to be modified and some totally new methods have been developed over the past couple of years. This chapter gives an extended survey of this area. Surfaces and solids designed in a computer graphics environment have many applications in modeling, animation, and visualization. The chapter concentrates on the visualization part. The chapter starts with the basics from differential geometry, which are essential for any variational method. Then, it surveys on variational surface modeling. The last step is the visualization part of geometric modeling. In this context, surface curves like geodesies and curvature lines play an important role. The corresponding differential equations are nonlinear, and in most cases numerical algorithms must be used. To be sure to visualize features at a high quality, algorithms with an inherent quality control are needed. The chapter presents the geometric algorithms, which satisfy this demand.

  • 18.
    Hege, Hans-Christian
    et al.
    Zuse Institute Berlin, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    Kasten, Jens
    Zuse Institute Berlin, Germany.
    Distillation and Visualization of Spatiotemporal Structures in Turbulent Flow Fields2011In: Journal of Physics: Conference Series, ISSN 1742-6588, Vol. 318, no 6, p. 1-6Article in journal (Refereed)
    Abstract [en]

    Although turbulence suggests randomness and disorder, organized motions that cause spatiotemporal 'coherent structures' are of particular interest. Revealing such structures in numerically given turbulent or semi-turbulent flows is of interest both for practically working engineers and theoretically oriented physicists. However, as long as there is no common agreement about the mathematical definition of coherent structures, extracting such structures is a vaguely defined task. Instead of searching for a general definition, the data visualization community takes a pragmatic approach and provides various tool chains implemented in flexible software frameworks that allow the user to extract distinct flow field structures. Thus physicists or engineers can select those flow structures which might advance their insight best. We present different approaches to distill important features from turbulent flows and discuss the necessary steps to be taken on the example of Lagrangian coherent structures.

  • 19.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Acceleration Feature Points of Unsteady Shear Flows2016In: Journal Archives of Mechanics, ISSN 0373-2029, Vol. 68, no 1, p. 55-80Article in journal (Refereed)
    Abstract [en]

    A framework for extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance is proposed in this paper. The minima of the acceleration magnitude (a superset of 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 feature points 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. We apply the acceleration feature extraction strategy 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 the pressure field and minima of λ2.

  • 20.
    Hotz, Ingrid
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Falk, MartinLinköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Proceedings of SIGRAD 2017, August 17-18, 2017 Norrköping, Sweden2017Conference proceedings (editor) (Refereed)
    Abstract [en]

    The annual meeting 2017 of the Swedish Computer Graphics Association (SIGRAD) took place at Linköping University, Campus Norrköping in Norrköping, Sweden in August 2017. SIGRAD is an event where researchers and industry professionals meet to discuss novel visions and developments in the field of computer graphics and related areas, such as visualization and human-computer interaction (HCI). Since SIGRAD was started in 1976, it has developed into the major annual appointment for the Nordic community of graphics and visual computing experts with a broad range of backgrounds. It thereby addresses the increasing need for visual computing solutions in both commercial and academic areas. SIGRAD 2017 offered a strong scientific program consisting of international keynote speakers from research and industry, presentations of recent scientific achievements in the field within Sweden, and novel technological results from international contributors. The topics covered present a nice cross-section across the diverse research efforts in the domains.

    Five original papers have been accepted for presentation after being peer-reviewed by an International Program Committee consisting of 22 highly qualified scientists. Each paper was reviewed, on average, by three reviewers from the committee. The accepted papers range from general computer graphics practices to practical applications and services that may benefit from the use of visualizations and computer graphics technologies. The extended participation of students at all levels of academia in research has been encouraged this year and 2 papers were selected which are first-authored by students studying at Master's Degree level.

    This year, we continued the “Swedish Research Overview Session” introduced at last year’s conference. In this session, Swedish research groups are given the opportunity to present their academically outstanding, previously published work at the annual conference. All papers in this session have been published in an academically outstanding journals or conferences not more than two years prior to the SIGRAD conference.

    We especially wish to thank our invited keynote speakers: Christoph Garth, University of Kaiserslautern, Germany, Ivan Viola, Vienna University of Technology, Austria, Claes Lundström, CMIV, Linköping University, and Samuel Ranta Eskola, Microsoft. Finally, we want to express our thanks to Gun-Britt Löfgren for helping us in organizing this event.

    The SIGRAD 2017 organizers

    Martin Falk, Daniel Jönsson, Ingrid Hotz

  • 21.
    Hotz, Ingrid
    et al.
    University of California, Davis, USA.
    Feng, Louis
    University of California, Davis, USA.
    Hagen, Hans
    University of Kaiserslautern.
    Hamann, Bernd
    University of California, Davis, USA.
    Joy, Ken
    University of California, Davis, USA.
    Tensor Field Visualization Using a Metric Interpretation2006In: Visualization and Image Processing of Tensor Fields / [ed] Joachim Weickert, Hans Hagen, Springer, 2006, p. 269-281Chapter in book (Refereed)
    Abstract [en]

    This chapter introduces a visualization method specifically tailored to the class of tensor fields with properties similar to stress and strain tensors. Such tensor fields play an important role in many application areas such as structure mechanics or solid state physics. The presented technique is a global method that represents the physical meaning of these tensor fields with their central features: regions of compression or expansion. The method consists of two steps: first, the tensor field is interpreted as a distortion of a flat metric with the same topological structure; second, the resulting metric is visualized using a texture-based approach. The method supports an intuitive distinction between positive and negative eigenvalues.

  • 22.
    Hotz, Ingrid
    et al.
    Universtiy of California,Davis, USA.
    Feng, Louis
    Universtiy of California,Davis, USA.
    Hagen, Hans
    University of Kaiserslautern,Germany.
    Hamann, Bernd
    University of California, Davis, USA.
    Joy, Ken
    University of California, Davis, USA.
    Jeremic, Boris
    University of California, Davis, USA.
    Physically Based Methods for Tensor Field Visualization2004Conference paper (Refereed)
    Abstract [en]

    The physical interpretation of mathematical features of tensor fields is highly application-specific. Existing visualization methods for tensor fields only cover a fraction of the broad application areas. We present a visualization method tailored specifically to the class of tensor field exhibiting properties similar to stress and strain tensors, which are commonly encountered in geomechanics. Our technique is a global method that represents the physical meaning of these tensor fields with their central features: regions of compression or expansion. The method is based on two steps: first, we define a positive definite metric, with the same topological structure as the tensor field; second, we visualize the resulting metric. The eigenvector fields are represented using a texture-based approach resembling line integral convolution (LIC) methods. The eigenvalues of the metric are encoded in free parameters of the texture definition. Our method supports an intuitive distinction between positive and negative eigenvalues. We have applied our method to synthetic and some standard data sets, and "real" data from earth science and mechanical engineering application.

  • 23.
    Hotz, Ingrid
    et al.
    Universtiy of California, Davis.
    Feng, Louis
    University of California, Davis.
    Hamann, Bernd
    University of California, Davis, USA.
    Joy, Ken
    University of California, Davis, USA.
    Tensor-fields Visualization using a Fabric like Texture on Arbitrary two-dimensional Surfaces2009In: Mathematical Foundations of Scientific Visualization / [ed] Torsten Möller,Bernd Hamann,Robert D. Russell, Springer, 2009, p. 139-155Chapter in book (Refereed)
    Abstract [en]

    We present a visualization method that for three-dimensional tensor fields based on the idea of a stretched or compressed piece of fabric used as a “texture” for a two-dimensional surfaces. The texture parameters as the fabric density reflect the physical properties of the tensor field. This method is especially appropriate for the visualization of stress and strain tensor fields that play an important role in many application areas including mechanics and solid state physics. To allow an investigation of a three-dimensional field we use a scalar field that defines a one-parameter family of iso-surfaces controlled by their iso-value. This scalar-field can be a “connected” scalar field, for example, pressure or an additional scalar field representing some symmetry or inherent structure of the dataset. Texture generation consists basically of three steps. The first is the transformation of the tensor field into a positive definite metric. The second step is the generation of an input for the final texture generation using line integral convolution (LIC). This input image consists of “bubbles” whose shape and density are controlled by the eigenvalues of the tensor field. This spot image incorporates the entire information content defined by the three eigenvalue fields. Convolving this input texture in direction of the eigenvector fields provides a continuous representation. This method supports an intuitive distinction between positive and negative eigenvalues and supports the additional visualization of a connected scalar field.

  • 24.
    Hotz, Ingrid
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. German Aerospace Center.
    Flatken, Markus
    German Aerospace Center - DLR.
    Berres, Anne
    University of Kaiserslautern.
    Merkel, Jonas
    University of Kaiserslautern.
    Gerndt, Andreas
    German Aeorspace Center (DLR).
    Hagen, Hans
    University Kaiserslautern.
    Dynamic Schedulig for Progressive Large-Scale Visualization2015Conference paper (Refereed)
  • 25.
    Hotz, Ingrid
    et al.
    University of Kaiserslautern.
    Hagen, Hans
    University of Kaiserslautern.
    Isometric Embedding for a Discrete Metric2004In: Geometric Modeling for Scientific Visualization / [ed] Guido Brunnett ,Bernd Hamann,Heinrich Müller ,Lars Linsen, Springer, 2004, 1, p. 19-36Chapter in book (Refereed)
  • 26.
    Hotz, Ingrid
    et al.
    Zuse Institute Berlin, Berlin, Germany.
    Peikert, Ronald
    ETH Zurich, Zurich, Switzerland .
    Definition  of  a  Multifield2014In: Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization / [ed] Charles D. Hansen; Min Chen; Christopher R. Johnson; Arie E. Kaufman; Hans Hagen, Springer London, 2014, p. 105-109Chapter in book (Refereed)
    Abstract [en]

    A challenge, visualization is often faced with, is the complex structure of scientific data. Complexity can arise in various ways, from high dimensionalities of domains and ranges, time series of measurements, ensemble simulations, to heterogeneous collections of data, such as combinations of measured and simulated data. Many of these complexities can be subsumed under a concept of multifields, and in fact, multifield visualization has been identified as one of the major current challenges in scientific visualization. In this chapter, we propose a multifield definition, which will allow us a systematic approach to discussing related research.

  • 27.
    Hotz, Ingrid
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Schultz, ThomasUniversity Bonn, Germany.
    Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (Dagstuhl’14)2015Collection (editor) (Refereed)
    Abstract [en]
    • Transfer result from one application to another between which there is otherwise not much exchange
    • Bringing together ideas from applications and theory: Applications can stimulate new basic research, as basic results can be of great use in the applications
    • Summarizing the state of the art and major open questions in the field
    • Presenting new and innovative work with the capabilities of advancing the field
  • 28.
    Hotz, Ingrid
    et al.
    University of California, USA.
    Sreevalsan-Nair, Jaya
    University of California, USA.
    Hagen, Hans
    Technical University of Kaiserslautern,Kaiserslautern, Germany.
    Hamann, Bernd
    University of California, USA.
    Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation2010In: Dagstuhl Follow-Ups, E-ISSN 1868-8977, Vol. 1, p. 110-123Article in journal (Refereed)
    Abstract [en]

    Interpolation is an essential step in the visualization process. While most data from simulations or experiments are discrete many visualization methods are based on smooth, continuous data approximation or interpolation methods. We introduce a new interpolation method for symmetrical tensor fields given on a triangulated domain. Differently from standard tensor field interpolation, which is based on the tensor components, we use tensor invariants, eigenvectors and eigenvalues, for the interpolation. This interpolation minimizes the number of eigenvectors and eigenvalues computations by restricting it to mesh vertices and makes an exact integration of the tensor lines possible. The tensor field topology is qualitatively the same as for the component wise-interpolation. Since the interpolation decouples the “shape” and “direction” interpolation it is shape-preserving, what is especially important for tracing fibers in diffusion MRI data.

  • 29.
    Kasten, Jens
    et al.
    Zuse Institute Berlin.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Hege, Hans-Christian
    Zuse Institute Berlin.
    On the Elusive Concept of Lagrangian Coherent Structures2012In: Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications / [ed] Ronald Peikert, Helwig Hauser, Hamish Carr, Raphael Fuchs, Springer, 2012, p. 207-220Chapter in book (Refereed)
    Abstract [en]

    Many of the recently developed methods for analysis and visualization of time-dependent flows are related to concepts, which can be subsumed under the term Lagrangian coherent structures (LCS). Thereby, no universal definition of LCS exists and different interpretations are used. Mostly, LCS are considered to be features linked to pathlines leading to the ideal conception of features building material lines. Such time-dependent features are extracted by averaging local properties of particles along their trajectories, e.g., separation, acceleration or unsteadiness. A popular realization of LCS is the finite-time Lyapunov exponent (FTLE) with its different implementations. The goal of this paper is to stimulate a discussion on the generality of the underlying assumptions and concepts. Using a few well-known datasets, the interpretation and usability of Lagrangian analysis methods are discussed.

  • 30.
    Kasten, Jens
    et al.
    Zuse Institute Berlin (ZIB), Berlin, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin (ZIB), Berlin, Germany.
    Noack, Bernd
    Berlin Institute of Technology MB1, Berlin, Germany .
    Hege, Hans-Christian
    Berlin Institute of Technology MB1, Berlin, Germany .
    On the Extraction of Long-living Features in Unsteady Fluid Flows2011In: Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications / [ed] Valerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny, Springer, 2011, p. 115-126Chapter in book (Refereed)
    Abstract [en]

    This paper proposes aGalilean invariant generalization of critical points ofvector field topology for 2D time-dependent flows. The approach is based upon a Lagrangian consideration of fluid particle motion. It extracts long-living features, likesaddles and centers, and filters out short-living local structures. This is well suited for analysis ofturbulent flow, where standard snapshot topology yields an unmanageable large number of topological structures that are barely related to the few main long-living features employed in conceptual fluid mechanics models. Results are shown for periodic and chaoticvortex motion.

  • 31.
    Kasten, Jens
    et al.
    Zuse Institute Berlin, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    Noack, Bernd R.
    Zuse Institute Berlin, Germany.
    Hege, Hans-Christian
    Zuse Institute Berlin, Germany.
    Vortex merge graphs in two-dimensional unsteady flow fields2012Conference paper (Refereed)
    Abstract [en]

    Among the various existing vortex definitions, there is one class that relies on extremal structures of derived scalar fields. These are, e.g., vorticity,λ<sub>2</sub>, or the acceleration magnitude. This paper proposes a method to identify and track extremal-based vortex structures in 2D time-dependent flows. It is based on combinatorial scalar field topology. In contrast to previous methods, merge events are explicitly handled and represented in the resulting graph. An abstract representation of this vortex merge graph serves as basis for the comparison of the different scalar identifiers. The method is applied to numerically simulated flows of a mixing layer and a planar jet.

  • 32.
    Kasten, Jens
    et al.
    Zuse Institute Berlin.
    Petz, Christoph
    Zuse Institue Berlin.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Hege, Hans-Christian
    Zuse Institute Berlin.
    Noack, Bernd R
    Institute Pprime, F-86036 Poitiers Cedex, France.
    Tadmor, Gilead
    Northeastern University, Boston,USA.
    Lagrangian Feature Extraction of the Cylinder Wake2010In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Physics of Fluids, Vol. 22, p. 091108-1-091108-1Article in journal (Refereed)
  • 33.
    Kasten, Jens
    et al.
    Zuse Institute Berlin (ZIB), Berlin, Germany.
    Petz, Christoph
    Zuse Institute Berlin (ZIB), Berlin, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin (ZIB), Berlin, Germany.
    Hege, Hans-Christian
    Zuse Institute Berlin (ZIB), Berlin, Germany.
    Noack, Bernd R
    Institute Pprime, Poitiers Cedex, France.
    Tadmor, Gilead
    Northeastern University, Boston, Massachusetts USA .
    Lagrangian Feature Extraction of the Cylinder Wake2010In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 22, no 9, p. 091108-091108-1Article in journal (Other academic)
    Abstract [en]

    n/a

  • 34.
    Kasten, Jens
    et al.
    Zuse Institute Berlin.
    Petz, Christoph
    Zuse Institue Berlin.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Noack, Bernd
    Hege, Hans-Christian
    Zuse Institute Berlin.
    Localized Finite-time Lyapunov Exponent for Unsteady Flow Analysis2009Conference paper (Refereed)
    Abstract [en]

    The Finite-time Lyapunov Exponent (FTLE) is a measure for the rate of separation of particles in time-dependent flow fields. It provides a valuable tool for the analysis of unsteady flows. Commonly it is defined based on the flow map, analyzing the separation of trajectories of nearby particles over a finite-time span. This paper proposes a localized definition of the FTLE using the Jacobian matrix along a pathline as generator of the separation. The localized FTLE (L-FTLE) definition makes only use of flow properties along the pathline. A fast computation algorithm is presented that efficiently reuses FTLE values from previous time steps, following an idea similar to FastLIC. The properties of L-FTLE are analyzed with focus on the sensitivity to the parameters of the algorithm. It is further compared to the flow map based version under consideration of robustness to noise.

  • 35.
    Kasten, Jens
    et al.
    Zuse Institute Berlin, Germany.
    Reininghaus, Jan
    Zuse Institute Berlin, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    Hege, Hans-Christian
    Zuse Institute Berlin, Germany.
    Two-dimensional Time-dependent Vortex Regions based on the Acceleration Magnitude2011In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 17, no 12, p. 2080-2087Article in journal (Refereed)
    Abstract [en]

    Acceleration is a fundamental quantity of flow fields that captures Galilean invariant properties of particle motion. Considering the magnitude of this field, minima represent characteristic structures of the flow that can be classified as saddle- or vortex-like. We made the interesting observation that vortex-like minima are enclosed by particularly pronounced ridges. This makes it possible to define boundaries of vortex regions in a parameter-free way. Utilizing scalar field topology, a robust algorithm can be designed to extract such boundaries. They can be arbitrarily shaped. An efficient tracking algorithm allows us to display the temporal evolution of vortices. Various vortex models are used to evaluate the method. We apply our method to two-dimensional model systems from computational fluid dynamics and compare the results to those arising from existing definitions.

  • 36.
    Kasten, Jens
    et al.
    IVU Traff Technology AG, Germany; Zuse Institute Berlin, Germany.
    Reininghaus, Jan
    IST Austria, Austria.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Hege, Hans-Christian
    Zuse Institute Berlin, Germany.
    Noack, Bernd R.
    LIMSI CNRS, France; Technical University of Carolo Wilhelmina Braunschweig, Germany.
    Daviller, Guillaume
    CNRS, France.
    Morzynski, Marek
    Poznan University of Tech, Poland.
    Acceleration feature points of unsteady shear flows2016In: ARCHIVES OF MECHANICS, ISSN 0373-2029, Vol. 68, no 1, p. 55-80Article in journal (Refereed)
    Abstract [en]

    A FRAMEWORK FOR EXTRACTING FEATURES IN 2D TRANSIENT FLOWS, based on the acceleration field to ensure Galilean invariance is proposed in this paper. The minima of the acceleration magnitude (a superset of 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 mea sure. These feature points 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. We apply the acceleration feature extraction strategy 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 the pressure field and minima of lambda(2). Copyright (C) 2016 by IPPT PAN

  • 37.
    Kasten, Jens
    et al.
    Berlin, Germany .
    Weinkauf, Tino
    Broadway, New York, NY, USA .
    Petz, Christoph
    Berlin, Germany .
    Hotz, Ingrid
    Berlin, Germany .
    Noack, Bernd R.
    Poitiers, France .
    Hege, Hans-Christian
    Berlin, Germany.
    Extraction of Coherent Structures from Natural and Actuated Flows2010In: Active Flow Control II / [ed] Rudibert King, Springer, 2010, p. 373-387Chapter in book (Refereed)
  • 38.
    Konig, Carolin
    et al.
    KTH Royal Inst Technol, Sweden.
    Skånberg, Robin
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Ynnerman, Anders
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Norman, Patrick
    KTH Royal Inst Technol, Sweden.
    Linares, Mathieu
    KTH Royal Inst Technol, Sweden; KTH Royal Inst Technol, Sweden.
    Binding sites for luminescent amyloid biomarkers from non-biased molecular dynamics simulations2018In: Chemical Communications, ISSN 1359-7345, E-ISSN 1364-548X, Vol. 54, no 24, p. 3030-3033Article in journal (Refereed)
    Abstract [en]

    A very stable binding site for the interaction between a pentameric oligothiophene and an amyloid-(1-42) fibril has been identified by means of non-biased molecular dynamics simulations. In this site, the probe is locked in an all-trans conformation with a Coulombic binding energy of 1200 kJ mol(-1) due to the interactions between the anionic carboxyl groups of the probe and the cationic epsilon-amino groups in the lysine side chain. Upon binding, the conformationally restricted probes show a pronounced increase in molecular planarity. This is in line with the observed changes in luminescence properties that serve as the foundation for their use as biomarkers.

  • 39.
    Kratz, Andrea
    et al.
    Zuse Institute Berlin.
    Auer, Cornelia
    Zuse Institute Berlin.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Tensor Invariants and Glyph Design2014In: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data / [ed] Carl-Fredrik Westin, Anna Vilanova, Bernhard Burgeth, Springer, 2014, p. 17-34Chapter in book (Refereed)
    Abstract [en]

    Tensors provide a mathematical language for the description of many physical phenomena. They appear everywhere where the dependence of multiple vector fields is approximated as linear. Due to this generality they occur in various application areas, either as result or intermediate product of simulations. As different as these applications, is the physical meaning and relevance of particular mathematical properties. In this context, domain specific tensor invariants that describe the entities of interest play a crucial role. Due to their importance, we propose to build any tensor visualization upon a set of carefully chosen tensor invariants. In this chapter we focus on glyph-based representations, which still belong to the most frequently used tensor visualization methods. For the effectiveness of such visualizations the right choice of glyphs is essential. This chapter summarizes some common glyphs, mostly with origin in mechanical engineering, and link their interpretation to specific tensor invariants.

  • 40.
    Kratz, Andrea
    et al.
    Zuse Institute Berlin, Germany.
    Auer, Cornelia
    Zuse Institute Berlin, Germany.
    Stommel, Markus
    Technical University Dortmund, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    Visualization and Analysis of Second-Order Tensors: Moving Beyond the Symmetric Positive-Definite Case: State of the Art Report2013In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 32, no 1, p. 49-74Article in journal (Refereed)
    Abstract [en]

    Tensors provide a powerful language to describe physical phenomena. Consequently, they have a long tradition in physics and appear in various application areas, either as the final result of simulations or as intermediate product. Due to their complexity, tensors are hard to interpret. This motivates the development of well-conceived visualization methods. As a sub-branch of scientific visualization, tensor field visualization has been especially pushed forward by diffusion tensor imaging. In this review, we focus on second-order tensors that are not diffusion tensors. Until now, these tensors, which might be neither positive-definite nor symmetric, are under-represented in visualization and existing visualization tools are often not appropriate for these tensors. Hence, we discuss the strengths and limitations of existing methods when dealing with such tensors as well as challenges introduced by them. The goal of this paper is to reveal the importance of the field and to encourage the development of new visualization methods for tensors from various application fields.

  • 41.
    Kratz, Andrea
    et al.
    Zuse Institute Berlin, Germany.
    Baum, Daniel
    Zuse Institute Berlin, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    Anisotropic Sampling of Planar and Two-Manifold Domains for Texture Generation and Glyph Distribution2013In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 19, no 11, p. 1782-1794Article in journal (Refereed)
    Abstract [en]

    We present a new method for the generation of anisotropic sample distributions on planar and two-manifold domains. Most previous work that is concerned with aperiodic point distributions is designed for isotropically shaped samples. Methods focusing on anisotropic sample distributions are rare, and either they are restricted to planar domains, are highly sensitive to the choice of parameters, or they are computationally expensive. In this paper, we present a time-efficient approach for the generation of anisotropic sample distributions that only depends on intuitive design parameters for planar and two-manifold domains. We employ an anisotropic triangulation that serves as basis for the creation of an initial sample distribution as well as for a gravitational-centered relaxation. Furthermore, we present an approach for interactive rendering of anisotropic Voronoi cells as base element for texture generation. It represents a novel and flexible visualization approach to depict metric tensor fields that can be derived from general tensor fields as well as scalar or vector fields.

  • 42.
    Kratz, Andrea
    et al.
    Zuse Institute Berlin.
    Meier, Björn
    Zuse Institue Berlin.
    Hotz, Ingrid
    Zuse Institue Berlin.
    A Visual Approach to Analysis of Stress Tensor Fields2011In: Scientific Visualization: Interactions, Features, Metaphors, Dagstuhl Follow-Ups, ISSN 1868-8977, Vol. 2, p. 188-211Article in journal (Refereed)
    Abstract [en]

    We present a visual approach for the exploration of stress tensor fields. In contrast to common tensor visualization methods that only provide a single view to the tensor field, we pursue the idea of providing various perspectives onto the data in attribute and object space. Especially in the context of stress tensors, advanced tensor visualization methods have a young tradition. Thus, we propose a combination of visualization techniques domain experts are used to with statistical views of tensor attributes. The application of this concept to tensor fields was achieved by extending the notion of shape space. It provides an intuitive way of finding tensor invariants that represent relevant physical properties. Using brushing techniques, the user can select features in attribute space, which are mapped to displayable entities in a three-dimensional hybrid visualization in object space. Volume rendering serves as context, while glyphs encode the whole tensor information in focus regions. Tensorlines can be included to emphasize directionally coherent features in the tensor field. We show that the benefit of such a multi-perspective approach is manifold. Foremost, it provides easy access to the complexity of tensor data. Moreover, including well-known analysis tools, such as Mohr diagrams, users can familiarize themselves gradually with novel visualization methods. Finally, by employing a focus-driven hybrid rendering, we significantly reduce clutter, which was a major problem of other three-dimensional tensor visualization methods. 

  • 43.
    Park, Sung
    et al.
    University of California, Davis, USA.
    Yu, Hongfeng
    University of California, Davis, USA.
    Hotz, Ingrid
    University of California, Davis, USA.
    Linsen, Lars
    Ernst-Moritz-Arndt-Universität Greifswald Greifswald, Germany.
    Hamann, Bernd
    University of California, Davis, USA.
    Structure-accentuating Dense Flow Visualization2006Conference paper (Refereed)
    Abstract [en]

    Vector field visualization approaches can broadly be categorized into approaches that directly visualize local orintegrated flow and approaches that analyze the topological structure and visualize extracted features. Our goal was to come up with a method that falls into the first category, yet brings out structural information. We have developed a dense flow visualization method that shows the overall flow behavior while accentuating structural information without performing a topological analysis. Our method is based on a geometry-based flow integration step and a texture-based visual exploration step. The flow integration step generates a density field, which is written into a texture. The density field is generated by tracing particles under the influence of the underlying vector field.When using a quasi-random seeding strategy for initialization, the resulting density is high in attracting regions and low in repelling regions. Density is measured by the number of particles per region accumulated over time. We generate one density field using forward and one using backward propagation. The density fields are explored using texture-based rendering techniques. We generate the two output images separately and blend the results, which allows us to distinguish between inflow and outflow regions. We obtained dense flow visualizations that display the overall flow behavior, emphasize critical and separating regions, and indicate flow direction in the neighborhood of these regions. We analyzed the results of our method for isolated first-order singularities and real data sets.

  • 44.
    Reininghaus, Jan
    et al.
    Zuse Institue Berlin.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Combinatorial 2D Vector Field Topology Extraction and Simplification2011In: Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications / [ed] Valerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny, Springer, 2011, p. 103-114Chapter in book (Refereed)
  • 45.
    Reininghaus, Jan
    et al.
    Zuse Institue Berlin.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Computational Discrete Morse Theory for Divergence-Free 2D Vector Fields2012In: Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications / [ed] Ronald Peikert, Helwig Hauser, Hamish Carr, Raphael Fuchs, Springer, 2012, p. 3-14Chapter in book (Refereed)
    Abstract [en]

    We present a simple approach to the topological analysis of divergence-free 2D vector fields using discrete Morse theory. We make use of the fact that the point-wise perpendicular vector field can be interpreted as the gradient of the stream function. The topology of the divergence-free vector field is thereby encoded in the topology of a gradient vector field. We can therefore apply a formulation of computational discrete Morse theory for gradient vector fields. The inherent consistence and robustness of the resulting algorithm is demonstrated on synthetic data and an example from computational fluid dynamics.

  • 46.
    Reininghaus, Jan
    et al.
    Zuse Institute Berlin, Germany.
    Kasten, Jens
    Zuse Institute Berlin, Germany.
    Weinkauf, Tino
    Saarbru¨cken, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    Efficient Computation of Combinatorial Feature Flow Fields2011In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 18, no 9, p. 1563-1573Article in journal (Refereed)
    Abstract [en]

    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 synthetic data and data sets from computational fluid dynamics and compare it to the stabilized continuous Feature Flow Field tracking algorithm.

  • 47.
    Reininghaus, Jan
    et al.
    Zuse Institute Berlin, Germany.
    Kotava, Natallia
    Kaiserslautern, Germany.
    Günther, David
    Zuse Institute Berlin, Germany.
    Kasten, Jens
    Zuse Institute Berlin, Germany.
    Hagen, Hans
    University of Kaiserslautern.
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    A Scale Space Based Persistence Measure for Critical Points in 2D Scalar Fields2011In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 17, no 12, p. 2045-2052Article in journal (Refereed)
    Abstract [en]

    This paper introduces a novel importance measure for critical points in 2D scalar fields. This measure is based on a combination of the deep structure of the scale space with the well-known concept of homological persistence. We enhance the noise robust persistence measure by implicitly taking the hill-, ridge- and outlier-like spatial extent of maxima and minima into account. This allows for the distinction between different types of extrema based on their persistence at multiple scales. Our importance measure can be computed efficiently in an out-of-core setting. To demonstrate the practical relevance of our method we apply it to a synthetic and a real-world data set and evaluate its performance and scalability.

  • 48.
    Reininghaus, Jan
    et al.
    Berlin-Dahlem, Germany.
    Löwen, Christian
    Berlin-Dahlem, Germany.
    Hotz, Ingrid
    Berlin-Dahlem, Germany.
    Fast Combinatorial Vector Field Topology2010In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 17, no 10, p. 1433-1443Article in journal (Refereed)
    Abstract [en]

    This paper introduces a novel approximation algorithm for the fundamental graph problem of combinatorial vector field topology (CVT). CVT is a combinatorial approach based on a sound theoretical basis given by Forman’s work on a discrete Morse theory for dynamical systems. A computational framework for this mathematical model of vector field topology has been developed recently. The applicability of this framework is however severely limited by the quadratic complexity of its main computational kernel. In this work we present an approximation algorithm for CVT with a significantly lower complexity. This new algorithm reduces the runtime by several orders of magnitude, and maintains the main advantages of CVT over the continuous approach. Due to the simplicity of our algorithm it can be easily parallelized to improve the runtime further.

  • 49.
    Rosanwo, Olifemi
    et al.
    Zuse Institute Berlin, Germany.
    Petz, Christoph
    Zuse Institute Berlin, Germany.
    Hotz, Ingrid
    Zuse Institute Berlin, Germany.
    Prohaska, Steffen
    Zuse Institute Berlin, Germany.
    Hege, Hans-Christian
    Zuse Institute Berlin, Germany.
    Dual Streamline Seeding2009Conference paper (Refereed)
    Abstract [en]

    This work introduces a novel streamline seeding technique based on dual streamlines that are orthogonal to the vector field, instead of tangential. The greedy algorithm presented here produces a net of orthogonal streamlines that is iteratively refined resulting in good domain coverage and a high degree of continuity and uniformity. The algorithm is easy to implement and efficient, and it naturally extends to curved surfaces.

  • 50.
    Schlemmer, Michael
    et al.
    University of Kaiserslautern, Germany.
    Bertram, Martin Hering
    Wirtschaftsmathematik (ITWM) in Kaiserslautern, Germany..
    Hotz, Ingrid
    Berlin (ZIB), FU Berlin, Germany..
    Garth, Christoph
    University of California, Davis, CA..
    Kollmann, Wolfgang
    University of California, Davis, CA..
    Hamann, Bernd
    University of California, Davis, CA..
    Hagen, Hans
    University of Kaiserslautern.
    Moment Invariants for the Analysis of 2D Flow Fields2007In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 13, no 6, p. 1743-1750Article in journal (Refereed)
    Abstract [en]

    We present a novel approach for analyzing two-dimensional (2D) flow field data based on the idea of invariant moments. Moment invariants have traditionally been used in computer vision applications, and we have adapted them for the purpose of interactive exploration of flow field data. The new class of moment invariants we have developed allows us to extract and visualize 2D flow patterns, invariant under translation, scaling, and rotation. With our approach one can study arbitrary flow patterns by searching a given 2D flow data set for any type of pattern as specified by a user. Further, our approach supports the computation of moments at multiple scales, facilitating fast pattern extraction and recognition. This can be done for critical point classification, but also for patterns with greater complexity. This multi-scale moment representation is also valuable for the comparative visualization of flow field data. The specific novel contributions of the work presented are the mathematical derivation of the new class of moment invariants, their analysis regarding critical point features, the efficient computation of a novel feature space representation, and based upon this the development of a fast pattern recognition algorithm for complex flow structures.

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