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  • 1.
    Abrikosov, Alexei I.
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Masood, Talha Bin
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Falk, Martin
    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.
    Topological analysis of density fields: An evaluation of segmentation methods2021In: Computers & graphics, ISSN 0097-8493, E-ISSN 1873-7684, Vol. 98, p. 231-241Article in journal (Refereed)
    Abstract [en]

    Topological and geometric segmentation methods provide powerful concepts for detailed field analysis and visualization. However, when it comes to a quantitative analysis that requires highly accurate geometric segmentation, there is a large discrepancy between the promising theory and the available computational approaches. In this paper, we compare and evaluate various segmentation methods with the aim to identify and quantify the extent of these discrepancies. Thereby, we focus on an application from quantum chemistry: the analysis of electron density fields. It is a scalar quantity that can be experimentally measured or theoretically computed. In the evaluation we consider methods originating from the domain of quantum chemistry and computational topology. We apply the methods to the charge density of a set of crystals and molecules. Therefore, we segment the volumes into atomic regions and derive and compare quantitative measures such as total charge and dipole moments from these regions. As a result, we conclude that an accurate geometry determination can be crucial for correctly segmenting and analyzing a scalar field, here demonstrated on the electron density field.

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  • 2.
    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.

  • 3.
    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.

  • 4.
    Behrendt, Benjamin
    et al.
    Department of Simulation and Graphics, University of Magdeburg, Germany.
    Engelke, Wito
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Berg, Philipp
    Department of Fluid Dynamics and Technical Flows, University of Magdeburg, Germany.
    Beuing, Oliver
    Institute of Neuroradiology, University Hospital Magdeburg, Germany.
    Preim, Bernhard
    Department of Simulation and Graphics, University of Magdeburg, Germany.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Saalfeld, Sylvia
    Department of Simulation and Graphics, University of Magdeburg, Germany.
    Evolutionary Pathlines for Blood Flow Exploration in Cerebral Aneurysms2019In: Eurographics Workshop on Visual Computing for Biology and Medicine / [ed] Kozlíková, Barbora and Linsen, Lars and Vázquez, Pere-Pau and Lawonn, Kai and Raidou, Renata Georgia, The Eurographics Association , 2019Conference paper (Refereed)
    Abstract [en]

    Blood flow simulations play an important role for the understanding of vascular diseases, such as aneurysms. However, analysis of the resulting flow patterns, especially comparisons across patient groups, are challenging. Typically, the hemodynamic analysis relies on trial and error inspection of the flow data based on pathline visualizations and surface renderings. Visualizing too many pathlines at once may obstruct interesting features, e.g., embedded vortices, whereas with too little pathlines, particularities such as flow characteristics in aneurysm blebs might be missed. While filtering and clustering techniques support this task, they require the pre-computation of pathlines densely sampled in the space-time domain. Not only does this become prohibitively expensive for large patient groups, but the results often suffer from undersampling artifacts. In this work, we propose the usage of evolutionary algorithms to reduce the overhead of computing pathlines that do not contribute to the analysis, while simultaneously reducing the undersampling artifacts. Integrated in an interactive framework, it efficiently supports the evaluation of hemodynamics for clinical research and treatment planning in case of cerebral aneurysms. The specification of general optimization criteria for entire patient groups allows the blood flow data to be batch-processed. We present clinical cases to demonstrate the benefits of our approach especially in presence of aneurysm blebs. Furthermore, we conducted an evaluation with four expert neuroradiologists. As a result, we report advantages of our method for treatment planning to underpin its clinical potential.  

  • 5.
    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.

  • 6.
    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)
  • 7.
    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.

  • 8.
    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.

  • 9.
    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.

  • 10.
    Dieckmann, Mark E
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Falk, Martin
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Folini, Doris
    Ecole Normale Supérieure, Lyon, CRAL, UMR CNRS 5574, Université de Lyon, 69622 Lyon, France.
    Walder, Rolf
    Ecole Normale Supérieure, Lyon, CRAL, UMR CNRS 5574, Université de Lyon, 69622 Lyon, France.
    Steneteg, Peter
    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.
    Collisionless Rayleigh–Taylor-like instability of the boundary between a hot pair plasma and an electron–proton plasma: The undular mode2020In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 27, no 11, p. 1-14, article id 112106Article in journal (Refereed)
    Abstract [en]

    We study with a two-dimensional particle-in-cell simulation the stability of a discontinuity or piston, which separates an electron–positron cloud from a cooler electron–proton plasma. Such a piston might be present in the relativistic jets of accreting black holes separating the jet material from the surrounding ambient plasma and when pair clouds form during an x-ray flare and expand into the plasma of the accretion disk corona. We inject a pair plasma at a simulation boundary with a mildly relativistic temperature and mean speed. It flows across a spatially uniform electron–proton plasma, which is permeated by a background magnetic field. The magnetic field is aligned with one simulation direction and oriented orthogonally to the mean velocity vector of the pair cloud. The expanding pair cloud expels the magnetic field and piles it up at its front. It is amplified to a value large enough to trap ambient electrons. The current of the trapped electrons, which is carried with the expanding cloud front, drives an electric field that accelerates protons. A solitary wave grows and changes into a piston after it saturated. Our simulations show that this piston undergoes a collisionless instability similar to a Rayleigh–Taylor instability. The undular mode grows and we observe fingers in the proton density distribution. The effect of the instability is to deform the piston but it cannot destroy it.

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  • 11.
    Dieckmann, Mark E
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Falk, Martin
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Steneteg, Peter
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Folini, Doris
    CRAL, École Normale Supérieure, 69622 Lyon, France.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Nordman, Aida
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Dell'Acqua, Pierangelo
    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.
    Walder, Rolf
    CRAL, École Normale Supérieure, 69622 Lyon, France.
    Structure of a collisionless pair jet in a magnetized electron-proton plasma: Flow-aligned magnetic field2019In: High Energy Phenomena in Relativistic Outflows VII (HEPRO VII): Formation and propagation of relativistic outflows, 2019, article id 006Conference paper (Refereed)
    Abstract [en]

    We present the results from a particle-in-cell (PIC) simulation that models the interaction between a spatially localized electron-positron cloud and an electron-ion plasma. The latter is permeated by a magnetic field that is initially spatially uniform and aligned with the mean velocity vector of the pair cloud. The pair cloud expels the magnetic field and piles it up into an electromagnetic piston. Its electromagnetic field is strong enough to separate the pair cloud from the ambient plasma in the direction that is perpendicular to the cloud propagation direction. The piston propagates away from the spine of the injected pair cloud and it accelerates the protons to a high nonrelativistic speed. The accelerated protons form an outer cocoon that will eventually become separated from the unperturbed ambient plasma by a fast magnetosonic shock. No electromagnetic piston forms at the front of the cloud and a shock is mediated here by the filamentation instability. The final plasma distribution resembles that of a hydrodynamic jet. Collisionless plasma jets may form in the coronal plasma of accreting black holes and the interaction between the strong magnetic field of the piston and the hot pair cloud may contribute to radio emissions by such objects.

  • 12.
    Dieckmann, Mark E
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Folini, Doris
    École Normale Supérieure, Lyon, CRAL, UMR CNRS 5574, Université de Lyon, Lyon, France .
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Nordman, Aida
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Dell'Acqua, Pierangelo
    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.
    Walder, Rolf
    École Normale Supérieure, Lyon, CRAL, UMR CNRS 5574, Université de Lyon, Lyon, France .
    Structure of a collisionless pair jet in a magnetized electron–proton plasma: flow-aligned magnetic field2019In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 621, article id A142Article in journal (Refereed)
    Abstract [en]

    Aims. We study the effect a guiding magnetic field has on the formation and structure of a pair jet that propagates through a collisionless electron–proton plasma at rest.

    Methods. We model with a particle-in-cell (PIC) simulation a pair cloud with a temperature of 400 keV and a mean speed of 0.9c (c - light speed). Pair particles are continuously injected at the boundary. The cloud propagates through a spatially uniform, magnetized, and cool ambient electron–proton plasma at rest. The mean velocity vector of the pair cloud is aligned with the uniform background magnetic field. The pair cloud has a lateral extent of a few ion skin depths.

    Results. A jet forms in time. Its outer cocoon consists of jet-accelerated ambient plasma and is separated from the inner cocoon by an electromagnetic piston with a thickness that is comparable to the local thermal gyroradius of jet particles. The inner cocoon consists of pair plasma, which lost its directed flow energy while it swept out the background magnetic field and compressed it into the electromagnetic piston. A beam of electrons and positrons moves along the jet spine at its initial speed. Its electrons are slowed down and some positrons are accelerated as they cross the head of the jet. The latter escape upstream along the magnetic field, which yields an excess of megaelectronvolt positrons ahead of the jet. A filamentation instability between positrons and protons accelerates some of the protons, which were located behind the electromagnetic piston at the time it formed, to megaelectronvolt energies.

    Conclusions. A microscopic pair jet in collisionless plasma has a structure that is similar to that predicted by a hydrodynamic model of relativistic astrophysical pair jets. It is a source of megaelectronvolt positrons. An electromagnetic piston acts as the contact discontinuity between the inner and outer cocoons. It would form on subsecond timescales in a plasma with a density that is comparable to that of the interstellar medium in the rest frame of the latter. A supercritical fast magnetosonic shock will form between the pristine ambient plasma and the jet-accelerated plasma on a timescale that exceeds our simulation time by an order of magnitude.

  • 13.
    Engelke, Wito
    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.
    Evolutionary Lines for Flow Visualization2018In: EuroVis 2018, 20th EG/VGTC Conference on Visualization, 4-8 June, Brno, Czech Republic / [ed] Jimmy Johansson and Filip Sadlo and Tobias Schreck, The Eurographics Association , 2018, p. 7-11Conference paper (Refereed)
    Abstract [en]

    In this work we explore evolutionary algorithms for selected a visualization application. We demonstrate its potential using an example from flow visualization showing promising first results. Evolutionary algorithms, as guided search approach, find close-to-optimal solutions with respect to some fitness function in an iterative process using biologically motivated mechanisms like selection, mutation and recombination. As such, they provide a powerful alternative to filtering methods commonly used in visualization where the space of possible candidates is densely sampled in a pre-processing step from which the best candidates are selected and visualized. This approach however tends to be increasingly inefficient with growing data size or expensive candidate computations resulting in large pre-processing times. We present an evolutionary algorithm for the problem of streamline selection to highlight features of interest in flow data. Our approach directly optimizes the solution candidates with respect to a user selected fitness function requiring significantly less computations. At the same time the problem of possible under-sampling is solved since we are not tied to a preset resolution. We demonstrate our approach on the well-known flow around an obstacle as case with a two-dimensional search space. The blood flow in an aneurysm serves as an example with a three-dimensional search space. For both, the achieved results are comparable to line filtering approaches with much less line computations.

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    Evolutionary Lines for Flow Visualization
  • 14.
    Engelke, Wito
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Lawonn, Kai
    Department of Simulation and Graphics, University of Magdeburg, Germany / Institute for Computational Visualistics, University of Koblenz‐Landau, Germany.
    Preim, Bernhard
    Department of Simulation and Graphics, University of Magdeburg, Germany.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Autonomous Particles for Interactive Flow Visualization2019In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, no 1, p. 248-259Article in journal (Refereed)
    Abstract [en]

    We present an interactive approach to analyse flow fields using a new type of particle system, which is composed of autonomous particles exploring the flow. While particles provide a very intuitive way to visualize flows, it is a challenge to capture the important features with such systems. Particles tend to cluster in regions of low velocity and regions of interest are often sparsely populated. To overcome these disadvantages, we propose an automatic adaption of the particle density with respect to local importance measures. These measures are user defined and the systems sensitivity to them can be adjusted interactively. Together with the particle history, these measures define a probability for particles to multiply or die, respectively. There is no communication between the particles and no neighbourhood information has to be maintained. Thus, the particles can be handled in parallel and support a real‐time investigation of flow fields. To enhance the visualization, the particles' properties and selected field measures are also used to specify the systems rendering parameters, such as colour and size. We demonstrate the effectiveness of our approach on different simulated vector fields from technical and medical applications.

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    Autonomous Particles for Interactive Flow Visualization
  • 15.
    Engelke, Wito
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Masood, Talha Bin
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Beran, Jakob
    Department of Meteorology (MISU)Stockholm University, Stockholm, Sweden.
    Caballero, Rodrigo
    Department of Meteorology (MISU)Stockholm University, Stockholm, Sweden.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Topology-Based Feature Design and Tracking for Multi-center Cyclones2021In: Topological Methods in Data Analysis and Visualization VI: Theory, Applications, and Software / [ed] Ingrid Hotz, Talha Bin Masood, Filip Sadlo and Julien Tierny, Springer, 2021, p. 71-85Chapter in book (Refereed)
    Abstract [en]

    In this paper, we propose a concept to design, track, and compare application-specific feature definitions expressed as sets of critical points. Our work has been inspired by the observation that in many applications a large variety of different feature definitions for the same concept are used. Often, these definitions compete with each other and it is unclear which definition should be used in which context. A prominent example is the definition of cyclones in climate research. Despite the differences, frequently these feature definitions can be related to topological concepts.

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  • 16.
    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.

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  • 17.
    Falk, Martin
    et al.
    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.
    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).
    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).
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Feature Exploration in Medical Volume Data using Local Frequency Distributions2020In: / [ed] B. Kozlíková, M. Krone, and N. N. Smit, 2020Conference paper (Refereed)
    Abstract [en]

    Frequency distributions (FD) are an important instrument when analyzing and investigating scientific data. In volumetric visualization, for example, frequency distributions visualized as histograms, often assist the user in the process of designing transfer function (TF) primitives. Yet a single point in the distribution can correspond to multiple features in the data, particularly in low-dimensional TFs that dominate time-critical domains such as health care. In this paper, we propose contributions to the area of medical volume data exploration, in particular Computed Tomography (CT) data, based on the decomposition of local frequency distributions (LFD). By considering the local neighborhood utilizing LFDs we can incorporate a measure for neighborhood similarity to differentiate features thereby enhancing the classification abilities of existing methods. This also allows us to link the attribute space of the histogram with the spatial properties of the data to improve the user experience and simplify the exploration step. We propose three approaches for data exploration which we illustrate with several visualization cases highlighting distinct features that are not identifiable when considering only the global frequency distribution. We demonstrate the power of the method on selected datasets.

  • 18.
    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.

  • 19.
    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.

  • 20.
    Friederici, Anke
    et al.
    Otto-von-Guericke-University Magdeburg, Magdeburg, Germany.
    Falk, Martin
    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.
    A Winding Angle Framework for Tracking and Exploring Eddy Transport in Oceanic Ensemble Simulations2021In: Workshop on Visualisation in Environmental Sciences (EnvirVis), The Eurographics Association , 2021Conference paper (Refereed)
    Abstract [en]

    Oceanic eddies, which are highly mass-coherent vortices traveling through the earth's waters, are of special interest for their mixing properties. Therefore, large-scale ensemble simulations are performed to approximate their possible evolution. Analyzing their development and transport behavior requires a stable extraction of both their shape and properties of water masses within. We present a framework for extracting the time series of full 3D eddy geometries based on an winding angle criterion. Our analysis tools enables users to explore the results in-depth by linking extracted volumes to extensive statistics collected across several ensemble members. The methods are showcased on an ensemble simulation of the Red Sea. We show that our extraction produces stable and coherent geometries even for highly irregular eddies in the Red Sea. These capabilities are utilized to evaluate the stability of our method with respect to variations of user-defined parameters. Feedback gathered from domain experts was very positive and indicates that our methods will be considered for newly simulated, even larger data sets.

  • 21.
    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..

    Download full text (pdf)
    Concepts of Hybrid Data Rendering
  • 22.
    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.

  • 23.
    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.

  • 24.
    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.

  • 25.
    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.

  • 26.
    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

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    Proceedings of SIGRAD 2017, August 17-18, 2017 Norrköping, Sweden
  • 27.
    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.

  • 28.
    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.

  • 29.
    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.

  • 30.
    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)
  • 31.
    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)
  • 32.
    Hotz, Ingrid
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Masood, Talha BinLinköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.Sadlo, FilipHeidelberg University, IWR, Heidelberg, Germany.Tierny, JulienCNRS, Department of Scientific Computing, Sorbonne Université, Paris, France.
    Topological Methods in Data Analysis and Visualization VI: Theory, Applications, and Software2021Collection (editor) (Refereed)
    Abstract [en]

    This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.  

  • 33.
    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.

  • 34.
    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
  • 35.
    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.

  • 36.
    Jankowai, Jochen
    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.
    Feature Level-Sets: Generalizing Iso-surfaces to Multi-variate Data2020In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 26, no 2, p. 1308-1319Article in journal (Refereed)
    Abstract [en]

    Iso-surfaces or level-sets provide an effective and frequently used means for feature visualization. However, they are restricted to simple features for uni-variate data. The approach does not scale when moving to multi-variate data or when considering more complex feature definitions. In this paper, we introduce the concept of traits and feature level-sets, which can be understood as a generalization of level-sets as it includes iso-surfaces, and fiber surfaces as special cases. The concept is applicable to a large class of traits defined as subsets in attribute space, which can be arbitrary combinations of points, lines, surfaces and volumes.  It is implemented into a system that provides an interface to define traits in an interactive way and multiple rendering options. We demonstrate the effectiveness of the approach using multi-variate data sets of different nature, including vector and tensor data, from different application domains.

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    fulltext
  • 37.
    Jankowai, Jochen
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Medicine and Health Sciences.
    Skånberg, Robin
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Jönsson, Daniel
    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.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Tensor volume exploration using attribute space representatives2020Conference paper (Refereed)
    Abstract [en]

    While volume rendering for scalar fields has been advanced into a powerful visualisation method, similar volumetric representations for tensor fields are still rare. The complexity of the data challenges not only the rendering but also the design of the transfer function. In this paper we propose an interface using glyph widgets to design a transfer function for the rendering of tensor data sets. Thereby the transfer function (TF) controls a volume rendering which represents sought after tensor-features and a texture that conveys directional information. The basis of the design interface is a two-dimensional projection of the attribute space. Characteristic representatives in the form of glyphs support an intuitive navigation through the attribute space. We provide three different options to select the representatives: automatic selection based on attribute space clustering, uniform sampling of the attribute space, or manually selected representatives. In contrast to glyphs placed into the 3D volume, we use glyphs with complex geometry as widgets to control the shape and extent of the representatives. In the final rendering the glyphs with their assigned colors play a similar role as a legend in an atlas like representation. The method provides an overview of the tensor field in the 3D volume at the same time as it allows the user to explore the tensor field in an attribute space. We demonstrate the flexibility of our approach on tensor fields for selected data sets with very different characteristics.

  • 38.
    Jönsson, Daniel
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Bergström, Albin
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Algström, Isac
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Simon, Rozalyn
    Linköping University, Department of Medical and Health Sciences, Division of Radiological Sciences. Linköping University, Faculty of Medicine and Health Sciences.
    Engström, Maria
    Linköping University, Department of Medical and Health Sciences, Division of Radiological Sciences. Linköping University, Faculty of Medicine and Health Sciences.
    Walter, Susanna
    Linköping University, Department of Clinical and Experimental Medicine, Division of Neuro and Inflammation Science. Linköping University, Faculty of Medicine and Health Sciences. Region Östergötland, Heart and Medicine Center, Department of Gastroentorology.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Visual analysis for understanding irritable bowel syndrome2019In: Biomedical visualisation / [ed] Paul Rea, Cham: Springer, 2019, p. 111-122Chapter in book (Refereed)
    Abstract [en]

    The cause of irritable bowel syndrome (IBS), a chronic disorder characterized by abdominal pain and disturbed bowel habits, is largely unknown. It is believed to be related to physical properties in the gut, central mechanisms in the brain, psychological factors, or a combination of these. To understand the relationships within the gut-brain axis with respect to IBS, large numbers of measurements ranging from stool samples to functional magnetic resonance imaging are collected from patients with IBS and healthy controls. As such, IBS is a typical example in medical research where research turns into a big data analysis challenge. In this chapter we demonstrate the power of interactive visual data analysis and exploration to generate an environment for scientific reasoning and hypothesis formulation for data from multiple sources with different character. Three case studies are presented to show the utility of the presented work.

  • 39.
    Jönsson, Daniel
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Bergström, Albin
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Forsell, Camilla
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Simon, Rozalyn
    Linköping University, Department of Medical and Health Sciences, Division of Radiological Sciences. Linköping University, Faculty of Medicine and Health Sciences.
    Engström, Maria
    Linköping University, Department of Medical and Health Sciences, Division of Radiological Sciences. Linköping University, Faculty of Medicine and Health Sciences.
    Ynnerman, Anders
    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.
    A Visual Environment for Hypothesis Formation and Reasoning in Studies with fMRI and Multivariate Clinical Data2019In: Eurographics Workshop on Visual Computing for Biology and Medicine, 2019Conference paper (Refereed)
    Abstract [en]

    We present an interactive visual environment for linked analysis of brain imaging and clinical measurements. The environment is developed in an iterative participatory design process involving neuroscientists investigating the causes of brain-related complex diseases. The hypotheses formation process about correlations between active brain regions and physiological or psychological factors in studies with hundreds of subjects is a central part of the investigation. Observing the reasoning patterns during hypotheses formation, we concluded that while existing tools provide powerful analysis options, they lack effective interactive exploration, thus limiting the scientific scope and preventing extraction of knowledge from available data.Based on these observations, we designed methods that support neuroscientists by integrating their existing statistical analysis of multivariate subject data with interactive visual explorationto enable them to better understand differences between patient groups and the complex bidirectional interplay between clinical measurement and the brain. These exploration concepts enable neuroscientists, for the first time during their investigations, to interactively move between and reason about questions such as ‘which clinical measurements are correlated with a specific brain region?’ or ‘are there differences in brain activity between depressed young and old subjects?’. The environment uses parallel coordinates for effective overview and selection of subject groups, Welch's t-test to filter out brain regions with statistically significant differences, and multiple visualizations of Pearson correlations between brain regions and clinical parameters to facilitate correlation analysis. A qualitative user study was performed with three neuroscientists from different domains. The study shows that the developed environment supports simultaneous analysis of more parameters, provides rapid pathways to insights, and is an effective support tool for hypothesis formation.

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  • 40.
    Jönsson, Daniel
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Steneteg, Peter
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Sundén, Erik
    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.
    Kottravel, Sathish
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Falk, Martin
    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.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Ropinski, Timo
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Inviwo - A Visualization System with Usage Abstraction Levels2020In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, Vol. 26, no 11, p. 3241-3254Article in journal (Refereed)
    Abstract [en]

    The complexity of todays visualization applications demands specific visualization systems tailored for the development of these applications. Frequently, such systems utilize levels of abstraction to improve the application development process, for insta

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  • 41.
    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.

  • 42.
    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.

  • 43.
    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.

  • 44.
    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)
  • 45.
    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

  • 46.
    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.

  • 47.
    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.

  • 48.
    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

  • 49.
    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)
  • 50.
    Klötzl, Daniel
    et al.
    Univ Stuttgart VISUS, Germany.
    Krake, Tim
    Univ Stuttgart VISUS, Germany.
    Zhou, Youjia
    Univ Utah SCI, UT USA.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Wang, Bei
    Univ Utah SCI, UT USA.
    Weiskopf, Daniel
    Univ Stuttgart VISUS, Germany.
    Local bilinear computation of Jacobi sets2022In: The Visual Computer, ISSN 0178-2789, E-ISSN 1432-2315, Vol. 38, p. 3435-3448Article in journal (Refereed)
    Abstract [en]

    We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

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