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  • 51.
    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.

  • 52.
    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. 

  • 53.
    Kuhn, Alexander
    et al.
    Zuse-Institute Berlin (ZIB), Berlin, Germany.
    Engelke, Wito
    Deutsches Zentrum für Luft- und Raumfahrt (DLR), Braunschweig, Germany.
    Flatken, Markus
    Deutsches Zentrum für Luft- und Raumfahrt (DLR), Braunschweig, Germany.
    Hans-Christian, Hege
    Zuse-Institute Berlin (ZIB), Berlin, Germany.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Topology-Based Analysis for Multimodal Atmospheric Data of Volcano Eruptions2015In: Topological Methods in Data Analysis and Visualization IV: Theory, Algorithms, and Applications / [ed] Hamish Carr, Christoph Garth and Tino Weinkauf, Springer, 2015, p. 35-50Conference paper (Refereed)
    Abstract [en]

    Many scientific applications deal with data from a multitude of different sources, e.g., measurements, imaging and simulations. Each source provides an additional perspective on the phenomenon of interest, but also comes with specific limitations, e.g. regarding accuracy, spatial and temporal availability. Effectively combining and analyzing such multimodal and partially incomplete data of limited accuracy in an integrated way is challenging. In this work, we outline an approach for an integrated analysis and visualization of the atmospheric impact of volcano eruptions. The data sets comprise observation and imaging data from satellites as well as results from numerical particle simulations. To analyze the clouds from the volcano eruption in the spatiotemporal domain we apply topological methods. We show that topology-related extremal structures of the data support clustering and comparison. We further discuss the robustness of those methods with respect to different properties of the data and different parameter setups. Finally we outline open challenges for the effective integrated visualization using topological methods.

  • 54.
    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.

  • 55.
    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)
  • 56.
    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.

  • 57.
    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.

  • 58.
    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.

  • 59.
    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.

  • 60.
    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.

  • 61.
    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.

  • 62.
    Schlemmer, Michael
    et al.
    Kaiserslautern, Germany.
    Hagen, Hans
    Kaiserslautern, Germany.
    Hotz, Ingrid
    Universtiy of California, Davis.
    Hamann, Bernd
    University of California, Davis, USA.
    Clifford Pattern Matching for Color Image Edge Detection2006In: Visualization of Large and Unstructured Data Sets: first workshop of the DFG's International Research Training Group Visualization of Large and Unstructured Data Sets - Applications in Geospatial Planning, Modeling, and Engineering, June 14-16, 2006, Dagstuhl Castle, Germany / [ed] Hans Hagen, Andreas Kerren, Peter Dannenmann, GI-Edition , 2006, p. 47-58Chapter in book (Refereed)
    Abstract [en]

    Feature detection and pattern matching play an important role in visualization.Originally developed for images and scalar fields, pattern matching methods become increasingly interesting for other applications, e.g., vector fields. To apply pattern matching to vector fields the basic concepts of convolution and fast Fourier transform (FFT) have to be generalized to vector fields. A formalism supporting an elegant generalization of these concepts is provided by the Clifford Algebra, originally developed for describing geometry and geometric operations. We discuss an application of the Clifford Pattern Matching (CPM). We apply CPM to images for ”Clifford Color Edge Detection” (C2ED), an approach for detecting edges and other features in color images. The basic idea is to treat color value tripels as vectors and apply the pattern matching algorithm to the resulting vector field. We introduce vector-valued filters for edge detection and present results.

  • 63.
    Schlemmer, Michael
    et al.
    Department of Computer Science, TU Kaiserslautern, Germany.
    Hotz, Ingrid
    Konrad-Zuse-Zentrum f¨ur Informationstechnik Berlin (ZIB), FU Berlin, Germany.
    Hamann, Bernd
    Institute for Data Analysis and Visualization (IDAV), University of California, Davis, CA.
    Hagen, Hans
    Department of Computer Science, TU Kaiserslautern, Germany.
    Comparative Visualization of Two-Dimensional Flow Data Using Moment Invariants2009Conference paper (Refereed)
    Abstract [en]

    The analysis of time-dependent data is often guided by the question of how dominant structures develop over time. It is important to understand how patterns or structures identified for one time step evolve over time, by changing or moving in the domain. To gain insight into such evolving structural change it is crucial to effectively compare different time steps. This paper proposes a comparison method for twodimensional flow fields. The method is based on a feature description using invariant moments. The specific strength of these moments is their invariance under scaling and rotation, thus facilitating an identification of features even if they occur at other positions, with changed orientation, and variation in size. In addition the moments themselves can beused to define a similarity measure. To evaluate the significance of this concept it has been applied to wind speed data from meteorological simulations.

  • 64.
    Schlemmer, Michael
    et al.
    University of Kaiserslautern, Germany.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Hamann, Bernd
    University of California, Davis, USA.
    Morr, Florian
    University of Kaiserslautern, Germany.
    Hagen, Hans
    University of Kaiserslautern, Germany.
    Priority Streamlines: A context-based Visualization of Flow Fields2007Conference paper (Refereed)
    Abstract [en]

    Flow vector fields contain a wealth of information that needs to be visualized. As an extension of the well-known streamline technique, we have developed a context-based method for visualizing steady flow vector fields in two and three dimensions. We call our method "Priority Streamlines". In our approach, the density of the streamlines is controlled by a scalar function that can be user-defined, or be given by additional information (e.g., temperature, pressure, vorticity, velocity) considering the underlying flow vector field. In regions, which are interesting the streamlines are drawn with increased density, while less interesting regions are drawn sparsely. Since streamlines in the most important regions are drawn first, we can use thresholding to obtain a streamline representation highlighting essential features. Color-mapping and transparency can be used for visualizing other information hidden in the flow vector field.

  • 65.
    Schlemmer, Michael
    et al.
    University of Kaiserslautern.
    Hotz, Ingrid
    Universtiy of California, Davis.
    Natarajan, Vijay
    University of California, Davis.
    Hamann, Bernd
    University of California, Davis, USA.
    Hagen, Hans
    University of Kaiserslautern.
    Fast Clifford Fourier transfor- mation for unstructured vector field data.2005Conference paper (Refereed)
    Abstract [en]

    Vector fields play an important role in many areas of computational physics and engineering. For effective visualization of vector fields it is necessary to identify and extract important features inherent in the data, defined by filters that characterize certain “patterns”. Our prior approach for vector field analysis used the Clifford Fourier transform for efficient pattern recognition for vector field data defined on regular grids [1,2]. Using the frequency domain, correlation and convolution of vectors can be computed as a Clifford multiplication, enabling us to determine similarity between a vector field and a pre-defined pattern mask (e.g., for critical points). Moreover, compression and spectral analysis of vector fields is possible using this method. Our current approach only applies to rectilinear grids. We combine this approach with a fast Fourier transform to handle unstructured scalar data [6]. Our extension enables us to provide a feature-based visualization of vector field data defined on unstructured grids, or completely scattered data. Besides providing the theory of Clifford Fourier transform for unstructured vector data, we explain how efficient pattern matching and visualization of various selectable features can be performed efficiently. We have tested our method for various vector data sets.

  • 66.
    Schultz, Thomas
    et al.
    Institute of Computer Science, University of Bonn, Bonn, Germany.
    Özarslan, EvrenLinköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering.Hotz, IngridLinköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Modeling, Analysis, and Visualization of Anisotropy2017Collection (editor) (Refereed)
    Abstract [en]

    This book focuses on the modeling, processing and visualization of anisotropy, irrespective of the context in which it emerges, using state-of-the-art mathematical tools. As such, it differs substantially from conventional reference works, which are centered on a particular application. It covers the following topics: (i) the geometric structure of tensors, (ii) statistical methods for tensor field processing, (iii) challenges in mapping neural connectivity and structural mechanics, (iv) processing of uncertainty, and (v) visualizing higher-order representations. In addition to original research contributions, it provides insightful reviews.This multidisciplinary book is the sixth in a series that aims to foster scientific exchange between communities employing tensors and other higher-order representations of directionally dependent data. A significant number of the chapters were co-authored by the participants of the workshop titled Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis, which was held in Dagstuhl, Germany in April 2016.

    It offers a valuable resource for those working in the field of multi-directional data, vital inspirations for the development of new models, and essential analysis and visualization techniques, thus furthering the state-of-the-art in studies involving anisotropy.

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  • 67.
    Schöneich, Mark
    et al.
    University Saarbrücken, Germany.
    Kratz, Andrea
    Zuse Institute Berlin.
    Hotz, Ingrid
    German Aerospace Center (DLR).
    Stommel, Markus
    Technical University Dortmund, Germany.
    Scheuermann, Gerik
    University of Leipzig.
    Zobel, Valentin
    University of Leipzig.
    Optimization strategy for the design of ribbed plastic components2014In: Journal of Plastics Technology, no 10, p. 160-175Article in journal (Refereed)
  • 68.
    Schöneich, Mark
    et al.
    University Saarbrücken, Saarbrücken, Germany.
    Kratz, Andrea
    Zuse Institute Berlin, Berlin, Germany.
    Zobel, Valentin
    Universität Leipzig, Leipzig, Germany .
    Scheuermann, Gerik
    Universität Leipzig, Leipzig, Germany.
    Stommel, Markus
    University Dortmund, Dortmund, Germany.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Tensor lines in engineering: success, failure, and open questions2015In: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data / [ed] Ingrid Hotz, Thomas Schultz, Cham: Springer, 2015, p. 339-351Chapter in book (Refereed)
    Abstract [en]

    Today, product development processes in mechanical engineering are almost entirely carried out via computer-aided simulations. One essential output of these simulations are stress tensors, which are the basis for the dimensioning of the technical parts. The tensors contain information about the strength of internal stresses as well as their principal directions. However, for the analysis they are mostly reduced to scalar key metrics. The motivation of this work is to put the tensorial data more into focus of the analysis and demonstrate its potential for the product development process. In this context we resume a visualization method that has been introduced many years ago, tensor lines. Since tensor lines have been rarely used in visualization applications, they are mostly considered as physically not relevant in the visualization community. In this paper we challenge this point of view by reporting two case studies where tensor lines have been applied in the process of the design of a technical part. While the first case was a real success, we could not reach similar results for the second case. It became clear that the first case cannot be fully generalized to arbitrary settings and there are many more questions to be answered before the full potential of tensor lines can be realized. In this chapter, we review our success story and our failure case and discuss some directions of further research.

  • 69.
    Skånberg, Robin
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology.
    Linares, Mathieu
    Linköping University, Department of Physics, Chemistry and Biology, Bioinformatics. Linköping University, Faculty of Science & Engineering.
    König, Carolin
    Division of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Sweden.
    Norman, Patrick
    Linköping University, Department of Physics, Chemistry and Biology. 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. 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. 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).
    VIA-MD: Visual Interactive Analysis of Molecular Dynamics2018In: Workshop on Molecular Graphics and Visual Analysis of Molecular Data, 2018Conference paper (Refereed)
  • 70.
    Sreevalsan-Nair, Jaya
    et al.
    Institute of Information Technology Bangalore, India (IIIT).
    Auer, Cornelia
    Zuse Institute Berlin.
    Hamann, Bernd
    University of California, Davis, USA.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Eigenvector-based Interpolation and Segmentation of 2D Tensor Fields2011In: Topological Methods in Data Analysis and Visualization. Theory, Algorithms, and Applications / [ed] Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, Ronald Peikert, Springer, 2011, p. 139-150Chapter in book (Refereed)
    Abstract [en]

    We propose a topology-based segmentation of 2D symmetric tensor fields, which results in cells bounded by tensorlines. We are particularly interested in the influence of the interpolation scheme on the topology, considering eigenvector-based and component-wise linear interpolation. When using eigenvector-based interpolation the most significant modification to the standard topology extraction algorithm is the insertion of additional vertices at degenerate points. A subsequent Delaunay re-triangulation leads to connections between close degenerate points. These new connections create degenerate edges and tri angles.When comparing the resulting topology per triangle with the one obtained by component-wise linear interpolation the results are qualitatively similar, but our approach leads to a less “cluttered” segmentation

  • 71.
    Sreevalsan-Nair, Jaya
    et al.
    Univ. of California, Davis.
    Nieuwenhuyse, Erwin Van
    U.S. Bureau of Reclamation.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Linsen, Lars
    International Univ. of Bremen (Germany).
    Hamann, Bernd
    Univ. of California, Davis.
    An Interactive Visual Exploration Tool for Northern California’s Water Monitoring Networks2007Conference paper (Refereed)
    Abstract [en]

    The water monitoring network in Northern California provides us with an integrated flow and water-quality dataset of the Sacramento-San Joaquin Delta, the reservoirs, and the two main rivers feeding the Delta, namely the Sacramento and the San Joaquin rivers. Understanding the dynamics and complex interactions among the components of this large water supply system and how they affect the water quality, and ecological conditions for fish and wildlife requires the assimilation of large amounts of data. A multivariate, time series data visualization tool which encompasses various components of the system, in a geographical context, is the most appropriate solution to this challenge. We have developed an abstract representation of the water system, which uses various information visualization techniques, like focus+context techniques, graph representation, 3D glyphs, and colormapping, to visualize time series data of multiple parameters.        

  • 72.
    Sreevalsan-Nair, Jaya
    et al.
    University of California, Davis, CA, USA .
    Verhoeven, Meike
    University of California, Davis, CA, USA .
    Woodruff, David L.
    University of California, Davis, CA, USA .
    Hotz, Ingrid
    Zuse Institue Berlin.
    Hamann, Bernd
    University of California, Davis, USA.
    Human-Guided Enhancement of a Stochastic Local Search: Visualization and Adjustment of 3D Pheromone2007Conference paper (Refereed)
    Abstract [en]

    In this paper, we describe user interaction with an optimization algorithm via a sophisticated visualization interface that we created for this purpose. Our primary interest is the tool itself. We demonstrate that a user wielding this tool can find ways to improve the performance of an ant colony optimization (ACO) algorithm as applied to a problem of finding 3D paths in the presence of impediments [14]. One part of a solution method can be to find a path on a grid. Of course, there are near linear time algorithms for the shortest path that have been applied to problems that are quite large. However, for a grid in three dimensions with arcs on the axes and diagonals, the problems can become extremely large as resolution is increased and heuristics thus make sense (see, e.g., [6] for state-of-the art algorithms where pre-processing is possible). Ant colony optimization (see, e.g., [4,5]) is ideally suited to such a problem.

  • 73.
    Valsangkar, Akash Anil
    et al.
    Indian Inst Sci, India.
    Monteiro, Joy Merwin
    Stockholm Univ, Sweden.
    Narayanan, Vidya
    Carnegie Mellon Univ, PA 15213 USA.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Natarajan, Vijay
    Indian Inst Sci, India.
    An Exploratory Framework for Cyclone Identification and Tracking2019In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 25, no 3, p. 1460-1473Article in journal (Refereed)
    Abstract [en]

    Analyzing depressions plays an important role in meteorology, especially in the study of cyclones. In particular, the study of the temporal evolution of cyclones requires a robust depression tracking framework. To cope with this demand we propose a pipeline for the exploration of cyclones and their temporal evolution. This entails a generic framework for their identification and tracking. The fact that depressions and cyclones are not well-defined objects and their shape and size characteristics change over time makes this task especially challenging. Our method combines the robustness of topological approaches and the detailed tracking information from optical flow analysis. At first cyclones are identified within each time step based on well-established topological concepts. Then candidate tracks are computed from an optical flow field. These tracks are clustered within a moving time window to distill dominant coherent cyclone movements, which are then forwarded to a final tracking step. In contrast to previous methods our method requires only a few intuitive parameters. An integration into an exploratory framework helps in the study of cyclone movement by identifying smooth, representative tracks. Multiple case studies demonstrate the effectiveness of the method in tracking cyclones, both in the northern and southern hemisphere.

  • 74.
    Zobel, Valentin
    et al.
    Zuse Institue Berlin.
    Reininghaus, Jan
    Zuse Institue Berlin.
    Hotz, Ingrid
    Zuse Institue Berlin.
    Visualization of Two-Dimensional Symmetric Tensor Fields Using the Heat Kernel Signature2014In: Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications / [ed] Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, Ronald Peikert, Springer, 2014, p. 249-262Chapter in book (Refereed)
    Abstract [en]

    We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set.

  • 75.
    Zobel, Valentin
    et al.
    Leipzig University, Leipzig, Germany.
    Reininghaus, Jan
    Institute of Science and Technology Austria, Klosterneuburg, Austria.
    Hotz, Ingrid
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Visualizing Symmetric Indefinite 2D Tensor Fields using the Heat Kernel Signature2015In: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data / [ed] Ingrid Hotz, Thomas Schultz, Cham: Springer, 2015, p. 257-267Chapter in book (Refereed)
    Abstract [en]

    The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece.

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