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Documents authored by Hotz, Ingrid

Document
DOI: 10.4230/LIPIcs.SoCG.2026.57
Singular Arrange and Traverse Algorithm for Computing Reeb Spaces of Bivariate PL Maps

Authors: Petar Hristov, Ingrid Hotz, and Talha Bin Masood

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We present an exact and efficient algorithm for computing the Reeb space of a bivariate PL map. The Reeb space is a topological structure that generalizes the Reeb graph to the setting of multiple scalar-valued functions defined over a shared domain, a situation that frequently arises in practical applications. While the Reeb graph has become a standard tool in computer graphics, shape analysis, and scientific visualization, the Reeb space is still in the early stages of adoption. Although several algorithms for computing the Reeb space have been proposed, none offer an implementation that is both exact and efficient, which has substantially limited its practical use. To address this gap, we introduce singular arrange and traverse, a new algorithm built upon the arrange and traverse framework [Hristov et al., 2025]. Our method exploits the fact that, in the bivariate case, only singular edges contribute to the structure of Reeb space, allowing us to ignore many regular edges [Tierny and Carr, 2017]. This observation results in substantial efficiency gains on datasets where most edges are regular, which is common in many numerical simulations of physical systems. We provide an implementation of our method and benchmark it against the original arrange and traverse algorithm, showing performance gains of up to four orders of magnitude on real-world datasets.
Cite as

Petar Hristov, Ingrid Hotz, and Talha Bin Masood. Singular Arrange and Traverse Algorithm for Computing Reeb Spaces of Bivariate PL Maps. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 57:1-57:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hristov_et_al:LIPIcs.SoCG.2026.57,
  author =	{Hristov, Petar and Hotz, Ingrid and Masood, Talha Bin},
  title =	{{Singular Arrange and Traverse Algorithm for Computing Reeb Spaces of Bivariate PL Maps}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{57:1--57:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.57},
  URN =		{urn:nbn:de:0030-drops-258644},
  doi =		{10.4230/LIPIcs.SoCG.2026.57},
  annote =	{Keywords: Computational topology, Reeb graph, Reeb space, Multivariate data, Multifield, Geometric arrangement}
}
Document
DOI: 10.4230/DagRep.6.4.16
Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis (Dagstuhl Seminar 16142)

Authors: Ingrid Hotz, Evren Özarslan, and Thomas Schultz

Published in: Dagstuhl Reports, Volume 6, Issue 4 (2016)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 16142, "Multidisciplinary Approaches to Multivalued Data: Modelling, Visualization, Analysis", which was attended by 27 international researchers, both junior and senior. Modelling multivalued data using tensors and higher-order descriptors has become common practice in neuroscience, engineering, and medicine. Novel tools for image analysis, visualization, as well as statistical hypothesis testing and machine learning are required to extract value from such data, and can only be developed within multidisciplinary collaborations. This report gathers abstracts of the talks held by participants on recent advances and open questions related to these challenges, as well as an account of topics raised within two of the breakout sessions.
Cite as

Ingrid Hotz, Evren Özarslan, and Thomas Schultz. Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis (Dagstuhl Seminar 16142). In Dagstuhl Reports, Volume 6, Issue 4, pp. 16-38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Article{hotz_et_al:DagRep.6.4.16,
  author =	{Hotz, Ingrid and \"{O}zarslan, Evren and Schultz, Thomas},
  title =	{{Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis (Dagstuhl Seminar 16142)}},
  pages =	{16--38},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{6},
  number =	{4},
  editor =	{Hotz, Ingrid and \"{O}zarslan, Evren and Schultz, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.6.4.16},
  URN =		{urn:nbn:de:0030-drops-61517},
  doi =		{10.4230/DagRep.6.4.16},
  annote =	{Keywords: visualization, image processing, statistical analysis, machine learning, tensor fields, higher-order descriptors, diffusion-weighted imaging (DWI), structural mechanics, fluid dynamics, microstructure imaging, connectomics, uncertainty visualization, feature extraction}
}
Document
DOI: 10.4230/DagRep.4.2.110
Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (Dagstuhl Seminar 14082)

Authors: Bernhard Burgeth, Ingrid Hotz, Anna Vilanova Bartroli, and Carl-Fredrik Westin

Published in: Dagstuhl Reports, Volume 4, Issue 2 (2014)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 14082 "Visualization and Processing of Higher Order Descriptors for Multi-Valued Data". The seminar gathered 26 senior and younger researchers from various countries in the unique atmosphere offered by Schloss Dagstuhl. The focus of the seminar was to discuss modern and emerging methods for analysis and visualization of tensor and higher order descriptors from medical imaging and engineering applications. Abstracts of the talks are collected in this report.
Cite as

Bernhard Burgeth, Ingrid Hotz, Anna Vilanova Bartroli, and Carl-Fredrik Westin. Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (Dagstuhl Seminar 14082). In Dagstuhl Reports, Volume 4, Issue 2, pp. 110-128, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Article{burgeth_et_al:DagRep.4.2.110,
  author =	{Burgeth, Bernhard and Hotz, Ingrid and Vilanova Bartroli, Anna and Westin, Carl-Fredrik},
  title =	{{Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (Dagstuhl Seminar 14082)}},
  pages =	{110--128},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2014},
  volume =	{4},
  number =	{2},
  editor =	{Burgeth, Bernhard and Hotz, Ingrid and Vilanova Bartroli, Anna and Westin, Carl-Fredrik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.4.2.110},
  URN =		{urn:nbn:de:0030-drops-45470},
  doi =		{10.4230/DagRep.4.2.110},
  annote =	{Keywords: visualization, image processing, tensor fields, diffusion tensor imaging (DTI), diffusion MRI (dMRI), fiber tractography, higher-order, tensors, partial differential equations (PDEs), structural mechanics, solid mechanics}
}
Document
DOI: 10.4230/DFU.Vol2.SciViz.2011.17
2D Tensor Field Segmentation

Authors: Cornelia Auer, Jaya Sreevalsan-Nair, Valentin Zobel, and Ingrid Hotz

Published in: Dagstuhl Follow-Ups, Volume 2, Scientific Visualization: Interactions, Features, Metaphors (2011)

Abstract
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.
Cite as

Cornelia Auer, Jaya Sreevalsan-Nair, Valentin Zobel, and Ingrid Hotz. 2D Tensor Field Segmentation. In Scientific Visualization: Interactions, Features, Metaphors. Dagstuhl Follow-Ups, Volume 2, pp. 17-35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InCollection{auer_et_al:DFU.Vol2.SciViz.2011.17,
  author =	{Auer, Cornelia and Sreevalsan-Nair, Jaya and Zobel, Valentin and Hotz, Ingrid},
  title =	{{2D Tensor Field Segmentation}},
  booktitle =	{Scientific Visualization: Interactions, Features, Metaphors},
  pages =	{17--35},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-26-2},
  ISSN =	{1868-8977},
  year =	{2011},
  volume =	{2},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.Vol2.SciViz.2011.17},
  URN =		{urn:nbn:de:0030-drops-32853},
  doi =		{10.4230/DFU.Vol2.SciViz.2011.17},
  annote =	{Keywords: Tensorfield visualization, surface topology}
}
Document
DOI: 10.4230/DFU.Vol2.SciViz.2011.188
A Visual Approach to Analysis of Stress Tensor Fields

Authors: Andrea Kratz, Björn Meyer, and Ingrid Hotz

Published in: Dagstuhl Follow-Ups, Volume 2, Scientific Visualization: Interactions, Features, Metaphors (2011)

Abstract
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.
Cite as

Andrea Kratz, Björn Meyer, and Ingrid Hotz. A Visual Approach to Analysis of Stress Tensor Fields. In Scientific Visualization: Interactions, Features, Metaphors. Dagstuhl Follow-Ups, Volume 2, pp. 188-211, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InCollection{kratz_et_al:DFU.Vol2.SciViz.2011.188,
  author =	{Kratz, Andrea and Meyer, Bj\"{o}rn and Hotz, Ingrid},
  title =	{{A Visual Approach to Analysis of Stress Tensor Fields}},
  booktitle =	{Scientific Visualization: Interactions, Features, Metaphors},
  pages =	{188--211},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-26-2},
  ISSN =	{1868-8977},
  year =	{2011},
  volume =	{2},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.Vol2.SciViz.2011.188},
  URN =		{urn:nbn:de:0030-drops-32962},
  doi =		{10.4230/DFU.Vol2.SciViz.2011.188},
  annote =	{Keywords: Tensor Field, Visualization and Analysis}
}
Document
DOI: 10.4230/DFU.SciViz.2010.110
Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation

Authors: Ingrid Hotz, Jaya Sreevalsan-Nair, Hans Hagen, and Bernd Hamann

Published in: Dagstuhl Follow-Ups, Volume 1, Scientific Visualization: Advanced Concepts (2010)

Abstract
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.
Cite as

Ingrid Hotz, Jaya Sreevalsan-Nair, Hans Hagen, and Bernd Hamann. Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation. In Scientific Visualization: Advanced Concepts. Dagstuhl Follow-Ups, Volume 1, pp. 110-123, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InCollection{hotz_et_al:DFU.SciViz.2010.110,
  author =	{Hotz, Ingrid and Sreevalsan-Nair, Jaya and Hagen, Hans and Hamann, Bernd},
  title =	{{Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation}},
  booktitle =	{Scientific Visualization: Advanced Concepts},
  pages =	{110--123},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-19-4},
  ISSN =	{1868-8977},
  year =	{2010},
  volume =	{1},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.SciViz.2010.110},
  URN =		{urn:nbn:de:0030-drops-27003},
  doi =		{10.4230/DFU.SciViz.2010.110},
  annote =	{Keywords: Tensor Field, Eigenvector, Eigenvalue, Interpolation}
}
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