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Christoph Schulz

Christoph Schulz

Herr Dr. rer. nat.

Wiss. Mitarbeiter
Visualisierungsinstitut der Universität Stuttgart (VISUS)
Arbeitsgruppe Weiskopf

Kontakt

+49 711 685 88619
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Visitenkarte (VCF)

Allmandring 19
70569 Stuttgart
Deutschland
Raum: 00.005

Fachgebiet

SFB-TRR 161: Quantitative Methods for Visual Computing

Meine Forschungsschwerpunkte sind:

Visualisierung
Computergrafik
Unsicherheit
Softwaretechnik

Man kann mich auf Google Scholar und per ORCID finden.

Publikationen

Publikationen:

2022
1. Rodrigues, Nils ; Schulz, Christoph ; Doring, Soren ; Baumgartner, Daniel ; Krake, Tim ; Weiskopf, Daniel: Relaxed Dot Plots: Faithful Visualization of Samples and Their Distribution. In: IEEE Transactions on Visualization and Computer Graphics, IEEE Transactions on Visualization and Computer Graphics. (2022), S. 59:1-59:7
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  @article{9904443, abstract = {We introduce relaxed dot plots as an improvement of nonlinear dot plots for unit visualization. Our plots produce more faithful data representations and reduce moire´ effects. Their contour is based on a customized kernel frequency estimation to match the shape of the distribution of underlying data values. Previous nonlinear layouts introduce column-centric nonlinear scaling of dot diameters for visualization of high-dynamic-range data with high peaks. We provide a mathematical approach to convert that column-centric scaling to our smooth envelope shape. This formalism allows us to use linear, root, and logarithmic scaling to find ideal dot sizes. Our method iteratively relaxes the dot layout for more correct and aesthetically pleasing results. To achieve this, we modified Lloyd's algorithm with additional constraints and heuristics. We evaluate the layouts of relaxed dot plots against a previously existing nonlinear variant and show that our algorithm produces less error regarding the underlying data while establishing the blue noise property that works against moire´ effects. Further, we analyze the readability of our relaxed plots in three crowd-sourced experiments. The results indicate that our proposed technique surpasses traditional dot plots.}, author = {Rodrigues, Nils and Schulz, Christoph and Doring, Soren and Baumgartner, Daniel and Krake, Tim and Weiskopf, Daniel}, doi = {10.1109/TVCG.2022.3209429}, journal = {IEEE Transactions on Visualization and Computer Graphics}, pages = {59:1-59:7}, title = {Relaxed Dot Plots: Faithful Visualization of Samples and Their Distribution}, url = {https://doi.org/10.1109/TVCG.2022.3209429}, year = 2022 }
  Link
  https://doi.org/10.1109/TVCG.2022.3209429
2. Hägele, David ; Schulz, Christoph ; Beschle, Cedric ; Booth, Hannah ; Butt, Miriam ; Barth, Andrea ; Deussen, Oliver ; Weiskopf, Daniel: Uncertainty Visualization: Fundamentals and Recent Developments. In: it - Information Technology, it - Information Technology. Bd. 64 (2022), Nr. 4–5, S. 121–132
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  @article{haegeleIt2022, abstract = {This paper provides a brief overview of uncertainty visualization along with some fundamental considerations on uncertainty propagation and modeling. Starting from the visualization pipeline, we discuss how the different stages along this pipeline can be affected by uncertainty and how they can deal with this and propagate uncertainty information to subsequent processing steps. We illustrate recent advances in the field with a number of examples from a wide range of applications: uncertainty visualization of hierarchical data, multivariate time series, stochastic partial differential equations, and data from linguistic annotation.}, author = {H\"agele, David and Schulz, Christoph and Beschle, Cedric and Booth, Hannah and Butt, Miriam and Barth, Andrea and Deussen, Oliver and Weiskopf, Daniel}, doi = {10.1515/itit-2022-0033}, journal = {it - Information Technology}, number = {4–5}, pages = {121–132}, title = {Uncertainty Visualization: Fundamentals and Recent Developments}, url = {https://doi.org/10.1515/itit-2022-0033}, volume = 64, year = 2022 }
  Link
  https://doi.org/10.1515/itit-2022-0033
2021
1. Schulz, Christoph ; Kwan, Kin Chung ; Becher, Michael ; Baumgartner, Daniel ; Reina, Guido ; Deussen, Oliver ; Weiskopf, Daniel: Multi-Class Inverted Stippling. In: ACM Trans. Graph., ACM Trans. Graph. Bd. 40. New York, NY, USA, Association for Computing Machinery (2021), Nr. 6
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  @article{10.1145/3478513.3480534, abstract = {We introduce inverted stippling, a method to mimic an inversion technique used by artists when performing stippling. To this end, we extend Linde-Buzo-Gray (LBG) stippling to multi-class LBG (MLBG) stippling with multiple layers. MLBG stippling couples the layers stochastically to optimize for per-layer and overall blue-noise properties. We propose a stipple-based filling method to generate solid color backgrounds for inverting areas. Our experiments demonstrate the effectiveness of MLBG in terms of reducing overlapping and intensity accuracy. In addition, we showcase MLBG with color stippling and dynamic multi-class blue-noise sampling, which is possible due to its support for temporal coherence.}, address = {New York, NY, USA}, articleno = {245}, author = {Schulz, Christoph and Kwan, Kin Chung and Becher, Michael and Baumgartner, Daniel and Reina, Guido and Deussen, Oliver and Weiskopf, Daniel}, doi = {10.1145/3478513.3480534}, issn = {0730-0301}, issue_date = {December 2021}, journal = {ACM Trans. Graph.}, month = dec, number = 6, numpages = {12}, publisher = {Association for Computing Machinery}, title = {Multi-Class Inverted Stippling}, url = {https://doi.org/10.1145/3478513.3480534}, volume = 40, year = 2021 }
  Link
  https://doi.org/10.1145/3478513.3480534
2. Müller, Thomas ; Schulz, Christoph ; Weiskopf, Daniel: Adaptive Polygon Rendering for Interactive Visualization in the Schwarzschild Spacetime. In: European Journal of Physics, European Journal of Physics. Bd. 43, IOP Publishing (2021), Nr. 1, S. 015601
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  @article{M_ller_2021, abstract = {Interactive visualization is a valuable tool for introductory or advanced courses in general relativity as well as for public outreach to provide a deeper understanding of the visual implications due to curved spacetime. In particular, the extreme case of a black hole where the curvature becomes so strong that even light cannot escape, benefits from an interactive visualization where students can investigate the distortion effects by moving objects around. However, the most commonly used technique of four-dimensional general-relativistic ray tracing is still too slow for interactive frame rates. Therefore, we propose an efficient and adaptive polygon rendering method that takes light deflection and light travel time into account. An additional advantage of this method is that it provides a natural demonstration of how multiple images occur and how light travel time affects them. Finally, we present our method using three example scenes: a triangle passing behind a black hole, a sphere orbiting a black hole and an accretion disk with different inclination angles.}, author = {Müller, Thomas and Schulz, Christoph and Weiskopf, Daniel}, doi = {10.1088/1361-6404/ac2b36}, journal = {European Journal of Physics}, number = 1, pages = 015601, publisher = {{IOP} Publishing}, title = {Adaptive Polygon Rendering for Interactive Visualization in the Schwarzschild Spacetime}, url = {https://iopscience.iop.org/article/10.1088/1361-6404/ac2b36/meta}, volume = 43, year = 2021 }
  Link
  https://iopscience.iop.org/article/10.1088/1361-6404/ac2b36/meta
3. Schatz, K. ; Müller, C. ; Gralka, P. ; Heinemann, M. ; Straub, A. ; Schulz, C. ; Braun, M. ; Rau, T. ; u. a.: 2019 IEEE Scientific Visualization Contest Winner: Visual Analysis of Structure Formation in Cosmic Evolution. In: IEEE Computer Graphics and Applications (CG&A), IEEE Computer Graphics and Applications (CG&A). Bd. 41 (2021), Nr. 06, S. 101–110
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  @article{9126163, abstract = {Simulations of cosmic evolution are a means to explain the formation of the universe as we see it today. The resulting data of such simulations comprise numerous physical quantities, which turns their analysis into a complex task. Here, we analyze such high-dimensional and time-varying particle data using various visualization techniques from the fields of particle visualization, flow visualization, volume visualization, and information visualization. Our approach employs specialized filters to extract and highlight the development of so-called active galactic nuclei and filament structures formed by the particles. Additionally, we calculate X-ray emission of the evolving structures in a pre-processing step to complement visual analysis. Our approach is integrated into a single visual analytics framework to allow for analysis of star formation at interactive frame rates. Finally, we lay out the methodological aspects of our work that led to success at the 2019 IEEE SciVis Contest.}, author = {Schatz, K. and Müller, C. and Gralka, P. and Heinemann, M. and Straub, A. and Schulz, C. and Braun, M. and Rau, T. and Becher, M. and Frey, S. and Reina, G. and Sedlmair, M. and Weiskopf, D. and Ertl, T. and Diehl, P. and Marcello, D. and Frank, J. and Müller, T.}, doi = {10.1109/MCG.2020.3004613}, issn = {1558-1756}, journal = {IEEE Computer Graphics and Applications (CG&A)}, month = nov, number = 06, pages = {101-110}, title = {2019 IEEE Scientific Visualization Contest Winner: Visual Analysis of Structure Formation in Cosmic Evolution}, url = {https://ieeexplore.ieee.org/document/9126163}, volume = 41, year = 2021 }
  Link
  https://ieeexplore.ieee.org/document/9126163
2020
1. Brich, Nicolas ; Schulz, Christoph ; Peter, Jörg ; Klingert, Wilfried ; Schenk, Martin ; Weiskopf, Daniel ; Krone, Michael: Visual Analysis of Multivariate Intensive Care Surveillance Data. In: Kozlíková, B. ; Krone, M. ; Smit, N. ; Nieselt, K. ; Raidou, R. G. (Hrsg.) ; Kozlíková, B. ; Krone, M. ; Smit, N. ; Nieselt, K. ; Raidou, R. G. (Hrsg.): Eurographics Workshop on Visual Computing for Biology and Medicine, Eurographics Workshop on Visual Computing for Biology and Medicine : The Eurographics Association, 2020 — ISBN 978-3-03868-109-0
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  @inproceedings{Nicolas2020Visual, author = {Brich, Nicolas and Schulz, Christoph and Peter, Jörg and Klingert, Wilfried and Schenk, Martin and Weiskopf, Daniel and Krone, Michael}, booktitle = {Eurographics Workshop on Visual Computing for Biology and Medicine}, doi = {10.2312/vcbm.20201174}, editor = {Kozlíková, Barbora and Krone, Michael and Smit, Noeska and Nieselt, Kay and Raidou, Renata Georgia}, isbn = {978-3-03868-109-0}, issn = {2070-5786}, publisher = {The Eurographics Association}, title = {Visual Analysis of Multivariate Intensive Care Surveillance Data}, year = 2020 }
2. Rodrigues, Nils ; Schulz, Christoph ; Lhuillier, Antoine ; Weiskopf, Daniel: Cluster-Flow Parallel Coordinates: Tracing Clusters Across Subspaces. In: Proceedings of the Graphics Interface Conference (GI) (forthcoming), Proceedings of the Graphics Interface Conference (GI) (forthcoming), 2020, S. 0:1-0:11
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  @inproceedings{rodrigues2020clusterflow, abstract = {We present a novel variant of parallel coordinates plots (PCPs) in which we show clusters in 2D subspaces of multivariate data and emphasize flow between them. We achieve this by duplicating and stacking individual axes vertically. On a high level, our cluster-flow layout shows how data points move from one cluster to another in different subspaces. We achieve cluster-based bundling and limit plot growth through the reduction of available vertical space for each duplicated axis. Although we introduce space between clusters, we preserve the readability of intra-cluster correlations by starting and ending with the original slopes from regular PCPs and drawing Hermite spline segments in between. Moreover, our rendering technique enables the visualization of small and large data sets alike. Cluster-flow PCPs can even propagate the uncertainty inherent to fuzzy clustering through the layout and rendering stages of our pipeline. Our layout algorithm is based on A*. It achieves an optimal result with regard to a novel set of cost functions that allow us to arrange axes horizontally (dimension ordering) and vertically (cluster ordering).}, author = {Rodrigues, Nils and Schulz, Christoph and Lhuillier, Antoine and Weiskopf, Daniel}, booktitle = {Proceedings of the Graphics Interface Conference (GI) (forthcoming)}, pages = {0:1-0:11}, title = {Cluster-Flow Parallel Coordinates: Tracing Clusters Across Subspaces}, url = {https://openreview.net/forum?id=oVHjlwLkl-}, year = 2020 }
  Link
  https://openreview.net/forum?id=oVHjlwLkl-
3. Sondag, Max ; Meulemans, Wouter ; Schulz, Christoph ; Verbeek, Kevin ; Weiskopf, Daniel ; Speckmann, Bettina: Uncertainty Treemaps. In: Proceedings of the IEEE Pacific Visualization Symposium (PacificVis), Proceedings of the IEEE Pacific Visualization Symposium (PacificVis), 2020, S. 111–120
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  @inproceedings{sondag2020uncertainty, abstract = {Rectangular treemaps visualize hierarchical numerical data by recursively partitioning an input rectangle into smaller rectangles whose areas match the data. Numerical data often has uncertainty associated with it. To visualize uncertainty in a rectangular treemap, we identify two conflicting key requirements: (i) to assess the data value of a node in the hierarchy, the area of its rectangle should directly match its data value, and (ii) to facilitate comparison between data and uncertainty, uncertainty should be encoded using the same visual variable as the data, that is, area. We present Uncertainty Treemaps, which meet both requirements simultaneously by introducing the concept of hierarchical uncertainty masks. First, we define a new cost function that measures the quality of Uncertainty Treemaps. Then, we show how to adapt existing treemapping algorithms to support uncertainty masks. Finally, we demonstrate the usefulness and quality of our technique through an expert review and a computational experiment on real-world datasets.}, author = {Sondag, Max and Meulemans, Wouter and Schulz, Christoph and Verbeek, Kevin and Weiskopf, Daniel and Speckmann, Bettina}, booktitle = {Proceedings of the IEEE Pacific Visualization Symposium (PacificVis)}, doi = {10.1109/PacificVis48177.2020.7614}, pages = {111-120}, title = {Uncertainty Treemaps}, url = {https://ieeexplore.ieee.org/document/9086235}, year = 2020 }
  Link
  https://ieeexplore.ieee.org/document/9086235
2019
1. Görtler, Jochen ; Spicker, Marc ; Schulz, Christoph ; Weiskopf, Daniel ; Deussen, Oliver: Stippling of 2D Scalar Fields. In: IEEE Transactions on Visualization and Computer Graphics, IEEE Transactions on Visualization and Computer Graphics. Bd. 25 (2019), Nr. 6, S. 2193–2204
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  @article{journals/tvcg/GortlerSSWD19, abstract = {We propose a technique to represent two-dimensional data using stipples. While stippling is often regarded as an illustrative method, we argue that it is worth investigating its suitability for the visualization domain. For this purpose, we generalize the Linde-Buzo-Gray stippling algorithm for information visualization purposes to encode continuous and discrete 2D data. Our proposed modifications provide more control over the resulting distribution of stipples for encoding additional information into the representation, such as contours. We show different approaches to depict contours in stipple drawings based on locally adjusting the stipple distribution. Combining stipple-based gradients and contours allows for simultaneous assessment of the overall structure of the data while preserving important local details. We discuss the applicability of our technique using datasets from different domains and conduct observation-validating studies to assess the perception of stippled representations}, author = {Görtler, Jochen and Spicker, Marc and Schulz, Christoph and Weiskopf, Daniel and Deussen, Oliver}, doi = {10.1109/TVCG.2019.2903945}, ee = {https://doi.org/10.1109/TVCG.2019.2903945}, journal = {IEEE Transactions on Visualization and Computer Graphics}, number = 6, pages = {2193-2204}, title = {Stippling of 2D Scalar Fields}, url = {https://ieeexplore.ieee.org/document/8667696}, volume = 25, year = 2019 }
  Link
  https://ieeexplore.ieee.org/document/8667696
2. Schatz, Karsten ; Müller, Christoph ; Gralka, Patrick ; Heinemann, Moritz ; Straub, Alexander ; Schulz, Christoph ; Braun, Matthias ; Rau, Tobias ; u. a.: Visual Analysis of Structure Formation in Cosmic Evolution. In: Proceedings of the IEEE Scientific Visualization Conference (SciVis), Proceedings of the IEEE Scientific Visualization Conference (SciVis), 2019, S. 33–41
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  @inproceedings{schatz2019visual, abstract = {The IEEE SciVis 2019 Contest targets the visual analysis of structure formation in the cosmic evolution of the universe from when the universe was five million years old up to now. In our submission, we analyze high-dimensional data to get an overview, then investigate the impact of Active Galactic Nuclei (AGNs) using various visualization techniques, for instance, an adapted filament filtering method for detailed analysis and particle flow in the vicinity of filaments. Based on feedback from domain scientists on these initial visualizations, we also analyzed X-ray emissions and star formation areas. The conversion of star-forming gas to stars and the resulting increasing molecular weight of the particles could be observed.}, author = {Schatz, Karsten and Müller, Christoph and Gralka, Patrick and Heinemann, Moritz and Straub, Alexander and Schulz, Christoph and Braun, Matthias and Rau, Tobias and Becher, Michael and Diehl, Patrick and Marcello, Dominic and Frank, Juhan and Müller, Thomas and Frey, Steffen and Reina, Guido and Weiskopf, Daniel and Ertl, Thomas}, booktitle = {Proceedings of the IEEE Scientific Visualization Conference (SciVis)}, doi = {10.1109/scivis47405.2019.8968855}, pages = {33-41}, title = {Visual Analysis of Structure Formation in Cosmic Evolution}, url = {https://ieeexplore.ieee.org/abstract/document/8968855}, year = 2019 }
  Link
  https://ieeexplore.ieee.org/abstract/document/8968855
3. Bruder, Valentin ; Schulz, Christoph ; Bauer, Ruben ; Frey, Steffen ; Weiskopf, Daniel ; Ertl, Thomas: Voronoi-Based Foveated Volume Rendering. In: Johansson, J. ; Sadlo, F. ; Marai, G. E. (Hrsg.) ; Johansson, J. ; Sadlo, F. ; Marai, G. E. (Hrsg.): Proceedings of the Eurographics Conference on Visualization - Short Papers (EuroVis), Proceedings of the Eurographics Conference on Visualization - Short Papers (EuroVis) : Eurographics Association, 2019 — ISBN 978-3-03868-090-1, S. 67–71
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  @inproceedings{conf/vissym/BruderSBFWE19, abstract = {Foveal vision is located in the center of the field of view with a rich impression of detail and color, whereas peripheral visionoccurs on the side with more fuzzy and colorless perception. This visual acuity fall-off can be used to achieve higher frame ratesby adapting rendering quality to the human visual system. Volume raycasting has unique characteristics, preventing a directtransfer of many traditional foveated rendering techniques. We present an approach that utilizes the visual acuity fall-off toaccelerate volume rendering based on Linde-Buzo-Gray sampling and natural neighbor interpolation. First, we measure gazeusing a stationary 1200 Hz eye-tracking system. Then, we adapt our sampling and reconstruction strategy to that gaze. Finally,we apply a temporal smoothing filter to attenuate undersampling artifacts since peripheral vision is particularly sensitive tocontrast changes and movement. Our approach substantially improves rendering performance with barely perceptible changes invisual quality. We demonstrate the usefulness of our approach through performance measurements on various data se}, author = {Bruder, Valentin and Schulz, Christoph and Bauer, Ruben and Frey, Steffen and Weiskopf, Daniel and Ertl, Thomas}, booktitle = {Proceedings of the Eurographics Conference on Visualization - Short Papers (EuroVis)}, doi = {10.2312/evs.20191172}, editor = {Johansson, Jimmy and Sadlo, Filip and Marai, G. Elisabeta}, ee = {https://doi.org/10.2312/evs.20191172}, isbn = {978-3-03868-090-1}, pages = {67-71}, publisher = {Eurographics Association}, title = {Voronoi-Based Foveated Volume Rendering}, url = {https://doi.org/10.2312/evs.20191172}, year = 2019 }
  Link
  https://doi.org/10.2312/evs.20191172
4. Gralka, Patrick ; Becher, Michael ; Braun, Matthias ; Frieß, Florian ; Müller, Christoph ; Rau, Tobias ; Schatz, Karsten ; Schulz, Christoph ; u. a.: MegaMol -- a comprehensive prototyping framework for visualizations. In: The European Physical Journal (Special Topics), The European Physical Journal (Special Topics). Bd. 227: Particle Methods in Natural Science and Engineering (2019), Nr. 14, S. 1817--1829
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  @article{Gralka2019Megamol, abstract = {We present MegaMol, a low-overhead prototyping framework for interactive visualization of large scientific data sets. We give a brief summary of related work for context and then focus on a comprehensive overview of the core architecture of the framework. This is followed by the existing and novel features and techniques in MegaMol that define its current functionality. MegaMol has originally been developed to support the visualization and analysis of particle-based data sets that, for instance, come from molecular dynamics simulations. Meanwhile, the software has evolved beyond that. New algorithms and techniques have been implemented to handle many diverse tasks, including information visualization. Additionally, improvements have been made on the software engineering side to make MegaMol more accessible for domain scientists, like an easy-to-handle scripting interface.}, author = {Gralka, Patrick and Becher, Michael and Braun, Matthias and Frieß, Florian and Müller, Christoph and Rau, Tobias and Schatz, Karsten and Schulz, Christoph and Krone, Michael and Reina, Guido and Ertl, Thomas}, doi = {10.1140/epjst/e2019-800167-5}, issn = {1951-6401}, journal = {The European Physical Journal (Special Topics)}, number = 14, pages = {1817--1829}, title = {MegaMol -- a comprehensive prototyping framework for visualizations}, url = {https://doi.org/10.1140/epjst/e2019-800167-5}, volume = {227: Particle Methods in Natural Science and Engineering}, year = 2019 }
  Link
  https://doi.org/10.1140/epjst/e2019-800167-5
5. Schulz, Christoph ; Rodrigues, Nils ; Amann, Marco ; Baumgartner, Daniel ; Mielke, Arman ; Baumann, Christian ; Sedlmair, Michael ; Weiskopf, Daniel: A Framework for Pervasive Visual Deficiency Simulation. In: Proceedings of the IEEE Conference on Virtual Reality and 3D User Interfaces (VR), Proceedings of the IEEE Conference on Virtual Reality and 3D User Interfaces (VR), 2019, S. 1852–1857
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  @inproceedings{schulz2019framework, abstract = {We present a framework for rapid prototyping of pervasive visual deficiency simulation in the context of graphical interfaces, virtual reality, and augmented reality. Our framework facilitates the emulation of various visual deficiencies for a wide range of applications, which allows users with normal vision to experience combinations of conditions such as myopia, hyperopia, presbyopia, cataract, nyctalopia, protanopia, deuteranopia, tritanopia, and achromatopsia. Our framework provides an infrastructure to encourage researchers to evaluate visualization and other display techniques regarding visual deficiencies, and opens up the field of visual disease simulation to a broader audience. The benefits of our framework are easy integration, configuration, fast prototyping, and portability to new emerging hardware. To demonstrate the applicability of our framework, we showcase a desktop application and an Android application that transform commodity hardware into glasses for visual deficiency simulation. We expect that this work promotes a greater understanding of visual impairments, leads to better product design for the visually impaired, and forms a basis for research to compensate for these impairments as everyday help}, author = {Schulz, Christoph and Rodrigues, Nils and Amann, Marco and Baumgartner, Daniel and Mielke, Arman and Baumann, Christian and Sedlmair, Michael and Weiskopf, Daniel}, booktitle = {Proceedings of the IEEE Conference on Virtual Reality and 3D User Interfaces (VR)}, doi = {10.1109/VR44988.2019.9044164}, pages = {1852-1857}, title = {A Framework for Pervasive Visual Deficiency Simulation}, url = {https://ieeexplore.ieee.org/document/9044164}, year = 2019 }
  Link
  https://ieeexplore.ieee.org/document/9044164
2018
1. Görtler, Jochen ; Schulz, Christoph ; Deussen, Oliver ; Weiskopf, Daniel: Bubble Treemaps for Uncertainty Visualization. In: IEEE Transactions on Visualization and Computer Graphics, IEEE Transactions on Visualization and Computer Graphics. Bd. 24 (2018), Nr. 1, S. 719–728
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  @article{Goertler2018Bubble, abstract = {We present a novel type of circular treemap, where we intentionally allocate extra space for additional visual variables. With this extended visual design space, we encode hierarchically structured data along with their uncertainties in a combined diagram. We introduce a hierarchical and force-based circle-packing algorithm to compute Bubble Treemaps, where each node is visualized using nested contour arcs. Bubble Treemaps do not require any color or shading, which offers additional design choices. We explore uncertainty visualization as an application of our treemaps using standard error and Monte Carlo-based statistical models. To this end, we discuss how uncertainty propagates within hierarchies. Furthermore, we show the effectiveness of our visualization using three different examples: the package structure of Flare, the S&P 500 index, and the US consumer expenditure survey}, author = {Görtler, Jochen and Schulz, Christoph and Deussen, Oliver and Weiskopf, Daniel}, doi = {10.1109/TVCG.2017.2743959}, journal = {IEEE Transactions on Visualization and Computer Graphics}, number = 1, pages = {719-728}, title = {Bubble Treemaps for Uncertainty Visualization}, url = {http://dx.doi.org/10.1109/TVCG.2017.2743959}, volume = 24, year = 2018 }
  Link
  http://dx.doi.org/10.1109/TVCG.2017.2743959
2. Goertler, Jochen ; Schulz, Christoph ; Deussen, Oliver ; Weiskopf, Daniel: Bubble Treemaps for Uncertainty Visualization. In: IEEE Transactions on Visualization and Computer Graphics, IEEE Transactions on Visualization and Computer Graphics. (2018)
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  @article{Goertler2018Bubble, author = {Goertler, Jochen and Schulz, Christoph and Deussen, Oliver and Weiskopf, Daniel}, journal = {IEEE Transactions on Visualization and Computer Graphics}, privnote = {uid:2408}, title = {Bubble Treemaps for Uncertainty Visualization}, url = {http://dx.doi.org/10.1109/TVCG.2017.2743959}, year = 2018 }
  Link
  http://dx.doi.org/10.1109/TVCG.2017.2743959
3. Schulz, Christoph ; Schatz, Karsten ; Krone, Michael ; Braun, Matthias ; Ertl, Thomas ; Weiskopf, Daniel: Uncertainty Visualization for Secondary Structures of Proteins. In: Proceedings of the IEEE Pacific Visualization Symposium (PacificVis), Proceedings of the IEEE Pacific Visualization Symposium (PacificVis) : IEEE, 2018, S. 96–105
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  @inproceedings{Schulz2018Uncertainty, abstract = {We present a technique that conveys the uncertainty in the secondary structure of proteins-an abstraction model based on atomic coordinates. While protein data inherently contains uncertainty due to the acquisition method or the simulation algorithm, we argue that it is also worth investigating uncertainty induced by analysis algorithms that precede visualization. Our technique helps researchers investigate differences between multiple secondary structure assignment methods. We modify established algorithms for fuzzy classification and introduce a discrepancy-based approach to project an ensemble of sequences to a single importance-weighted sequence. In 2D, we depict the aggregated secondary structure assignments based on the per-residue deviation in a collapsible sequence diagram. In 3D, we extend the ribbon diagram using visual variables such as transparency, wave form, frequency, or amplitude to facilitate qualitative analysis of uncertainty. We evaluated the effectiveness and acceptance of our technique through expert reviews using two example applications: the combined assignment against established algorithms and time-dependent structural changes originating from simulated protein dynamics.}, author = {Schulz, Christoph and Schatz, Karsten and Krone, Michael and Braun, Matthias and Ertl, Thomas and Weiskopf, Daniel}, booktitle = {Proceedings of the IEEE Pacific Visualization Symposium (PacificVis)}, doi = {10.1109/PacificVis.2018.00020}, pages = {96-105}, publisher = {IEEE}, title = {Uncertainty Visualization for Secondary Structures of Proteins}, url = {https://ieeexplore.ieee.org/document/8365980}, year = 2018 }
  Link
  https://ieeexplore.ieee.org/document/8365980
4. Schulz, Christoph ; Zeyfang, Adrian ; van Garderen, Mereke ; Ben Lahmar, Houssem ; Herschel, Melanie ; Weiskopf, Daniel: Simultaneous Visual Analysis of Multiple Software Hierarchies. In: Proceedings of the IEEE Working Conference on Software Visualization (VISSOFT), Proceedings of the IEEE Working Conference on Software Visualization (VISSOFT) : IEEE, 2018, S. 87–95
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  @inproceedings{Schulz2018Simultaneous, abstract = {We propose a tree visualization technique for comparison of structures and attributes across multiple hierarchies. Many software systems are structured hierarchically by design. For example, developers subdivide source code into libraries, modules, and functions. This design propagates to software configuration and business processes, rendering software hierarchies even more important. Often these structural elements are attributed with reference counts, code quality metrics, and the like. Throughout the entire software life cycle, these hierarchies are reviewed, integrated, debugged, and changed many times by different people so that the identity of a structural element and its attributes is not clearly traceable. We argue that pairwise comparison of similar trees is a tedious task due to the lack of overview, especially when applied to a large number of hierarchies. Therefore, we strive to visualize multiple similar trees as a whole by merging them into one supertree. To merge structures and combine attributes from different trees, we leverage the Jaccard similarity and solve a matching problem while keeping track of the origin of a structure element and its attributes. Our visualization approach allows users to inspect these supertrees using node-link diagrams and indented tree plots. The nodes in these plots depict aggregated attributes and, using word-sized line plots, detailed data. We demonstrate the usefulness of our method by exploring the evolution of software repositories and debugging data processing pipelines using provenance data.}, author = {Schulz, Christoph and Zeyfang, Adrian and van Garderen, Mereke and {Ben Lahmar}, Houssem and Herschel, Melanie and Weiskopf, Daniel}, booktitle = {Proceedings of the IEEE Working Conference on Software Visualization (VISSOFT)}, doi = {10.1109/VISSOFT.2018.00017}, pages = {87-95}, publisher = {IEEE}, title = {Simultaneous Visual Analysis of Multiple Software Hierarchies}, url = {https://ieeexplore.ieee.org/document/8530134/}, year = 2018 }
  Link
  https://ieeexplore.ieee.org/document/8530134/
2017
1. Schulz, Christoph ; Nocaj, Arlind ; Goertler, Jochen ; Deussen, Oliver ; Brandes, Ulrik ; Weiskopf, Daniel: Probabilistic Graph Layout for Uncertain Network Visualization. In: IEEE Transactions on Visualization and Computer Graphics, IEEE Transactions on Visualization and Computer Graphics. Bd. 23 (2017), Nr. 1
  - BibTeX
  - Link
  BibTeX
  @article{Schulz2016ProbabilisticGraphLayout, author = {Schulz, Christoph and Nocaj, Arlind and Goertler, Jochen and Deussen, Oliver and Brandes, Ulrik and Weiskopf, Daniel}, journal = {IEEE Transactions on Visualization and Computer Graphics}, number = 1, privnote = {uid:2281}, title = {Probabilistic Graph Layout for Uncertain Network Visualization}, url = {http://dx.doi.org/10.1109/TVCG.2016.2598919}, volume = 23, year = 2017 }
  Link
  http://dx.doi.org/10.1109/TVCG.2016.2598919
2. Srulijes, Karin ; Schulz, Christoph ; Mack, David J. ; Jarosch, Rafael ; Klenk, Jochen ; Schwickert, Lars ; Schwenk, Michael ; Maetzler, Walter ; u. a.: Visualization of Eye-Head Coordination While Walking in Healthy Subjects and Patients with Neurodegenerative Diseases. In: Poster (reviewed) presented on Symposium of the International Society of Posture and Gait Research (ISPGR), Poster (reviewed) presented on Symposium of the International Society of Posture and Gait Research (ISPGR). (2017)
  - BibTeX
  BibTeX
  @article{srulijes2017visualization, author = {Srulijes, Karin and Schulz, Christoph and Mack, David J. and Jarosch, Rafael and Klenk, Jochen and Schwickert, Lars and Schwenk, Michael and Maetzler, Walter and Weiskopf, Daniel and Becker, Clemens}, booktitle = {Poster (reviewed) presented on Symposium of the International Society of Posture and Gait Research (ISPGR)}, eventtitle = {Symposium of the International Society of Posture and Gait Research (ISPGR)}, title = {Visualization of Eye-Head Coordination While Walking in Healthy Subjects and Patients with Neurodegenerative Diseases}, year = 2017 }
3. Gralka, Patrick ; Schulz, Christoph ; Reina, Guido ; Weiskopf, Daniel ; Ertl, Thomas: Visual Exploration of Memory Traces and Call Stacks. In: Proceedings of the IEEE Working Conference on Software Visualization (VISSOFT), Proceedings of the IEEE Working Conference on Software Visualization (VISSOFT) : IEEE, 2017, S. 54–63
  - BibTeX
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  BibTeX
  @inproceedings{Gralka2017Visual, abstract = {Analysis of software performance typically takes into account clock cycles and memory consumption at each sampling point in time. Although this is a valid strategy, we argue that it is also worth investigating data and control flow structures, as observed using memory traces and call stacks, because of their importance for performance engineering. In this work, we present a visual approach to memory profiling that supports analysis of memory layout, access patterns, and aliasing in correlation to program execution. Our method leverages language-agnostic dynamic code instrumentation to minimize the impact of tracing on performance, i.e., the application remains usable on commodity hardware. The profiled data is then clustered and visualized using a density-based scatter plot. If debug symbols are available, the scatter plot is augmented by a flame graph to ease linking to the high-level source code. Our visualization helps software engineers to identify runtime behavior by relating memory addresses to instruction execution. We demonstrate our approach using a set of examples revealing different memory access patterns and discuss their influence on software performance.}, author = {Gralka, Patrick and Schulz, Christoph and Reina, Guido and Weiskopf, Daniel and Ertl, Thomas}, booktitle = {Proceedings of the IEEE Working Conference on Software Visualization (VISSOFT)}, doi = {10.1109/VISSOFT.2017.15}, pages = {54-63}, publisher = {IEEE}, title = {Visual Exploration of Memory Traces and Call Stacks}, url = {https://dx.doi.org/10.1109/VISSOFT.2017.15}, year = 2017 }
  Link
  https://dx.doi.org/10.1109/VISSOFT.2017.15
4. Schulz, Christoph ; Burch, Michael ; Beck, Fabian ; Weiskopf, Daniel: Visual Data Cleansing of Low-Level Eye Tracking Data. In: Burch, M. ; Chuang, L. ; Fisher, B. ; Schmidt, A. ; Weiskopf, D. (Hrsg.) ; Burch, M. ; Chuang, L. ; Fisher, B. ; Schmidt, A. ; Weiskopf, D. (Hrsg.): Eye Tracking and Visualization: Foundations, Techniques, and Applications. ETVIS 2015, Eye Tracking and Visualization: Foundations, Techniques, and Applications. ETVIS 2015 : Springer International Publishing, 2017
  - BibTeX
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  BibTeX
  @inbook{Schulz2017VDA, author = {Schulz, Christoph and Burch, Michael and Beck, Fabian and Weiskopf, Daniel}, booktitle = {Eye Tracking and Visualization: Foundations, Techniques, and Applications. ETVIS 2015}, editor = {Burch, Michael and Chuang, Lewis and Fisher, Brian and Schmidt, Albrecht and Weiskopf, Daniel}, privnote = {uid:2246}, publisher = {Springer International Publishing}, title = {Visual Data Cleansing of Low-Level Eye Tracking Data}, url = {http://dx.doi.org/10.1007/978-3-319-47024-5_12}, year = 2017 }
  Link
  http://dx.doi.org/10.1007/978-3-319-47024-5_12
5. Schulz, Christoph ; Rodrigues, Nils ; Damarla, Krishna ; Henicke, Andreas ; Weiskopf, Daniel: Visual Exploration of Mainframe Workloads. In: Proceedings of the SIGGRAPH Asia Symposium on Visualization, Proceedings of the SIGGRAPH Asia Symposium on Visualization : ACM, 2017, S. 4:1-4:7
  - BibTeX
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  BibTeX
  @inproceedings{Schulz2017Visual, abstract = {We present a visual analytics approach to support the workload management process for z/OS mainframes at IBM. This process typically requires the analysis of records consisting of 100 to 150 performance-related metrics, sampled over time. We aim at replacing the previous spreadsheet-based workflow with an easier, faster, and more scalable one regarding measurement periods and collected performance metrics. To achieve this goal, we collaborate with a developer embedded at IBM in a formative process. Based on that experience, we discuss the application background and formulate requirements to support decision making based on performance data for large-scale systems. Our visual approach helps analysts find outliers, patterns, and relations between performance metrics by data exploration through various visualizations. We demonstrate the usefulness and applicability of line plots, scatter plots, scatter plot matrices, parallel coordinates, and correlation matrices for workload management. Finally, we evaluate our approach in a qualitative user study with IBM domain experts.}, author = {Schulz, Christoph and Rodrigues, Nils and Damarla, Krishna and Henicke, Andreas and Weiskopf, Daniel}, booktitle = {Proceedings of the SIGGRAPH Asia Symposium on Visualization}, pages = {4:1-4:7}, publisher = {ACM}, title = {Visual Exploration of Mainframe Workloads}, url = {http://dx.doi.org/10.1145/3139295.3139312}, venue = {Article No. 4}, year = 2017 }
  Link
  http://dx.doi.org/10.1145/3139295.3139312
2016
1. Schulz, Christoph ; Nocaj, Arlind ; El-Assady, Mennatallah ; Frey, Steffen ; Hlawatsch, Marcel ; Hund, Michael ; Karch, Grzegorz Karol ; Netzel, Rudolf ; u. a.: Generative Data Models for Validation and Evaluation of Visualization Techniques. In: Proceedings of the Workshop on Beyond Time and Errors: Novel Evaluation Methods for Visualization (BELIV), Proceedings of the Workshop on Beyond Time and Errors: Novel Evaluation Methods for Visualization (BELIV) : ACM, 2016, S. 112–124
  - BibTeX
  - Link
  BibTeX
  @inproceedings{2016SchulzGenerativeDataModels, abstract = {We argue that there is a need for substantially more research on the use of generative data models in the validation and evaluation of visualization techniques. For example, user studies will require the display of representative and uncon-founded visual stimuli, while algorithms will need functional coverage and assessable benchmarks. However, data is often collected in a semi-automatic fashion or entirely hand-picked, which obscures the view of generality, impairs availability, and potentially violates privacy. There are some sub-domains of visualization that use synthetic data in the sense of generative data models, whereas others work with real-world-based data sets and simulations. Depending on the visualization domain, many generative data models are "side projects" as part of an ad-hoc validation of a techniques paper and thus neither reusable nor general-purpose. We review existing work on popular data collections and generative data models in visualization to discuss the opportunities and consequences for technique validation, evaluation, and experiment design. We distill handling and future directions, and discuss how we can engineer generative data models and how visualization research could benefit from more and better use of generative data models.}, author = {Schulz, Christoph and Nocaj, Arlind and El-Assady, Mennatallah and Frey, Steffen and Hlawatsch, Marcel and Hund, Michael and Karch, Grzegorz Karol and Netzel, Rudolf and Schätzle, Christin and Butt, Miriam and Keim, Daniel A. and Ertl, Thomas and Brandes, Ulrik and Weiskopf, Daniel}, booktitle = {Proceedings of the Workshop on Beyond Time and Errors: Novel Evaluation Methods for Visualization (BELIV)}, doi = {10.1145/2993901.2993907}, pages = {112-124}, publisher = {ACM}, title = {Generative Data Models for Validation and Evaluation of Visualization Techniques}, url = {http://dx.doi.org/10.1145/2993901.2993907}, year = 2016 }
  Link
  http://dx.doi.org/10.1145/2993901.2993907
2015
1. Schulz, Christoph ; Burch, Michael ; Weiskopf, Daniel: Visual Data Cleansing of Eye Tracking Data. In: Proceedings of the Symposium on Eye Tracking and Visualization (ETVIS), Proceedings of the Symposium on Eye Tracking and Visualization (ETVIS), 2015. — Rezensiertes Abstract
  - BibTeX
  - Link
  BibTeX
  @inproceedings{Schulz2015Visual, abstract = {Analysis and visualization of eye movement data from eye tracking studies typically take into account gazes, fixations,and saccades of both eyes filtered and fused into a combined eye. Although this is a valid strategy, we argue that it is also worthinvestigating low-level eye tracking data prior to high-level analysis, since today’s eye tracking systems measure and infer data fromboth eyes separately. In this work, we present an approach that supports visual analysis and cleansing of low-level time-varying datafor a wide range of eye tracking experiments. The visualization helps researchers get insights into the quality in terms of uncertainty—not only for both eyes in combination but each eye individually. Furthermore, we discuss uncertainty originating from eye tracking,how to reveal it for visualization and illustrate its usefulness using our approach by applying it to eye movement data formerly recordedwith a Tobii T60XL stationary eye tracker using a prototypical implementation.}, author = {Schulz, Christoph and Burch, Michael and Weiskopf, Daniel}, booktitle = {Proceedings of the Symposium on Eye Tracking and Visualization (ETVIS)}, note = {Rezensiertes Abstract}, title = {Visual Data Cleansing of Eye Tracking Data}, url = {http://etvis.visus.uni-stuttgart.de/etvis2015/papers/etvis15_schulz.pdf}, year = 2015 }
  Link
  http://etvis.visus.uni-stuttgart.de/etvis2015/papers/etvis15_schulz.pdf
2013
1. Krone, Michael ; Reina, Guido ; Schulz, Christoph ; Kulschewski, Tobias ; Pleiss, Jürgen ; Ertl, Thomas: Interactive Extraction and Tracking of Biomolecular Surfaces Features. In: Computer Graphics Forum, Computer Graphics Forum. Bd. 32 (2013), Nr. 3
  - BibTeX
  - Link
  BibTeX
  @article{Krone2013EuroVis, author = {Krone, Michael and Reina, Guido and Schulz, Christoph and Kulschewski, Tobias and Pleiss, Jürgen and Ertl, Thomas}, journal = {Computer Graphics Forum}, number = 3, privnote = {uid:1663}, title = {Interactive Extraction and Tracking of Biomolecular Surfaces Features}, url = {http://dx.doi.org/10.1111/cgf.12120}, volume = 32, year = 2013 }
  Link
  http://dx.doi.org/10.1111/cgf.12120

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Visual Analysis of Time-Dependent Motion-Capturing and Eye-Tracking Data (Bachelor)
Analysis of Impossible Figures (Bachelor)
Comparison of Virtual Reality Headsets (Technical Report)
Visualizing the Uncertainty of the Secondary Structure of Proteins (Diplom)
Visual Exploration of Workload Performance Data (Master)
Using the Smartphone-Headset as an Integrated Eye Tracker (Bachelor)
Visual Analysis of Evolution and Uncertainty in Hierarchical Data (Bachelor)
Foveated Volume Rendering (Bachelor)
Analysis and Comparison of Projection Techniques for Dimension Reduction (Technical Report)
Sparse Table Data in MegaMol (Technical Report)
Visual Analysis of Multidimensional Data and Attributes with Order Statistics (Master)
Simultaneous Visual Analysis of Multidimensional Data and Attributes (Bachelor)
GPU-Accelerated Stippling (Bachelor)
Analysis and Comparison of Visual Refactoring Techniques (Technical Report)
Visualization of Time-Continuous High-Dimensional Data using MegaMol (Bachelor)
Color-Vision Helper for Color Blind in AR (Bachelor)
Measurement and Simulation of Vision in VR (Bachelor)
Visual Analysis of Time-Dependent Intensive Care Data (Master)
Interaction for Cluster-Flow Parallel Coordinates (Bachelor)
Measurement of Retinal Sensitivity in VR (Bachelor)
Visual Analysis of Droplet Trajectories (Technical Report)
General-relativistic Polygon Rendering (Bachelor)
Visualization of Differences in Perception Caused by Vision Deficiency (Master)

Lehrveranstaltungen

Practical Course Visual Computing (WS15)
Practical Course Visual Computing (SS16)
Visualisierung von Bäumen und Graphen (WS16)
Studienprojekt: Fehlsichtigkeitssimulator (SS17 – WS17)
Verlässlichkeit in der Visualisierung: Fake oder Fakt? (WS17)
Scientific Visualization (SS18)
Seminar Visuelle Text Analytik (WS18)
SimTech – Master B (SS19)
Programmierung für Medieninformatik (WS19)
SimTech – Master B (SS20)
Audio Post-Processing für Online-Lehre (WS20)

Christoph Schulz

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