Wrangling consumes a disproportionate share of the effort associated with any data project. While a variety of tools support it, relatively little is known about how their differing interface forms shape the way people actually wrangle. We conduct a between-subjects (N=40) observational study of representative data cleaning tasks performed with four tools spanning distinct interface paradigms: Jupyter (notebook), Excel (spreadsheet), ChatGPT (conversational AI), and OpenRefine (visual wranglers). We situate our observations within the Technical Dimensions of Programming Systems framework, which we use as a conceptual scaffold for comparing across interface paradigms. Our results reveal no consistent advantage of any single tool, nor convergence of results within tools, suggesting that tool affordances steer user strategies but do not determine outcomes. Instead, we identify trade-offs and connect them with observed practice. For example, a key tension is between data- and abstraction-centered interfaces, where data-centered interfaces encourage opportunistic cleaning rather than systematic, planned transformations found in abstraction-focused tools (but come with a cognitive burden). Tool design, beyond mere functionality, plays a structuring role in how data work unfolds.

Shiyi He, El Kindi Rezig, Paul Rosen, and Andrew M. McNutt. How Wranglers Shape Wrangling: A Technical Dimensions Analysis. IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC) (to appear), 2026.

@inproceedings{he2026wranglers,
  title = {How Wranglers Shape Wrangling: A Technical Dimensions Analysis},
  author = {He, Shiyi and Rezig, El Kindi and Rosen, Paul and McNutt, Andrew M.},
  booktitle = {IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)
    (to appear)},
  year = {2026},
  abstract = {Wrangling consumes a disproportionate share of the effort associated with
    any data project. While a variety of tools support it, relatively little is known about
    how their differing interface forms shape the way people actually wrangle. We conduct a
    between-subjects (N=40) observational study of representative data cleaning tasks
    performed with four tools spanning distinct interface paradigms: Jupyter (notebook),
    Excel (spreadsheet), ChatGPT (conversational AI), and OpenRefine (visual wranglers). We
    situate our observations within the Technical Dimensions of Programming Systems
    framework, which we use as a conceptual scaffold for comparing across interface
    paradigms. Our results reveal no consistent advantage of any single tool, nor
    convergence of results within tools, suggesting that tool affordances steer user
    strategies but do not determine outcomes. Instead, we identify trade-offs and connect
    them with observed practice. For example, a key tension is between data- and
    abstraction-centered interfaces, where data-centered interfaces encourage opportunistic
    cleaning rather than systematic, planned transformations found in abstraction-focused
    tools (but come with a cognitive burden). Tool design, beyond mere functionality, plays
    a structuring role in how data work unfolds.}
}

Simplifying line charts for responsive displays typically applies a single algorithm uniformly across devices, despite the availability of multiple techniques that preserve different signal characteristics (e.g., peaks, trends, periodicity). We investigate whether users benefit from algorithmic choice when adapting charts across screen sizes. In a within-subjects study (N=30), participants simplified nine datasets under three conditions: single pre-assigned technique (C1), multiple techniques (C2), and multiple techniques with manual point selection (C3), each with control over simplification level. We found that users adapted technique selections across datasets rather than devices, leveraging dataset-level strategies rather than per-device optimization. Additionally, interaction complexity did not always increase engagement uniformly, suggesting that responsive simplification tools should balance algorithmic flexibility with progressive disclosure and strong defaults. Supplemental materials are available at url{https://osf.io/yjp76/?view_only=b77b5e97f0cc4f689fbf48ad0d965af3}.

Rifat Ara Proma, and Paul Rosen. Beyond One-Size-Fits-All: User Strategies For Simplification Technique And Level Selection In Responsive Line Charts. EuroVis Short Papers, 2026.

@inproceedings{proma2026beyond,
  title = {Beyond One-Size-Fits-All: User Strategies for Simplification Technique and
    Level Selection in Responsive Line Charts},
  author = {Proma, Rifat Ara and Rosen, Paul},
  booktitle = {EuroVis Short Papers},
  year = {2026},
  abstract = {Simplifying line charts for responsive displays typically applies a single
    algorithm uniformly across devices, despite the availability of multiple techniques that
    preserve different signal characteristics (e.g., peaks, trends, periodicity). We
    investigate whether users benefit from algorithmic choice when adapting charts across
    screen sizes. In a within-subjects study (N=30), participants simplified nine datasets
    under three conditions: single pre-assigned technique (C1), multiple techniques (C2),
    and multiple techniques with manual point selection (C3), each with control over
    simplification level. We found that users adapted technique selections across datasets
    rather than devices, leveraging dataset-level strategies rather than per-device
    optimization. Additionally, interaction complexity did not always increase engagement
    uniformly, suggesting that responsive simplification tools should balance algorithmic
    flexibility with progressive disclosure and strong defaults. Supplemental materials are
    available at url{https://osf.io/yjp76/?view_only=b77b5e97f0cc4f689fbf48ad0d965af3}.}
}

Annotation is a central mechanism in visualization design that enables people to communicate key insights. Prior research has provided essential accounts of the visual forms annotations take, but less attention has been paid to the decisions behind them. This paper examines how annotations are designed in practice and how educators reflect on those practices. We conducted a two-phase qualitative study: interviews with ten practitioners from diverse backgrounds revealed the heuristics they draw on when creating annotations, and interviews with seven visualization educators offered complementary perspectives situated within broader concerns of clarity, guidance, and viewer agency. These studies provide a systematic account of annotation design knowledge in professional settings, highlighting the considerations, trade-offs, and contextual judgments that shape the use of annotations. By making this tacit expertise explicit, our work complements prior form-focused studies, strengthens understanding of annotation as a design activity, and points to opportunities for improved tool and guideline support.

Md Dilshadur Rahman, Devin Lange, Ghulam Jilani Quadri, and Paul Rosen. Designing Annotations In Visualization: Considerations From Visualization Practitioners And Educators. EuroVis Full Papers, 2026.

@article{rahman2026designing,
  title = {Designing Annotations in Visualization: Considerations from Visualization
    Practitioners and Educators},
  author = {Rahman, Md Dilshadur and Lange, Devin and Quadri, Ghulam Jilani and Rosen,
    Paul},
  journal = {EuroVis Full Papers},
  year = {2026},
  abstract = {Annotation is a central mechanism in visualization design that enables
    people to communicate key insights. Prior research has provided essential accounts of
    the visual forms annotations take, but less attention has been paid to the decisions
    behind them. This paper examines how annotations are designed in practice and how
    educators reflect on those practices. We conducted a two-phase qualitative study:
    interviews with ten practitioners from diverse backgrounds revealed the heuristics they
    draw on when creating annotations, and interviews with seven visualization educators
    offered complementary perspectives situated within broader concerns of clarity,
    guidance, and viewer agency. These studies provide a systematic account of annotation
    design knowledge in professional settings, highlighting the considerations, trade-offs,
    and contextual judgments that shape the use of annotations. By making this tacit
    expertise explicit, our work complements prior form-focused studies, strengthens
    understanding of annotation as a design activity, and points to opportunities for
    improved tool and guideline support.}
}

Peer review is an underutilized yet potentially powerful strategy for fostering evaluative judgment and design literacy in visualization education. Critiquing visual work requires domain-specific competencies that extend beyond generic peer feedback; however, widely adopted platforms such as Canvas provide limited support for the cognitive and visual demands of visualization critique. We introduce VisPeerReview, a visualization-specific learning analytics dashboard (LAD) designed to scaffold peer feedback through an integrated visualization display, rubric-guided prompts, and inline annotation tools. We evaluated VisPeerReview through a three-phase mixed-methods study conducted in an undergraduate data visualization course, comparing it with Canvas’s default peer-review workflow. Drawing on interaction logs, peer-review text, and survey responses, we found that VisPeerReview elicited significantly longer and more linguistically rich feedback and was consistently preferred by students. Sentiment analysis further indicated more positive evaluative language and clearer reviewer intent under the dashboard-supported condition. Beyond tool evaluation, this study offers the first systematic comparison between Canvas and a visualization-specific LAD, demonstrating how theory-aligned instructional interface design—grounded in representational competence and learningsciences frameworks—can meaningfully improve the quality of peer feedback in computing education.

Alon Friedman, Ly Dinh, Md Dilshadur Rahman, and Paul Rosen. Designing For Engagement: A Comparison Of Canvas And A Visual Peer Review Dashboard. ACM Transactions on Computing Education, 2026.

@article{friedman2026designing,
  title = {Designing for Engagement: A Comparison of Canvas and a Visual Peer Review
    Dashboard},
  author = {Friedman, Alon and Dinh, Ly and Rahman, Md Dilshadur and Rosen, Paul},
  journal = {ACM Transactions on Computing Education},
  year = {2026},
  abstract = {Peer review is an underutilized yet potentially powerful strategy for
    fostering evaluative judgment and design literacy in visualization education. Critiquing
    visual work requires domain-specific competencies that extend beyond generic peer
    feedback; however, widely adopted platforms such as Canvas provide limited support for
    the cognitive and visual demands of visualization critique. We introduce VisPeerReview,
    a visualization-specific learning analytics dashboard (LAD) designed to scaffold peer
    feedback through an integrated visualization display, rubric-guided prompts, and inline
    annotation tools. We evaluated VisPeerReview through a three-phase mixed-methods study
    conducted in an undergraduate data visualization course, comparing it with Canvas’s
    default peer-review workflow. Drawing on interaction logs, peer-review text, and survey
    responses, we found that VisPeerReview elicited significantly longer and more
    linguistically rich feedback and was consistently preferred by students. Sentiment
    analysis further indicated more positive evaluative language and clearer reviewer intent
    under the dashboard-supported condition. Beyond tool evaluation, this study offers the
    first systematic comparison between Canvas and a visualization-specific LAD,
    demonstrating how theory-aligned instructional interface design—grounded in
    representational competence and learningsciences frameworks—can meaningfully improve the
    quality of peer feedback in computing education.}
}

Deep neural networks (DNNs) achieve state-of-the-art performance in many vision tasks, yet understanding their internal behavior remains challenging, particularly how different layers and activation channels contribute to class separability. We introduce ChannelExplorer, an interactive visual analytics tool for analyzing image-based outputs across model layers, emphasizing data-driven insights over architecture analysis for exploring class separability. ChannelExplorer summarizes activations across layers and visualizes them using three primary coordinated views: a Scatterplot View to reveal inter- and intra-class confusion, a Jaccard Similarity View to quantify activation overlap, and a Heatmap View to inspect activation channel patterns. Our technique supports diverse model architectures, including CNNs, GANs, ResNet and Stable Diffusion models. We demonstrate the capabilities of ChannelExplorer through four use-case scenarios: (1) generating class hierarchy in ImageNet, (2) finding mislabeled images, (3) identifying activation channel contributions, and(4) locating latent states’ position in Stable Diffusion model. Finally, we evaluate the tool with expert users.

Rahat Zaman, Bei Wang, and Paul Rosen. Channelexplorer: Visualizing Cnn Activation Channels For Exploring Class Separability. IEEE Transactions on Visualization and Computer Graphics (to appear), 2026.

@article{zaman2026cnn,
  title = {ChannelExplorer: Visualizing CNN Activation Channels for Exploring Class
    Separability},
  author = {Zaman, Rahat and Wang, Bei and Rosen, Paul},
  journal = {IEEE Transactions on Visualization and Computer Graphics  (to appear)},
  year = {2026},
  abstract = {Deep neural networks (DNNs) achieve state-of-the-art performance in many
    vision tasks, yet understanding their internal behavior remains challenging,
    particularly how different layers and activation channels contribute to class
    separability. We introduce ChannelExplorer, an interactive visual analytics tool for
    analyzing image-based outputs across model layers, emphasizing data-driven insights over
    architecture analysis for exploring class separability. ChannelExplorer summarizes
    activations across layers and visualizes them using three primary coordinated views: a
    Scatterplot View to reveal inter- and intra-class confusion, a Jaccard Similarity View
    to quantify activation overlap, and a Heatmap View to inspect activation channel
    patterns. Our technique supports diverse model architectures, including CNNs, GANs,
    ResNet and Stable Diffusion models. We demonstrate the capabilities of ChannelExplorer
    through four use-case scenarios: (1) generating class hierarchy in ImageNet, (2) finding
    mislabeled images, (3) identifying activation channel contributions, and(4) locating
    latent states' position in Stable Diffusion model. Finally, we evaluate the tool with
    expert users.}
}

In this paper, we study the propagation of data uncertainty through the marching cubes algorithm for isosurface visualization for correlated uncertain data. Consideration of correlation has been shown paramount for avoiding errors in uncertainty quantification and visualization in multiple prior studies. Although the problem of isosurface uncertainty with spatial data correlation has been previously addressed, there are two major limitations to prior treatments. First, there are no analytical formulations for uncertainty quantification of isosurfaces when the data uncertainty is characterized by a Gaussian distribution with spatial correlation. Second, as a consequence of the lack of analytical formulations, existing techniques resort to a Monte Carlo sampling approach, which is expensive and difficult to integrate into visualization tools. To address these limitations, we present a closed-form framework to efficiently derive uncertainty in marching cubes level-sets for Gaussian uncertain data with spatial correlation (MAGIC). To derive closed-form solutions, we leverage the Hinkley’s derivation on the ratio of Gaussian distributions. With our analytical framework, we achieve a significant speed-up and enhanced accuracy of uncertainty quantification over classical Monte Carlo methods. We further accelerate our analytical solutions using many-core processors to achieve speed-ups up to 585x and integrability with production visualization tools for broader impact. We demonstrate the effectiveness of our correlation-aware uncertainty framework through experiments on meteorology, urban flow, and astrophysics simulation datasets.

Tushar M. Athawale, Kenneth Moreland, David Pugmire, Chris R. Johnson, Paul Rosen, Matthew Norman, Antigoni Georgiadou, and Alireza Entezari. Magic: Marching Cubes Isosurface Uncertainty Visualization For Gaussian Uncertain Data With Spatial Correlation. IEEE Transactions on Computer Graphics and Visualization, 2026.

@article{athawale2026magic,
  title = {MAGIC: Marching Cubes Isosurface Uncertainty Visualization for Gaussian
    Uncertain Data with Spatial Correlation},
  author = {Athawale, Tushar M. and Moreland, Kenneth and Pugmire, David and Johnson,
    Chris R. and Rosen, Paul and Norman, Matthew and Georgiadou, Antigoni and Entezari,
    Alireza},
  journal = {IEEE Transactions on Computer Graphics and Visualization},
  year = {2026},
  abstract = {In this paper, we study the propagation of data uncertainty through the
    marching cubes algorithm for isosurface visualization for correlated uncertain data.
    Consideration of correlation has been shown paramount for avoiding errors in uncertainty
    quantification and visualization in multiple prior studies. Although the problem of
    isosurface uncertainty with spatial data correlation has been previously addressed,
    there are two major limitations to prior treatments. First, there are no analytical
    formulations for uncertainty quantification of isosurfaces when the data uncertainty is
    characterized by a Gaussian distribution with spatial correlation. Second, as a
    consequence of the lack of analytical formulations, existing techniques resort to a
    Monte Carlo sampling approach, which is expensive and difficult to integrate into
    visualization tools. To address these limitations, we present a closed-form framework to
    efficiently derive uncertainty in marching cubes level-sets for Gaussian uncertain data
    with spatial correlation (MAGIC). To derive closed-form solutions, we leverage the
    Hinkley’s derivation on the ratio of Gaussian distributions. With our analytical
    framework, we achieve a significant speed-up and enhanced accuracy of uncertainty
    quantification over classical Monte Carlo methods. We further accelerate our analytical
    solutions using many-core processors to achieve speed-ups up to 585x and integrability
    with production visualization tools for broader impact. We demonstrate the effectiveness
    of our correlation-aware uncertainty framework through experiments on meteorology, urban
    flow, and astrophysics simulation datasets.}
}

Overplotted line charts can obscure trends in temporal data and hinder prediction. We conduct a user study comparing three alternatives-aggregated, trellis, and spiral line charts against standard line charts on tasks involving trend identification, making predictions, and decision-making. We found aggregated charts performed similarly to standard charts and support more accurate trend recognition and prediction; trellis and spiral charts generally lag. We also examined the impact on decision-making via a trust game. The results showed similar trust in standard and aggregated charts, varied trust in spiral charts, and a lean toward distrust in trellis charts. These findings provide guidance for practitioners choosing visualization strategies for dense temporal data.

Rifat Ara Proma, Ghulam Jilani Quadri, and Paul Rosen. Evaluating Line Chart Strategies For Mitigating Density Of Temporal Data: The Impact On Trend, Trust, And Prediction. Lecture Notes in Computer Science, 2026.

@article{proma2025linechart,
  title = {Evaluating Line Chart Strategies for Mitigating Density of Temporal Data: The
    Impact on Trend, Trust, and Prediction},
  author = {Proma, Rifat Ara and Quadri, Ghulam Jilani and Rosen, Paul},
  journal = {Lecture Notes in Computer Science},
  year = {2026},
  note = {textit{Presented at the International Symposium on Visual Computing 2025}},
  abstract = {Overplotted line charts can obscure trends in temporal data and hinder
    prediction. We conduct a user study comparing three alternatives-aggregated, trellis,
    and spiral line charts against standard line charts on tasks involving trend
    identification, making predictions, and decision-making. We found aggregated charts
    performed similarly to standard charts and support more accurate trend recognition and
    prediction; trellis and spiral charts generally lag. We also examined the impact on
    decision-making via a trust game. The results showed similar trust in standard and
    aggregated charts, varied trust in spiral charts, and a lean toward distrust in trellis
    charts. These findings provide guidance for practitioners choosing visualization
    strategies for dense temporal data.}
}

Data wrangling—the process of cleaning, transforming, and preparing data for analysis—is a well-known bottleneck in data science workflows. Existing tools either rely on manual scripting, which is error-prone and hard to debug, or automate cleaning through opaque black-box pipelines that offer limited control. We present Buckaroo, a scalable visual data wrangling system that restructures data preparation as a direct manipulation task over visualizations. Buckaroo enables users to explore and repair data anomalies—such as missing values, outliers, and type mismatches—by interacting directly with coordinated data visualizations. The system extensibly supports user-defined error detectors and wranglers, tracks provenance for undo/redo, and generates reproducible scripts for downstream tasks. Buckaroo maintains efficient indexing data structures and differential storage to localize anomaly detection and minimize recomputation. To demonstrate the applicability of our model, Buckaroo is integrated with the Hopara pan-and-zoom engine, which enables multi-layered navigation over large datasets without sacrificing interactivity. Through empirical evaluation and an expert review we show that Buckaroo makes visual data wrangling scalable—bridging the gap between visual inspection and programmable repairs.

El Kindi Rezig, Mir Mahathir Mohammad, Nicolas Baret, Ricardo Mayerhofer, Andrew McNutt, and Paul Rosen. Towards Scalable Visual Data Wrangling Via Direct Manipulation. Conference on Innovative Data Systems Research (CIDR), 2026.

@article{rezig2026cidr,
  title = {Towards Scalable Visual Data Wrangling via Direct Manipulation},
  author = {Rezig, El Kindi and Mohammad, Mir Mahathir and Baret, Nicolas and Mayerhofer,
    Ricardo and McNutt, Andrew and Rosen, Paul},
  journal = {Conference on Innovative Data Systems Research (CIDR)},
  year = {2026},
  abstract = {Data wrangling—the process of cleaning, transforming, and preparing data
    for analysis—is a well-known bottleneck in data science workflows. Existing tools either
    rely on manual scripting, which is error-prone and hard to debug, or automate cleaning
    through opaque black-box pipelines that offer limited control. We present Buckaroo, a
    scalable visual data wrangling system that restructures data preparation as a direct
    manipulation task over visualizations. Buckaroo enables users to explore and repair data
    anomalies—such as missing values, outliers, and type mismatches—by interacting directly
    with coordinated data visualizations. The system extensibly supports user-defined error
    detectors and wranglers, tracks provenance for undo/redo, and generates reproducible
    scripts for downstream tasks. Buckaroo maintains efficient indexing data structures and
    differential storage to localize anomaly detection and minimize recomputation. To
    demonstrate the applicability of our model, Buckaroo is integrated with the Hopara
    pan-and-zoom engine, which enables multi-layered navigation over large datasets without
    sacrificing interactivity. Through empirical evaluation and an expert review we show
    that Buckaroo makes visual data wrangling scalable—bridging the gap between visual
    inspection and programmable repairs.}
}

Line charts surface many features in time series data, from trends to periodicity to peaks and valleys. However, not every potentially important feature in the data may correspond to a visual feature which readers can detect or prioritize. In this study, we conducted a visual stenography task, where participants re-drew line charts to solicit information about the visual features they believed to be important. We systematically varied noise levels (SNR ~5-30 dB) across line charts to observe how visual clutter influences which features people prioritize in their sketches. We identified three key strategies that correlated with the noise present in the stimuli: the Replicator attempted to retain all major features of the line chart including noise; the Trend Keeper prioritized trends disregarding periodicity and peaks; and the De-noiser filtered out noise while preserving other features. Further, we found that participants tended to faithfully retain trends and peaks and valleys when these features were present, while periodicity and noise were represented in more qualitative or gestural ways: semantically rather than accurately. These results suggest a need to consider more flexible and human-centric ways of presenting, summarizing, pre-processing, or clustering time series data.

Rifat Ara Proma, Michael Correll, Ghulam Jilani Quadri, and Paul Rosen. Visual Stenography: Feature Recreation And Preservation In Sketches Of Line Charts. IEEE Transactions on Visualization and Computer Graphics, 2026.

@article{proma2025stenography,
  title = {Visual Stenography: Feature Recreation and Preservation in
Sketches of Line Charts},
  author = {Proma, Rifat Ara and Correll, Michael and Quadri, Ghulam Jilani and Rosen,
    Paul},
  journal = {IEEE Transactions on Visualization and Computer Graphics},
  year = {2026},
  abstract = {Line charts surface many features in time series data, from trends to
    periodicity to peaks and valleys. However, not every potentially important feature in
    the data may correspond to a visual feature which readers can detect or prioritize. In
    this study, we conducted a visual stenography task, where participants re-drew line
    charts to solicit information about the visual features they believed to be important.
    We systematically varied noise levels (SNR ~5-30 dB) across line charts to observe how
    visual clutter influences which features people prioritize in their sketches. We
    identified three key strategies that correlated with the noise present in the stimuli:
    the Replicator attempted to retain all major features of the line chart including noise;
    the Trend Keeper prioritized trends disregarding periodicity and peaks; and the
    De-noiser filtered out noise while preserving other features. Further, we found that
    participants tended to faithfully retain trends and peaks and valleys when these
    features were present, while periodicity and noise were represented in more qualitative
    or gestural ways: semantically rather than accurately. These results suggest a need to
    consider more flexible and human-centric ways of presenting, summarizing,
    pre-processing, or clustering time series data.}
}

Reeb graphs are an important tool for abstracting and representing the topological structure of a function defined on a manifold. We have identified three properties for faithfully representing Reeb graphs in a visualization. Namely, they should be constrained to the boundary, compact, and aligned with the function gradient. Existing algorithms for drawing Reeb graphs are agnostic to or violate these properties. In this paper, we introduce an algorithm to generate Reeb graph visualizations, called textit{GASP}, that is cognizant of these properties, thereby producing visualizations that are more representative of the underlying data. To demonstrate the improvements, the resulting Reeb graphs are evaluated both qualitatively and quantitatively against the geometric barycenter algorithm, using its implementation available in the Topology ToolKit (TTK), a widely adopted tool for calculating and visualizing Reeb graphs.

Sefat Rahman, Tushar M. Athawale, and Paul Rosen. Gasp: A Gradient-Aware Shortest Path Algorithm For Boundary-Confined Visualization Of 2-Manifold Reeb Graphs. Topological Data Analysis and Visualization (TopoInVis), 2025.

@article{rahman2025reeb,
  title = {GASP: A Gradient-Aware Shortest Path Algorithm for Boundary-Confined
    Visualization of 2-Manifold Reeb Graphs},
  author = {Rahman, Sefat and Athawale, Tushar M. and Rosen, Paul},
  journal = {Topological Data Analysis and Visualization (TopoInVis)},
  year = {2025},
  abstract = {Reeb graphs are an important tool for abstracting and representing the
    topological structure of a function defined on a manifold. We have identified three
    properties for faithfully representing Reeb graphs in a visualization. Namely, they
    should be constrained to the boundary, compact, and aligned with the function gradient.
    Existing algorithms for drawing Reeb graphs are agnostic to or violate these properties.
    In this paper, we introduce an algorithm to generate Reeb graph visualizations, called
    textit{GASP}, that is cognizant of these properties, thereby producing visualizations
    that are more representative of the underlying data. To demonstrate the improvements,
    the resulting Reeb graphs are evaluated both qualitatively and quantitatively against
    the geometric barycenter algorithm, using its implementation available in the Topology
    ToolKit (TTK), a widely adopted tool for calculating and visualizing Reeb graphs.}
}