Modeling Color Difference for Visualization Design

Color Maps: Facilitating the Clinical Impact of Quantitative MRI

Presenting quantitative data using non-standardized color maps potentially results in unrecognized misinterpretation of data. Clinically meaningful color maps should intuitively and inclusively represent data without misleading interpretation. Uniformity of the color gradient for color maps is critically important. Maximal color and lightness contrast, readability for color vision-impaired individuals, and recognizability of the color scheme are highly desirable features. This article describes the use of color maps in five key quantitative MRI techniques: relaxometry, diffusion-weighted imaging (DWI), dynamic contrast-enhanced (DCE)-MRI, MR elastography (MRE), and water-fat MRI. Current display practice of color maps is reviewed and shortcomings against desirable features are highlighted. EVIDENCE LEVEL: 5 TECHNICAL EFFICACY: Stage 2.

Visualization-Driven Illumination for Density Plots

We present a novel visualization-driven illumination model for density plots, a new technique to enhance density plots by effectively revealing the detailed structures in high- and medium-density regions and outliers in low-density regions, while avoiding artifacts in the density field's colors. When visualizing large and dense discrete point samples, scatterplots and dot density maps often suffer from overplotting, and density plots are commonly employed to provide aggregated views while revealing underlying structures. Yet, in such density plots, existing illumination models may produce color distortion and hide details in low-density regions, making it challenging to look up density values, compare them, and find outliers. The key novelty in this work includes (i) a visualization-driven illumination model that inherently supports density-plot-specific analysis tasks and (ii) a new image composition technique to reduce the interference between the image shading and the color-encoded density values. To demonstrate the effectiveness of our technique, we conducted a quantitative study, an empirical evaluation of our technique in a controlled study, and two case studies, exploring twelve datasets with up to two million data point samples.

Shape It Up: An Empirically Grounded Approach for Designing Shape Palettes

Shape is commonly used to distinguish between categories in multi-class scatterplots. However, existing guidelines for choosing effective shape palettes rely largely on intuition and do not consider how these needs may change as the number of categories increases. Unlike color, shapes can not be represented by a numerical space, making it difficult to propose general guidelines or design heuristics for using shape effectively. This paper presents a series of four experiments evaluating the efficiency of 39 shapes across three tasks: relative mean judgment tasks, expert preference, and correlation estimation. Our results show that conventional means for reasoning about shapes, such as filled versus unfilled, are insufficient to inform effective palette design. Further, even expert palettes vary significantly in their use of shape and corresponding effectiveness. To support effective shape palette design, we developed a model based on pairwise relations between shapes in our experiments and the number of shapes required for a given design. We embed this model in a palette design tool to give designers agency over shape selection while incorporating empirical elements of perceptual performance captured in our study. Our model advances understanding of shape perception in visualization contexts and provides practical design guidelines that can help improve categorical data encodings.

Quantifying Emotional Responses to Immutable Data Characteristics and Designer Choices in Data Visualizations

Emotion is an important factor to consider when designing visualizations as it can impact the amount of trust viewers place in a visualization, how well they can retrieve information and understand the underlying data, and how much they engage with or connect to a visualization. We conducted five crowdsourced experiments to quantify the effects of color, chart type, data trend, data variability and data density on emotion (measured through self-reported arousal and valence). Results from our experiments show that there are multiple design elements which influence the emotion induced by a visualization and, more surprisingly, that certain data characteristics influence the emotion of viewers even when the data has no meaning. In light of these findings, we offer guidelines on how to use color, scale, and chart type to counterbalance and emphasize the emotional impact of immutable data characteristics.

Causal Priors and Their Influence on Judgements of Causality in Visualized Data

"Correlation does not imply causation" is a famous mantra in statistical and visual analysis. However, consumers of visualizations often draw causal conclusions when only correlations between variables are shown. In this paper, we investigate factors that contribute to causal relationships users perceive in visualizations. We collected a corpus of concept pairs from variables in widely used datasets and created visualizations that depict varying correlative associations using three typical statistical chart types. We conducted two MTurk studies on (1) preconceived notions on causal relations without charts, and (2) perceived causal relations with charts, for each concept pair. Our results indicate that people make assumptions about causal relationships between pairs of concepts even without seeing any visualized data. Moreover, our results suggest that these assumptions constitute causal priors that, in combination with visualized association, impact how data visualizations are interpreted. The results also suggest that causal priors may lead to over- or under-estimation in perceived causal relations in different circumstances, and that those priors can also impact users' confidence in their causal assessments. In addition, our results align with prior work, indicating that chart type may also affect causal inference. Using data from the studies, we develop a model to capture the interaction between causal priors and visualized associations as they combine to impact a user's perceived causal relations. In addition to reporting the study results and analyses, we provide an open dataset of causal priors for 56 specific concept pairs that can serve as a potential benchmark for future studies. We also suggest remaining challenges and heuristic-based guidelines to help designers improve visualization design choices to better support visual causal inference.

Toward the validation of crowdsourced experiments for lightness perception

Crowdsource platforms have been used to study a range of perceptual stimuli such as the graphical perception of scatterplots and various aspects of human color perception. Given the lack of control over a crowdsourced participant's experimental setup, there are valid concerns on the use of crowdsourcing for color studies as the perception of the stimuli is highly dependent on the stimulus presentation. Here, we propose that the error due to a crowdsourced experimental design can be effectively averaged out because the crowdsourced experiment can be accommodated by the Thurstonian model as the convolution of two normal distributions, one that is perceptual in nature and one that captures the error due to variability in stimulus presentation. Based on this, we provide a mathematical estimate for the sample size needed to produce a crowdsourced experiment with the same power as the corresponding in-person study. We tested this claim by replicating a large-scale, crowdsourced study of human lightness perception with a diverse sample with a highly controlled, in-person study with a sample taken from psychology undergraduates. Our claim was supported by the replication of the results from the latter. These findings suggest that, with sufficient sample size, color vision studies may be completed online, giving access to a larger and more representative sample. With this framework at hand, experimentalists have the validation that choosing either many online participants or few in person participants will not sacrifice the impact of their results.

What Does the Chart Say? Grouping Cues Guide Viewer Comparisons and Conclusions in Bar Charts

Reading a visualization is like reading a paragraph. Each sentence is a comparison: the mean of these is higher than those; this difference is smaller than that. What determines which comparisons are made first? The viewer's goals and expertise matter, but the way that values are visually grouped together within the chart also impacts those comparisons. Research from psychology suggests that comparisons involve multiple steps. First, the viewer divides the visualization into a set of units. This might include a single bar or a grouped set of bars. Then the viewer selects and compares two of these units, perhaps noting that one pair of bars is longer than another. Viewers might take an additional third step and perform a second-order comparison, perhaps determining that the difference between one pair of bars is greater than the difference between another pair. We create a visual comparison taxonomy that allows us to develop and test a sequence of hypotheses about which comparisons people are more likely to make when reading a visualization. We find that people tend to compare two groups before comparing two individual bars and that second-order comparisons are rare. Visual cues like spatial proximity and color can influence which elements are grouped together and selected for comparison, with spatial proximity being a stronger grouping cue. Interestingly, once the viewer grouped together and compared a set of bars, regardless of whether the group is formed by spatial proximity or color similarity, they no longer consider other possible groupings in their comparisons.

psudo: Exploring Multi-Channel Biomedical Image Data with Spatially and Perceptually Optimized Pseudocoloring

Over the past century, multichannel fluorescence imaging has been pivotal in myriad scientific breakthroughs by enabling the spatial visualization of proteins within a biological sample. With the shift to digital methods and visualization software, experts can now flexibly pseudocolor and combine image channels, each corresponding to a different protein, to explore their spatial relationships. We thus propose psudo, an interactive system that allows users to create optimal color palettes for multichannel spatial data. In psudo, a novel optimization method generates palettes that maximize the perceptual differences between channels while mitigating confusing color blending in overlapping channels. We integrate this method into a system that allows users to explore multi-channel image data and compare and evaluate color palettes for their data. An interactive lensing approach provides on-demand feedback on channel overlap and a color confusion metric while giving context to the underlying channel values. Color palettes can be applied globally or, using the lens, to local regions of interest. We evaluate our palette optimization approach using three graphical perception tasks in a crowdsourced user study with 150 participants, showing that users are more accurate at discerning and comparing the underlying data using our approach. Additionally, we showcase psudo in a case study exploring the complex immune responses in cancer tissue data with a biologist.

Interactive polar diagrams for model comparison

OBJECTIVE

Evaluating the performance of multiple complex models, such as those found in biology, medicine, climatology, and machine learning, using conventional approaches is often challenging when using various evaluation metrics simultaneously. The traditional approach, which relies on presenting multi-model evaluation scores in the table, presents an obstacle when determining the similarities between the models and the order of performance.

METHODS

By combining statistics, information theory, and data visualization, juxtaposed Taylor and Mutual Information Diagrams permit users to track and summarize the performance of one model or a collection of different models. To uncover linear and nonlinear relationships between models, users may visualize one or both charts.

RESULTS

Our library presents the first publicly available implementation of the Mutual Information Diagram and its new interactive capabilities, as well as the first publicly available implementation of an interactive Taylor Diagram. Extensions have been implemented so that both diagrams can display temporality, multimodality, and multivariate data sets, and feature one scalar model property such as uncertainty. Our library, named polar-diagrams, supports both continuous and categorical attributes.

CONCLUSION

The library can be used to quickly and easily assess the performances of complex models, such as those found in machine learning, climate, or biomedical domains.

The Effects of Visual Complexity and Task Difficulty on the Comprehensive Cognitive Efficiency of Cluster Separation Tasks

Cluster separation is required to perform multi-class visual statistics tasks and plays an essential role in information processing in visualization. This cognition behavioral study investigated the cluster separation task and the effects of visual complexity and task difficulty. A total of 32 college students (18 men and 14 women, with ages ranging from 18 to 25 years; mean = 21.2, SD = 3.9) participated in this study. The observers' average response accuracy, reaction time, mental effort, and comprehensive cognitive efficiency were measured as functions of three levels of visual complexity and task difficulty. The levels of visual complexity and task difficulty were quantified via an optimized complexity evaluation method and discrimination judgment task, respectively. The results showed that visual complexity and task difficulty significantly influenced comprehensive cognitive efficiency. Moreover, a strong interaction was observed between the effects of visual complexity and task difficulty. However, there was no positive linear relationship between the mental effort and the complexity level. Furthermore, two-dimensional color × shape redundant coding showed higher cognitive efficiency at low task difficulty levels. In contrast, the one-dimensional color encoding approach showed higher cognitive efficiency at increased task difficulty levels. The findings of this study provide valuable insights into designing more efficient and user-friendly visualization in the future.

Automatic Scatterplot Design Optimization for Clustering Identification

Scatterplots are among the most widely used visualization techniques. Compelling scatterplot visualizations improve understanding of data by leveraging visual perception to boost awareness when performing specific visual analytic tasks. Design choices in scatterplots, such as graphical encodings or data aspects, can directly impact decision-making quality for low-level tasks like clustering. Hence, constructing frameworks that consider both the perceptions of the visual encodings and the task being performed enables optimizing visualizations to maximize efficacy. In this article, we propose an automatic tool to optimize the design factors of scatterplots to reveal the most salient cluster structure. Our approach leverages the merge tree data structure to identify the clusters and optimize the choice of subsampling algorithm, sampling rate, marker size, and marker opacity used to generate a scatterplot image. We validate our approach with user and case studies that show it efficiently provides high-quality scatterplot designs from a large parameter space.

Trend judgment as a perceptual building block of graphicacy and mathematics, across age, education, and culture

Data plots are widely used in science, journalism and politics, since they efficiently allow to depict a large amount of information. Graphicacy, the ability to understand graphs, has thus become a fundamental cultural skill comparable to literacy or numeracy. Here, we introduce a measure of intuitive graphicacy that assesses the perceptual ability to detect a trend in noisy scatterplots ("does this graph go up or down?"). In 3943 educated participants, responses vary as a sigmoid function of the t-value that a statistician would compute to detect a significant trend. We find a minimum level of core intuitive graphicacy even in unschooled participants living in remote Namibian villages (N = 87) and 6-year-old 1st-graders who never read a graph (N = 27). The sigmoid slope that we propose as a proxy of intuitive graphicacy increases with education and tightly correlates with statistical and mathematical knowledge, showing that experience contributes to refining graphical intuitions. Our tool, publicly available online, allows to quickly evaluate and formally quantify a perceptual building block of graphicacy.

EnConVis: A Unified Framework for Ensemble Contour Visualization

Ensemble simulation is a crucial method to handle potential uncertainty in modern simulation and has been widely applied in many disciplines. Many ensemble contour visualization methods have been introduced to facilitate ensemble data analysis. On the basis of deep exploration and summarization of existing techniques and domain requirements, we propose a unified framework of ensemble contour visualization, EnConVis (Ensemble Contour Visualization), which systematically combines state-of-the-art methods. We model ensemble contour visualization as a four-step pipeline consisting of four essential procedures: member filtering, point-wise modeling, uncertainty band extraction, and visual mapping. For each of the four essential procedures, we compare different methods they use, analyze their pros and cons, highlight research gaps, and attempt to fill them. Specifically, we add Kernel Density Estimation in the point-wise modeling procedure and multi-layer extraction in the uncertainty band extraction procedure. This step shows the ensemble data's details accurately and provides abstract levels. We also analyze existing methods from a global perspective. We investigate their mechanisms and compare their effects, on the basis of which, we offer selection guidelines for them. From the overall perspective of this framework, we find choices and combinations that have not been tried before, which can be well compensated by our method. Synthetic data and real-world data are leveraged to verify the efficacy of our method. Domain experts' feedback suggests that our approach helps them better understand ensemble data analysis.

Unifying Effects of Direct and Relational Associations for Visual Communication

People have expectations about how colors map to concepts in visualizations, and they are better at interpreting visualizations that match their expectations. Traditionally, studies on these expectations (inferred mappings) distinguished distinct factors relevant for visualizations of categorical vs. continuous information. Studies on categorical information focused on direct associations (e.g., mangos are associated with yellows) whereas studies on continuous information focused on relational associations (e.g., darker colors map to larger quantities; dark-is-more bias). We unite these two areas within a single framework of assignment inference. Assignment inference is the process by which people infer mappings between perceptual features and concepts represented in encoding systems. Observers infer globally optimal assignments by maximizing the "merit," or "goodness," of each possible assignment. Previous work on assignment inference focused on visualizations of categorical information. We extend this approach to visualizations of continuous data by (a) broadening the notion of merit to include relational associations and (b) developing a method for combining multiple (sometimes conflicting) sources of merit to predict people's inferred mappings. We developed and tested our model on data from experiments in which participants interpreted colormap data visualizations, representing fictitious data about environmental concepts (sunshine, shade, wild fire, ocean water, glacial ice). We found both direct and relational associations contribute independently to inferred mappings. These results can be used to optimize visualization design to facilitate visual communication.

InfoColorizer: Interactive Recommendation of Color Palettes for Infographics

When designing infographics, general users usually struggle with getting desired color palettes using existing infographic authoring tools, which sometimes sacrifice customizability, require design expertise, or neglect the influence of elements' spatial arrangement. We propose a data-driven method that provides flexibility by considering users' preferences, lowers the expertise barrier via automation, and tailors suggested palettes to the spatial layout of elements. We build a recommendation engine by utilizing deep learning techniques to characterize good color design practices from data, and further develop InfoColorizer, a tool that allows users to obtain color palettes for their infographics in an interactive and dynamic manner. To validate our method, we conducted a comprehensive four-part evaluation, including case studies, a controlled user study, a survey study, and an interview study. The results indicate that InfoColorizer can provide compelling palette recommendations with adequate flexibility, allowing users to effectively obtain high-quality color design for input infographics with low effort.

A Survey of Perception-Based Visualization Studies by Task

Knowledge of human perception has long been incorporated into visualizations to enhance their quality and effectiveness. The last decade, in particular, has shown an increase in perception-based visualization research studies. With all of this recent progress, the visualization community lacks a comprehensive guide to contextualize their results. In this report, we provide a systematic and comprehensive review of research studies on perception related to visualization. This survey reviews perception-focused visualization studies since 1980 and summarizes their research developments focusing on low-level tasks, further breaking techniques down by visual encoding and visualization type. In particular, we focus on how perception is used to evaluate the effectiveness of visualizations, to help readers understand and apply the principles of perception of their visualization designs through a task-optimized approach. We concluded our report with a summary of the weaknesses and open research questions in the area.

Rainbow Colormaps: What are they good and bad for?

Guidelines for color use in quantitative visualizations have strongly discouraged the use of rainbow colormaps, arguing instead for smooth designs that do not induce visual discontinuities or implicit color categories. However, the empirical evidence behind this argument has been mixed and, at times, even contradictory. In practice, rainbow colormaps are widely used, raising questions about the true utility or dangers of such designs. We study how color categorization impacts the interpretation of scalar fields. We first introduce an approach to detect latent categories in colormaps. We hypothesize that the appearance of color categories in scalar visualizations can be beneficial in that they enhance the perception of certain features, although at the cost of rendering other features less noticeable. In three crowdsourced experiments, we show that observers are more likely to discriminate global, distributional features when viewing colorful scales that induce categorization (e.g., rainbow or diverging schemes). Conversely, when seeing the same data through a less colorful representation, observers are more likely to report localized features defined by small variations in the data. Participants showed awareness of these different affordances, and exhibited bias for exploiting the more discriminating colormap, given a particular feature type. Our results demonstrate costs and benefits for rainbows (and similarly colorful schemes), suggesting that their complementary utility for analyzing scalar data should not be dismissed. In addition to explaining potentially valid uses of rainbow, our study provides actionable guidelines, including on when such designs can be more harmful than useful. Data and materials are available at https://osf.io/xjhtf.

Visualization in Motion: A Research Agenda and Two Evaluations

We contribute a research agenda for visualization in motion and two experiments to understand how well viewers can read data from moving visualizations. We define visualizations in motion as visual data representations that are used in contexts that exhibit relative motion between a viewer and an entire visualization. Sports analytics, video games, wearable devices, or data physicalizations are example contexts that involve different types of relative motion between a viewer and a visualization. To analyze the opportunities and challenges for designing visualization in motion, we show example scenarios and outline a first research agenda. Motivated primarily by the prevalence of and opportunities for visualizations in sports and video games we started to investigate a small aspect of our research agenda: the impact of two important characteristics of motion-speed and trajectory on a stationary viewer's ability to read data from moving donut and bar charts. We found that increasing speed and trajectory complexity did negatively affect the accuracy of reading values from the charts and that bar charts were more negatively impacted. In practice, however, this impact was small: both charts were still read fairly accurately.

Rainbow Dash: Intuitiveness, Interpretability and Memorability of the Rainbow Color Scheme in Visualization

After demonstrating that rainbow colors are still commonly used in scientific publications, we comparatively evaluate the rainbow and sequential color schemes on choropleth and isarithmic maps in an empirical user study with 544 participants to examine if a) people intuitively associate order for the colors in these schemes, b) they can successfully conduct perceptual and semantic map reading and recall tasks with quantitative data where order may have implicit or explicit importance. We find that there is little to no agreement in ordering of rainbow colors while sequential colors are indeed intuitively ordered by the participants with a strong dark is more bias. Sequential colors facilitate most quantitative map reading tasks better than the rainbow colors, whereas rainbow colors competitively facilitate extracting specific values from a map, and may support hue recall better than sequential. We thus contribute to dark- versus light is more bias debate, demonstrate why and when rainbow colors may impair performance, and add further nuance to our understanding of this highly popular, yet highly criticized color scheme.

Which emphasis technique to use? Perception of emphasis techniques with varying distractors, backgrounds, and visualization types

Emphasis effects are visual changes that make data elements distinct from their surroundings. Designers may use computational saliency models to predict how a viewer's attention will be guided by a specific effect; however, although saliency models provide a foundational understanding of emphasis perception, they only cover specific visual effects in abstract conditions. To address these limitations, we carried out crowdsourced studies that evaluate emphasis perception in a wider range of conditions than previously studied. We varied effect magnitude, distractor number and type, background, and visualization type, and measured the perceived emphasis of 12 visual effects. Our results show that there are perceptual commonalities of emphasis across a wide range of environments, but also that there are limitations on perceptibility for some effects, dependent on a visualization's background or type. We developed a model of emphasis predictability based on simple scatterplots that can be extended to other viewing conditions. Our studies provide designers with new understanding of how viewers experience emphasis in realistic visualization settings.

Braid Plot-A Mixed Palette Plotting Method as an Extension of Contour Plot

In this article, we propose a new method of three-dimensional data plotting based on the use of mixed hue palettes, which makes it possible to distinguish simultaneously both huge and subtle changes in the value of the presented quantity at the same plot. This method called "braid plot" is based on the alternating use of multiple palettes of colors (a kind of interlacing), which greatly increases the sharpness of the graph and allows us to define areas of equal values more accurately than using traditional graphs with a single palette or contour plot. We present here an algorithm of preparing braid plot composed of any number of initial color sets. As a result of using this type of plot, it was possible to detect, e.g., weak perturbation effects or subtle oscillations of the spectral density function, which is very hard to observe using classical plots.

An Automated Approach to Reasoning About Task-Oriented Insights in Responsive Visualization

Authors often transform a large screen visualization for smaller displays through rescaling, aggregation and other techniques when creating visualizations for both desktop and mobile devices (i.e., responsive visualization). However, transformations can alter relationships or patterns implied by the large screen view, requiring authors to reason carefully about what information to preserve while adjusting their design for the smaller display. We propose an automated approach to approximating the loss of support for task-oriented visualization insights (identification, comparison, and trend) in responsive transformation of a source visualization. We operationalize identification, comparison, and trend loss as objective functions calculated by comparing properties of the rendered source visualization to each realized target (small screen) visualization. To evaluate the utility of our approach, we train machine learning models on human ranked small screen alternative visualizations across a set of source visualizations. We find that our approach achieves an accuracy of 84% (random forest model) in ranking visualizations. We demonstrate this approach in a prototype responsive visualization recommender that enumerates responsive transformations using Answer Set Programming and evaluates the preservation of task-oriented insights using our loss measures. We discuss implications of our approach for the development of automated and semi-automated responsive visualization recommendation.

The Weighted Average Illusion: Biases in Perceived Mean Position in Scatterplots

Scatterplots can encode a third dimension by using additional channels like size or color (e.g. bubble charts). We explore a potential misinterpretation of trivariate scatterplots, which we call the weighted average illusion, where locations of larger and darker points are given more weight toward x- and y-mean estimates. This systematic bias is sensitive to a designer's choice of size or lightness ranges mapped onto the data. In this paper, we quantify this bias against varying size/lightness ranges and data correlations. We discuss possible explanations for its cause by measuring attention given to individual data points using a vision science technique called the centroid method. Our work illustrates how ensemble processing mechanisms and mental shortcuts can significantly distort visual summaries of data, and can lead to misjudgments like the demonstrated weighted average illusion.

Modeling Just Noticeable Differences in Charts

One of the fundamental tasks in visualization is to compare two or more visual elements. However, it is often difficult to visually differentiate graphical elements encoding a small difference in value, such as the heights of similar bars in bar chart or angles of similar sections in pie chart. Perceptual laws can be used in order to model when and how we perceive this difference. In this work, we model the perception of Just Noticeable Differences (JNDs), the minimum difference in visual attributes that allow faithfully comparing similar elements, in charts. Specifically, we explore the relation between JNDs and two major visual variables: the intensity of visual elements and the distance between them, and study it in three charts: bar chart, pie chart and bubble chart. Through an empirical study, we identify main effects on JND for distance in bar charts, intensity in pie charts, and both distance and intensity in bubble charts. By fitting a linear mixed effects model, we model JND and find that JND grows as the exponential function of variables. We highlight several usage scenarios that make use of the JND modeling in which elements below the fitted JND are detected and enhanced with secondary visual cues for better discrimination.

Rethinking the Ranks of Visual Channels

Data can be visually represented using visual channels like position, length or luminance. An existing ranking of these visual channels is based on how accurately participants could report the ratio between two depicted values. There is an assumption that this ranking should hold for different tasks and for different numbers of marks. However, there is surprisingly little existing work that tests this assumption, especially given that visually computing ratios is relatively unimportant in real-world visualizations, compared to seeing, remembering, and comparing trends and motifs, across displays that almost universally depict more than two values. To simulate the information extracted from a glance at a visualization, we instead asked participants to immediately reproduce a set of values from memory after they were shown the visualization. These values could be shown in a bar graph (position (bar)), line graph (position (line)), heat map (luminance), bubble chart (area), misaligned bar graph (length), or 'wind map' (angle). With a Bayesian multilevel modeling approach, we show how the rank positions of visual channels shift across different numbers of marks (2, 4 or 8) and for bias, precision, and error measures. The ranking did not hold, even for reproductions of only 2 marks, and the new probabilistic ranking was highly inconsistent for reproductions of different numbers of marks. Other factors besides channel choice had an order of magnitude more influence on performance, such as the number of values in the series (e.g., more marks led to larger errors), or the value of each mark (e.g., small values were systematically overestimated). Every visual channel was worse for displays with 8 marks than 4, consistent with established limits on visual memory. These results point to the need for a body of empirical studies that move beyond two-value ratio judgments as a baseline for reliably ranking the quality of a visual channel, including testing new tasks (detection of trends or motifs), timescales (immediate computation, or later comparison), and the number of values (from a handful, to thousands).

Visualization as a stimulus domain for vision science

Traditionally, vision science and information/data visualization have interacted by using knowledge of human vision to help design effective displays. It is argued here, however, that this interaction can also go in the opposite direction: the investigation of successful visualizations can lead to the discovery of interesting new issues and phenomena in visual perception. Various studies are reviewed showing how this has been done for two areas of visualization, namely, graphical representations and interaction, which lend themselves to work on visual processing and the control of visual operations, respectively. The results of these studies have provided new insights into aspects of vision such as grouping, attentional selection and the sequencing of visual operations. More generally yet, such results support the view that the perception of visualizations can be a useful domain for exploring the nature of visual cognition, inspiring new kinds of questions as well as casting new light on the limits to which information can be conveyed visually.

The Making of Continuous Colormaps

Continuous colormaps are integral parts of many visualization techniques, such as heat-maps, surface plots, and flow visualization. Despite that the critiques of rainbow colormaps have been around and well-acknowledged for three decades, rainbow colormaps are still widely used today. One reason behind the resilience of rainbow colormaps is the lack of tools for users to create a continuous colormap that encodes semantics specific to the application concerned. In this paper, we present a web-based software system, CCC-Tool (short for Charting Continuous Colormaps) under the URL https://ccctool.com, for creating, editing, and analyzing such application-specific colormaps. We introduce the notion of "colormap specification (CMS)" that maintains the essential semantics required for defining a color mapping scheme. We provide users with a set of advanced utilities for constructing CMS's with various levels of complexity, examining their quality attributes using different plots, and exporting them to external application software. We present two case studies, demonstrating that the CCC-Tool can help domain scientists as well as visualization experts in designing semantically-rich colormaps.

Semantic Discriminability for Visual Communication

To interpret information visualizations, observers must determine how visual features map onto concepts. First and foremost, this ability depends on perceptual discriminability; observers must be able to see the difference between different colors for those colors to communicate different meanings. However, the ability to interpret visualizations also depends on semantic discriminability, the degree to which observers can infer a unique mapping between visual features and concepts, based on the visual features and concepts alone (i.e., without help from verbal cues such as legends or labels). Previous evidence suggested that observers were better at interpreting encoding systems that maximized semantic discriminability (maximizing association strength between assigned colors and concepts while minimizing association strength between unassigned colors and concepts), compared to a system that only maximized color-concept association strength. However, increasing semantic discriminability also resulted in increased perceptual distance, so it is unclear which factor was responsible for improved performance. In the present study, we conducted two experiments that tested for independent effects of semantic distance and perceptual distance on semantic discriminability of bar graph data visualizations. Perceptual distance was large enough to ensure colors were more than just noticeably different. We found that increasing semantic distance improved performance, independent of variation in perceptual distance, and when these two factors were uncorrelated, responses were dominated by semantic distance. These results have implications for navigating trade-offs in color palette design optimization for visual communication.

LineSmooth: An Analytical Framework for Evaluating the Effectiveness of Smoothing Techniques on Line Charts

We present a comprehensive framework for evaluating line chart smoothing methods under a variety of visual analytics tasks. Line charts are commonly used to visualize a series of data samples. When the number of samples is large, or the data are noisy, smoothing can be applied to make the signal more apparent. However, there are a wide variety of smoothing techniques available, and the effectiveness of each depends upon both nature of the data and the visual analytics task at hand. To date, the visualization community lacks a summary work for analyzing and classifying the various smoothing methods available. In this paper, we establish a framework, based on 8 measures of the line smoothing effectiveness tied to 8 low-level visual analytics tasks. We then analyze 12 methods coming from 4 commonly used classes of line chart smoothing-rank filters, convolutional filters, frequency domain filters, and subsampling. The results show that while no method is ideal for all situations, certain methods, such as Gaussian filters and TOPOLOGY-based subsampling, perform well in general. Other methods, such as low-pass CUTOFF filters and Douglas-peucker subsampling, perform well for specific visual analytics tasks. Almost as importantly, our framework demonstrates that several methods, including the commonly used UNIFORM subsampling, produce low-quality results, and should, therefore, be avoided, if possible.

A Design Space of Vision Science Methods for Visualization Research

A growing number of efforts aim to understand what people see when using a visualization. These efforts provide scientific grounding to complement design intuitions, leading to more effective visualization practice. However, published visualization research currently reflects a limited set of available methods for understanding how people process visualized data. Alternative methods from vision science offer a rich suite of tools for understanding visualizations, but no curated collection of these methods exists in either perception or visualization research. We introduce a design space of experimental methods for empirically investigating the perceptual processes involved with viewing data visualizations to ultimately inform visualization design guidelines. This paper provides a shared lexicon for facilitating experimental visualization research. We discuss popular experimental paradigms, adjustment types, response types, and dependent measures used in vision science research, rooting each in visualization examples. We then discuss the advantages and limitations of each technique. Researchers can use this design space to create innovative studies and progress scientific understanding of design choices and evaluations in visualization. We highlight a history of collaborative success between visualization and vision science research and advocate for a deeper relationship between the two fields that can elaborate on and extend the methodological design space for understanding visualization and vision.

Modeling the Influence of Visual Density on Cluster Perception in Scatterplots Using Topology

Scatterplots are used for a variety of visual analytics tasks, including cluster identification, and the visual encodings used on a scatterplot play a deciding role on the level of visual separation of clusters. For visualization designers, optimizing the visual encodings is crucial to maximizing the clarity of data. This requires accurately modeling human perception of cluster separation, which remains challenging. We present a multi-stage user study focusing on four factors-distribution size of clusters, number of points, size of points, and opacity of points-that influence cluster identification in scatterplots. From these parameters, we have constructed two models, a distance-based model, and a density-based model, using the merge tree data structure from Topological Data Analysis. Our analysis demonstrates that these factors play an important role in the number of clusters perceived, and it verifies that the distance-based and density-based models can reasonably estimate the number of clusters a user observes. Finally, we demonstrate how these models can be used to optimize visual encodings on real-world data.

Synergy between research on ensemble perception, data visualization, and statistics education: A tutorial review

In the age of big data, we are constantly inventing new data visualizations to consolidate massive amounts of numerical information into smaller and more digestible visual formats. These data visualizations use various visual features to convey quantitative information, such as spatial position in scatter plots, color saturation in heat maps, and area in dot maps. These data visualizations are typically composed of ensembles, or groups of related objects, that together convey information about a data set. Ensemble perception, or one's ability to perceive summary statistics from an ensemble, such as the mean, has been used as a foundation for understanding and explaining the effectiveness of certain data visualizations. However, research in data visualization has revealed some perceptual biases and conceptual difficulties people face when trying to utilize the information in these graphs. In this tutorial review, we will provide a broad overview of research conducted in ensemble perception, discuss how principles of ensemble encoding have been applied to the research in data visualization, and showcase the barriers graphs can pose to learning statistical concepts, using histograms as a specific example. The goal of this tutorial review is to highlight possible connections between three areas of research-ensemble perception, data visualization, and statistics education-and to encourage research in the practical applications of ensemble perception in solving real-world problems in statistics education.

The relation between color and spatial structure for interpreting colormap data visualizations

Interpreting colormap visualizations requires determining how dimensions of color in visualizations map onto quantities in data. People have color-based biases that influence their interpretations of colormaps, such as a dark-is-more bias—darker colors map to larger quantities. Previous studies of color-based biases focused on colormaps with weak data spatial structure, but color-based biases may not generalize to colormaps with strong data spatial structure, like “hotspots” typically found in weather maps and neuroimaging brain maps. There may be a hotspot-is-more bias to infer that colors within hotspots represent larger quantities, which may override the dark-is-more bias. We tested this possibility in four experiments. Participants saw colormaps with hotspots and a legend that specified the color-quantity mapping. Their task was to indicate which side of the colormap depicted larger quantities (left/right). We varied whether the legend specified dark-more mapping or light-more mapping across trials and operationalized a dark-is-more bias as faster response time (RT) when the legend specified dark-more mapping. Experiment 1 demonstrated robust evidence for the dark-is-more bias, without evidence for a hotspot-is-more bias. Experiments 2 to 4 suggest that a hotspot-is-more bias becomes relevant when hotspots are a statistically reliable cue to “more” (i.e., the locus of larger quantities) and when hotspots are more perceptually pronounced. Yet, comparing conditions in which the hotspots were “more,” RTs were always faster for dark hotspots than light hotspots. Thus, in the presence of strong spatial cues to the locus of larger quantities, color-based biases still influenced interpretations of colormap data visualizations.

The misuse of colour in science communication

The accurate representation of data is essential in science communication. However, colour maps that visually distort data through uneven colour gradients or are unreadable to those with colour-vision deficiency remain prevalent in science. These include, but are not limited to, rainbow-like and red-green colour maps. Here, we present a simple guide for the scientific use of colour. We show how scientifically derived colour maps report true data variations, reduce complexity, and are accessible for people with colour-vision deficiencies. We highlight ways for the scientific community to identify and prevent the misuse of colour in science, and call for a proactive step away from colour misuse among the community, publishers, and the press.

Exploring Casual COVID-19 Data Visualizations on Twitter: Topics and Challenges

Social networking sites such as Twitter have been a popular choice for people to express their opinions, report real-life events, and provide a perspective on what is happening around the world. In the outbreak of the COVID-19 pandemic, people have used Twitter to spontaneously share data visualizations from news outlets and government agencies and to post casual data visualizations that they individually crafted. We conducted a Twitter crawl of 5409 visualizations (from the period between 14 April 2020 and 9 May 2020) to capture what people are posting. Our study explores what people are posting, what they retweet the most, and the challenges that may arise when interpreting COVID-19 data visualization on Twitter. Our findings show that multiple factors, such as the source of the data, who created the chart (individual vs. organization), the type of visualization, and the variables on the chart influence the retweet count of the original post. We identify and discuss five challenges that arise when interpreting these casual data visualizations, and discuss recommendations that should be considered by Twitter users while designing COVID-19 data visualizations to facilitate data interpretation and to avoid the spread of misconceptions and confusion.

Measuring the Effects of Scalar and Spherical Colormaps on Ensembles of DMRI Tubes

We report empirical study results on the color encoding of ensemble scalar and orientation to visualize diffusion magnetic resonance imaging (DMRI) tubes. The experiment tested six scalar colormaps for average fractional anisotropy (FA) tasks (grayscale, blackbody, diverging, isoluminant-rainbow, extended-blackbody, and coolwarm) and four three-dimensional (3D) spherical colormaps for tract tracing tasks (uniform gray, absolute, eigenmaps, and Boy's surface embedding). We found that extended-blackbody, coolwarm, and blackbody remain the best three approaches for identifying ensemble average in 3D. Isoluminant-rainbow colormap led to the same ensemble mean accuracy as other colormaps. However, more than 50 percent of the answers consistently had higher estimates of the ensemble average, independent of the mean values. The number of hues, not luminance, influences ensemble estimates of mean values. For ensemble orientation-tracing tasks, we found that both Boy's surface embedding (greatest spatial resolution and contrast) and absolute colormaps (lowest spatial resolution and contrast) led to more accurate answers than the eigenmaps scheme (medium resolution and contrast), acting as the uncanny-valley phenomenon of visualization design in terms of accuracy. Absolute colormap broadly used in brain science is a good default spherical colormap. We could conclude from our study that human visual processing of a chunk of colors differs from that of single colors.

Color Crafting: Automating the Construction of Designer Quality Color Ramps

Visualizations often encode numeric data using sequential and diverging color ramps. Effective ramps use colors that are sufficiently discriminable, align well with the data, and are aesthetically pleasing. Designers rely on years of experience to create high-quality color ramps. However, it is challenging for novice visualization developers that lack this experience to craft effective ramps as most guidelines for constructing ramps are loosely defined qualitative heuristics that are often difficult to apply. Our goal is to enable visualization developers to readily create effective color encodings using a single seed color. We do this using an algorithmic approach that models designer practices by analyzing patterns in the structure of designer-crafted color ramps. We construct these models from a corpus of 222 expert-designed color ramps, and use the results to automatically generate ramps that mimic designer practices. We evaluate our approach through an empirical study comparing the outputs of our approach with designer-crafted color ramps. Our models produce ramps that support accurate and aesthetically pleasing visualizations at least as well as designer ramps and that outperform conventional mathematical approaches.

Estimating Color-Concept Associations from Image Statistics

To interpret the meanings of colors in visualizations of categorical information, people must determine how distinct colors correspond to different concepts. This process is easier when assignments between colors and concepts in visualizations match people's expectations, making color palettes semantically interpretable. Efforts have been underway to optimize color palette design for semantic interpretablity, but this requires having good estimates of human color-concept associations. Obtaining these data from humans is costly, which motivates the need for automated methods. We developed and evaluated a new method for automatically estimating color-concept associations in a way that strongly correlates with human ratings. Building on prior studies using Google Images, our approach operates directly on Google Image search results without the need for humans in the loop. Specifically, we evaluated several methods for extracting raw pixel content of the images in order to best estimate color-concept associations obtained from human ratings. The most effective method extracted colors using a combination of cylindrical sectors and color categories in color space. We demonstrate that our approach can accurately estimate average human color-concept associations for different fruits using only a small set of images. The approach also generalizes moderately well to more complicated recycling-related concepts of objects that can appear in any color.

Common Fate for Animated Transitions in Visualization

The Law of Common Fate from Gestalt psychology states that visual objects moving with the same velocity along parallel trajectories will be perceived by a human observer as grouped. However, the concept of common fate is much broader than mere velocity; in this paper we explore how common fate results from coordinated changes in luminance and size. We present results from a crowdsourced graphical perception study where we asked workers to make perceptual judgments on a series of trials involving four graphical objects under the influence of conflicting static and dynamic visual factors (position, size and luminance) used in conjunction. Our results yield the following rankings for visual grouping: motion > (dynamic luminance, size, luminance); dynamic size > (dynamic luminance, position); and dynamic luminance > size. We also conducted a follow-up experiment to evaluate the three dynamic visual factors in a more ecologically valid setting, using both a Gapminder-like animated scatterplot and a thematic map of election data. The results indicate that in practice the relative grouping strengths of these factors may depend on various parameters including the visualization characteristics and the underlying data. We discuss design implications for animated transitions in data visualization.

Evaluating Perceptual Bias During Geometric Scaling of Scatterplots

Scatterplots are frequently scaled to fit display areas in multi-view and multi-device data analysis environments. A common method used for scaling is to enlarge or shrink the entire scatterplot together with the inside points synchronously and proportionally. This process is called geometric scaling. However, geometric scaling of scatterplots may cause a perceptual bias, that is, the perceived and physical values of visual features may be dissociated with respect to geometric scaling. For example, if a scatterplot is projected from a laptop to a large projector screen, then observers may feel that the scatterplot shown on the projector has fewer points than that viewed on the laptop. This paper presents an evaluation study on the perceptual bias of visual features in scatterplots caused by geometric scaling. The study focuses on three fundamental visual features (i.e., numerosity, correlation, and cluster separation) and three hypotheses that are formulated on the basis of our experience. We carefully design three controlled experiments by using well-prepared synthetic data and recruit participants to complete the experiments on the basis of their subjective experience. With a detailed analysis of the experimental results, we obtain a set of instructive findings. First, geometric scaling causes a bias that has a linear relationship with the scale ratio. Second, no significant difference exists between the biases measured from normally and uniformly distributed scatterplots. Third, changing the point radius can correct the bias to a certain extent. These findings can be used to inspire the design decisions of scatterplots in various scenarios.

Discriminability Tests for Visualization Effectiveness and Scalability

The scalability of a particular visualization approach is limited by the ability for people to discern differences between plots made with different datasets. Ideally, when the data changes, the visualization changes in perceptible ways. This relation breaks down when there is a mismatch between the encoding and the character of the dataset being viewed. Unfortunately, visualizations are often designed and evaluated without fully exploring how they will respond to a wide variety of datasets. We explore the use of an image similarity measure, the Multi-Scale Structural Similarity Index (MS-SSIM), for testing the discriminability of a data visualization across a variety of datasets. MS-SSIM is able to capture the similarity of two visualizations across multiple scales, including low level granular changes and high level patterns. Significant data changes that are not captured by the MS-SSIM indicate visualizations of low discriminability and effectiveness. The measure's utility is demonstrated with two empirical studies. In the first, we compare human similarity judgments and MS-SSIM scores for a collection of scatterplots. In the second, we compute the discriminability values for a set of basic visualizations and compare them with empirical measurements of effectiveness. In both cases, the analyses show that the computational measure is able to approximate empirical results. Our approach can be used to rank competing encodings on their discriminability and to aid in selecting visualizations for a particular type of data distribution.

A Study of Colormaps in Network Visualization

Color is a widely used visual channel for encoding data in visualization design. It is important to select the appropriate type of color mapping to better understand the data. While several studies have investigated the effects of colormaps in various types of information visualization, there have been no studies on their effects on network visualization. Thus, in this paper, we investigate the effects of several colormaps in network visualization using node-link diagrams. Specifically, we compare four different single- and multi-hue colormaps for node attributes, and evaluate their effectiveness in terms of task completion time and correctness rate. Our results show that participants complete their tasks significantly faster with blue (single-hue, sequential) as compared to viridis (multi-hue, sequential), RdYlBu (divergent, red-yellow-blue), and jet (rainbow) colormaps. Additionally, the overall correctness rate shows significant differences between colormaps, with viridis being the least error-prone among the colormaps studied.

Measuring and Modeling the Feature Detection Threshold Functions of Colormaps

Pseudocoloring is one of the most common techniques used in scientific visualization. To apply pseudocoloring to a scalar field, the field value at each point is represented using one of a sequence of colors (called a colormap). One of the principles applied in generating colormaps is uniformity and previously the main method for determining uniformity has been the application of uniform color spaces. In this paper we present a new method for evaluating the feature detection threshold function across a colormap. The method is used in crowdsourced studies for the direct evaluation of nine colormaps for three feature sizes. The results are used to test the hypothesis that a uniform color space (CIELAB) will accurately model colormapped feature detection thresholds compared to a model where the chromaticity components have reduced weights. The hypothesis that feature detection can be predicted solely on the basis of luminance is also tested. The results reject both hypotheses and we demonstrate how reduced weights on the green-red and blue-yellow terms of the CIELAB color space creates a more accurate model when the task is the detection of smaller features in colormapped data. Both the method itself and modified CIELAB can be used in colormap design and evaluation.

Stippling of 2D Scalar Fields

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.

Correlation Judgment and Visualization Features: A Comparative Study

Recent visualization research efforts have incorporated experimental techniques and perceptual models from the vision science community. Perceptual laws such as Weber's law, for example, have been used to model the perception of correlation in scatterplots. While this thread of research has progressively refined the modeling of the perception of correlation in scatterplots, it remains unclear as to why such perception can be modeled using relatively simple functions, e.g., linear and log-linear. In this paper, we investigate a longstanding hypothesis that people use visual features in a chart as a proxy for statistical measures like correlation. For a given scatterplot, we extract 49 candidate visual features and evaluate which best align with existing models and participant judgments. The results support the hypothesis that people attend to a small number of visual features when discriminating correlation in scatterplots. We discuss how this result may account for prior conflicting findings, and how visual features provide a baseline for future model-based approaches in visualization evaluation and design.