Color Crafting: Automating the Construction of Designer Quality Color Ramps

TL;DR

This paper introduces an algorithmic method to automatically generate high-quality color ramps for visualizations by modeling expert designer practices from a corpus of 222 ramps, improving upon traditional mathematical approaches.

Contribution

It presents a novel data-driven approach that learns from expert-designed color ramps to automate the creation of effective, aesthetically pleasing color schemes for data visualization.

Findings

Models produce ramps supporting accurate visualizations

Generated ramps outperform conventional mathematical methods

Approach supports novice visualization developers

Abstract

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.

Equations

$$w\times f_{SRVF}(c_i,c_j)+(1-w)\times |L(c_i)-L(c_j)|$$

$$\frac{1}{n(n-1)}\sum _{i=1}^n\sum _{j=1}^n\sum _{x=1}^{l}dist(c_i(x),c_j(x))$$

$$c^{\prime }(x)=\frac{{\sum }_{i=1}^n{c}_i(x)}{n}$$

Full text

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K.6.1Management of Computing and Information SystemsProject and People ManagementLife Cycle; \CCScatK.7.mThe Computing ProfessionMiscellaneousEthics

\teaser

Our approach uses design mining and unsupervised clustering techniques to produce automatically generated color ramps that capture designer practices. The four choropleth maps shown above utilize color ramps generated from our approach. Developers select a single guiding seed color, shown in the squares below each map, to generate a ramp. We then fit curves capturing structural patterns in designer practices in CIELAB (bottom) to these seed colors to generate ramps (middle, seed colors indicated by a black dot). We embody this technique in Color Crafter, a web-based tool that enables designers of all ability levels to generate high-quality custom color ramps.

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1 Introduction

Visualizations commonly use color ramps to encode ordered or continuous numeric data. The specific colors used in a given visualization determine how accurately that visualization communicates the underlying data and influence subjective impressions of a visualization, such as affect [6], topical alignment [30, 41], and aesthetic quality [37]. Heuristics for constructing effective encodings have evolved from years of experience by designers. However, these heuristics are often qualitative, ill-defined, and require sufficient expertise to implement. For example, Sloan & Brown [70] recommends that color ramps should use “a set of colors with an easily remembered order.” While recent efforts mathematically formalize these heuristics into constraints (e.g., Bujack et al. [12]), these formalizations still require substantial manual guiding to get from abstract constraints to concrete encodings. Novice visualization designers are currently left with two choices for generating color ramps: to rely on their limited intuitions to craft color ramps of unverified quality or to choose from a small, predefined set of high-quality ramps in tools such as ColorBrewer [27].

Existing approaches assert that crafting effective color ramps requires substantial color design expertise and recommend that those lacking this experience should instead draw from preconstructed ramps [83, 64]. However, this approach restricts the set of available ramps to a small, finite collection, limiting the designers’ agency and control in creating their visualizations. These limitations are especially prohibitive in situations where specific colors, such as brand colors or semantically meaningful colors [41] are required. Our work aims to give visualization designers of all skill levels an easy way to craft custom designer-quality color ramps. Rather than build up from quantified heuristics, we achieve this goal by modeling designer practices to automatically generate high-quality color ramps from a single seed color. We mine characteristic structures that a ramp’s sequence of colors traverse in a perceptual color space. These structures capture key variations and patterns that are often overlooked by or difficult to describe using conventional heuristics.

Color ramps traverse an ordered path through color space that can be modeled as a curve. Common approaches to generating these ramps require designers to select two or more control points and interpolate these control points along either a linear path [51, 11] or spline [5]. More sophisticated approaches use heuristics from designer practices as constraints applied to interpolating these control points [83, 77, 8]. However, these approaches require formalizing a sufficiently complete set of heuristics and rely heavily on the control points to determine the length and direction of the path traversed by the ramp. Our discussions with designers and preliminary analyses of handcrafted ramps reveal features of handcrafted ramps not well-captured by these heuristics (Figure 1). Our approach instead builds on the ground truth practices embodied by handcrafted designs to generate a set of curves modeling designer practices, including the direction and structure of colors within the ramp. Designers can seed these curves using a single desired color to generate a collection of ramps reflecting expert practices (Figure Color Crafting: Automating the Construction of Designer Quality Color Ramps).

We generate models of common design practices in ramps through design mining: using knowledge discovery techniques to understand design demographics, automate design curation, and support data-driven design tools [34]. We assembled and mined a repository of 222 designer-crafted color ramps from popular visualization tools and used these ramps as inputs to two clustering algorithms to construct models that capture common design patterns. Our models represent the continuous paths color encodings traverse in color space in order to capture structural features used by designers such as the twists and kinks in the designer curves shown in Figure 1. These continuous paths, modeled as interpolating cubic B-spline curves in CIELAB, can be anchored in color space by seeding each curve with a single guiding color and interpolating around this color to construct a set of ramps. We embed these models in Color Crafter, a tool that allows visualization developers to specify individual seed colors to automatically generate high-quality color ramps. Developers can edit these ramps by freely rotating, translating, and scaling the seeded curve models in CIELAB.

We conducted a crowdsourced experiment with designers to compare ramps generated using our approach to both designer-crafted and linearly interpolated ramps. Our experiment measures how accurately people can identify values using color-coded scatterplots, heatmaps, and choropleth maps as well as the aesthetic value of each visualization. Our findings show that our automatically-generated color ramps perform at least as well as designer color ramps at supporting accurate interpretation and positive aesthetics and outperform linear approaches used in common tools. We also show how this approach can readily reproduce common designer ramps (Figure 9) and create high-quality ramps with traditionally “ugly” colors (Figure 10). The clusters and models from our approach open new directions for future work in understanding what makes encodings effective, including a theoretical evaluation of the structures modeled and missed by our approach.

Contributions: Our primary contribution is an approach to automate the construction of color ramps that provide high data interpretation accuracy and aesthetic value. Our approach models designer practices by capturing key features of the paths that designer-crafted color ramps traverse through color space. This approach allows novice visualization developers to readily craft high-quality ramps. We evaluate this approach in a formal experimental evaluation with expert designers and pair of use cases illustrating the utility of our approach. We embody these results in Color Crafter, an interactive tool for color ramp construction and editing.

2 Related Work

Building effective color ramps requires an understanding of human visual perception as well as the effect of aesthetics in visualization. While the terminology used to describe color encodings varies across the literature, we refer to colormaps as any set of colors used to encode data. Color palettes use discrete colors to encode categorical data while color ramps use sequential or diverging colors to encode quantitative data. We survey prior work related to color perception and aesthetics in visualization to inform our work. We also discuss common guidelines and current techniques for constructing color encodings and recent methods for design mining and automation in visualization.

2.1 Color Perception and Aesthetics in Visualization

Color ramps sample colors along a continuous path through a color space. These spaces provide mathematical representations that allow designers to computationally reason about the relationship between colors. There are artistic color spaces that focus on intuitive parameters of aesthetics (e.g., HSV [24, 23]) and perceptually-based spaces derived from empirical studies of color difference perceptions (e.g., CIELUV and CIELAB [13, 49]). Heer & Stone [28] developed models for color naming that enhance visualizations by leveraging the link between visual perception and symbolic cognition. Other models attempt to balance both perceptual and artistic approaches (e.g., Munsell [35]) or to increase the precision with which they approximate perception (e.g., CIE94 [47] and CIECAM02 [55]). However, these models introduce non-euclidean components that make it difficult to interpolate across. Zeyen et al. [89] present a method for interpolating in non-Euclidean color spaces. While these models correct for imprecisions in color spaces, their increased complexity is a trade-off that designers often consider reasonable for visualization applications [21].

Empirical studies of color perception in data visualizations evaluate several different aspects of color’s utility (see Kovesi [33] and Silva et al. [69] for surveys). Several such studies focus on individual features of color perception. For example, Cleveland & McGill [15] found that different color channels communicate data less precisely than other visual channels such as size and position. MacEachren et al. [45] measure the effectiveness of color and other channels at communicating uncertainty in visualizations. Others studies measure how visual channels such as size [74] and shape [71] affect color perception.

Other work evaluates full color encodings such as evaluating performance across different color ramps and palettes [44, 6, 82, 81, 17]. For example, Padilla et al. [57] assess trade-offs in binning color ramps, finding that binned ramps often allow analysts to more accurately estimate values in visualizations. Correll et al. [16] show how manipulating ramp structure can support uncertainty estimation. Schloss et al. [66] found that the background color in a visualization affects the inferred color mapping between color ramps and data, depending on whether the color ramp varies in apparent opacity. Liu & Heer [44] evaluate how different design parameters, such as color name and perceptual distance, influence encoding accuracy for popular color ramps. These studies provide grounded perceptual insight into aspects of effective color encodings that designers can draw upon when creating encodings.

However, leveraging color perception alone is insufficient to create high-quality color ramps. Visual aesthetics significantly affect factors such as the perceived usability, satisfaction, and pleasure related to a visual representation [56]. Several models of aesthetics in visualization have been proposed. These models identify general aspects of aesthetic that are key to positive perceptions of a visualization [37, 22, 36, 56, 7]. Palmer et al. [59] surveys the aesthetic preferences that have been empirically studied in cognitive science. For example, Western individuals generally prefer cooler colors such as blue and green over warmer colors such as red and orange [29, 43] and more saturated colors compared to less saturated colors [58]. These effects change according to demographic factors such as age, gender, and culture [59]. Professional designers use knowledge from aesthetic studies to build pleasurable and engaging color encodings. However, models of aesthetic preference focus more on evaluating rather than generating effective visualizations. Our approach allows us to capture aspects of aesthetics functionally embedded into encodings by designers.

2.2 Guidelines and Techniques

Approaches to color ramp design combine aspects of color perception and aesthetics. Guidelines about what makes color ramps effective are often derived from designer experience or empirical data (see Bujack et al [12] and Zhou & Hansen [92] for surveys). These guidelines can be either perceptual (e.g., colors should be discriminable) or aesthetic (e.g., colors should be harmonious). For example, Brewer [10] offers qualitative perceptual and aesthetic considerations for designing effective encodings based on her own practices. Tools such as ColorMeasures [12] and colorspace [87] use mathematical abstractions of such guidelines to provide quantitative insight into colormap quality.

Perceptual guidelines emphasize ways to make ramps intuitively mirror the underlying data. Sloan & Brown [70] stress that colors in a ramp should be maximally distinguishable and follow an easily remembered order. Wainer & Francolini [79] note that defining an intuitive order can be challenging. Trumbo [78] explains that an effective univariate color ramp should have an ordering in one or more retinal variables and contain sufficient separation between colors. Levkowitz & Herman [40] emphasize a need for perceptual uniformity: the concept that colors should convey the differences between the values they are representing. Zhang & Montag [90] evaluate the performance of colormaps constructed in CIELAB and stress the importance of perceptual uniformity. Mittelstädt et al. [50, 52] states that high discriminative power is important for effective color ramps and that highly saturated colors help achieve this goal.

Aesthetic guidelines help designers consider how colors might work together to increase the appeal of visualizations. For example, Meier et al. [48] recommend using harmonious colors that are not limited to a single planar slice of the HSV color space. Moreland [53] describes ways to utilize aspects of color such as hue and saturation to create aesthetically pleasing diverging color ramps. Zeileis et al. [88] offers advice for choosing colors that are appealing, cooperate with each other, and work in any context. Schloss & Palmer [67] identify preferable color pairs by decomposing empirical factors in aesthetic preference. Most of these design guidelines are qualitatively defined, involve explicit trade-offs between aesthetics and perception, and require considering the context of a visualization and sophisticated knowledge of color spaces to implement correctly.

In practice, many conventional guidelines, such as a preference towards linearity or uniform differences [39, 40, 61, 75] may not be followed by experts [10]. This deviation makes it complex for less experienced designers to utilize these guidelines for building effective color ramps. Several tools have been developed to aid visualization developers in using color. Samsel et al. [65] leverages the author’s artistic experience to craft ramps explicitly for earth science data. ColorBrewer [27] is a widely-used tool for delivering high-quality color ramps for both categorical and ordered encodings. Models in ColorBrewer were manually crafted using expert knowledge to select and adjust colors over perceptually-ordered spaces.

Other tools aim to support visualization developers in crafting color encodings. For example, Wijffelaars et al. [83] developed a technique to construct univariate lightness-ordered color ramps as curves parameterized according to qualitative observations of designer ramps. Tominski et al. [77] describes a color encoding technique that maximizes effectiveness with respect to specific visualization tasks such as comparison, localization, and identification. ColorCAT [51] uses constraints regarding analysis tasks and color-vision deficiencies to select colors and linearly interpolates these colors in CIECAM02. Tools such as Colorgorical [26], PRAVDAColor [8], Tree Colors [76], iWantHue [3], and VizPalettes [4] use rule-based methods to help craft color encodings that adhere to design guidelines. These approaches allow visualization designers to construct effective encodings; however, they generally require designers to manually specify multiple control points or to tune automatically generated parameters. Generally speaking, increasing the points and parameters necessary to generate an encoding exchanges flexibility for simplicity: designers require more expertise to effectively use the tool. Further, these approaches do not capture nuanced elements of designer practices, such as the features in Figure 1. In this work, we hope to simplify the visualization design process for designers of all skill levels using a design-mining approach that models designer practices without the need for a precise translation from design practice to mathematical rules.

2.3 Automated Design & Design Mining in Visualization

Automating the visualization design process computationally applies design guidelines to generate effective visualizations. Many tools and methods exist for automating or aiding particular aspects of visualization design such as computing mappings between data and predefined colormaps [62, 42, 38], general perceptual optimization [18], chart type selection [80], and transfer function design [68]. Other tools and methods focus on fully or partially automating the visualization design process [32, 20]. For example, Mackinlay [46] developed an application-independent tool that uses expressiveness and effectiveness principles to automatically build effective visualizations. Wongsuphasawat et al [84, 85, 86] created Voyager, a system that uses both manual and automated chart specification to support data analysis. Draco [54] uses a set of constraints derived from empirical studies in visualizations to formalize visualization design knowledge.

These tools and methods effectively automate several aspects of visualization design. However, some design principles, especially related to aesthetics, are less understood and are difficult to define mathematically. We can instead use data mining principles to computationally infer these principles from existing artifacts, a concept known as design mining [34]. For example, Jahanian et al. leverage design mining to model color semantics from magazine cover designs [30] and visual balance from aesthetically pleasing photographs [31]. Samsel et al. [63] use color schemes from well-known paintings to generate more engaging and expressive scientific visualizations. Our approach builds on these works, utilizing the principles of design mining to infer aspects of color ramp design directly from high-quality examples.

3 Modeling Designer Practice

To allow visualization developers of all skill levels to easily craft high-quality color ramps, we developed an approach that models designer practices by analyzing the general structure of the continuous curves that designer-crafted color ramps traverse through color space. Mathematically, color ramps are an ordered list of points in a three-dimensional space. By treating color ramps as continuous curves fit through the individual colors in a source ramp, we can analyze the relationships between colors and the general structure that designers craft when creating high-quality ramps. While prior approaches have used qualitative observations of curve structures in ramps to formulate explicit constraints on encoding design [5, 83, 8], we instead use a design mining approach to implicitly model designer practices to generate color ramps using techniques from unsupervised machine learning. This approach first computes a set of normalized curves from a corpus of designer ramps. We cluster these curves according to their structural patterns and generate representative curves for each cluster. We anchor these representative curves in color space using a seeding color positioned according to the luminance distribution of the component curves to generate the final ramp. Once seeded, users can optionally edit ramps by applying standard affine transforms (i.e., rotating, translating, reflecting, and scaling) to the seeded curves.

Our approach can be described in five major steps (Figure 2):

Corpus Construction 2. 2.

Curve Normalization 3. 3.

Curve Clustering 4. 4.

Model Construction 5. 5.

Seeding

3.1 Corpus Construction

Our algorithm uses designer crafted ramps as input data to construct models of effective design. We manually assembled a corpus of 222 unique designer-crafted color ramps from known high-quality sources to provide a ground truth dataset. This corpus contains 53 ramps from ColorBrewer [27], 20 ramps from R,111https://www.r-project.org/ 31 ramps from Tableau,222https://www.tableau.com/ and 118 ramps from the online designer community ColourLovers333https://www.colourlovers.com/. As ColourLovers is not exclusively for visualization, we only selected color sets that reflected an ordered linear or diverging series of values. This corpus is available at https://tinyurl.com/colorcrafting.

42 of the 222 were diverging color ramps, while 180 were sequential color ramps. We construct our primary models using the sequential ramps and use additional data from the diverging ramps to provide supplementary parameters for generating diverging ramps (c.f. §3.6).

3.2 Curve Normalization

The hand-crafted ramps in our corpus contained between 5 and 13 colors. To provide uniform inputs into our clustering algorithms, we resampled these ramps to normalize the number of color points per ramp. We first fit an interpolating cubic B-spline 444[https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/

scipy.interpolate.splprep.html](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/%5C%5C%0Ascipy.interpolate.splprep.html) through the colors of each ramp in CIELAB. The original ramp colors acted as control points to guide the curve fitting. We then used arc length interpolation to select nine equidistant points along each curve as the colors in our normalized ramps. We chose nine colors as we wish to provide as many control points for our input curves as is reasonable to retain fine-grained features. Designers have previously found nine colors to be a reliable upper bound for the number of perceptually distinct colors in sequential ramps [27]. We use the normalized curves as inputs to a set of clustering functions to elicit common design patterns across ramps.

3.3 Curve Clustering

We observed common design patterns occurring across subsets of ramps, such as characteristic twists in hue space or smaller changes in chroma at the ends of ramps (Figure 1). Key features of these patterns are difficult to express mathematically, but are salient in the structures ramps traverse through color space. Our models aim to capture these structures in order to replicate designer practices in constructing color encodings. We cluster the normalized curves computed from our corpus according to different aspects of their shape to group color ramps with similar structures. We compute these clusters agnostic of the specific colors used in order to elicit common relative relationships between colors regardless of where those specific colors reside in color space. We used two different unsupervised clustering techniques: one that uses elastic shape descriptors to match weighted features of the curve structures (Bayesian curve clustering [91]) and a second that uses structural features related to known color ramp heuristics (k-means clustering).

3.3.1 Bayesian Clustering

Our Bayesian clustering approach leverages the algorithm introduced in Zhang et al. [91] which uses an elastic shape metric—the square root velocity function, or $SRVF$ [72] —to compute structural relationships between curves. One advantage of this clustering algorithm is that it infers the number of clusters rather than needing to specify a number a priori, allowing natural structural patterns to emerge from the data. The algorithm infers these clusters by computing a posterior distribution on the number of clusters through a Markov Chain Monte Carlo procedure based on the Chinese restaurant process [60].

While this metric focuses on structural features, one challenge of applying this algorithm to color ramps is that the clustering is designed to be scale invariant (i.e., all curves are scaled to the same length). In color ramps, the length of a curve corresponds with the difference between adjacent colors, a critical component of discriminability. To include curve length in the clustering, we adapted the algorithm to use a weighted sum of both the original shape invariant metric and an added term, $L$, reflecting the curve length. $L$ was computed by summing the distance (in absolute $\Delta E$) between each color in the ramp. $f_{SRVF}$ represents the distance metric described in Zhang et al. [91] which calculates the difference between $SRVF$ values for a pair of curves, $c_{i}$ and $c_{j}$. The resulting algorithm computes the distance between any two color ramp curves, $c_{i}$ and $c_{j}$, as:

[TABLE]

To find the optimal $w$, we clustered the set of color ramps using ten different values for $w$: 0.0 to 1.0 in 0.1 step increments. For each value of $w$, we evaluated the clustering result by computing the tightness—mean summed distance between corresponding control points —of each cluster. To compute the tightness of a cluster, first we aligned all of the curves within each cluster by translating each curve to a common starting point, rotating each curve such that the curves are oriented in the same direction (i.e., the vector passing through each curve’s first and middle control color point in the same direction), and, if needed, reflecting the curve with respect to this aligned vector to minimize the distance between other curves in the cluster. As we cluster based on color-agnostic structures in the curves, this reflection allows us to cluster curves of different handedness [81]. Tightness is computed as:

[TABLE]

where $c_{i}$ and $c_{j}$ correspond to ramps in the cluster, $c(x)$ is the current control point color in the aligned ramp, $n$ is the number of ramps in the cluster, $l$ is the number of control point colors in a normalized ramp ($l=9$ for our implementation), and $dist$ computes the Euclidean distance between two corresponding colors. After running this clustering algorithm for the ten tested $w$ values, $w=0.5$ resulted in the tightest clusters. This weight balances length and shape equally, whereas smaller $w$ more heavily considers ramp lengths (correlating with bias towards relative discriminability) and larger favors shape (correlating with bias towards relative aesthetic). The algorithm generated 9 clusters of between 5 and 42 ramps.

3.3.2 K-means Clustering

While the Bayesian clustering approach leverages elastic shape descriptors to cluster curves based on their overall structures, many established heuristics for color ramps explicitly consider features related to the structure of the ramp. For example, discriminability correlates to the distance between sampled color points along the ramp’s curve. To prioritize these structural features, we computed a second set of clusters using k-means clustering, where the features used to compute clusters correspond to common design recommendations selected from Bujack et al. [12] and qualitative observations of our corpus. This approach pairs implicit and explicit features of ramp design, allowing us to analyze curves based on how designers implement guiding heuristics while measuring cluster quality using our tightness metric captures residual aspects of structural similarity outside of these heuristics.

We computed eight features describing various curve characteristics:

Local Angles: The angle between each color, which captures local variations in curve trajectory 2. 2.

Sum of Angles: Sum of all angles between adjacent colors, approximating overall trajectory 3. 3.

Local Discriminability: Distance between each set of adjacent colors in $\Delta E$ 4. 4.

Length: Sum of all distances between adjacent colors in $\Delta E$ 5. 5.

Speed: First derivative of the curve at each color 6. 6.

Acceleration: Second derivative of the curve at each color 7. 7.

Curvature: Curvature of the curve approximated as $1/r$, where $r$ corresponds to the radius of the sphere of best fit to the 3D curve 8. 8.

Turning Points: Number of local minima and maxima in the curve. This metric captures small-scale variations and “kinks” in the curve not well modeled by conventional heuristics

We then conducted an exhaustive feature selection by computing 255 feature vectors for each curve for $k\in[2,15]$, with larger $k$ preserving finer differences between models. We evaluate each cluster configuration using tightness as described in Section 3.3.1. For our corpus, the ideal configuration of clusters set $k=9$ and used the sum of angles between curve control colors, length, curvature, and number of turning points as features.

3.4 Model Construction

Each cluster produced from the approaches described in Sections 3.3.1 and 3.3.2 captures a specific design pattern found in expert-crafted ramps. We model these patterns by constructing a representative curve for each cluster that we can then use to generate ramps reflecting each pattern. We first align and reflect the curves within a cluster using the approach described in Section 3.3.1. We then construct a representative curve by computing the mean curve from the set of aligned curves in each cluster. We compute the mean curve as the mean relative position of each control point:

[TABLE]

where $c_{i}(x)$ is the $x$th color in ramp $i$ and $c^{\prime}(x)$ is the $x$th control point color in the representative curve. While averaging can compress variation from extremely long or high curvature ramps, characteristic curves tend to qualitatively align well with component curves while making it easier to keep seeded models inside of the gamut. Manual editing can enhance these characteristic curves during ramp design.

3.5 Seeding

Aligning the clustered curves before computing the representative curve means that representative curves capture relative structures measured in CIELAB: control points reflect the relationship between adjacent colors including the distances and angles between points and the global curve trajectory, but not the actual values of those colors. We can anchor these curves in color space by seeding the model using a single target color. We refer to this color as a seed color.

We use a user-specified seed color to translate the representative model curves to a desired region of color space. As design guidelines heavily emphasize luminance variations in ramp design [10], we first anchor the $L^{*}$ distribution of the representative curve by translating in $L^{*}$ to match the average $L^{*}$ distribution within the corresponding cluster. We fit a representative curve to a seed color by translating the curve in $L^{*}$ by $s_{L}-c_{i,L}(x)$, where $c_{i,L}(x)$ is closest $L^{*}$ value of a control point color to the seed color. This translation minimizes the amount of displacement from the luminance distribution of the original representative curve. We then translate the curve in the $a^{*}-b^{*}$ plane to fit the ramp to the seed color. All subsequent colors in the ramp are computed according to the relative positions of the remaining control points to the seed color. For example, if the representative curve contains nine colors differing uniformly in $L*$ from 10 to 90 and the seed color is (78, -45, 32), we shift the model curve along $L*$ such that one of the colors contains a lightness of 78, adjusting the $L*$ range to [8,88], with the eighth control color matching the seed color. We then translate the representative curve in the hue plane ($a^{*}$ and $b^{*}$) such that the eighth color in the curve is precisely the seed color (78, -45, 32) and calculate the remaining colors from the new coordinates of the curve’s control points. Once seeded, developers can rotate, translate, reflect, and scale the curve to edit the curve’s appearance while retaining the desired structural properties (c.f., §3.7).

3.6 Constructing Diverging Ramps

Mathematically, diverging color ramps are two sequential ramps joined at a neutral center (or zero) point. We can extend sequential models to construct diverging color ramps based on this observation. We derived parameters from the set of 42 designer diverging ramps to pair sequential curves to form diverging ramps. We accomplish this by first computing a sequential ramp using the above algorithm, duplicating the ramp’s representative curve, and rotating the duplicated curve by a controlled amount. As clustering the diverging curves did not provide meaningful clusters, we can instead use statistics describing the angles between sequential arms of designer models to guide rotations. By default, our approach selects rotations between sequential ramps such that the angle between the curves is equal to 115 degrees—the mean angle between the sequential arms of the 42 designer-crafted diverging ramps in our corpus. This resulting diverging ramp is then translated in the $a^{*}-b^{*}$ plane such that the central point is a shade of gray.

Designers can rotate the arms of the ramp to adjust the hues of the end points and translate the ramp in $L^{*}$ to adjust the shade of the center point. We constrain hue rotation to between $\pm 60^{\circ}$ to reflect the bounds placed on diverging ramps by designers in our corpus. Figure 4 shows an example diverging ramp constructed using this approach.

3.7 Color Crafter

We embody our approach in Color Crafter, a web-based tool that allows users to seed our representative curves using a specified color, edit that color using a series of affine transformations, and copy the resulting color ramps to the user’s clipboard in several common color formats. The basic interface focuses on providing simple mechanisms for ramp generation (Figure 5a). Users input a desired target color and the tool seeds a set of representative curves using that color. Users can edit the curves by translating, rotating, reflecting, or scaling the component curves (Figure 5b). Results of model editing are shown in the curve view alongside a copy of the current ramp. Curves reaching beyond the bounds of the gamut revert to the most recent valid ramp. In future work, we intend to increase the flexibility of the tool to allow expert designers to more freely manipulate the curves and control points.

4 Evaluation

We evaluated our approach in three ways: 1. an empirical study measuring accuracy and subjective preference with graphic designers, as in Gramazio et al. [26]; 2. a replication case study showing how our method can readily reproduce ramps echoing popular designer sources, as in Wijffelaars et al. [83]; and 3. a use case evaluation demonstrating the utility of our approach even with conventionally “ugly” colors.

4.1 Empirical Study

We conducted a 3 (visualization type) x 4 (color ramp type) full factorial within-subjects study drawing on the methodology from Gramazio et al. [26] to compare our automatically generated sequential color ramps (from both the k-means and Bayesian clustering techniques) with linearly interpolated ramps (as in chroma.js [1] and Color Picker for Data [2]) and designer-crafted ramps. We recruited 35 designers from professional design communities to compare how these ramps support accurate data interpretation and aesthetic preference.

Stimuli: Participants were shown a series of visualizations that encoded data using a sequential color ramp and were asked to identify marks in the visualization with a given value and to rate how pleasant they found the visualization. We tested four categories of ramps—designer ramps, ramps constructed using both clustering techniques (k-means and Bayesian), and ramps constructed using linear interpolation in CIELAB—using three different visualizations: a scatterplot, a heatmap, and a choropleth map (Fig. 6). Scatterplots used 10 16-pixel diameter circular marks rendered at randomly selected x and y coordinates with no overlap between marks. Heatmaps consisted of a $10\times 10$ grid where each square was $30\times 30$ pixels in size. Choropleth maps were $550\times 450$ pixel maps of the United States, providing stimuli testing targets of varying size [73, 74]. Each mark in a visualization was assigned a value between zero and eight. We visualized these values using one of 108 color ramps (27 per ramp type). We chose nine distinct colors to match the length of our normalized color ramps (c.f., §3.2). Each visualization contained exactly one mark of the target value. All other marks were mapped to a different, randomly selected value.

Our stimuli drew from a fixed corpus of 108 color ramps. This corpus contained four sets of 27 ramps reflecting the four categories of ramps used in our experiments: designer, k-means, Bayesian, and linear. Our designer ramps were randomly selected from the corpus of 180 sequential ramps used to guide our models. K-means ramps were generated using our k-means clustering models with 27 unique seeding colors without manual ramp refinement. Bayesian ramps were generated using our unedited Bayesian curves with 27 additional colors. Linear ramps linearly interpolated between two control points selected from 27 pairs of pseudorandomly selected colors in CIELAB, reflecting current approaches in many popular tools [1, 2]. We chose seeding colors for these linear ramps that separated the two ends of each linear ramp by a minimum of 40 units in lightness to provide a reasonable comparison to how a developer might craft ramps using this approach (mean $\Delta L^{*}=61.3\pm 9.2$).

Seeding colors in the k-means, Bayesian, and linear conditions were drawn from a set of 15,581 colors. This color set contains all integer colors within $\Delta E=3$ of each color in our corpus of 180 designer ramps to avoid confounds from hue preferences. For example, people tend to find yellow-green tones less appealing overall [26], and designers tend to avoid these colors when creating ramps. We sample near the designer colors to help avoid confounds introduced as a result of the seed color choice: people may rate blue ramps higher overall simply because they prefer blue rather than as a result of the quality of the ramp itself. Given the seed colors are still drawn from a large corpus of possible colors, we anticipate these results reflect choices novice designers might make, and we explore poor color choices in the case study in Section 4.2. Our method does not explicitly exclude colors as in tools like Colorgorical as we want to provide novice designers with sufficient flexibility in crafting ramps according to their needs (e.g., fitting a corporate brand color). Our evaluation instead aims to measure the overall efficiency of our approach in generating ramps that support accurate and aesthetically pleasing visualizations. The distance between ramp endpoints averaged $73.2\pm 7.8\Delta E$ for linear ramps, $65.8\pm 11.9\Delta E$ for designer ramps, $70.1\pm 8.6\Delta E$ for K-Means ramps, and $66.2\pm 3.0\Delta E$ for Bayesian ramps.

Procedure: Our experiment consisted of five phases: (1) informed consent and screening, (2) preview of visualizations, (3) tutorial, (4) formal study, and (5) demographics questionnaire. Participants first provided informed consent for their participation and completed a series of digitally rendered Ishihara plates to help screen for color vision deficiencies [14]. Upon successfully completing the screening, participants then were shown a preview of the full set of 39 visualizations used in the formal study. As noted in prior studies of aesthetics, this preview allows participants to develop a preliminary intuition for the aesthetics of all of the stimuli to help anchor the end-points of their aesthetic preferences prior to beginning the study and to mitigate transfer effects [59, 26]. After the preview, participants completed three tutorial questions to clarify any possible ambiguities in the instructions.

In the formal study, each participant completed 39 trials—36 test stimuli plus three engagement checks—presented sequentially in random order to mitigate transfer (e.g., learning or fatigue) effects. Participants clicked on the mark (either a scatterplot point, heatmap square, or U.S. state) that they thought encoded a target value. Below the visualization, we included a slider that participants used to report their responses to ”How pleasant looking is the color ramp?”. The slider was always initially set to 0. Participants could move the slider to the left, which was labeled Not Pleasant with a minimum value of -100, or to the right, which was labeled Very Pleasant with a maximum value of +100. After each trial, a gray box covered the visualization for 2 seconds to mitigate potential contrast effects between subsequent trials. To ensure honest participation, each experiment contained three trials that were considerably easier to identify the target mark, and any participants that failed to correctly answer any of these engagement checks were excluded from our analysis. The full study infrastructure, set of stimulus ramps, and anonymized data is available at https://tinyurl.com/colorcrafting.

**Participant Recruitment: ** We recruited 35 design practitioners through social media, design interest groups, and online forums. Our participants included designers from the United States, the United Kingdom, India, and China. We excluded four participants from our analysis for either failing to correctly answer the engagement checks (trials that were considerably easier than normal trials), or self-reporting a color vision deficiency or abnormal vision. We analyzed data from the remaining 31 participants ($\mu_{age}=32.5$ years; 13 female, 17 male, 1 DNR), who had an average of 6.2 years of formal design experience.

**Results: ** We analyzed task performance and aesthetic ratings using a two-factor repeated measures ANCOVA treating interparticipant variation as a random covariate. All post-hoc analyses used Tukey’s Honest Significant Difference Test (HSD, $\alpha$ = .05). To provide transparency into our effects, we include all data in our supplemental materials and provide both inferential and descriptive statistics in the form of means and 95% confidence intervals to describe all effects in our study [19]. Figures 7 and 8 summarize our results. We include the anonymized study data in our OSF supplement for further exploration.

Error. We measured error as the absolute value of the difference between the reported and target value. We found a significant effect of color ramp type on accuracy ($F(3,90)=2.835,\ p<.05$). While not significant, our generated ramps performed as well or better on average than designer ramps. However, color ramps generated from our k-means clustering technique ($\mu_{error}=0.495\ \pm\ 0.073$) significantly outperformed linear color ramps ($\mu_{error}=0.649\ \pm\ 0.088$) at supporting accurate data interpretation (Figure 7).

We also found a significant effect of visualization type on accuracy ($F(2,60)=5.399,\ p<.01$). Trials involving heatmaps ($\mu_{error}=0.659\ \pm\ 0.063$) were significantly harder than trials involving scatterplots ($\mu_{error}=0.519\ \pm\ 0.086$) and choropleth maps ($\mu_{error}=0.511\ \pm\ 0.058$). Ramps did not perform significantly differently across visualizations.

Aesthetics. We measured aesthetic performance as the reported pleasantness of each visualization, with positive values corresponding to positive aesthetics and negative values corresponding to negative aesthetics. We found a significant effect of color ramp type on aesthetic rating ($F(3,90)=8.163,\ p<.001$). Color ramps generated from our k-means ($\mu_{ar}=9.99\ \pm\ 5.101$) and Bayesian ($\mu_{ar}=5.48\ \pm\ 4.621$) clustering techniques as well as designer color ramps ($\mu_{ar}=2.817\ \pm\ 5.358$) were viewed as significantly more aesthetically pleasing than linear ($\mu_{ar}=-7.409\ \pm\ 5.331$) color ramps (Figure 8).

We also found a significant effect of visualization type on aesthetic rating ($F(2,60)=7.289,\ p<.001$). Color encodings in heatmaps ($\mu_{ar}=-4.129\ \pm\ 4.443$) were generally perceived as less pleasing than color encodings used in scatterplots ($\mu_{ar}=5.038\ \pm\ 4.428$) and choropleth maps ($\mu_{ar}=7.247\ \pm\ 4.444$). While future work should explore these differences, visualizations did not significantly affect ramp aesthetics.

4.2 Use Case: Recreating Designer Ramps

Our clustering approach is intended to capture characteristic design patterns employed in expert-crafted color ramps. However, computing a representative curve may aggregate away fine-scale details present in any individual designer ramp. To evaluate the effects of this aggregation, we reconstructed the set of designer-crafted color ramps seen in Figure 1. We selected a random seed color from the designer ramp as the input to our algorithm. Using our tool, Color Crafter (Section 3.7), we applied simple affine transformations to the model curves and selected the model that produced a color ramp most similar to the original designer ramp. A side-by-side comparison of the original designer ramps and the model-generated ramps are shown in Figure 9. While there are some variations from the original ramps, we were able to derive close matches to each of the hand-crafted encodings This replication shows that our models are capable of capturing common design patterns and allows users to readily craft designer-caliber ramps.

4.3 Use Case: Unpleasant Seed Colors

While our empirical evaluation focused on a large corpus of designer colors to avoid hue biases, novice designers may select colors with significantly lower aesthetic values to seed ramps. Our method must be robust to poor seed color selection in order to truly support this population. We evaluated this robustness using a worst case design scenario. We collected a set of “ugly” colors from the ColourLovers design community555https://www.colourlovers.com/palette/1416250/The_Ugliest_Colors to use as seed colors representing actively poor color choices. These ramps are shown in Figure 10. The ramps generated using these colors provide aesthetically reasonable color ramps with logical ordering and sufficient discriminability even though they use colors conventionally thought of as unpleasant.

Our approach likely creates pleasing encodings from even “ugly” individual colors as the model curves prioritize luminance to anchor the generated ramps. As a result, though individual colors are unpleasant, the resulting ramps create aesthetically pleasant combinations of colors—the combinations vary according to designer preferences in lightness and chroma with small, smooth hue adjustments [67]. Colorgorical [26] uses this same idea to estimate pairwise aesthetics. While the colors selected here represent only one community’s aesthetic, future studies should evaluate how robust the contrasts in this model are to different seed colors (e.g., yellow-greens [67, 26, 58]).

5 Discussion

Most guidelines for effective color ramp design are qualitative heuristics often originating from years of designer experience and intuition. It is difficult for novice visualization designers to apply these guidelines as they are often ill-defined and require significant expertise to understand and correctly implement. Theoretical formalizations of these guidelines [12] help reduce the breadth of knowledge required for them to be effectively applied; however, these formalizations form an incomplete set of constraints better suited to evaluating encodings. Our approach recognizes the practices that designers have developed over many years and leverages a design mining approach to model implicit patterns in these practices to provide visualization designers and developers of all skill levels the ability to easily craft color ramps that support accurate data interpretation and positive aesthetics. Through developing and evaluating our approach, we found:

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Design patterns in color ramps can be quantified using ramp structure: We can cluster and aggregate the paths traversed by expert color ramps to capture common structural features in design. We computed 18 different patterns to reproduce expert-caliber ramps using individual seed colors.

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Our generated ramps performed at least as well as designer ramps at supporting accuracy: Color ramps generated using our approach performed at least as well as designer-crafted color ramps at supporting accurate data interpretation. Our k-means clustering technique generated ramps that significantly out-performed linearly interpolated color ramps in a perceptual color space.

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Our generated ramps performed at least as well as designer ramps at supporting positive aesthetics: Design practitioners rated ramps from our method as at least as aesthetically pleasing as designer ramps. Both our Bayesian and k-means clustering techniques resulted in ramps that were viewed as significantly more aesthetically pleasing than linearly interpolated color ramps.

Our findings indicate that the relative structure of the color ramp is the most important factor to generating effective and aesthetically pleasing encodings. While the overall aesthetic quality of our automated ramps may vary, we found that our approach predominantly generated color ramps with pleasing patterns even using random seeding colors. In a pilot study, designers found ramps generated using completely random colors aesthetically comparable to designer ramps ($\mu_{k-means}=7.548\ \pm\ 6.464,\ \mu_{bayesian}=8.691\ \pm\ 6.288,\ \mu_{designer}=12.718\ \pm 6.433$) despite potential confounds from hue preference. These preliminary results coupled with our evaluation show that the relationship between colors in a ramp is critical to establishing positive aesthetic. While this finding aligns with prior studies [67], increasing the number of colors a designer must specify increases the complexity of the design problem, making it harder for those with limited experience to build effective ramps. By capturing the diversity of structures and the nuanced color relationships replicated implicitly in designer encodings, we simplify the design process and empower more people to engage in effective visualization practices. We anticipate these findings might extend to other encoding design tasks, such as selecting shape configurations. Confirming this hypothesis is important future work.

While we aim to empower novice color designers, our goal is not to replace the designer but rather leverage their expertise to enable novices to produce high-quality color ramps. While explicit, constraint-based methods generate encodings guaranteed to follow good practices, constraint models are often hard to use and miss key, hard-to-define patterns, such as the kinks seen in designer-crafted ramps (Figure 1) that are critical to effective encoding design. Our approach allows us to detect these features implicitly and provide both novice and skilled designers with a strong and editable baseline. We anticipate that designers could use this approach to quickly generate preliminary encodings and hand-tune those encodings to fit their ideal needs.

Our approach is most similar to rule-based approaches such as PRAVDAcolor [8] and Colorgorical [26]. These tools computationally apply perceptual and aesthetic heuristics to derive color encodings for particular tasks. However, most rule-driven tools either require sufficient expertise as the constraint set is incomplete or focus on evaluating rather than generating encodings (e.g., ColorMeasures [12] and Pals [87]). Our approach attempts to reduce the expertise needed to craft ramps by minimizing required inputs: ramps can be generated using a single color. While our study suggests this approach results in reasonably high quality ramps, our method can generate ramps violating common practices, such as ramps lacking a logical order, but does not do so often. We qualitatively analyzed of the 81 random ramps from our random seed color pilot (https://tinyurl.com/colorcrafting) and found that while six linear ramps lacked a logical order, our method only generated order-preserving ramps.

Pairing constraint-based evaluative approaches with our generative model would allow systems to both generate and evaluate encodings at design time. This approach would allow tools to immediately winnow undesirable options from our 18 design patterns before presenting them to users. We could also incorporate additional constraints such as a size-sensitive discriminability [74] or color-boosting to mitigate curvature compression in characteristic curves (Figure 9). Exploring the utility of these generate-and-evaluate paradigms is important future work.

A significant body of research reflects on what makes color ramps effective [92, 69, 33]. While our clustering features build on this work, theories around effective perceptual, aesthetic, and cognitive characteristics for color encodings are too numerous to effectively embody in any single tool, yet they are also rife with disagreement and exceptions: ramp design is an art that blends expertise, serendipity, and structured thinking grounded in decades of theory. For example, both designer ramps and our technique often break the convention that a ramp should include a starting color with zero chroma (e.g., a gray), instead using yellow or another light hue appropriate to the ramp’s theme (Fig. 9). Few ramps in our corpus contain a zero-chroma color. This exemplifies the promise of design-mining methods for generative encodings—our approach breaks conventions in ways similar to designer approaches while preserving common practices such as introducing subtle hue twists. While we focus on optimizing for functionality and design support, our models capture nuanced design structures and offer a lens to explore ramp design theory and heuristics. A full qualitative theoretical analysis of the clusters and structures generated (and not) by this approach is valuable future work but falls outside of the current scope.

5.1 Limitations & Future Work

The performance of our approach is determined by the quality of the designer-crafted color ramps that we collect. Expanding this corpus may improve the quality of the models being used and provide deeper insight into patterns used in color encoding design. We have released the corpus as an open-source repository (https://tinyurl.com/colorcrafting) for curated extensibility.

Our approach allows us to regenerate our models as this corpus grows. However, the success of this technique depends on the models extracted from the corpus: poor quality ramps result in models that reflect poor practices. For example, ramps with high hue variation, such as rainbows, create models with large hue variations and noisy L+C curves leading to undesirable color name and luminance variation. In preliminary experiments, such ramps tend to cluster together; however, to generate ramps with unique structures, such as the cubehelix map 666https://jiffyclub.github.io/palettable/cubehelix/, we may wish to preserve high-variance structures. While our current approaches create ramps with smooth hue, chroma, and luminance variations, ramps with dramatic structural variations would require manual tuning or reweighting of the corpus. Future work should explore how sensitive our approach is to the training ramp distribution.

As many as 8% of men and 0.5% of women suffer from color vision deficiencies [9]. At present, our approach does not consider CVD as part of the modeling process. Without explicitly considering CVD models as either added constraints to the generation process or as a filter for output ramps, we cannot guarantee that our encodings will be robust for this population. Increasing the robustness of our approach for color vision deficiencies is important future work.

Our evaluation study uses an intentionally simple task to concretely measure perceptual discriminability by how well people can read data values. However, color maps can also be tuned to certain tasks, such as comparison [77], and factors like cognitive load. Future work should further explore how different characteristics of ramp design affect different tasks to better understand how designers might tailor encodings towards specific goals. Further, our linear ramps use only two seed colors, whereas many linear interpolation tools allow designers to specify multiple points. We use two points to most closely mimic the single-seed approach used in our technique, but future work could compare against linear interpolation with improved seeding.

Our approach uses unsupervised clustering methods to identify common structures. However, more sophisticated data mining and generation approaches such as Generalized Adversarial Networks (GANs) [25] may offer alternative methods to clustering. Future work should explore how these methods support effective design automation.

6 Conclusion

We present an approach for automatically generating designer-quality color ramps. Our approach utilizes design mining and unsupervised clustering techniques to implicitly learn design patterns from designer color encodings rather than expressing design guidelines as mathematical constraints. We evaluated color ramps generated using our approach through an empirical crowdsourced study with design practitioners. Our results show that ramps generated using our approach performed at least as well as designer-crafted color ramps at supporting accurate data interpretation and positive aesthetics and significantly outperformed color ramps produced using linear interpolation through perceptual color spaces. Our findings also suggest that the relative structure of the curve that a color ramp traverses through color space is more important than the specific colors used for constructing effective color ramps and allows us to capture implicit patterns in expert-caliber visualization design. We hope this work will spark future research on how design mining can empower more people to develop effective visualizations.

Acknowledgements.

We thank Maureen Stone and the anonymous reviewers for their feedback. This work was supported by NSF Award # 1657599.