A Testing Environment for Continuous Colormaps

1 INTRODUCTION

• The suite addresses colormap evaluation often relying on evaluator-chosen proprietary data, while complementing rather than abandoning user-centered studies.It can help designers test options before or after a usability study.Source: §1 · p. 1
• Its local test functions model features such as jumps, gradients, critical points, ridges, and different signal frequencies.The paper gives mathematical reasoning for selecting these functions.Source: §1 · p. 2
• Global test functions model complex regional variations, including large smooth jumps, volatile small jumps, and differing signal-to-noise levels.The paper draws some global-test functions from continuous optimization literature.Source: §1 · p. 2
• The third suite component is an extensible collection of real-world datasets from different applications.The paper expects this collection to continue expanding.Source: §1 · p. 2
• Integration into the open-access CCC-Tool provides a design and test environment for application-specific colormaps and visualization datasets.The tool enables users to create, edit, and analyze colormaps.Source: §1 · p. 2

2.1 Color Mapping

• Colormap quality has been assessed quantitatively and experimentally, but application-specific semantics remain important to practical design.These semantics can include key values, critical ranges, value distributions, and spatial relationships.Source: §2.1 · p. 2

2.2 Colormap Test Data

• The literature lacked a colormap test suite, despite examples of datasets used to compare colormaps and demonstrate algorithms.The work aims to support application-specific colormap design.Source: §2.2 · p. 2, §2.1 · p. 2
• Analytic datasets such as gradients, ridges, jumps, and frequency variations are common because they expose specific colormap properties.Cartographic maps and data from scientific visualization applications are also common test data.Source: §2.2 · p. 3
• The test suite follows these literature patterns with expressive analytic data and real-world datasets from different scientific applications.Table 1 is identified as summarizing popular colormap test data in the literature.Source: §2.2 · p. 3, Table 1 · p. 3

3 MOTIVATION

• The initial test functions address common scalar-field challenges, with scope intended to expand toward more complex or specialized cases.Examples include jumps, extrema, ridges or valleys, varying gradients and frequencies, and noise levels.Source: §3 · p. 3
• Tests are designed as intuitive functions that each address one challenge and can be interpreted and customized by experts or non-experts.Their simplicity could support future automatic test reports or colormap optimization.Source: §3 · p. 3
• Parameterized, usually resolution-independent test functions let users examine how colormaps handle features resembling anticipated application data.Finding and defining a suitable test function is usually easier than manually creating a dataset.Source: §3 · p. 3
• The suite is also intended to include extensible real-world datasets from applications, potentially modified where appropriate.The collection could draw on popular data used for colormap testing in visualization literature.Source: §3 · p. 3

• Three design goals are intuitive and mathematically reproducible test behavior, comparability with prior analytic examples, and easy access through the CCC-Tool.The integration lets users test colormaps immediately after creating or editing a specification.Source: §4 · p. 3
• The suite combines local tests of scalar-field properties, global tests such as signal-to-noise ratio and topological properties, and application-specific data sets.The real-world data sets reflect the need to evaluate colormaps with application data.Source: §4 · pp. 3–4
• The neighborhood variation test uses four elements, with odd columns repeating a value and even columns containing the ordered set of test values.The figure also shows the test as a three-dimensional visualization encoding values through height.Source: Figure 2 · p. 4
• The gradient tests visualize linear, convex, and concave gradient types in color and as three-dimensional height maps.The illustrated examples use r = 0 and R = 1.0, with Tx = Ty.Source: Figure 3 · p. 4
• Common parameters let users set the test-function range, choose a polynomial exponent, and select among enumerated cases.The range parameters r and R determine the test function's minimum and maximum.Source: §4 · p. 4

4.1.1 Step Functions

• Step functions arrange increasing test values in a rectangular grid, with alternating columns providing adjacent comparisons across step heights and value levels.Observers can identify a column’s test value and compare it with the adjacent column.Source: §4.1.1 · p. 4

4.1.2 Gradient Variation

• Gradient Variation tests linear, concave, or convex behavior along both axes, with increasing or decreasing values set by the endpoint values R and r.For b ≥ 2, the y-direction concave case has a decreasing gradient and the convex case an increasing gradient; the x-direction is defined similarly.Source: §4.1.2 · pp. 4–5

4.1.3 Local Topology: Minimum, Maximum, and Saddle

• Quadratic test functions create user-defined minima, maxima, and saddles by choosing the signs of o and p, with m setting the structure’s starting value.Fig. 4 shows the corresponding 2D color mappings and 3D height maps.Source: Figure 4 · p. 4, §4.1.3 · p. 5

4.1.4 Local Topology: Ridge and Valley Lines

• Ridge and valley tests place a vertical line at x = 0 and vary its shape across linear, concave, and convex profiles.R > r yields a ridge, while R < r yields a valley; the profiles can vary along y as well.Source: Figure 5 · p. 4, §4.1.4 · p. 5

4.1.5 Frequency Variation

• Frequency Variation tests wave-like fields with increasing spatial frequency in x and decreasing amplitude in y, and noise can be shown with several distributions.High-frequency tests require attention to image resolution because aliasing can occur when D is large.Source: §4.1.5 · pp. 5–6, Figure 10 · p. 6

4.1.6 Threshold Variation

• Threshold Variation tests a user-defined threshold t at x = 0, using linear, flat, or steep gradient behavior around the isoline.Values are lower on the left and higher on the right; the examples show the three types in color-mapped and height-map views.Source: Figure 7 · p. 5, §4.1.6 · p. 6

4.2 Global Tests

• Global tests model broader scalar-field behavior, including multiple local extrema, small relevant variations amid wide value ranges, and noise.They also include test functions drawn from other computer science disciplines.Source: §4.2 · pp. 6–7

4.2.1 Global Topological Structures

• Perlin noise combined with other test functions creates fields with many critical points and varied spatial structures.Options can focus noise on small or high values, scale it to the field range, or replace field values with a custom noise range.Source: §4.2.1 · p. 7

4.2.2 Little Bit Variation

• The Little Bit Variation test adds grooves of varying depths to a linear background to test whether colormaps resolve small changes within a larger data range.Grooves alternate with unchanged stripes, and their depths vary between user-defined minimum and maximum values.Source: §4.2.2 · p. 7

4.2.3 Signal-Noise Variation

• Noise tests vary the affected pixel fraction and support uniform, normal, and beta-like distributions.Noise can be applied to test functions from the local and global suites, with several noise-behavior options.Source: §4.2.3 · p. 7

4.2.4 Function Collection

• The function collection adds established tests from other computer science domains, including optimization functions, and is intended to expand over time.The values can be scaled to the colormap range or a user-defined range; the Bukin Function, for example, has many small local minima along a valley line.Source: §4.2.4 · p. 7

4.3 Application-Specific Tests

• Real-world data can combine several of the challenges modeled by analytic test functions, so the authors include application data to cover realistic challenges across domains.The authors regard real-world data as indispensable to completing the suite.Source: §4.3 · p. 8
• The authors distinguish real-world tests from theory-based functions because real data’s varied sources, measurement methods, and attributes can present multiple challenges together.Source: §4.3 · p. 8
• The application-data collection is intended to cover different scientific disciplines so users can find cases resembling their own data.The current tool offers medical-, flow-, and photograph-specific data, and the collection is planned to expand over time.Source: §4.3 · p. 8

5 TEST EVALUATION

• A general automatic colormap score may be uninformative because meaningful evaluation depends on the colormap’s intended use.The proposed evaluation instead derives information from test functions for users to analyze and rate.Source: §5 · p. 8
• The method computes normalized neighboring-value differences for the test field and for its color mapping, storing them as Value Difference and Color Difference Fields.Color differences can use Lab, DIN99, DE94, or CIEDE2000 measures.Source: §5 · p. 8
• Subtracting the normalized fields produces a Subtraction Field that shows local uniformity and highlights areas of nonlinear mapping.Users can inspect it alongside the Color Difference Field.Source: §5 · p. 8
• Fixed Black-White or Custom normalization makes Color Difference Fields comparable across colormaps.Custom normalization is useful when the black-white difference is too large relative to the field’s color differences.Source: §5 · p. 8

6 APPLICATION CASE

• Small temperature variations near freezing were difficult to see in flat regions such as oceans because their horizontal gradients are much smaller than those in mountainous regions.Source: §6 · p. 9
• A discontinuous transition at 0°C separated negative from positive temperatures that the locally uniform cool-warm colormap did not distinguish near freezing.The Subtraction Field marked the transition’s spatial position.Source: §6 · p. 9
• The colormap path was extended through color space to provide more distinguishable colors for positive temperatures, with additional keys for temperature subranges.The design allocated more of the mapping to positive values because much of the full range occurred below 0°C, mostly in Antarctica.Source: §6 · p. 9

7 CONCLUSION

• Test functions are proposed as a standard evaluation method alongside user testimonies and empirical studies, allowing quick, controlled, and repeatable comparisons across colormaps and data sets.The authors note that this approach avoids recruiting participants and organizing user-study logistics.Source: §7 · p. 9
• The suite covers scalar-field challenges including steps, gradients, extrema, saddle points, ridges, valleys, topology, thresholds, frequencies, and small value changes.Noise can be added to extend the basic functions, but the authors note that the test functions cannot cover every possible challenge.Source: §7 · p. 9
• The collection combines newly designed functions with functions used in other computer science fields and real-world data sets from different application areas.The real-world data sets present individual scalar-field analysis challenges and are intended to reduce dependence on external data.Source: §7 · p. 9
• The test suite is integrated into the open-access CCC-Tool, which supports visual and numerical evaluation of test-function results.The paper also presents an example of evaluating and enhancing a user-designed colormap for a specific application problem.Source: §7 · p. 9
• The authors plan to extend the collection and explore an open-source real-world data database and automatic test reports for user-selected tests.Automatic reports are proposed as a future step toward adopting the suite as a standard evaluation method.Source: §7 · p. 9