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Good Colour Maps: How to Design Them

Peter Kovesi

arXiv:1509.03700v1cs.GR

TL;DR

Colour maps can distort data interpretation through uneven perceptual contrast and limitations of CIELAB at relevant spatial frequencies. The paper develops lightness-focused design techniques and shows how they support more consistent map perception, relief shading, and ternary-image structures.

  • Problem

    Vendor colour maps often have uneven perceptual contrast, creating false anomalies or obscuring data features, while prior designs overlook CIELAB’s spatial-frequency limitations.

  • Method

    The paper develops lightness-focused design techniques for linear, diverging, rainbow, and cyclic maps, with test images, relief-shading analysis, and ternary-image basis colours.

  • Results

    The proposed designs provide consistent structure salience across ternary channel permutations, while colour maps can complement relief shading when their frequency content is sufficiently lower.

  • Takeaways & Limitations

    Perceptual lightness variation should guide colour-map construction, with map choice and frequency content considered alongside relief shading and channel assignment.

  • Takeaways & Limitations

    Smoothing a diverging map’s lightness reversal removes a false feature but introduces a small perceptual flat spot where structures are harder to see.

Abstract

from arXiv · show

Many colour maps provided by vendors have highly uneven perceptual contrast over their range. It is not uncommon for colour maps to have perceptual flat spots that can hide a feature as large as one tenth of the total data range. Colour maps may also have perceptual discontinuities that induce the appearance of false features. Previous work in the design of perceptually uniform colour maps has mostly failed to recognise that CIELAB space is only designed to be perceptually uniform at very low spatial frequencies. The most important factor in designing a colour map is to ensure that the magnitude of the incremental change in perceptual lightness of the colours is uniform. The specific requirements for linear, diverging, rainbow and cyclic colour maps are developed in detail. To support this work two test images for evaluating colour maps are presented. The use of colour maps in combination with relief shading is considered and the conditions under which colour can enhance or disrupt relief shading are identified. Finally, a set of new basis colours for the construction of ternary images are presented. Unlike the RGB primaries these basis colours produce images whereby the salience of structures are consistent irrespective of the assignment of basis colours to data channels.

1 Introduction

Effective continuous colour maps should reveal data structure and communicate metric values through near-uniform perceptual contrast and intuitive colour ordering. The introduction identifies uneven contrast in vendor maps, explains its perceptual consequences, and presents a simple test image for detecting such faults.

  • Design goals: Effective colour maps should provide near-uniform perceptual contrast and intuitive perceptual ordering to reveal structure and communicate metric values [44].
  • Motivation: Vendor colour maps can create false anomalies through locally high contrast and hide real features in low-contrast flat spots.These problems are linked to highly uneven perceptual contrast across the map.
  • Perceptual analysis: A rainbow map constructed as a straight path in RGB space produces CIELAB clustering, near-constant lightness, and kinks that generate flat spots and false anomalies.The cited example shows these effects in the green, cyan–yellow, yellow, and red regions.
  • Scope: The paper concerns colour maps for continuous data ranges, while categorical displays are directed to Brewer’s work.
  • Evaluation: A sine wave superimposed on a ramp provides constant-magnitude features at different offsets for quickly evaluating colour-map faults.The test image cannot replace detailed psychophysical evaluation but reveals serious flat spots and false features under typical uncontrolled viewing conditions.

2 The Importance of Lightness

For fine image structures, perceptual contrast in colour maps is dominated by lightness differences because chromatic acuity declines at high spatial frequencies. Consequently, equal lightness increments are more effective than equal CIELAB-distance spacing, while constant-lightness maps can make features nearly invisible.

  • 2 The Importance of Lightness: CIELAB colour-difference formulas are limited for colour-map design because they were derived from large isolated patches and do not represent fine image spatial scales.These formulas are based on the CIE 1931 2° and CIE 1964 10° Standard Observers, while a 10 mm object viewed at 600 mm subtends only about 1°.
  • 2 The Importance of Lightness: Fine-scale colour-map contrast is dominated by lightness differences, whereas hue and chroma differences are relatively unimportant.Chromatic-grating acuity decreases above about 3 cycles/degree and ultimately fails around 11–12 cycles/degree, so lightness differences govern the resolution of fine image structures.
  • 2 The Importance of Lightness: Equal CIELAB-distance spacing can produce reduced feature contrast where the lightness gradient is small, whereas equal lightness increments render the test image more uniformly.Figure 4 compares maps built from the same path: the equispaced map renders one section poorly, while the equal-lightness map avoids that reduced contrast.
  • 2 The Importance of Lightness: A constant-lightness colour map makes the test image’s sine-wave pattern almost impossible to discern.The map is generated from equispaced points on a CIELAB curve at lightness 70, demonstrating the importance of a nonzero lightness gradient.

3 Prior Work

Prior work explored perceptual colour maps using colour-space distance, luminance, saturation, lightness profiles, and structured paths, but results were inconsistent and hue-based or rainbow maps often performed poorly. Several studies also examined spatial-frequency effects, perceptual ordering, diverging maps, and evaluation methods.

  • Colour-space uniformity: CIELAB- and CIELUV-distance methods often failed because their assumed perceptual uniformity does not hold at fine spatial scales.This limitation led to inconsistent success in generating good colour maps.
  • Magnitude maps: Rogowitz et al. found luminance and saturation better suited to representing magnitude than hue, whose maps performed poorly; one optimized map was less effective than linearized grey scale despite traversing six times its CIELUV distance.Their colour maps followed controlled paths through Munsell and CIELAB spaces and were evaluated on medical images.
  • Spatial frequency and rainbow maps: Rogowitz and Treinish linked chromatic and achromatic responses to spatial frequency, suggesting saturation for low-frequency data and luminance for high-frequency information while identifying ordering and banding problems in rainbow maps.They noted that rainbow-map colour ordering can be confused and images can be partitioned into uneven bands.
  • Alternative construction methods: Other approaches used face-based luminance matching to construct isoluminant and monotonically increasing-lightness maps, directed RGB-cube paths for perceptual ordering, and spiral RGB paths for colour- and grey-scale reproduction.The spiral RGB map had monotonically increasing lightness, but its colour variations were not perceptually smooth.
  • Lightness and diverging maps: Niccoli emphasized linear or cube-law lightness profiles, while Spence and Efendov found that 90° hue differences often performed well in isoluminant diverging maps, rather than 180° differences.Niccoli’s cube-law rationale was unclear given CIELAB’s intended perceptual linearity.

4 Colour Map Design

The section presents a colour-map design process that defines paths in CIELAB space and equalizes perceptual contrast along them, while addressing limitations and design requirements for linear, diverging, rainbow, and cyclic maps.

  • General design method: Colour maps are constructed by fitting first- or second-order B-splines through CIELAB control points, then remapping samples using cumulative perceptual-contrast differences to obtain equalized contrast.Contrast differences are usually based on lightness differences, while CIE76 is used for isoluminant or low-lightness-contrast maps.
  • General design method: Extended regions with little lightness gradient can create hue or chroma discontinuities when paths are sampled at equal lightness changes.The perceptual contrast formula must therefore be chosen carefully; CIEDE2000 adds correction factors for lightness, chroma, and hue, although its lightness correction may be useful.
  • Diverging colour maps: Diverging maps can produce false features and hard-to-resolve structures when their lightness gradient reverses at the reference value.A linear-diverging blue-grey-yellow map avoids the central flat spot by eliminating the lightness-gradient reversal.
  • Rainbow colour maps: Rainbow maps require contrived lightness-gradient reversals that disrupt perceptual colour ordering, so they are generally not recommended despite their continued use.Their shortcomings are well documented.
  • Cyclic colour maps: The HSV hue-circle cyclic map has uneven perceptual contrast, including low-lightness-contrast regions and false anomalies from its lighter secondary colours.Alternative cyclic paths use alternating light and dark colours; a diamond-shaped path through magenta, yellow green, and blue is reported as successful.

5 Colour Maps for Relief Shading

Colour can complement relief shading by conveying data values while preserving or enhancing perceived 3D structure, but frequency-matched or very dark colour variations can disrupt or mask the shading. When image and shading spectra differ substantially, ordinary colour maps are generally safe; otherwise, isoluminant or very low-contrast maps are advisable.

  • 5 Colour Maps for Relief Shading: Relief shading conveys surface shape but not absolute data values, whereas combining it with a data-derived colour image communicates both structure and metric information.This combination can reveal fine structures while also conveying feature magnitudes, including deviations above and below zero.
  • 5 Colour Maps for Relief Shading: An isoluminant colour map prevents disruption when frequency content matches the shading, but produces little apparent 3D amplification once the relief pattern is sufficiently rich.A constant-lightness map is theoretically orthogonal to shading information, while misaligned colour and shading gradients can amplify 3D perception in simple synthetic cases.
  • 5 Colour Maps for Relief Shading: The strongest interference occurs in a synthetic worst case when colour-lightness and relief-shading variations share similar spatial frequencies, unlike typical natural-data spectra.Natural-data amplitude spectra generally decay with frequency, so the single-frequency synthetic example is not representative.
  • 5 Colour Maps for Relief Shading: When colour and shading have closely matched frequency spectra, colour can substantially disrupt 3D perception; shifting colour variation toward lower frequencies largely avoids interference.For the DEM example, 1/f^1.2 noise caused considerable disruption, whereas 1/f^1.8 noise produced almost no interference aside from locally masked regions.
  • 5 Colour Maps for Relief Shading: If colour-image and shading spectra differ significantly, no special isoluminance precautions are generally needed, provided non-isoluminant maps avoid very dark colours that can mask shading.The required caution also depends on the scaling of gradient values used to generate the shading; smaller gradient scaling increases sensitivity to nonisoluminance.

6 Colours for Ternary Images

The section introduces near-isoluminant basis colours for ternary images so that data channels and their combinations have more consistent perceptual prominence than with RGB primaries. The design matches lightness and chroma as closely as possible while accepting reduced gamut and subdued colours.

  • Motivation: RGB primaries can bias ternary images because red, green, and blue have unequal perceptual sensitivity and CIELAB lightness values of approximately 53, 88, and 32, respectively.The eye is particularly insensitive to blue because it has many fewer blue cones than green and red ones.
  • Basis-colour design: The proposed basis colours are ‘red’ RGB [0.90 0.17 0.00] with lightness 50 and chroma 92, ‘green’ [0.00 0.50 0.00] with lightness 46 and chroma 71, and ‘blue’ [0.10 0.33 1.00] with lightness 44 and chroma 100.The corresponding ‘cyan’, ‘magenta’, and ‘yellow/orange’ secondary colours have lightness values 79, 72, and 73, respectively, with chroma values 43, 78, and 77.
  • Basis-colour design: The design keeps maximum lightness differences among basis or secondary colours to about 6, while maximum chroma difference reaches 35 because of gamut limitations.The compromise was accepted because lightness differences matter more at fine spatial scales; stronger manual constraints could reduce lightness differences further but would reduce chroma and gamut.
  • Evaluation: Across six colour-channel permutations, the proposed basis colours closely preserve feature salience, whereas RGB primaries make different structures most noticeable and give green-encoded structures excessive prominence.The proposed colours avoid channel-assignment bias, producing a more consistent representation of the data.
  • Limitations: The near-isoluminant basis colours represent a reduced subset of the RGB cube, producing more subdued ternary images in exchange for more consistent data representation.The representable gamut is shown within the RGB cube in Figure 24.

7 Conclusion

The paper presents principled techniques for designing perceptually uniform colour maps while accounting for CIELAB’s limited uniformity beyond very low spatial frequencies. It also provides practical evaluation images, guidance for relief shading, and basis colours that stabilize ternary-image perception across channel assignments.

  • Conclusion: Principled colour-map design must account for CIELAB’s perceptual-uniformity limitations beyond very low spatial frequencies.The paper identifies this limitation as a reason previous approaches have had inconsistent success.
  • Conclusion: Lightness-gradient reversals in diverging, rainbow, and cyclic maps must be smoothed to prevent false features, although they can still create local perceptual flat spots.Linear-diverging maps may therefore be preferable to classical reversing maps; minimally bad rainbow maps can still be constructed, despite lacking perceptual ordering.
  • Conclusion: Simple test images reveal serious deficiencies in many vendor-supplied colour maps and support further experimentation with colour-map design.The presented images are simple to generate and facilitate readily accessible evaluation.
  • Conclusion: Relief shading can combine metric information from colour with form information from shading when the coloured image has substantially different, preferably lower, frequency content.Under that condition, no particular precautions are needed in choosing the colour map.
  • Conclusion: RGB primaries are unsuitable ternary-image basis colours because channel assignments can produce different perceptions, whereas matched-lightness basis colours stabilize perceived structures across channel permutations.The basis colours and their secondary colours are closely matched in lightness.

A The Colour Map Test Image

The test image combines a ramp with a sine wave whose amplitude decreases across the image, exposing whether a colour map resolves features spanning 10% of the data range. Its 8-pixel wavelength targets peak human contrast sensitivity, while an equivalent circular spiral-ramp test evaluates cyclic maps.

  • A The Colour Map Test Image: The test image superimposes a sine wave on a ramp, with peak-to-trough features equal to 10% of the total data range and amplitude decreasing to zero downward.The amplitude increases with the square of distance from the bottom, creating a broad low-contrast region; each row is normalized to span 0–255, slightly reducing the top ramp slope.
  • A The Colour Map Test Image: The sine wave uses an 8-pixel wavelength, producing 64 cycles across a 512-pixel image and approximately 5.2 cycles per degree at the stated viewing conditions.This lies within the 3–7 cycles-per-degree range of maximal contrast sensitivity for most observers.
  • A The Colour Map Test Image: This spatial frequency biases the test toward light–dark discrimination rather than chromatic discrimination, while reflecting the need to resolve features at this scale and finer.
  • A The Colour Map Test Image: The cyclic-map test uses a circular image with a 100-cycle sine wave superimposed on a spiral ramp from 0 to 2π, with amplitude decreasing from the outside to the centre.The spiral creates a 2π discontinuity on the right side of the image.
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