Cube-Root Color Spaces and Chromatic Adaptation

The recommendations of the International Commission on Illumination (CIE) on the CIELUV 1976 and CIELAB 1976 color spaces are discussed. A cube-root chromaticity diagram (a',b') for CIELAB 1976 is added. A slightly modified cube-root chromaticity diagram (A',B') is proposed which takes care of the CIE corrections (1978) for saturated yellow and red colors in CIELAB 1976 color space. Important advantages of the corresponding cube-root color space labeled LABHNU 1977 are shown and compared to the CIELUV 1976 and CIELAB 1976 color spaces. Chromatic adaptation can be described approximately as an equal (cube-root) chromaticity shift for all test colors defined by the two chromaticities of the adaptation illuminants. These properties are discussed and compared to our own chromatic-adaptation data and data published by Bartleson (1978). Color-appearance attributes and differences are studied for CIE standard illuminants D₆₅ and A. The Munsell data and OSA data and the main properties of different experiments of Evans and Swenholt (1968) and Pointer (1974) lead to the LABHNU 1977 color space which is evaluated for chromatic adaptation to different illuminants and is compared to the CIELAB 1976 and CIELUV 1976 color spaces.     

Determination of constant Hue Loci for a CRT gamut and their predictions using color appearance spaces

A colorimetrically characterized computer-controlled CRT display was used to determine 24 loci of constant perceived hue for pseudo-object related stimuli, sampling the display's interior color gamut at constant lightness and the edge of its gamut at variable lightness. Nine observers performed three replications generating matching data at 132 positions. the constant hue loci were used to evaluate the correlation between perceived hue and hue angle of CIELAB, CIELUV, Hunt, and Nayatani color appearance spaces. the CIELAB, CIELUV, and Hunt spaces exhibited large errors in the region of the blue CRT primary, while the Nayatani and CIELUV spaces produced large errors in the region of the red primary for constant lightness stimuli. Along the edge of the CRT's color gamut (variable lightness stimuli), all the spaces had a similar trend, large errors in the cyan region. the differences in performance between the four spaces were not statistically significant for the constant lightness stimuli. For the variable lightness stimuli, CIELAB and CIELUV had statistically superior performance in comparison with the Nayatani space and equal performance in comparison with the Hunt space. It was concluded that for imaging applications, a new color appearance space needs to be developed that will produce small hue error artifacts when used for gamut mapping along loci of constant hue angle. © 1995 John Wiley & Sons, Inc.     

Correspondence Between CIELAB and CIELUV Color Differences

The CIE presently recommends two uniform color spaces, the CIE 1976 (L*u*v*)-space (CIELUV) and the CIE 1976 (L*a*b*)-space (CIELAB). With each of these spaces is associated a color-difference formula. Color differences calculated by one formula cannot readily be converted to color differences calculated by the other formula. A conversion factor such as ρ = ΔE_uv*/ΔE_ab* cannot be determined uniquely. However, for any given location in color space, it is possible to determine a range, ρ_min ? ρ ? ρ_max, within which ρ must lie. Lines of constant ρ_min and ρ_max can be plotted in (L*a*b*)-space which indicate the range of ρ in (L*u*v*)-space.     

CIELAB color space boundaries under theoretical spectra and 99 test color samples

A color space is a three-dimensional representation of all the possible color percepts. The CIE 1976 L*a*b* is one of the most widely used object color spaces. In CIELAB, lightness L* is limited between 0 and 100, while a* and b* coordinates have no fixed boundaries. The outer boundaries of CIELAB have been previously calculated using theoretical object spectral reflectance functions and the CIE 1931 and 1964 observers under the CIE standard illuminants D50 and D65. However, natural and manufactured objects reflect light smoothly as opposed to theoretical spectral reflectance functions. Here, data generated from a linear optimization method are analyzed to re-evaluate the outer boundaries of the CIELAB. The color appearance of 99 test color samples under theoretical test spectra has been calculated in the CIELAB using CIE 1931 standard observer. The lightness L* boundary ranged between 6 and 97, redness-greenness a* boundary ranged between −199 and 270, and yellowness-blueness b* boundary ranged between −74 and 161. The boundary in the direction of positive b* (yellowness) was close to the previous findings. While the positive a* (redness) boundary exceeded previously known limits, the negative a* (greenness) and b* (blueness) boundaries were lower than the previously calculated CIELAB boundaries. The boundaries found here are dependent on the color samples used here and the spectral shape of the test light sources. Irregular spectral shapes and more saturated color samples can result in extended boundaries at the expense of computational time and power.     

A comparison of the CIE 1976 colour spaces

The CIE 1976 colour spaces, CIELUV and CIELAB, have been compared by recalculating the results of a number of reported sets of experimental data. These include the results of just-noticeable-difference observations, colour difference scaling, colour matching ellipses, and acceptability ellipses. As a means of representing the colour difference data uniformly, it is shown that neither colour space is significantly better than the other. Attention is drawn to some anomalies in the CIELAB space.     

A Euclidean color space in high agreement with the CIE94 color difference formula

Many consider it futile to try to create color spaces that are significantly more uniform than the CIELAB space, and, therefore, efforts concentrate on developing estimates of perceived color differences based on non‐Euclidean distances for this color space. A Euclidean color space is presented here, which is derived from the CIELAB by means of a simple adjustment of the a* and b* axes, and in which small Euclidean distances agree to within 10.5% with the non‐Euclidean distances given by the CIE94 formula. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 64–65, 2000     

Evaluation of Uniform Color Spaces Developed after the Adoption of CIELAB and CIELUV

Since the adoption of the color spaces CIELAB and CIELUV by the CIE in 1976, several other uniform spaces have been developed. We studied most of these spaces and evaluated their uniformity for small as well as larger color differences. Therefore, several criteria have been defined based on color discrimination data and appearance systems. The main difference between color spaces based on discrimination data and spaces that model appearance systems is reflected in a different size of the chroma distance unit compared with the lightness unit. If spaces based on the same kind of data (discrimination data or appearance systems) are compared with each other, they are all almost equally uniform. BFD (l:c), for example, is said to be more uniform than CMC(l:c), but, based on confidence intervals of 65%, there is no significant difference between them. If the proposed color difference formula of the CIE is compared with these distance functions, it also performs equally well. The SVF space and OSA 90 space on the other hand should be better than OSA 74. However, as opposed to what was expected, OSA 74 is slightly better; but, also in this case, the difference between the spaces is insignificant.     

Estimation of chromaticness of constant-luminance central-field colors on a D65 surround

Eight observers estimated chromaticness for central-field colors of different chromaticity and constant luminance in a surround of the chromaticity of D₆₅. The perceived chromaticness was scaled relatively and absolutely. The experimental results are compared with chromaticness as defined in different color spaces. In the CIELUV, CIELAB, LABHNU, and LABHNU2 spaces, colors of equal visual chromaticness are located approximately on circles. The LABHNU and LABHNU2 color spaces seem to describe the relative and absolute scalings in the best way for all observers.     

Uniform colour spaces based on the DIN99 colour‐difference formula

Several colour‐difference formulas such as CMC, CIE94, and CIEDE2000 have been developed by modifying CIELAB. These formulas give much better fits for experimental data based on small colour differences than does CIELAB. None of these has an associated uniform colour space (UCS). The need for a UCS is demonstrated by the widespread use of the a*b* diagram despite the lack of uniformity. This article describes the development of formulas, with the same basic structure as the DIN99 formula, that predict the experimental data sets better than do the CMC and CIE94 colour‐difference formulas and only slightly worse than CIEDE2000 (which was optimized on the experimental data). However, these formulas all have an associated UCS. The spaces are similar in form to L*a*b*. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 282–290, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10066     

A fallacy in the definition of ΔH*

When a color differs from the reference, it is desirable to ascribe the difference to differences in the perceptual attributes of hue, chroma, and/or lightness through psychometric correlates of these attributes. To this end, the CIE has recommended the quantity ΔH* as a psychometric correlate of hue as defined by ΔH* = [(ΔE*)² - (ΔL*)² - (ΔC*)²]^1/2, where the correlates correspond to either the 1976 CIELAB or CIELUV color spaces. Since ΔH* is defined as a “leftover,” this definition is valid only to the extent that ΔE* comprises exclusively ΔL*, ΔC*, and ΔH* and that ΔL*, ΔC*, and ΔH* are mutually independent compositionally, both psychophysically and psychometrically. It will be shown that as now defined ΔH* lacks psychometric independence of chroma and always leads to incorrect hue difference determination. Such a deficiency causes problems, especially in the halftone color printing industry, since it can suggest an incorrect adjustment for the hue of the inks. A revised definition herein of ΔH* provides a psychometric hue difference independent of chroma, valid for large and small psychometric color differences regardless of chroma. However, for small chromas, the seldom used metric ΔC might be a better color difference metric than ΔH* because complex appearance effects make the perceptual discrimination of lightness, chroma, and hue components more difficult than for high chromas.     

A study in black: The cielab and cieluv L* function for very low values of Y

Four approximations to the CIELAB and CIELUV metric lightness function L* for values of Y < 1% have been examined. It is shown that the requirement of equality in both value and first derivative at the point of transfer results in considerably poorer fit to the Munsell Renotation Value function than approximations that do not demand continuity at the point of transfer.     

Which color is more colorful,the lighter one or the darker one?

To answer a question often asked in industrial color reproduction, a series of highly chromatic color samples of the same CIELAB hue but of small variations of CIELAB chroma and lightness were prepared and scaled for perceived colorfulness. The results indicate that lightness contributes to the perceived colorfulness as defined by the observers according to their everyday color experiences. For the samples used, colorfulness can be modeled by factoring in the CIELAB L* value in addition to CIELAB C*. The results show that colorfulness, as implied in our everyday color experiences, can be a complex perceptual attribute. A newer psychophysical scaling model is also presented, since Thurstone's Case V model was shown to be inadequate. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 168–174, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10142     

An integrated color‐appearance model using CIELUV and its applications

A new type of color‐appearance model is presented together with its formulations. It is named In‐CAM(CIELUV), which means the integrated color‐appearance model using CIELUV space. Using the In‐CAM(CIELUV), we can integrate its fields of applications in both colorimetric engineering and artistic color design. Various applications are introduced in colorimetric and color design fields. The In‐CAM(CIELUV) connects directly colorimetric color space and perceptual Hue‐Tone color order systems. In other words, the In‐CAM (CIELUV) gives a colorimetric basis for Hue‐Tone system. The three color attributes in the In‐CAM(CIELUV) space are mutually independent. This is a very convenient feature for selecting color combinations. Some two‐color combinations selected systematically in the In‐CAM(CIELUV) space are shown. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 125–134, 2008     

Geodesic calculation of color difference formulas and comparison with the munsell color order system

Riemannian metric tensors of color difference formulas are derived from the line elements in a color space. The shortest curve between two points in a color space can be calculated from the metric tensors. This shortest curve is called a geodesic. In this article, the authors present computed geodesic curves and corresponding contours of the CIELAB ( ), the CIELUV ( ), the OSA‐UCS (ΔE_E) and an infinitesimal approximation of the CIEDE2000 (ΔE₀₀) color difference metrics in the CIELAB color space. At a fixed value of lightness L*, geodesic curves originating from the achromatic point and their corresponding contours of the above four formulas in the CIELAB color space can be described as hue geodesics and chroma contours. The Munsell chromas and hue circles at the Munsell values 3, 5, and 7 are compared with computed hue geodesics and chroma contours of these formulas at three different fixed lightness values. It is found that the Munsell chromas and hue circles do not the match the computed hue geodesics and chroma contours of above mentioned formulas at different Munsell values. The results also show that the distribution of color stimuli predicted by the infinitesimal approximation of CIEDE2000 (ΔE₀₀) and the OSA‐UCS (ΔE_E) in the CIELAB color space are in general not better than the conventional CIELAB (ΔE) and CIELUV (ΔE) formulas. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 259–266, 2013     

Color determination in olive oils

Color characterization of olive oil may be of great importance to the industry. To determine the color of a solution, it is necessary to accurately measure a series of tristimulus coordinates for which several methods exist. This study analyzes the errors in the calculation of tristimulus values of olive oil color based on methods, by using several selected ordinates and an increasing number of weighted ordinates, and how these errors affect the values of the chromatic parameters defined in the various chromatic systems. The above analysis shows that the use of a large number of ordinates will lead to better results in the color definition of oils. For its determination, we have used the CIE 1931, CIELUV 1976 and CIELAB 1976 spaces; the latter yields the best results.     

Visual Evaluation of Daylight Simulators for the Colorimetry of Luminescent Materials

The accuracy of several methods for assessing the colorimetric performance of daylight simulators as practical realizations of CIE standard daylight illuminants such as D₆₅ was studied by visual methods. Eight luminescent samples containing various fluorescent whitening agents were used. Visual differences between sample pairs, each consisting of a luminescent sample and its nonluminescent substrate, were judged under a reference source simulating D₆₅ and six test sources with different ultraviolet content from the reference source but nearly the same spectral irradiance in the visible region. Over 3000 observations were made by eight observers. Visual scale values were derived and compared to indices calculated by five published methods. The results show that four methods based on colorimetric weighting gave significantly better correlations than one based on radiometric weighting, with little choice among them; that the CIELAB color-difference equation was preferred to CIELUV; and that the choice of 2° or 10° standard observer had no effect.     

Image color-appearance specification through extension of CIELAB

An extension of the CIE 1976 (L*, a*, b*) color space, CIELAB is described for applications in color reproduction. This extension incorporates a more accurate model of chromatic adaptation, capability to distinguish between the modes of appearance of reflective and self-luminous stimuli, and adjustments to account for changes in surround. The extension of CIELAB is referred to as the RLAB color space. This color space can be used for calculating metrics of lightness, chroma, hue, and color difference. It can also be used to determine the required colors for reproduction across changes in media and viewing conditions. A pilot experiment testing the RLAB model for cross-media color reproduction is also described.     

Metric coefficients for chromatic discrimination of surface colors

The values of the coefficients of the metric tensor (g₁₁, g₂₂, and 2g₁₂) have been determined graphically at any point on the CIE-1964 chromatic diagram, by using Luo and Rigg's chromatic discrimination data. Chromatic-discrimination thresholds obtained by this method and those predicted by the CIELUV, CIELAB; and LABNHU color-difference formulas are compared with different sets of experimental results. The predictions made by the formulas do not fit the experimental results as well as the graphical predictions.     

Some aspects of the visual scaling of large colour differences—II

In an earlier article the authors related visually‐ scaled large colour differences to ΔE* values calculated using four colour‐difference formulae. All four metrics yielded linear regressions from plots of visual colour difference against ΔE*, and ΔE gave the best linear fit, but the correlations were rather low. In an effort to clarify matters, the previous investigation is expanded to include data not hitherto examined. The link between visual colour difference and ΔE* colour metrics is further explored in terms of a power law relationship over a wide range of lightness, hue, and chroma variations within CIELAB colour space. It is shown that power‐law fits are superior to linear regressions in all cases, although correlations over large regions of the colour space are not very high. Partitioning of the experimental results to give reduced data sets in smaller regions is shown to improve correlations markedly, using power‐law fits. Conclusions are drawn concerning the uniformity of CIELAB space in the context of both linear and power‐law behavior. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 116–122, 2000