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Kuehni et al. Vol. 27, No. 2 /February 2010 /J. Opt. Soc. Am. A 159

Perceptual prominence of Hering’s chromaticprimaries

Rolf G. Kuehni, Renzo Shamey,* Mara Mathews, and Brandi Keene

Polymer and Color Chemistry Program, Department of Textile Engineering, Chemistry, and Science,North Carolina State University, 2104 Research Drive, Raleigh, North Carolina 27695-8301, USA

*Corresponding author: [email protected]

Received April 23, 2009; revised October 12, 2009; accepted October 27, 2009;posted December 3, 2009 (Doc. ID 110415); published January 11, 2010

Reported are results of an experiment involving perceptual assessment of very large color differences usingsamples representing approximate mean Hering opponent generic unique hues (guHs) based on subject selec-tions, intermediate hues (iHs) using Munsell samples intermediate between guHs, and pairings of both guHsand iHs with a neutral gray. Sample pairs were assessed by 28 color normal subjects twice, with a gap of atleast 24 hours between assessments. Results were calculated for individual subjects and the entire group. Thehypothesis was that perceived chromatic differences of Hering’s guHs are larger than those of iHs, and thiswas found to be statistically valid at the 99% confidence level based on a t-test. In addition, gray as a perceptwas found to have prominence comparable to that of generic unique hues. © 2010 Optical Society of America

OCIS codes: 330.1690, 330.1720, 330.5020, 330.7310.

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. INTRODUCTIONwidely accepted point of view in regard to the percep-

ual nature of colors is one proposed by Ewald Hering in878 [1]. According to his hypothesis there are two per-eptual chromatic opponent-color processes that result inour fundamental color percepts: yellow and blue as onepponent pair, red and green as the other. The hues of theundamental percepts are the unique hues (uHs). Forost subjects the uH pairs are not complementary, how-

ver. All other pure hues are mixtures of two adjoiningundamental colors, their veiled versions the result of ad-ixtures with white or black percepts, or both. Hering’sypothesis appears intuitively veridical to most people,nd it has support from scaling experiments of interme-iate hues in terms of uHs [2,3]. We are not aware of ex-eriments in the opposite direction: attempting to scaleue percepts based on iH primaries. So far, Hering’s per-eptual hypothesis lacks support from a neurophysiologi-al model and corresponding experimental evidence, asonceded, for example, by Abramov and Gordon [3] and byacLeod [4], although some potentially promising devel-

pment has recently been reported [5]. If uHs are excep-ional, their perceptual differences might be larger thanhose between iHs, adding experimental support to theering hypothesis. We are not aware that this possibilityas been experimentally investigated in the past.In the experiment described here an attempt has beenade to assess the perceptual prominence, if any, of theering chromatic primaries in comparison with that of

Hs by comparing very large color differences. Perceptualifferences between two color stimuli begin at the thresh-ld difference level (“just noticeable differences”). Of com-ercial importance are small but supra-threshold differ-

nces. Large differences are those between neighboringamples in color atlases, such as the Munsell system orhe Optical Society of America Uniform Color Scales

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OSA-UCS). As the differences judged in this experimentre much larger than those of OSA-UCS we name themvery large differences.” It is well known that large differ-nces are not just scaled up versions of threshold differ-nces, but that there are what appear to be parametrichanges [6,7]. We think it is likely that very large differ-nces deviate even more from scaled up small differences,ith the intrinsic qualitative nature becoming more im-ortant.The hypothesis investigated in the current experiment

s: Average perceived differences between Hering uHs arearger than those between iHs because the uHs are per-eptually more prominent than the iHs. It has beenhown [8–10] that there can be significant inter-subjectariation in the stimuli selected to represent uHs. Pastublished experiments [10], as well as unpublished ex-eriments in our own laboratory, show the same for iHs.onsequently, samples representing approximately aver-ge uH percepts based on previously assessed individualH stimulus choices rather than those representing indi-idual subjects’ uH percepts have been employed. Thesere here named generic unique hues (guHs). They areepresented by the Munsell hue samples of the highesthroma available in the system. The selected iH samplesre those that in the Munsell system are halfway betweenhe guHs. Thus, the samples selected are considered in-ermediate in terms of the hue scaling of the Munsell sys-em.

. METHOD. Subjectstotal of 28 subjects including fifteen females (mean age

2.0, range 19–29 years) and 13 males (mean age6.1 years, range 19–51 years) participated in the experi-ent. Most subjects were university students and did not

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160 J. Opt. Soc. Am. A/Vol. 27, No. 2 /February 2010 Kuehni et al.

ave any previous experience in making color differenceudgments. All subjects had normal color vision accordingo results of the Neitz Test of Color Vision [11].

. Samples and Sample Presentationable 1 lists the approximate mean guHs [8,9] yellow (Y),ed (R), blue (B), and green (G), and the iHs orange (O),urple (P), blue-green (BG), and yellow-green (GY) basedn the Munsell color atlas samples employed. A Munsellample was also used as neutral gray (NG). The letter no-ations shown in Table 1 are used to identify the variousues throughout.Sheets of the corresponding Munsell papers were cut

nto 2.5�2.5 cm size samples and mounted on sheets of1.6 cm�28.0 cm N5.5 gray cardboards �L*=57� in 12 tri-ngular and six double pair arrangements. As a result ofhe lightness crispening effect the gray samples werelearly distinguishable from their surround. The arrange-ent of samples is described in the following subsections.

. Double Pair Setshe psychometric method of pair comparison was firstsed for color comparisons by J. Cohn [12]. It is the stan-ard methodology used in establishing data for color-ifference formulas. Double pair samples shown in Tablewere used for the purpose of establishing the perceptualifference between the arbitrarily selected reference pair–BG and pairs of guHs and iHs in a manner comparableith the widely used method of judging the size of small

olor differences against a gray reference pair. Figure 1(a)hows an example of a mounted pair with designationair O–BG versus pair Y–B.

. Triangular Setsriangular evaluation of color differences is a well-stablished method having, in color, found its most exten-ive application in mid-20th century in the scaling of theSA-UCS [13]. Table 3 shows the guHs, iHs and NG setsf samples used in this part of the study. All sets wereeparately mounted on N5.5 gray cardboards in triangu-ar patterns. Because of the lightness crispening effect14] there is clear perceptual distinction between the NGample and the surround.

The difference between the first and the second samplen each group was given the letter A, between the secondnd the third sample the letter B, and between the third

Table 1. Munsell Colors Used as Genericand Intermediate Hues

Hue NotationMunsell Color Notation

of Samples Used

eneric unique yellow Y 5Y8/14eneric unique red R 5R4/14eneric unique green G 2.5G5/12eneric unique blue B 2.5PB5/12

ntermediate purple P 10P5/12ntermediate orange O 5YR6/14ntermediate green–yellow GY 2.5GY7/12ntermediate blue–green BG 7.5BG5/10eutral Gray NG N6

nd first sample the letter C. The layout of the triangularisplay is shown in Fig. 1(b). The first four triangles es-ablish the perceptual difference relations between guHs,he second four between iHs. Each difference appearswice in these sets. The last set of four triangular pairsontains generic unique and intermediate hue samples asell as achromatic gray samples, so that comparison of

he perceptual differences can also be made between chro-atic and central gray samples.

. Procedureubjects were adapted to simulated D65 daylight using apectraLight III standard calibrated viewing booth (X-ite) illuminated with filtered tungsten light at a color

emperature of 6504 K and at 1400 lux intensity for 2 minith all extraneous light excluded. Subjects sat in front of

he booth with sample display charts approximately at0° from the normal and at an approximate distance of

Table 2. Double Pair Samples Compared

First pair Second Pair

O–BG G–BO–BG Y–BO–BG Y–GO–BG R–GO–BG R–YO–BG B–R

ig. 1. (Color online) Sample schemes: (a) Double pair arrange-ent. (b) Triangle sample arrangement.

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0 cm. The subject was shown the first triangular chartnd asked to identify the pair that exhibited the smallesterceptual color difference among the three differences A,, and C. This difference was given the arbitrary value of.0 and the subject was then asked to assess the magni-ude of the difference for the other two pairs as incremen-al fractions, e.g., 1.4 of the first difference.

In the case of the pair comparisons the larger of the twoifferences was given the arbitrary value of 1.0 and themaller difference was scaled as a decremental fraction,.g., 0.75. The experiment was repeated once for each sub-ect, with at least a 24 h interval between the judgments.

All sample sets were assessed by all subjects in randomrder. Although assessments of very large color differ-nces, such as those used in this experiment, have beenescribed as difficult [15], none of the subjects employedn this study indicated significant difficulty in makinguch judgments. In addition intra- and inter-subject vari-bility of assessments was found to be well within those ofmall color-difference judgments [16].

. ANALYSIS

Table 3. Triangular Sample Sets

eneric Hue Sets Intermediate Hue Sets Hue–Gray Sets

R–G–Y O–BG–P Y–NG–BR–B–Y O–GY–P R–NG–GR–G–B O–GY–BG P–NG–GYY–G–B P–GY–BG BG–NG–O

Table 4. Mean Values from Double-Pair Data

Pair Mean Difference Standard Deviation

Y–B 1.33 0.17B–R 1.18 0.18Y–R 1.09 0.19R–G 1.04 0.18G–Y 1.02 0.26B–G 0.50 0.18

ata from both sets of tests were analyzed separately and

nified around the value of 1.0 assigned to difference–BG in the double pair test.Double-pair data: Mean relative color difference values

f the two trials were calculated from the individual meanata of the 28 subjects and normalized to a value of 1.0 forhe difference O–BG. The results are shown in Table 4nd indicate that on average, with the exception of theifference B–G, all differences are larger than the differ-nce O–BG.

Triangular set data: Comparable mean data by indi-idual and in total were calculated from the four assess-ents for each difference pair. For example, for the differ-

nce between Y and B, the mean response for sampleairs Y and B in sets R–B–Y and Y–G–B, each evaluatedwo times, was calculated in a manner comparable to cal-ulations performed in the evaluation of the OSA-UCS ex-erimental data involving triangular sets. The iH resultsere normalized so that the mean result for the O–BGair has the arbitrarily chosen value of 1.0. Normaliza-ion of the guH pairs was separately calculated so thathe triangular mean difference agrees with the corre-ponding double pair mean difference for all six guHairs, and the results were then averaged. The chromatic-ray mean color difference values were also normalized inhe same manner using a factor that set the mean Y–Bifference in those data also to a value of 1.30.The resulting normalized mean perceptual difference

alues of all subjects for the three groups of differencesorted by magnitude of difference, their standard devia-ions, and the range of values by subject are shown inable 5.Figures 2–5 show graphical representations of the re-

ults from Table 5 in schematic perceptual hue circles. Inig. 2 the results for the diagonal guH and iH pairs arehown. Figure 3 compares the mean values for the differ-nces between neighboring guHs. Figure 4 shows the dif-erences between pairs of iHs and Fig. 5 those of guHsnd iHs compared with the central gray. It is evident fromhese figures that the perceptual plane implicit in the re-ults is non-Euclidean.

Before discussing these results in greater detail infor-ation concerning the intra- and inter-subject variability

f the experimental data is provided.

Table 5. Mean Normalized Relative Perceptual Color Differences

Generic Hues Intermediate Hues Hue: Gray

PairMeanDiff.

Std.Dev. Range Pair

MeanDiff.

Std.Dev. Range Pair

MeanDiff.

Std.Dev. Range

Y–B 1.30 0.64 0.58–2.63 O–BG 1.00 0.59 0.35–2.39 R–NG 1.31 0.82 0.37–3.71Y–R 1.27 0.65 0.43–2.83 GY–P 0.91 0.48 0.30–2.00 O–NG 1.25 0.81 0.37–3.53

–G 1.20 0.83 0.38–3.50 P–O 0.82 0.41 0.32–1.74 P–NG 1.23 0.78 0.37–3.16B–R 1.07 0.61 0.38–2.55 GY–BG 0.61 0.28 0.26–1.29 GY–NG 1.21 0.74 0.37–2.97

–Y 0.92 0.57 0.38–2.50 BG–P 0.56 0.28 0.26–1.42 Y–NG 1.21 0.88 0.37–3.71–G 0.49 0.21 0.38–1.32 O–GY 0.51 0.26 0.26–1.10 B–NG 0.93 0.70 0.37–3.16

G–NG 0.86 0.61 0.37–2.23BG–NG 0.84 0.58 0.38–2.79

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. Intra- and Inter-Subject Variabilityata on intra- and inter-subject variability in color-ifference judgments are rarely provided in the literature.ntra-subject variability for each subject is the change inis/her judgments among repetitions. Inter-subject vari-bility, however, is the variation in the mean results ofne subject against the mean results of others. Assuminghat the grand mean perceived color difference for eachair is the true value, the inter-subject (or intra-group)ariability is the degree to which each subject’s assess-ent of each pair agrees with the true value of such pair.measure of inter-subject variability can be obtained us-

ng the accuracy concept defined as the degree to whichssessments Y agree with a “true value” Ym as shown inq. (1) [17].

Accuracy = Ym − Y. �1�

For the analysis, the inter-subject variability was cal-ulated separately for each subject. Equation (2) can besed to obtain the individualized sum of squares repre-enting inter-subject variability [18,19].

Inter-subject sum of squares = � �Yik − Y� i�2. �2�

he subscript i represents the sample pair number (i=1o 36) for 12 panels of triangular sets, k denotes the trialumber (k=1 to 2), Yik represents the perceived color dif-erence of a pair for a subject in a particular trial, and Y� iepresents the grand mean perceived color differencerom all trials and all subjects for a given pair. In order tobtain an objective assessment, inter-subject sum ofquares can be converted to standard deviation using

ig. 2. Mean normalized perceived difference values for diago-al comparisons.

ig. 3. Mean normalized perceived difference values for neigh-oring guH pairs.

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mong his or her trials, or intra-subject variability, canlso be calculated by obtaining the sum of squares of theeviation of assessments using each subject’s mean judg-ents for each pair from all trials Yi as shown in

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In order to obtain the overall intra-subject variabilityhe mean intra-subject standard deviation can be ob-ained. Table 6 shows a summary of intra- and inter-ubject variability for the triangular color difference as-essments carried out in this study. For all subjects andample pairs the mean intra-subject standard deviation oferceived color difference assessments between trials is.81 units, with a range of 0.15–1.89 units. The meannter-subject standard deviation is 2.0 with a range of ap-roximately 1.2–4.1 units. These values are well within

ig. 4. Mean normalized perceived difference values for neigh-oring iH pairs.

ig. 5. Mean normalized perceived difference values betweenentral gray and guH or iHs.

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he range of comparable data recently calculated for twondependent experiments in small-color-difference judg-

ents [16].Subjects also differed in how they judged the magni-

ude of difference of specific pairs. To provide an indica-ion of the variability, the six pairs of normalized guH dif-erences and those of iH differences were ranked for eachubject on a scale of 1–12. Table 7 gives the ranks for all8 subjects and each of the 12 differences, providing anndication of variability in assessment.

Separate summing of ranks for the guH differences andhe iH differences for each subject indicates that all 28ubjects judged the guH differences on average to bearger than the iH differences, if to varying degree. Cal-ulation of the ratio between the two rank sums resultedn a mean value of 1:1.57, with a standard deviation of.35.

. Generic Unique Hues and Intermediate Huesalculations of the mean perceived differences using theesults given in Table 5 show guH differences are approxi-ately 41% larger than those between iHs. Diagonal per-

eptual differences between guHs (Y–B plus R–G) haveeen judged on average to be 31% larger than those be-ween iHs (O–BG plus GY–P). The mean difference be-

Table 6. Summary of Intra- and Inter-SubjectVariability for Triangular Judgments

Subject Intra-Subject SD Inter-Subject SD

M1a 0.43 1.53M2 0.27 1.69M3 0.67 1.63M4 0.57 1.48M5 0.28 1.35M6 0.37 1.42M7 0.15 1.77M8 1.89 3.22M9 1.34 3.01M10 0.58 1.26M11 0.17 1.37M12 0.96 1.67M13 1.34 3.01F1 0.50 1.16F2 0.57 1.29F3 0.22 1.68F4 0.63 1.36F5 1.07 2.25F6 1.86 4.12F7 1.43 2.81F8 0.70 1.54F9 1.63 3.08F10 1.09 3.21F11 1.26 2.28F12 0.70 1.69F13 0.53 1.54F14 0.57 1.26F15 1.03 2.27

Grand Mean 0.81 2.00Range 0.15–1.89 1.16–4.12

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ween the four neighboring guH pairs is approximately0% larger than that between the four iH pairs, evenhough the difference between B and G is judged themallest of all 12 differences. With the exception of Y–R,erceived differences between opposing guHs are largerhan those between neighboring ones. When comparingor the 28 observers the mean normalized values for theix guH differences derived from triangular data withhose of the six iH difference in a two-tailed paired t-testre statistically significant at the 99% confidence level,onfirming the basic hypothesis.

In Figs. 6 and 7 the relative differences between neigh-oring guHs and iHs obtained in this experiment are com-ared with those of the Munsell hue diagram, with thengular distances representing the hue difference values.he 12 o’clock position was normalized for R in the firstase and O in the second. As evident from Fig. 6 there arearge discrepancies in the relative locations of Y and G.nterestingly, there is little relative difference in scalingf iHs between the results of the experiment and theunsell system.

. Difference from Grayhe non-Euclidean nature of the perceptual plane is evi-ent from the fact that the diagonal sums of differencesetween gray and opponent hues are approximately 1.6 to.8 times larger than the direct differences between thepponent hues. The judged differences between NG and Rr O rival in magnitude those between Y–B and R–G. Theerceptual character of NG is in these comparisons seeno be as distinct as those of the most distinct chromaticolors. The largest perceptual difference is between R andG (1.31) and the smallest between BG and NG (0.84).

. Index of Distinctness Predicateo obtain a measure of the comparative distinctness ofach of the four guHs and iHs, as well as gray, the meanerceptual differences for each of the four cases where aiven hue is a component of the difference (eight cases in-olving gray), was calculated and defined as the index ofistinctness predicate as shown in Table 8.Based on these results R has comparatively the most

istinctive perceptual character, followed by Y, NG, andG shares the next place with O and P. In direct compari-ons the perceptual distinctness of gray is in the range ofhose of guHs and larger than those of iHs.

. DISCUSSIONince antiquity, certain hues have been regarded as pri-ary or “generic,” while others were considered interme-

iate. This applies to the visual arts and philosophy, asell as science. Most authors limited generics to Y, R, and, based on experience with colorants; G was considered

o be a mixture of Y and B. Early proponents of three ge-eric chromatic colors such as d’Aguilon [20] or Boyle [21]enerally agreed that hues transition smoothly from oneo the next. They selected Y, R, and B as the generic huesith the argument that only with those can all other huese generated, an argument not valid, either for light mix-ure or colorant mixture.

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As pointed out in the introduction, in 1878 Hering pro-osed that, perceptually, colors are a mixture of one orwo fundamental hue percepts plus those of white andlack. The fundamental hue percepts, in English termedHs, are Y, R, B, and G, each one defined as a hue thatoes not contain traces of a second hue percept, uniqueed for example being the red that is neither yellowishor bluish, but purely red. Other hues can perceptually benderstood as composed of two unique hues, but uniqueues cannot be understood as composed of iHs. The per-

Table 7. Ranks of the guH and

ubject

Generic Unique Hue Sets

R–G Y–B G–Y Y–R B–R B–

M1 9 1 2 3 4M2 2 3 7 4 1M3 2 1 7 3 5M4 1 3 9.5 2 6 9M5 1 3 9 2 4M6 1.5 3 4 8 1.5M7 4 1 3 2 5.5 5M8 4 1 2.5 2.5 7M9 1.5 1.5 12 6 3M10 10 2 5 4 1M11 1 3 4.5 6 4.5M12 10 1 3 2 7 11M13 4 1 10 2 3 11F1 9 2.5 1 2.5 6F2 7.5 1 7.5 2.5 2.5F3 7.5 1.5 1.5 3 7.5F4 11 2 4 1 7F5 1 6 8 5 3F6 1 4.5 9 2 4.5F7 7.5 2 3 1 7.5F8 6 2 3 1 8.5 8F9 1 6.5 10 6.5 2F10 2 11 8 5 1F11 7 2 1 3 4F12 9 4 1 2 8 11F13 8.5 2.5 2.5 1 8.5F14 1 2 12 7 5F15 1 6 8 2 3

Range 1–10 1–11 1–12 1–7 1–9 5–Mean 4.68 2.86 5.64 3.25 4.66 9.

SD 3.60 2.24 3.50 1.96 2.37 2.

ig. 6. Comparison of the location of the same guH color chipsn the Munsell system (dashed lines M) and as a result of the ex-eriment (solid lines), both scales normalized at R (5R).

eptual validity of this hypothesis has generally been ac-epted. Tests have shown that individual subjects differ toconsiderable extent in the stimuli they select as repre-

enting for them the uHs [3,9,22]. In addition, as men-ioned, at this time there is no generally accepted neuro-hysiological model for the generation of uH percepts.he experimentally confirmed neurons with opponent-olor properties in the lateral geniculate nuclei do notave response properties in agreement with uH percepts23]. Thus, it remains unresolved whether uHs have sin-ular neurophysiological correlates.

ifferences for All 28 Subjects

Intermediate Hue Sets

O–BG GY–P O–GY GY–BG BG–P P–O

8 5 12 6 7 1110 5 11.5 11.5 8 66 4 9 10 12 114 7 12 8 11 55 7 11 11 11 86 7 10.5 12 10.5 58 11 12 9.5 7 9.55 6 12 9 10 8

4.5 4.5 9 10 11 73 6 12 9 11 72 7 12 11 10 88 4 5 11.5 6 96 9 7.5 7.5 5 11.57 4.5 10 12 8 4.59 4 12 10 6 55 6 10 12 11 4

8.5 8.5 5.5 10 5.5 32 4 12 9 10 73 7 8 10 11 64 10 11 9 5 6

10 11 12 5 4 73 4.5 12 8 11 4.53 4 9 10 12 65 6 8 11 9.5 9.55 3 7 11.5 10 6

6.5 10 11 5 6.5 44 3 8 9 10.5 10.5

4.5 9 10 7 12 4.5

2–9 3–11 5–12 5–12 5–12 3–115.54 6.32 10.04 9.45 8.98 6.912.31 2.40 2.12 2.00 2.49 2.38

ig. 7. Comparison in the same manner as Fig. 6 of the iH colorhip locations, normalized at O (5YR).

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The idea behind our experiment is that the special per-eptual nature of uHs (averaged as guHs) will result onverage in larger perceived differences between themhan those between intermediate hues, because of highererceptual distinctness of the guHs. Our results supporthe validity of this idea for the average subject andhereby provide support for the special nature of guHs. Asn all such kinds of judgments there is considerable inter-ubject variability in the results, but the concept wasound to apply, on average, to each of our 28 subjects.here can be differences of opinion about the specific de-ign of any experiment. Further investigation involvingifferent experimental methodologies may help elucidatehe question addressed in this experiment.

. CONCLUSIONShe question arises if there is a methodology with whicho provide objective, perceptual support for the specialole of the guHs. This is the basis of the present experi-ent. It needs to be kept in mind that the property of

uHs of interest is their unique perceptual character, buthat the methodology used is color difference assessment,ecause there is no direct, objective method to describehe perceptual character of the hues. The results provideupport for the hypothesis stated in the introduction asollows:

1. Diagonal perceptual differences between guHs haveeen judged on average to be 31% larger than those be-ween iHs.

2. The mean difference between neighboring guHs is0% larger than that between iHs, even though the dif-erence between B and G is judged the smallest of the 12ifferences.3. For all chromatic differences those between guHs

re on average 41% larger than those between iHs.4. On the basis of a two-tailed paired t-test the differ-

nce between the normalized mean guH and the iH trian-ular differences is found to be statistically significant athe 99% confidence level.

5. An index calculated as the mean of four differencesn which guHs and iHs are involved places R, Y, and B inront, with G falling between O and P.

In addition, the data show that NG, as a perceptual

Table 8. Distinctness Index

Color Index

R 1.21Y 1.18

NG 1.11B 0.95O 0.90P 0.89G 0.87

GY 0.82BG 0.76

oncept, is in the same class of distinctness as the guHs,

ith an index of 1.11. Of all eight differences involvingray, the largest is that between NG and R, also support-ng the role of R as the most distinctive hue percept.

CKNOWLEDGMENTShe authors would like to express their appreciation to-Rite Inc. for the donation of the sheets of Munsell pa-ers used in the experiment. We also thank all subjectsor participating in the study.

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perceptual prominence of hering's chromatic primaries

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