Color appearance: hue and saturation scaling

Figures 1a and 1b show, for the Newtonian-View and Maxwellian-View, respectively, group mean hue scaling data as a function of wavelength. The hue values have been re-scaled by their associated saturation functions such that the hues sum, not to 100%, but to the associated saturation values (see above); the means for females are shown by symbols and the means for males by continuous lines. The error bars are SEMs; for clarity, those for males extend only below the data points, while those for females extend only above the data points. At each wavelength, the group means, and their SEMs, were obtained by averaging the R, Y, G, B values obtained from each participant.

Figure 1 Color appearance in the fovea of monochromatic lights. Group means of individual hue functions re-scaled by the associated saturation values; hue values sum to the saturation values. (a) Stimuli seen in Newtonian view. Error bars (SEMs) extend above the symbols for females and below the lines for males. (b) Maxwellian view. (c) Data from Newtonian view smoothed and re-plotted on a two-dimensional color space (Uniform Appearance Diagram; see text for details). (d) Data from Maxwellian view smoothed and re-plotted on a Uniform Appearance Diagram. Full size image

There appear to be sex-related differences, but they seem small, and it is not easy to appreciate their magnitude or direction. The effects are clearer when the data in Figure 1a, b are displayed in a color space, the UAD, in Figure 1c, d. The data for females are rotated slightly with respect to those of males: in most parts of the spectrum, the rotation of the female data is clockwise with respect to the male data – this rotation is implicit in the data and is not the result of an analytic manipulation. Consider, for example, the points labeled 510 nm in Figure 1c; for females, the point is almost on the G-R vertical axis, meaning that the sensation is close to unique G; but for males, the same wavelength is still within the BG quadrant, meaning that its wavelength must increase by a few nanometers in order for it to appear unique G.

We are dealing with data from two viewing conditions. We have previously shown that these conditions result in systematic differences in the hues elicited by each wavelength [25]. We digress to show that the sex-related differences that are the central point of this paper are not due to any differences in viewing conditions.

Although the results were qualitatively similar, there is a problem that prevents us from simply amalgamating the two data sets. Despite having the same retinal illuminance there is an important difference: our stimuli were presented as brief flashes with a minimum ITI of 20 s in a darkened testing room, which meant that participants’ pupils were widely dilated. Thus, in the Newtonian-View much of the light entered through the periphery of the pupil and therefore struck the receptors at angles greater than those for light entering through the pupil center, as is the case in the Maxwellian-View. Such "edge" rays are known to produce changes on color appearance of monochromatic lights (Type-II Stiles-Crawford Effect (SC-II); [46, 47]).

Figure 2 compares our data from the two viewing conditions. The abscissa shows, for Maxwellian-view, the wavelengths that elicited a series of hue sensations, ranging from 100%B to 20%Y & 80%R, in 5% hue steps. (The range of hue ratios is restricted to those that were seen by all participants.) The ordinate shows the change in wavelength needed to produce the same hue sensation in Newtonian-view as from Maxwellian-view. The solid, group-mean, curve is re-drawn from our earlier paper comparing these viewing conditions; possible reasons for the effect are discussed fully in that paper [25]. The other two curves in Figure 2, from the data in this paper (Figure 1c, d), break down the effect by sex: there appear to be some sex-related differences, but they are not significant (see statistical analysis below).

Figure 2 Shift in stimulus wavelength required to make color appearance seen in Newtonian same as when seen in Maxwellian view. Group mean functions disaggregated by sex. Error bars (SEMs) extend above the symbols for females and below the symbols for males. Full size image

Statistical analysis of sex differences

Although the effects of sex on color appearance seemed consistent between the two viewing conditions, they were small and not identical. To demonstrate that the sex effects are real, we used an accepted way to amalgamate data sets that have different means: computation of individual differences from the means for each condition.

Because there were almost twice as many female participants as males, averaging across all participants would grossly bias the result towards the wavelengths required by females for each hue. Therefore, for each viewing condition, a global mean of the wavelengths required to elicit each hue was derived: Optical-System Mean = (Mean for males + mean for females)/2. Means were computed separately for each sex to remove the effects of differences in sample sizes between males and females.

Then, for each hue sensation from one of the two viewing conditions (Newtonian or Maxwellian), each participant’s required wavelength was subtracted from the mean wavelength for that participant’s sex. These differences from each Optical-System Mean, were combined into one large matrix, that was organized to retain sex and optical system descriptors.

The male–female differences in the wavelength required for a specific hue are shown in Figure 3. This figure shows clearly the central point of this paper: males require a slightly longer wavelength than do females to experience the same hue.

Figure 3 Sex differences in shifts in wavelengths (combined data from Newtonian and Maxwellian views; see text for description of combination procedure) associated with specific hue sensations. Wavelengths required for females to experience a specific hue ratio (blue, blue/green, green/yellow, yellow/red) subtracted from the wavelengths required by males for the same hue ratios. Full size image

In Figure 3 the abscissa is a series of hue sensations, ranging from 100%B to 20%Y & 80%R, in 5% hue steps; the range of hue ratios is restricted to those that were seen by all participants. (For example, only 30 females reported a sensation of 5%R & 95%B, and only 24 had a sensation of 25%R & 75%B; of the males, only 18 reported a sensation of 5%R & 95%B, and only 14 had a sensation of 25%R & 75%B.) The results from the matrix combining all the data were averaged separately for males and females: the mean wavelength needed to elicit each hue for females was then subtracted from that for males. The results are plotted on the ordinate of Figure 3. For 56 out of 57 of these sensations, covering most of the visible spectrum, males require a longer wavelength than do females to experience a given hue sensation. This difference is also shown in Figure 1c, d: as we have noted (see above), for each viewing condition, the female data are rotated clockwise with respect to the male data.

An ANOVA (SPSS; general linear model, repeated measures, mixed design) was run using the above global matrix: the factors were hue, sex, and optical system. (See Table 1.) While the sex effects were small, the effect of sex was significant: F(1, 92) = 7.004, p = 0.010. The degrees of freedom (92) were slightly less than the degrees of freedom expected from the total number of participants (105); this was due to some missing data points caused by minor errors in the computerized data acquisition. Data from participants with such missing data were excluded from the statistical analysis.

Table 1 Analysis of Sex and Color Appearance Between-Subjects Effects Full size table

In Figure 3 the mean effect-size of the male-female differences in wavelength required to elicit each hue is 2.2 nm. Although, across the hues, there are variations in the differences, they are not significantly different from this mean (ANOVA: no significant effect of hue, see Table 1). That is, regardless of the particular hue, males required, on average, a wavelength 2.2 nm longer than the wavelength needed to elicit the same sensation from females. Similarly, there was no significant effect on the difference scores due to optical system: the results were the same when each participant’s data-set was compared to the appropriate mean for a given optical system. Among other things, this means that the possible sex differences in the data from the two viewing condition (see Figure 2) are not statistically significant. There were no other significant effects or interactions.

Rayleigh anomaloscope matches

Humans are polymorphic for the L- and M-cones (e.g. [13]). Furthermore, individuals may express more than one of these alleles, and there are sex differences in the relative numbers of L- and M-cones [14, 48, 49]. It is generally agreed that many females have phenotypes with multiple L- and M-photopigments. However there is some consensus that males may express only one of each (e.g. [50]). These findings may be the basis for the significant sex effects on hue that we report here.

Inter-individual variations in spectral sensitivities of L- and M-cones in individuals should affect their Rayleigh anomaloscope matches. In this test a bipartite filed is illuminated on one side with a light that appears Y; the task is to match its appearance with an additive mix on the other side with two lights, one appearing G and the other appearing R. (Because all the wavelengths we used were longer than 520 nm, S-cones contributed essentially nothing to the outcome.) Most participants who scaled the appearances of monochromatic lights seen in Newtonian-view also used our anomaloscope to make Rayleigh matches.

Following the convention of Neitz and Jacobs [48], we derived an average measure of the matching RG value as follows. We pooled the RG ratios for all participants, regardless of sex, and weighted the R and G values so that the group average for the quantity R/(R + G) equaled 0.5. This value is the midpoint of the abscissae in Figures 4a, b; these figures show the frequency distributions of this ratio for females and males respectively. High values of the ratio imply less effective R in the matching mix and low values imply less effective G. Individuals who lack the L-cone will have extremely high values for the ratio, while those who lack the M-cone will have extremely low values; these individuals exhibit a form of color blindness (dichromacy) referred to as protanopia or deuteranopia respectively; moderately high values indicate less severe (anomalous) forms of these deficiencies. All of our observers had ratios far from these extremes – they were color-normal.

Figure 4 Frequency distributions of anomaloscope matching ratios: R/(R + G), where R and G are re-weighted to produce a group mean of 0.5 (see text for details). (Only participants who also scaled hue and saturation of stimuli seen in Newtonian view.) (a) females. (b) males. Full size image

Because humans, particularly females, are polymorphic for the L- and M-cone genes, population Rayleigh matches might be expected to show multiple modes, as was shown in published data based on large samples: males had a bi-modal distribution, while females had a largely tri-modal distribution (e.g., [14]). Even though our distributions of matching RG ratios (Figure 4) do not differ greatly by sex, they do show, especially for the females, some of the sex-related differences reported previously. Each graph also includes the normal distributions expected (based on group means and variances) if only random variations were involved. Applying the Kolmogorov-Smirnov test (as included in SPSS), the frequency distribution for males was not significantly different from normality (p = 0.134), perhaps due to small sample size; for females there was a significant difference from normality (p = 0.016).

We considered the distributions of Rayleigh matches because significant multiple modes point to possible sub-populations; each sub-population could be associated with multiple modes in spectral distributions of unique hues. We examine this below.

Unique hues

Single cones can only report the rate at which their photopigments are absorbing photons – once a photon is absorbed, all information about its wavelength is lost. To provide information about wavelength (color), the nervous system must compare the responses of cones that contain different photopigments; this comparison is done by spectrally-opponent cells in the retina – for example, a cone type that is more sensitive to longer wavelengths might excite these cells, while another cone type, more sensitive to shorter wavelengths, would inhibit them.

Spectrally-opponent systems seem ubiquitous in species with color vision, ranging from assorted shallow-water mullets of the family Mugilidae [51], to eels [52], to macaque monkeys [53]. In the macaque, four types of spectrally-opponent cells have been identified in the retina and visual area of the thalamus (lateral geniculate nucleus) [53–56]. These opponent cells have spectral points at which excitation and inhibition are equal and there is no net response (null point). Psychological sensations of color also have spectral nulls – for example, the sensation that is only Y (unique Y) coincides with the null point for R vs. G (see Figure 1). However, the psychophysical null points (unique hues) do not coincide with the nulls of the spectrally-opponent cells. Sensations must ultimately depend on re-processing of these neural inputs to determine opponent hue (sensory) mechanisms [30].

The spectral loci of the unique hues are especially interesting because they define the null points of spectrally-opponent sensations – i.e., hue mechanisms. We argue that hue mechanisms are opponent, based on a variety of evidence, including observations that one half of an opponent system can be used to cancel the sensation of its opponent [57, 58]. Thus, unique Y occurs at the wavelength that elicits a sensation of neither R nor G; this is the null point of the RG mechanism. The precise values of these loci therefore play an important role in constraining many models of color vision based on spectrally opponent processing of visual information (e.g., [30, 57, 59–61]).

UADs were plotted for each individual; the wavelength for each unique hue was found by interpolation on the fitted spline. Figures 5a–c show the frequency distributions of the spectral loci of unique Y, G, and B. In these figures, for simplicity, we show only data for the Newtonian-view – the results and conclusions for the Maxwellian-view are very similar (e.g., see Table 2). For comparability across these three graphs, bin widths were set at 0.33 of the standard deviation for each distribution. (Some of the data points in these figures were included in [41], but here we have added a substantial number of new participants.) Note that for most individuals there is no spectral wavelength that corresponds to unique R – the longest wavelengths elicit a sensation that contains some Y. For each hue, we also show the expected distribution if the loci were normally distributed. From Kolmogorov-Smirnov tests (as included in SPSS), all the group data distributions differ significantly from their expected normal distributions: for Y, p = 0.0043; for G, p = 0.0004; for B, p = 0.0003. The significant differences from normality and the existence of sub-peaks suggest that for the unique hues, humans are not a homogeneous population. In particular the distribution of Y is very narrow, a finding that has also been reported by others using comparable sample sizes but very different psychophysical techniques [62].

Figure 5 Frequency distributions of spectral loci of unique hues (Newtonian view), together with normal distributions based on means and standard deviations of the data. Bin widths = 0.33 of SD for given distribution. (a) Yellow. (b) Green. (c) Blue. Full size image

Table 2 Spectral Loci (nm) of Unique Hues for Newtonian and Maxwellian Views Full size table

The multiple peaks seen in the distributions in Figure 5 may be sex-related; Figures 6a–c show the same data, but split between males and females to examine this. Applying the Kolmogorov-Smirnov test, the frequency distributions of females show significant deviations from normality: Y, p = 0.01; G, p = 0.0005; B, p = 0.0002. However, none of the male distributions differ significantly from expected normal distributions (possibly due to small sample size): Y, p = 0.152; G, p = 0.2; B, p = 0.119. But in all these cases, males have their loci shifted towards longer wavelengths, which reiterates the general finding that males require a longer wavelength than females to experience the same hue sensation (Figure 3).

Figure 6 Frequency distributions of spectral loci of unique hues (Newtonian view), disaggregated by sex. Bin widths = 0.33 of SD for given distribution. (a) Yellow. (b) Green. (c) Blue. Full size image

The similarity of the findings for the two viewing conditions is shown in Table 2: Regarding the spectral loci of the unique hues, the group mean wavelengths, for Newtonian and Maxwellian views, are given in Table 2. Not only are the values similar, but in all cases the values for males are shifted to longer wavelengths.

To examine whether there were any correlations among individuals’ spectral loci and their associated anomaloscope ratios, we computed R2 values separately for males and females. None of the correlations, for any of the unique hues, was significant; most were essentially flat lines with R2 ranging from 0.001 (males, B-unique) to 0.17 (males, Y-unique). The lack of any clear correlations is interesting. Given the relatively broad range of the anomaloscope ratios, and the indications of sub-peaks, possibly related to expression of different L- and M-cone alleles, we might have expected a closer relation between a participant’s anomaloscope ratio and his or her locus of a spectral hue. Unique Y in particular is a function only of L- and M-cone inputs to the G-R opponent hue mechanism; it coincides with the spectral null point of the G-R system. But, these cone inputs must be weighted relative to each other: specifically, the input from the M-cones must be weighted more strongly than that from the L-cones in order to shift unique Y to its observed spectral locus.

Furthermore, the relative weights of these inputs must be quite tightly constrained because the distribution of unique Y shown in Figure 5 is narrow (see [30] for a more complete discussion). This narrowness is remarkable for two reasons: firstly, there are differences in sensitivity among L- and M-cone spectral sensitivities, as shown by the range of anomaloscope ratios; secondly, there are large variations among individuals in the relative numbers of these cones [33]. The cortical weighting of the cone inputs to the G-R system must compensate for these individual differences.

Finally, we looked for any possible correlations between the spectral loci of each pair of unique hues. We found none, confirming similar earlier conclusions [61, 63].

Wavelength discrimination

Because an individual’s UAD for a particular viewing condition has a uniform metric, it can be used to derive a wavelength- discrimination function [23–27]. Participants’ functions were derived by measuring, for each stimulus, (along the spline function fitted to each individual's UAD – see above) the change in wavelength needed to produce a fixed, criterion change in sensation; these wavelength shifts were averaged across participants to obtain group wavelength-discrimination functions for males and females.

Figure 7 shows wavelength-discrimination functions for the two optical viewing conditions broken down by sex. In Figure 7a we show the curves for the Newtonian View, and in Figure 7b the same for the Maxwellian View. The general trends are remarkably similar. While there are no statistically significant sex differences, the male and female curves are not identical. Applying Exploratory Data Analysis [64] to these data: there appear to be systematic differences between the sexes. In the middle of the spectrum, males have a slightly broader range of relatively poor discrimination (540–560 nm for Newtonian-view; 530–570 nm for Maxwellian-view). We suggest that the sex differences in wavelength discrimination are real.