Are red, yellow, green, and blue perceptual categories?

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Are red, yellow, green, and blue perceptual categories? ⁎

Christoph Witzel , Karl R. Gegenfurtner Department of Psychology, Giessen University, Otto-Behaghel-Str. 10, 35394 Giessen, Germany

A R T I C LE I N FO

A B S T R A C T

Number of Reviews = 2

This study investigated categorical perception for unique hues in order to establish a relationship between color appearance, color discrimination, and low-level (second-stage) mechanisms. We tested whether pure red, yellow, green, and blue, (unique hues) coincide with troughs, and their transitions (binary hues) with peaks of sensitivity in DKL-space. Results partially confirmed this idea: JNDs demarcated perceptual categories at the binary hues around green, blue and less clearly around yellow, when colors were isoluminant with the background and when accounting for the overall variation of sensitivity by fitting an ellipse. The categorical JND pattern for those three categories was in line with the effect of the second-stage mechanisms. In contrast, the results for unique red, binary red-yellow, and the JNDs for dark colors clearly contradicted categorical perception. There was a JND maximum around the center of red and JNDs strongly decreased away from the center. Although this observation alone would also be in line with categorical perception; unique red was shifted away from the center towards yellow so that unique red was close to the minimum instead of the maximum JND, hence contradicting categorical perception. In addition, we also showed that observers do not adjust unique hues more consistently than binary hues, confirming a previous study. Taken together, our findings suggest that some of the unique hues could be inherent in the early stages of color processing. At the same time, they also raise questions about complex effects of lightness, chroma and instructions on the measurements of JNDs and unique hues.

Keywords: Categorical perception Color vision Color appearance Color discrimination Unique hues

1. Introduction In this study, we investigated the relationship between the basic mechanisms of color vision, the subjective appearance of colors, and the color terms used to communicate about colors. For this purpose, we investigated whether red, yellow, green, and blue categories result from color processing at the early, sensory stages of color processing. 1.1. Background Red, yellow, green, and blue play a particular role in color appearance and color language. With respect to color appearance, pure red, yellow, green, and blue are assumed to be elementary colors, called unique hues. The subjective appearance of any other color may be composed by a mixture of the unique hues (Abramov & Gordon, 1994, p. 1647; Sternheim & Boynton, 1966; Valberg, 2001). Unique hues consist of two opponent pairs of hue, namely unique red and green, and unique blue and yellow. Besides the chromatic unique hues there are black and white, which, however, are not the focus of this study. Red, yellow, green, and blue also play a particular role in color language. Human observers are able to perceive a multitude of different

⁎

colors (Krauskopf & Gegenfurtner, 1992; Linhares, Pinto, & Nascimento, 2008; Pointer & Attridge, 1998). However, when communicating about colors we use color terms that assign the discernable colors to a few categories, such as red, orange, and yellow. These categories may be called “linguistic categories” because they correspond to linguistic color terms. Several studies observed a tendency across fundamentally different languages to have color terms that refer to the most typical red, yellow, green, and blue (Kay & Regier, 2003; Lindsey & Brown, 2009; Regier, Kay, & Khetarpal, 2007). More precisely, the prototypes of the categories of different languages cluster around the prototypes of the English red, yellow, green, and blue categories, which in turn coarsely correspond to the unique hues (Regier, Kay, & Cook, 2005). Assuming that typical red, yellow, green, and blue have particular perceptual properties, they have been glossed focal colors. The second-stage mechanisms are the basic mechanisms responsible for color opponency and the three-dimensionality (trichromacy) of human color vision. These mechanisms are known to a degree that allows for modeling them by color spaces, such as the DerringtonKrauskopf-Lennie (DKL) space (Derrington, Krauskopf, & Lennie, 1984). The second-stage mechanisms produce three cone-opponent channels. Each of these channels combines information provided by the

Corresponding author. E-mail address: [email protected] (C. Witzel).

https://doi.org/10.1016/j.visres.2018.04.002 Received 31 January 2017; Received in revised form 20 February 2018; Accepted 6 April 2018 0042-6989/ © 2018 Elsevier Ltd. All rights reserved.

Please cite this article as: Witzel, C., Vision Research (2018), https://doi.org/10.1016/j.visres.2018.04.002

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O'Regan, 2006; Vazquez-Corral, O'Regan, Vanrell, & Finlayson, 2012). However, the coincidence of high chroma and category prototypes is a feature of the stimulus set, rather than a property of human color perception (Witzel, in press; Witzel & Franklin, 2014; Witzel, Maule, & Franklin, under revision), and the constancy of categorizing typical colors seems to be a consequence of categorization rather than a feature of perceptual color constancy (Weiss, Witzel, & Gegenfurtner, 2017; Witzel, van Alphen, Godau, & O'Regan, 2016). Finally, although there is a similarity between empirical measurements of unique hues and typical red, yellow, green, and blue (Kuehni, 2001; Miyahara, 2003; Witzel & Franklin, 2014; Witzel et al., under revision); their precise relationship remains unclear (for a detailed theoretical discussion see Witzel, in press). Taken together, the origin of unique hues (Mollon, 2009; Valberg, 2001) and linguistic color categories (Kay & Regier, 2006; Witzel, accepted) is still unknown. Their relationship to known mechanisms of color vision remains unclear and doubt has been casted on the idea that unique hues and focal colors play a particular role in color perception (Witzel & Gegenfurtner, in press). Instead, the idea that red, yellow, green, and blue are elementary might be solely the result of linguistic color naming (Bosten & Boehm, 2014). In particular, those four color terms and their prototypical colors might gain their significance from colored objects or lights in the natural or cultural environment (e.g. Broackes, 2011; Mollon, 2006). Such linguistically defined unique hues might not have any particular implications for color perception and color appearance.

photoreceptors in different ways. A luminance channel mainly adds the excitation of long- (L) and middle-wavelength (M) cones (L + M). A chromatic channel contrasts the L- to the M-cone excitation (L-M), and a second chromatic channel contrasts the excitation of the short-wavelength cones (S) to the combined L- and M-cone excitation (S(L + M)). The L-M channel produces a color contrast between a bluish green and red, and the S(-L + M) channel contrasts a greenish yellow to purple. In this way, these channels lay the basis for a kind of color opponency that could potentially be linked to the color opponency of unique hues. However, it is not clear how the sensory color signal of the secondstage mechanisms is further processed at the cortical level to produce the colors in the way they ultimately appear to us (Gegenfurtner, 2003; Witzel & Gegenfurtner, in press). Several observations contradict a direct relationship between unique hues and cone-opponent mechanisms. First, the poles of the cone-opponent channels do not correspond to the opponent pairs of unique hues (Abramov & Gordon, 1994; De Valois, De Valois, Switkes, & Mahon, 1997; Hansen & Gegenfurtner, 2006; Krauskopf, Williams, & Heeley, 1982; Malkoc, Kay, & Webster, 2005; Wuerger, Atkinson, & Cropper, 2005). Second, the inter-individual variation in unique hues is not related to inter-individual variations in sensitivity of those channels, either (Webster, Miyahara, Malkoc, & Raker, 2000). Third, Danilova and Mollon (2010, 2012) found evidence that sensitivity to hue difference decreases towards the cerulean line, the line that connects unique blue to unique yellow through the adapting white-point. The authors suggest that there is a perceptual mechanism for discrimination away from the cerulean line, which coarsely corresponds to a contrast between blue and yellow. However, the contrary was found for unique green (Danilova & Mollon, 2014), and results were ambiguous for unique red (Danilova & Mollon, 2016). A neural basis of unique hues has been suggested (Stoughton & Conway, 2008), but these results have been contested (Mollon, 2009). Other studies did not find neurophysiological evidence for unique hues (Bohon, Hermann, Hansen, & Conway, 2016; Wool et al., 2015). A recent ERP study (Forder, Bosten, He, & Franklin, 2017) observed shorter latencies for unique than for intermediate hues in the P2 component. Since this is a post-perceptual component (including e.g. effects of attention and working memory) the link between unique hues and mechanisms of color perception remains open. In addition, the special status of red, yellow, green, and blue in color appearance has been questioned. A recent study showed that, instead of red, yellow, green, and blue, other reference colors (notably lime, orange, purple, and teal) can be used to describe the appearance of all colors (Bosten & Boehm, 2014). That study also showed that unique hue adjustments are sensitive to the comparison colors used in the instructions; for example, it yielded different choices of unique red when asking observers to adjust a red that is neither blue nor orange than when asking for a red that is neither blue nor yellow. Another study (Bosten & Lawrance-Owen, 2014) proposed that unique hues should be more reliable across measurements than other colors if they are the basis and reference for the appearance of all colors. However, the study found that lower within-individual variability (i.e. higher consistency) is not a general property of unique hues. Other studies observed that unique hues do not have higher salience than other colors (Witzel & Franklin, 2014; Wool et al., 2015). Despite many attempts the link between particular perceptual properties and the prototypes of linguistic categories could not yet be established either (Witzel & Gegenfurtner, in press; Witzel, under review). It has been found that category prototypes are categorized more consistently than other colors across illumination changes (Olkkonen, Witzel, Hansen, & Gegenfurtner, 2009; Olkkonen, Witzel, Hansen, & Gegenfurtner, 2010), that the regularities in color categorization across cultures correlate with the chroma of colors (Lindsey, Brown, Brainard, & Apicella, 2016; Witzel, 2016; Witzel, Cinotti, & O'Regan, 2015), and that the highly saturated category prototypes correspond to surfaces that have particular properties under illumination change (Philipona &

1.2. Objective Categorical perception of color has been one of the major approaches to link color perception and language (Kay & Regier, 2006; Witzel, accepted). According to the idea of categorical perception, the perceived differences between colors increase at the category borders, leading to an abrupt change in perceived color at category boundaries (Bornstein & Korda, 1984). If color perception is inherently categorical the resulting perceptual categories may provide the perceptual origin of the linguistic categories used in color naming. The existence of perceptual categories would thus explain statistical regularities in color categorization across different languages (Kay & Regier, 2003; Lindsey & Brown, 2009; Regier et al., 2007). The sensitivity to color differences is the basic ability to see a difference between two colors. If color perception was inherently categorical the sensitivity to color differences should be higher at category boundaries when compared to the continuous change of the sensory color signal. This idea may be called categorical sensitivity (Witzel & Gegenfurtner, 2013). However, sensitivity is not categorical when considering the categories of all eight chromatic basic color terms (Witzel & Gegenfurtner, 2013; Witzel & Gegenfurtner, 2016). The orange-pink and the green–blue category boundaries coarsely coincide with increases in sensitivity while other categories show the contrary pattern. Instead of categories, the changes in sensitivity across hues could be explained by the second-stage mechanisms. This was particularly true when accounting for the global modulation of sensitivity through a fitted ellipse, and inspecting the local variation of the residuals. Evidence for a relationship between sensitivity and secondstage mechanisms was in line with previous findings (Brown, Lindsey, & Guckes, 2011; Giesel, Hansen, & Gegenfurtner, 2009; Krauskopf & Gegenfurtner, 1992; Lindsey et al., 2010). The increase of sensitivity at the orange-pink and the green–blue boundaries could be explained by the coincidence of these boundaries with the second-stage mechanisms (see also Malkoc et al., 2005). The evidence against categorical sensitivity at the boundaries of the linguistic categories (Witzel & Gegenfurtner, 2013; Witzel & Gegenfurtner, 2016) does not contradict the idea that there could be categorical perception at the transition between unique hues. The transitions between unique hues are called binary hues. Binary hues are 2

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also allowed us to reevaluate the question of whether unique hues are more consistent than binary hues. Bosten and Lawrance-Owen (2014) estimated sensitivity based on the global modulation of their unique and binary hue measurements across hues, and then examined the local variation of those same measurements to test for differences between unique and binary hues. Here, our JND measurements provide a measure of sensitivity that is independent of the measurements of unique and binary hues. We calculate the variation of unique and binary hues in terms of discriminable differences, which are differences in terms of the number of JNDs that fit between colors. We tested whether the standard deviation in terms of discriminable differences is lower for unique than for binary hues.

those hues, to which two adjacent unique hues contribute to the same amount. For example, the red-yellow binary hue appears to 50% as red and to 50% as yellow. The concept of binary hues is based on the observation that observers can estimate the proportions of unique hues in a given hue, as shown by hue scaling (Jameson & Hurvich, 1959; Sternheim & Boynton, 1966). These binary hues differ in several ways from the boundaries of the linguistic categories. In particular, linguistic categories include categories whose prototypes and boundaries do not correspond to unique and binary hues, such as pink, orange, and purple. Hence, the results on categorical sensitivity for linguistic categories are not necessarily representative for binary and unique hues. Categorical sensitivity at the transitions between unique hues could result from two kinds of determinants, perceptual learning and secondstage mechanisms. If unique red, yellow, green, and blue play a particular role in the physical or cultural environment, observers might have repeated experience and training with discriminating those colors. As a result, perceptual learning might produce an increase of sensitivity at category boundaries (e.g. Özgen, 2004). At the same time, the sensitivity to color differences is related to the second-stage mechanisms (Giesel et al., 2009; Krauskopf & Gegenfurtner, 1992; Witzel & Gegenfurtner, 2013). Hence, categorical sensitivity for unique hues would link unique hues to those low-level mechanisms. If unique hues correspond to perceptual categories that result from second-stage mechanisms this would suggest that unique and binary hues are inbuilt in the early stages of color processing rather than being the product of perceptual learning. Since second-stage mechanisms exist independently of language and culture, categorical perception for unique hues would also explain the prevalence of color categories for red, yellow, green, and blue across languages. Following the idea of categorical perception, the present study investigated whether sensitivity increases (i.e. JNDs decrease) towards the binary hues. The transition between unique hues may be more gradual and continuous (e.g. Abramov & Gordon, 1994; Hansen & Gegenfurtner, 2006; Sternheim & Boynton, 1966) than the boundaries of the linguistic categories (e.g. Bornstein & Korda, 1984; Olkkonen et al., 2010; Witzel & Gegenfurtner, 2013). While a gradual transition between unique hues could be considered as a form of categorical perception, the perceptual magnet effect might be a better framework for the relationship between perception and unique hues. According to this idea, the prototypes of categories function like a perceptual magnet for other category members in that neighboring stimuli look more similar to the prototype (Kuhl, 1991). In contrast to categorical perception, perceptual magnet effects may decrease gradually rather than abruptly with the distance from the prototype. If unique hues work like perceptual magnets, sensitivity should gradually decrease towards unique hues, making colors close to prototypes look more similar. Similar to categorical perception, sensitivity should be highest at the binary hues because increasing proximity to binary hues is equivalent to decreasing proximity to unique hues. If changes in sensitivity predict the transition between unique and binary hues, the red, yellow, green, and blue categories are grounded in perception and may be considered as “perceptual categories”. In this study, we investigated categorical perception and perceptual magnet effects by testing whether sensitivity patterns are specific to the unique hue categories (category effects). For this purpose, we compared just-noticeable differences (JNDs) with unique and binary hues. A JND is the minimum difference between two colors that an observer is just able to perceive or “notice”. The lower a JND, the higher is the sensitivity. We had previously provided thorough measurements of JNDs along an isoluminant hue circle in DKL-space (Witzel & Gegenfurtner, 2013, 2015). Here, we supplement and compare these measurements with new data on unique and binary hues. In the case of categorical perception JNDs should specifically decrease towards binary hues and in the case of perceptual magnet effects, JNDs should continuously decrease towards binary and increase towards unique hues. In addition, the combination of JNDs with unique and binary hues

2. Method We focused on colors that were isoluminant with the background in order to control for possible effects of luminance on discrimination thresholds. At the same time, it could be argued that the measurement of unique hues might depend on lightness. This is particularly true for red since the red color category only exists at lower lightness (Fig. 9.a in Witzel & Gegenfurtner, 2013). For this reason, we also examined possible effects of lightness on unique hue measurements and JNDs for dark colors that include examples of red according to previous color naming measurements (see fig. 9.b in Witzel & Gegenfurtner, 2013). We included two sets of JND measurements for isoluminant colors, one from Witzel and Gegenfurtner (2013) and one from Witzel and Gegenfurtner (2015). The latter set allows us to verify the general validity of our results. A third set of JNDs for dark colors from Witzel and Gegenfurtner (2013) was added to examine the role of lightness. Unique and binary hues were measured in two different ways. First, they were measured in DKL-space with observers who had also participated in the extensive measurements of JNDs (Witzel & Gegenfurtner, 2013). However, the number of participants available for these measurements were limited. For this reason, we measured a second sample of participants. This second sample was measured with colors sampled along isoluminant hue circles with different radii (i.e. chroma) in CIELUV-space. The advantage of sampling in CIELUV-space is that CIELUV is more homogenous in sensitivity and chroma than DKL-space (details follow below) and hence color sampling in CIELUV allows better disentangling measurements of unique hues from measurements of sensitivity and chroma. This approach also allowed us to examine the role of stimulus sampling for the measurement of unique and binary hues and to check the general validity of these measurements. 2.1. Participants Measurements were done with three groups of observers. Group 1 included ten German observers (eight women, 22 ± 3y). The first set of JNDs for isoluminant colors was measured by Witzel and Gegenfurtner (2013) for these ten observers. The JNDs for the dark colors were obtained from four of these observers (cw, f1, f2, & f3; cf. Witzel & Gegenfurtner, 2013). For the present study, six observers from Group 1 (cw, m1, f1, f2, f3, f4) also participated in the unique and binary hue measurements in DKL-space. In addition, we thoroughly measured unique and binary hues in CIELUV-space with a second group of participants (Group 2). This group consisted of 19 observers (13 women, 24 ± 5y). 18 of these observers took part in the main measurements in which colors where (close to) isoluminant with the background (L∗ = 76). Unique and binary hues at lower lightness levels were measured for 17 (L∗ = 60), 19 (L∗ = 50), and 4 (L∗ = 38) observers of Group 2. Group 3 consisted of six observers (two women, age 26.5 ± 3y) who provided the second set of JNDs for isoluminant colors in DKLspace (Witzel & Gegenfurtner, 2015). All participants were paid for participation, and were not color deficient as tested through the Ishihara plates (Ishihara, 2004). The work was carried out in accordance 3

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Fig. 1. Stimulus sampling. Panel a: Measurement of JNDs by Witzel and Gegenfurtner (2013). The colored circle illustrates the hue circle from which stimuli were sampled for the measurements in DKL-space. The distance of the grey curve from the center illustrates the size of average JNDs (in degree azimuth) for different hue directions. For illustration purposes JNDs are rescaled (divided by 13) to fit into the hue circle. The black ellipse is fitted to the JNDs (cf. Witzel & Gegenfurtner, 2013). For comparison, the dashed curves show CIELUV- (blue) and CIELAB- (red) chroma, rescaled (i.e. divided by 90 and 80, respectively) to fit into the hue circle. Panel b: Adjustments of unique (colored lines and symbols) and binary hues (black lines and symbols) in DKL-space. Disks correspond to the hue adjustments of individual observers. The size of the disks corresponds the frequency with which that hue has been adjusted. The line indicates the hue direction of the average across observers and the bars at the end of the lines correspond to standard errors of mean. The length of the lines is slightly lower than the radius of the test colors to avoid covering single dots. Fig. S1 provides corresponding figures for the measurements of unique and binary hues in CIELUV-space. Panel c: The fat grey ellipse corresponds to a circle of radius 50 at L* = 76 in CIELUV-space. The thin dotted ellipses inside the grey ellipse correspond to a CIELUV-circle with radius 55 at L* = 60, with radius 50 at L* = 50, and with radius 34 at L* = 38. The grey disk in the center is the adapting white-point and the origin of the DKL-space. Unique hues measured in DKL-space and at the four lightness levels in CIELUV-space are shown as colored disks with initials of their color names (R = red, Y = yellow, G = green, B = blue). Binary hues are shown as black discs. Adjustments in CIELUV are averaged across the 3 levels of chroma.

2.2. Apparatus For the measurements in DKL-space, the same apparatus as for the measurements of JNDs was used (Witzel & Gegenfurtner, 2013). For the measurements in CIELUV-space with the new participants the apparatus was the one of Witzel and Franklin (2014). 2.3. Stimuli For the measurements of JNDs and for the measurements of unique hues in the first group of participants, colors were defined through an isoluminant hue circle in DKL-space (cf. Fig. 1.a-b). The hue circle was also isoluminant with the background, which had a luminance of 27.9 cd/m2, and it was fit into the monitor gamut so as to maximize cone-contrasts and chroma at equal radius. Note that DKL-space controls for cone-contrasts, not perceived chroma and the axes in our implementation of DKL-space are scaled relative to the monitor gamut. Perceived chroma varies along the hue circle in DKL-space. This is illustrated by chroma in CIELUV- and CIELAB-space (blue and red curves in Fig. 1.a) that provide coarse estimations of perceived chroma. The variation of chroma across hue implies that the isoluminant circle in DKL-space may not fully disentangle perceived hue and chroma. This is the reason why it was important to re-measure unique hues in CIELUVspace, which better approximates perceived chroma than DKL-space. The first set of JNDs included measurements for 72 test colors of different hue (for details see Witzel & Gegenfurtner, 2013). The second set, i.e. the JNDs for Group 3, was done for 20 test colors with different hues along the isoluminant hue circle (for details see Witzel & Gegenfurtner, 2015). JNDs for dark colors were measured with the luminance of the background set twice as high as the stimuli (59.4 cd/ m2). Due to the lighter background, colors appear darker and a red category appears at this lightness level (Fig. 9.b in Witzel & Gegenfurtner, 2013). For the second group of participants, unique and binary hues were determined along isoluminant hue circles in CIELUV-space. The CIE1931 chromaticity coordinates and luminance of the background were [0.3101, 0.3162, 20.4 cd/m2], which corresponds to standard illuminant C. The chromaticity coordinates of the background were taken for the adapting white point in the calculation of CIELUV-coordinates. The white point luminance was set to 50 cd/m2 to avoid L∗ values above 100 when colors were lighter than the background. Calculated in this

with the Code of Ethics of the World Medical Association (Declaration of Helsinki) and informed consent was obtained for experimentation with human subjects. 4

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way, background lightness was L∗= 70; details are as in Witzel and Franklin (2014). Chroma was defined by the radius in CIELUV and at each lightness level colors were measured at three different chroma levels (see Fig. S1). The main measurements involved colors that coarsely corresponded in lightness to those used for the first group, but were slightly lighter (L∗ = 76) than the background (L∗ = 70). The three hue circles at this lightness had radii of 30, 40 and 50. At lower lightness, unique and binary hues were also measured at L∗ = 60 with radii of 35, 45, and 55, at L∗ = 50 with radii of 30, 40, and 50, and at L∗ = 38 with 14, 24, and 34. Fig. 1.c illustrates the relationship between the two sampling methods in DKL- and in CIELUV-space, respectively. Circles in CIELUVspace correspond to ellipses when converted to DKL-space (cf. grey fat and black dotted lines). These ellipses also illustrate that higher lightness levels in CIELUV imply higher radius in DKL-space since ellipses are wider the higher L∗, even when CIELUV radii are equal. In the experiment, colors were shown as colored discs at the center of the screen. The diameter of the discs was 1.9 deg visual angle in the measurements with the first group of participants (in -space), and 3.2 deg visual angle in those with the second group (in CIELUV-space).

JNDs [in

azimuth degree]

a.)

JNDs for Group 1

14

n1 = 10 n2 = 18

12 10 8 6 4 2 0 0

90

b.) azimuth degree]

To determine unique and binary hues, participants adjusted the hue on the disk. When the experiment started, observers read the instructions (written on the grey background of the screen to control adaptation). The instructions explained how to adjust unique and binary hues. The instructions for adjusting unique hues followed the logic of the hue cancelation technique (Hurvich & Jameson, 1955) and asked participants to adjust the unique hues that are neither one nor the other adjacent hue, for example the red that is neither yellowish nor bluish. To produce a binary hue the instructions asked observers to adjust the hue that contains 50% of two adjacent hues, for example 50% red and 50% blue. Instructions emphasized that unique and binary hues do not necessarily have to correspond to prototypes of color names, such as typical yellow or red, or to intermediate prototypes, such as purple or orange, respectively. Before each trial, a short message on the screen indicated which unique or binary hue observers were to adjust in that trial. Observers could recall that message during a trial by pressing a key. A trial began with the presentation of the disk in a random hue. Observers could adjust the hue of the disk to one or the other direction of the azimuth by pressing one of two keys. A third key confirmed the adjustments and continued with the message for the next trial. Each unique and binary hue adjustment was done three times at each of the three levels of chroma. JNDs were measured through a classical 4-alternative forced-choice task (Krauskopf & Gegenfurtner, 1992; Witzel & Gegenfurtner, 2013). In each trial, four discs were shown around the central fixation point. One of the discs differed in hue from the other ones. Participants had to indicate, which disks had a different color by pressing one of 4 keys that corresponded to the 4 locations of the discs. Each trial began with a fixation point for 1 s, continued with the stimulus displayed for 0.5 s, and ended with a feedback for 0.5 s. Hue differences were adapted through a 3-down-1-up staircase that stopped after 7 reversal points. Resulting JNDs correspond to a probability of correct responses of 0.79. For a 4AFC, this corresponds to a probability of 0.72 of seeing the differences. In the first JND set, JNDs were measured four times for each test color and each hue direction, in the second set three times.

270

360

270

360

JNDs2 for Group 3 15

JNDs [in

2.4. Procedure

180

5

n2 = 18 n3 = 6

10

0 0

90

180

Hue [DKL azimuth in degree] Fig. 2. Category effects for isoluminant colors in DKL-space. (a) Results with JNDs for the n1 = 10 observers of Group 1 (Witzel & Gegenfurtner, 2013). (b) Results with the JNDs for the 6 observers of Group 3. The x-axis represents hue as azimuth degree along the isoluminant hue circle in DKL-space; the y-axis and the solid black curve above the area corresponds to JNDs in azimuth degree; the grey area around the solid curve indicates standard errors of mean for JND measurements across observers. Solid vertical lines illustrate binary, dotted vertical lines unique hues. These vertical lines show data that is averaged across the measurements in DKL and CIELUV. The white disks and diamonds illustrate the results for the measurements in DKL (diamonds, n = 6), and CIELUV (disks, n2 = 18), separately. Horizontal error bars around disks and diamonds refer to standard errors of mean (but are small and only visible for red). Sample sizes are given in the upper left corner (n1 ∼ Group1, n2 ∼ Group2 at L* = 76, n3 ∼ Group3). The solid lines connecting the binary hues are the boundary lines used for the analyses.

(Schütt, Harmeling, Macke, & Wichmann, 2016). The resulting profile was largely the same as for average reversal points (see Fig. S2 in the Supplementary material). The individual datasets of JNDs for Group 1 and 3 (solid curves in Figs. 2 and 5) and the unique and binary hues measured for Group 2 at L∗ = 76 (diamonds in Fig. 2) are provided in the Supplementary material (Tables S1–S4) for further use. 3.1. Variation of unique and binary hue adjustments Fig. 1.b illustrates the average and individual variability of the unique and binary hue adjustments in DKL-space (Group 1). Fig. S1 in the Supplementary material provides corresponding diagrams for the adjustments in CIELUV space (Group 2), which also illustrate the variation of adjustments across chroma. Fig. 1.c illustrates the variation of unique (colored dots) and binary (black dots) hue adjustments across lightness and across DKL- and CIELUV-space. In Fig. 1.c, measurements for different lightness levels with Group 2 in CIELUV-space (ellipses) were averaged across the three levels of chroma within each lightness

3. Results Figs. 1.a and 2 illustrate aggregated JNDs in DKL-space. JNDs were calculated as the average across the reversal points of each staircase. The first 3 reversal points were discarded to avoid distortions of reversal points through spurious answers. To double-check we had also calculated JNDs based on psychophysical functions fitted with psignifit 5

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between the hue adjustments in CIELUV and the JND measurements in DKL-space (see ellipses in Fig. 1.c). Although, the effect of chroma was negligible for average adjustments, it might play a role for the consistency of adjustments. In fact, Bosten and Lawrance-Owen (2014; see their Experiment 2) report that consistency decreases with lower chroma. For these reasons, we also analyzed effects of chroma, when testing for differences in consistency between unique and binary hues. We calculated a two-way repeated measures analysis of variance to compare standard deviations across 8 (4 unique and 4 binary) hues and the 3 levels of chroma (Table S9). Standard deviations differed across hues (F(7,119) = 2.7, p = 0.01); but there was neither an effect of chroma (F(2,34) = 0.5, p = 0.64) nor an interaction between hue and levels of chroma (F(14,238) = 0.7, p = 0.79). According to Fig. 3, the average standard deviations were highest for red, orange and green–blue, and lowest for green. We compared average standard deviations between unique and binary hues in a paired t-test (Table S10), but there was no significant difference (t(17) = 0.8, p = 0.42). These observations show that the effect of hue was not specific to the difference between unique and binary hues. Considering that the consistency of hue adjustments might depend on lightness, we explored the consistency of hue adjustments at the other lightness levels (L∗ = [38, 50 60]); but the results looked very similar to those at L∗ = 76 (Fig. S3). Further examination of the effect of chroma on the consistency of hue adjustments did not show clear relationships between adjustments and chroma for any hue (Table S11).

level. We tested whether unique and binary hues varied across different levels of lightness, chroma, and across the measurements in two different color spaces (DKL and CIELUV). Section 2.1 of Supplementary material provides detailed analyses. In sum, analyses on the effects of lightness and chroma indicated that the adjustments of red, yellow, yellow-green, and green–blue change systematically with lightness (Table S5). These results suggest that it might be important to distinguish results for different levels of lightness. The analyses also show that blue, blue-red, and possibly green–blue change towards a higher azimuth (more reddish and more bluish, respectively) with increasing chroma (Table S6). This, however, was only true for lightness L∗ = 50. There were no systematic effects of chroma at lightness L∗ = 76, which is in the focus of our tests for category effects (Table S6). There was also no evidence for a difference between measuring unique and binary hues in DKL- and in CIELUV-space (colored circle vs. ellipses in Fig. 1.c; see Table S7 for detailed analyses). We then examined the variation of unique and binary hue adjustments and tested whether the consistency of hue adjustments differs between unique and binary hues (cf. Bosten & Lawrance-Owen, 2014). For details on analyses see Section 2.2 of the Supplementary material. In a first approach to that question, we considered that the variation of adjustments may be partly due to the variation of sensitivity across color space. However, according to our Supplementary analyses (Table S8) the standard deviations of unique and binary hue adjustments were not correlated to JNDs, suggesting that the variation of hue adjustments is shaped by factors beyond sensitivity. Second, we assessed the consistency of unique and binary hues in terms of discriminable color differences. For this, we calculated distances of each hue adjustment in JND-space following the approach of. We used the hue measurements in CIELUV- space at L∗ = 76 because they were done for a larger number of participants and the lightness was almost the same as the lightness of the JND measurements in DKLspace. For each unique and binary hue, each participant, and each level of chroma, we calculated the standard deviation across the three repeated measurements to obtain a measure of consistency. Fig. 3 illustrates the consistencies across unique and binary hues averaged across chroma and observers. Note that the sampling of chroma differed

3.2. Category effects in DKL-space Category effects may consist in an increase of sensitivity at the transition between categories (boundary effect), a decrease of sensitivity around the prototypes of the categories (prototype effect), or both (cf. Witzel & Gegenfurtner, 2013). For unique hues, this implies that JNDs would decrease towards binary hues, or increase towards unique hues. At the same time, JNDs may be globally modulated by factors other than categories, such as the color space used to represent colors and the relative scaling of its axes (cf. Witzel & Gegenfurtner, 2013). To account for global modulations JNDs within categories (category JNDs) are compared to the boundary line. The boundary line is the line that connects the data at the 2 boundaries of a category (see solid black lines in Fig. 2.a and b). Boundary effects were examined through paired, twotailed t-tests across observers that tested whether JNDs within categories lay above the boundary line, both on average and in relative frequency (boundary test). To test for prototype effects, we used paired, two-tailed t-tests that compared the JNDs at the unique hue with the average JNDs within the respective category (prototype test). We also examined the JND patterns with a third kind of test (triangle tests). We report details on triangle tests in the Supplementary material only because the results of the triangle tests are largely overlapping with those of the other tests. The logic behind all these tests has been explained in great detail by Witzel and Gegenfurtner (2013, p. 18). Fig. 2 compares unique hues and JNDs in DKL-space. The combination of the data from the three groups of observers resulted in three kinds of datasets: The first dataset included the aggregated unique and binary hues (white diamonds in Fig. 2.a and b) and the individual JNDs (cf. solid black curve above the colored areas in Fig. 2.a) both measured with Group 1. For this dataset, tests were calculated across the 10 individual JND measurements. The second dataset combined the individual unique and binary hues of Group 2 originally measured in CIELUV (white disks in Fig. 2) with the aggregated JNDs of Group 1. The third dataset combined the unique and binary measurements of Group 2 with the aggregated JNDs of Group 3 (Fig. 2.b). For these two datasets, tests were calculated across the individual unique and binary hue measurements. In general, all three datasets yielded the same results. Results of all the tests for each dataset are reported in detail in Supplementary Table S12. The boundary tests for the three datasets (two upper parts of Table

Fig. 3. Consistency of unique and binary hues. The x-axis lists unique and binary hues ordered by their azimuth; R = red, Y = yellow, G = green, and B = blue. The y-axis represents the standard deviation of hue adjustments in JND space where one unit corresponds to one JND. Standard deviations represented by the bars were calculated across 3 repeated measurements and then averaged across observers and levels of chroma. Results are shown for the adjustments at L* = 76; results for other lightness levels are provided in Fig. S3. Note that unique hues (R, Y, G, and B) do not always have lower standard deviations than binary hues (RY, YG, GB, and BR). 6

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S12) showed that category JNDs were on average and more frequently above the boundary line for the red (all p < 0.003) and the green category (all p < 0.02), with the exception of Group 3 that yielded opposite effects in the frequency test for red (t(17) = −5.0, p < 0.001). The first and the second datasets with the JNDs of Group 1 (solid curve in Fig. 2.a) yielded JNDs that were on average above the boundary line in the yellow and blue categories. However, none of those differences from the boundary line were significant for the blue and yellow category in any of the datasets (min. p > 0.08). Prototype tests for all three datasets (third part of Table S12) showed that JNDs for unique blue were higher above the boundary line than the average blue category JNDs (all p < 0.01). For the green category, this was only the case in the first two datasets (both p < 0.02), but not in the third (t(17) = −1.2, p = 0.26). The JNDs at unique red contradicted a prototype effect because they were lower than the average category JNDs in all three datasets. This negative difference just missed significance (i.e. p < 0.1) in the first dataset (t (9) = −2.0, p = 0.07), but was significant in the second (t (17) = −4.0, p < 0.001) and third dataset (t(17) = −2.6, p < 0.02). JNDs at unique yellow also contradicted a prototype effect because they were significantly lower than yellow category JNDs with the third dataset (t(17) = −3.3, p = 0.004) and did not produce significant effects with the other two datasets (both p > 0.53). Unique yellow, green, and blue are close to the center of the binary hues (cf. Fig. 2), but unique red is shifted away from the center towards yellow. In Fig. 2 it looks as if the peaks of JNDs in the red category are closer to the center than to unique red. This would explain why the results of the prototype tests for the red category contradicted a prototype effect. To test the idea that JNDs increase towards the category centers, we recalculated the prototype tests using the category centers instead of the unique hues as “prototypes” (center tests). These center tests yielded significant effects for the red center with all datasets (all p < 0.001). JNDs at the green and blue centers were on average higher than the respective category JNDs, but not in every dataset this difference was significant. For yellow results were mainly the same as with the prototype test and contradicted both a prototype and a center effect. For details see last part of Table S12 in the Supplementary material. In sum, green yielded clear boundary effects, and some non-significant tendencies towards boundary effects were also found for yellow and blue and partial evidence for boundary effects was found for red. Prototype effects were found for unique blue, and to some extent for unique green. While JNDs for unique red contradicted a prototype effect, JNDs at the center of red strongly supported a center effect. Finally, yellow did not yield any consistent effect. Taken together, these results are ambiguous with respect to both boundary and prototype effects.

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Fig. 4. Category effects when accounting for global variation. (a) Results with residuals of ellipse. The y-axis corresponds to the residuals of the elliptical fit of the JNDs for Group 1. (b–c) Results represented in CIELUV and CIELAB. JNDs in panels b-c are re-calculated as Euclidean distances in CIELUV- and CIELABspace. Dotted curves correspond to results obtained with the JNDs of Group 3 (solid line in Fig. 2.b). Apart from that, format is as in Fig. 2.

The study of Witzel and Gegenfurtner (2013) showed that the global modulation of JNDs in DKL-space may cover local patterns. In that study local patterns and their relationship to perceptual mechanisms could be revealed by modelling global variations through a fitted ellipse, and examining local patterns in the residuals of the ellipse fit (see Fig. 5 in Witzel & Gegenfurtner, 2013). To target specifically these local patterns, we tested boundary and prototype effects for the residuals of the ellipse fit. For the same reason, we also inspected category effects in CIELUV- and CIELAB-space. CIELUV and CIELAB have been developed to compensate variations in discriminability across color space. These spaces equalize discriminability through algorithmic transformations, which imply transformations at a global rather than local level. In particular, CIELUV compensates modulations in sensitivity across DKLspace in a similar way as the ellipse fit (cf. ellipses in Fig. 1). Fig. 4.a shows the residuals of the elliptical fit. The ellipse was fitted to the aggregated JNDs (of Group 1). The ellipse fit accounts for the main variation along the second diagonal (cf. Figs. 1 and 5.a in Witzel &

Gegenfurtner, 2013). For the tests with Group 1, residuals were calculated for JNDs of each individual observer (cf. grey area in Fig. 4.a). Detailed results of all tests are provided in Table S13 of the Supplementary material. Boundary tests with residuals revealed that the category JNDs were on average and most frequently above the boundary line for yellow, green, and blue (first and second part of Table S13). These differences were significant in both kinds of boundary tests (i.e. for averages and frequencies of category JNDs), with all three datasets and for all three categories (all p < 0.02). The only exception from this was the first (Group 1) and the second dataset (Group 2) for the green category in that the the first dataset did not yied significant results in both 7

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effects for blue (all p < 0.004), negative effects for red, non-significant effects for yellow (all p > 0.12), and inconsistent effects for green across the three datasets. As with the residuals, the prototype tests for category centers provided more promising results (last part of Table S14). Red and blue showed significant positive effects in all three datasets (all p < 0.03). Center effects for green went in the positive direction, but were only significant in the second dataset (t(17) = 4.1, p < 0.01), not in the other two datasets (both p > 0.44). For yellow, effects were not significant in any of the three datasets (all p > 0.20). In CIELAB (Fig. 4.c), the profile of JNDs looks different from the profile of the residuals and the JNDs in CIELUV. However, the main troughs and peaks of JNDs remain, and are actually more pronounced than for the residuals and the JNDs in CIELUV. The two boundary tests showed positive effects for yellow, green, and blue, but these were not always significant in all three datasets (first and second part of Table S15). Red showed inconsistent effects, some of the three datasets producing significantly positive effects, while other datasets showed significant effects in the opposite direction. As for the residuals and in CIELUV, prototype tests for unique hues provided inconsistent results, in particular because the red category produced effects that contradicted prototype effects (third part of Table S15). Instead, the center tests (last part of Table S15) were again significantly positive for red, green, and blue in all three datasets (all p < 0.05), except for green in the third dataset, for which the positive effect was not significant (t (17) = 0.5, p = 0.61). As for CIELUV, there were no significant center effects for yellow in any of the three datasets (all p > 0.15). In sum, results in CIELUV (Fig. 4.b) and CIELAB (Fig. 4.c) produce similar results as the residuals (Fig. 4.a). Adjustments of binary yellowgreen, green–blue, and blue-red tended to coincide with local peaks in sensitivity (troughs in JNDs). Evidence for troughs in sensitivity (peaks in JNDs) around unique hues was ambiguous. In particular, unique blue clearly coincided with a peak in JNDs. In contrast, unique red was closer to a local trough than to a peak in JNDs. Instead of boundary and prototype effects at binary and unique hues, red showed a consistent trough of sensitivity at the center between red binary hues.

Fig. 5. Unique hues and JNDs for dark colors. The main curve corresponds to average JNDs for dark colors (made darker by using a background that was twice as light, i.e. 59.4 cd/m2). Diamonds show average adjustments of unique and binary hues at isoluminance in DKL-space. Disks show adjustments at different lightness (L*) levels in CIELUV after conversion to DKL-space. Disks and diamonds are ordinally arranged by their lightness levels. The lightness of the symbols also illustrates their relative lightness. The legend indicates the different datasets and their sample sizes. Apart from that, format as in Fig. 2. Note that there are no categorical patterns for these JNDs.

boundary tests (both p > 0.12) and the second dataset just missed significance in the frequency test (t(17) = 2.0, p = 0.07). The red category provided contradictory results in the boundary tests: It did not yield significant results with the the first and second dataset (all p > 17), and negative effects with the third dataset (both p < 0.004). Prototype tests for unique hues produced inconsistent results (third part of Table S13). Only unique blue yielded a positive prototype effect that was consistent across all three datasets (all p < 0.001). Unique yellow produced a positive prototype effect only in the second dataset (t (17) = 4.9, p < 0.001), and unique green did not yield a significant effect (all p > 0.05). Results for unique red contradicted a prototype effect in all three datasets, with the second and third resulting in significantly negative effects (both p < 0.001). The center tests yielded more promising results (Last part of Table S13). In this test all three datasets produced significantly positive prototype effects at the centers of all four categories. The only exception form this were non-significant results for yellow (t(17) = −1.3, p = 0.22) and green (t(17) = 0.7, p = 0.49) in the third dataset. Fig. 4.b and c illustrates unique hues and JNDs in CIELUV and CIELAB. To determine JNDs in CIELUV and CIELAB, we converted test colors and reversal points to CIELUV and CIELAB, respectively, and calculated their average Euclidean distances (ΔE). Detailed results from boundary and prototype tests are provided by Tables S14 and S15 in the Supplementary material. In CIELUV (Fig. 4.b), the profile of JNDs looks similar to the residuals of the ellipse fit (Fig. 4.a), and JNDs yielded similar categorical patterns as the residuals (Table S14). All categories showed on average positive boundary effects in both boundary tests (average and frequency) and with all three datasets. However, not all of these effects were significant (first and second part of Table S14). In addition, the frequency test of the red category with the third dataset yielded significant negative effects (t(17) = 21.1, p < 0.001). The prototype tests for unique hues (third part of Table S14) resulted in significant positive

3.4. Differences in lightness The pattern of JNDs across hue depends on the lightness of the background (Witzel & Gegenfurtner, 2013). At the same time, we observed above (Section 3.1) that some unique and binary hues may vary with lightness, in particular red, yellow, yellow-green, and green–blue. For this reason, we examined category effects at different lightness levels. Fig. 5 illustrates the JNDs for dark colors, and compares unique and binary hue measurements across lightness (L*) levels. The symbols in this figure correspond to the data of the symbols in Fig. 1.c. In Fig. 5, they are ordered by increasing lightness from bottom to top and illustrate potential variation of unique and binary hues choices across lightness levels. Deviations of the diamonds from the disks indicate potential effects of the stimulus sampling in DKL and CIELUV, respectively. Since the stimuli in DKL-space are just slightly lower in lightness than the CIELUV colors at L* = 76, deviations of these stimuli indicate that it is rather the variation in chroma or the overall stimulus sampling (circle vs. ellipse) than the differences in lightness that produce these shifts. However, the variation of unique and binary hues across different lightness levels was not large enough to produce different results concerning their relationship with the JND profile for dark colors. In fact, the JNDs for dark colors do not exhibit either systematic troughs at any of the binary hues or peaks at the unique hues or at the centers between the binary hues. The data looks noisier for dark than for isoluminant colors, in particular in the green category. This is probably due to the smaller sample of participants. While evidence for category effects might seem ambiguous in the green and red category due to noise, the yellow and blue clearly contradict the idea of category effects. Finally, 8

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the nonlinearities across chroma and lightness, such as the Abney effect and the Bezold–Brücke hue shift (for review see Pridmore & Melgosa, 2015). To examine such nonlinear effects, we had measured unique and binary hues at several levels of lightness and chroma. Unique and binary hues were similar across lightness levels (Fig. 1.c and disks in Fig. 5). However, yellow, yellow-green, and green–blue were shifted towards green with increasing lightness, and unique red tended to be shifted towards yellow at lower lightness (disks in Fig. 5). The shifts for yellow-green and green–blue are generally in line with Bezold-Brücke hue shifts; but with increasing lightness yellow should be either invariant or shifted towards red, and unique red should be shifted in the opposite direction according to the Bezold-Brücke shift (e.g. Fig. 2 in Pridmore & Melgosa, 2015). Increasing chroma shifted adjustments of unique blue and binary blue-red towards reddish hues, contrary to what is predicted by the Abney effect (cf. Figs. 4 & 9 in O'Neil et al., 2012). Another factor that might affect measurements of unique and binary hues is differences in the variation of chroma across hues. The largest sample of unique hue and binary hue measurements (Group 2) was conducted for hues along circles in CIELUV-space while JNDs were always measured in DKL-space. CIELUV and DKL differ in their control of chroma (as obvious from the ellipses in Fig. 1.c), and none of these spaces completely controls perceived chroma. As a consequence perceived chroma varies across hue in both spaces and may affect the precise measurements of unique hues (Witzel, in press, accepted; Witzel & Hammermeister, 2017). Nevertheless, the unique and binary hues measured in this study generally agreed between the two groups of participants despite the differences in stimulus sampling (Figs. 1.c and 5). In particular, unique red, yellow, and blue are almost identical for both groups at comparable lightness levels (cf. white disks and white diamonds in Fig. 5). We also did not find significant differences between the unique hues measured with Group 1 in DKL- and those measured with Group 2 at an equivalent lightness level (L∗ = 76) in CIELUV space. At the same time, statistical power of those analyses was low because Group 1 was small (n = 6). Hence, we cannot completely exclude possible differences between the measurements in the two spaces. In particular, there might be differences between the two groups for yellow-green, unique green, green-blue, and blue-red (white disks and white diamonds in Fig. 5). Instructions and tasks might also affect the measurements of unique and binary hues across studies (Bosten & Boehm, 2014). In particular, most measurements of unique hues, such as hue cancelation and hue scaling, require the communication of unique hues through color names. This is also true for our study when we asked observers to adjust for example the yellow that is neither red nor green, or the hue that contains equal amounts of green and blue. For this reason, it is difficult to completely disentangle measurements of color appearance and color naming. Yet, it is known that the typical colors of color terms and linguistic color categories are not independent of lightness and chroma (for a discussion see Witzel, in press, accepted; Witzel & Gegenfurtner, in press). While blue and green exist at almost all levels of lightness and chroma, red and yellow only exist at high chroma and specific levels of lightness (e.g. Fig. 8 of Olkkonen et al., 2010). When yellow is darker and desaturated it becomes brown, which has different category prototypes and boundaries than yellow. At the same time, colors along the hue circle in DKL- (Witzel & Gegenfurtner, 2013) and at equivalent lightness (L∗ = 76) in CIELUV-space (Witzel et al., under revision; Witzel & Franklin, 2014) are too light and too desaturated to be called red. Instead, they are called orange or pink (for a thorough discussion see Witzel in press). Those linguistic categories are implied in the color terms used in the instructions and might affect the measurements of unique and binary hues. This could explain why our measurements of red, yellow and yellow-green were affected by differences in lightness. It may also explain why adjustments of unique red varied strongly at high lightness levels (cf. Figs. 3 and S3). In addition, the variation of unique red across studies might be related to differences in the instructions since we

as noted previously (Fig. S5 and S14 in Witzel & Gegenfurtner, 2013), residuals for the dark colors (not shown) did not show pronounced peaks and troughs, either. In sum, JNDs for dark colors do not show any categorical patterns. 4. Discussion Our results revealed that some unique and binary hues coincided with the peaks and troughs of JNDs. This was particularly true of JNDs with colors that are isoluminant with the background and when accounting for global variation (Fig. 4). However, unique red completely contradicted any prototype effect since it coincided with a peak rather than a trough in sensitivity. No categorical patterns were observed with JNDs at lower lightness levels. We also found that some of the unique and binary hue adjustments were more consistent across repeated measurements than others (Fig. 3). At the same time, unique hue adjustments were not generally more consistent than binary hue adjustments. The questions arise of whether the binary and unique hues measured in the present study are reliable and allow for general conclusions; whether JNDs are in line with the idea of categorical sensitivity and perceptual categories; and how these findings are related to perceptual mechanisms. 4.1. Color appearance, unique and binary hues In general, our measurements were very much in line with previous measurements of unique and binary hues in cone-opponent (or equivalent) spaces (cf. Fig. 2.d in Bosten & Boehm, 2014; Fig. 1.a in Bosten & Lawrance-Owen, 2014; Fig. 1 in Malkoc et al., 2005; Fig. 4 in Webster et al., 2000; Fig. 1 in Wool et al., 2015; Fig. 1 in Wuerger et al., 2005). In all studies, unique yellow, green, and blue did not coincide with the cone-opponent axes; instead they were close to the diagonal directions −S/(L-M), −S/(M-L), and +S/(M-L), i.e. close to the diagonal of the first, second, and third quadrants in Fig. 1. Binary yellowgreen, green–blue, and blue-red were located close to the –S pole of the S-(L + M) dimension, to the +M pole of the L-M mechanism, and to the +S pole of the S-(L + M) dimensions, respectively. Finally, in all those studies binary red-yellow has been observed in the first quadrant (in Fig. 1), close to the –S/(L-M) diagonal. At a closer look, some differences between studies appear. The distances of unique and binary hues from the diagonal directions differ across studies (e.g. unique yellow, green, and blue in De Valois et al., 1997; Hansen & Gegenfurtner, 2006; Malkoc et al., 2005). Differences with respect to the diagonal might simply be due to differences in the relative scaling of the two cone-opponent axis across studies. However, there were also differences that cannot be explained by axis scaling. In particular, in our and in most of the above studies unique red was slightly shifted away from the L-M axis towards –S (more yellowish). In contrast some studies (De Valois et al., 1997; Hansen & Gegenfurtner, 2006; Wool et al., 2015) found unique red to be slightly shifted towards +S. In our measurements, adjustments of unique green yielded highest, and adjustments of unique red and blue-green lowest consistency. At a first glimpse this observation seems to contrast prior findings according to which unique green varies most strongly across observers (Kuehni & Charlotte, 2004). In our study, unique green adjustments in DKL and CIELUV seem to strongly vary across both repeated measurements and observers (cf. Figs. 1.b and S1). However, JNDs were also higher for unique green than for other unique and binary hues (cf. Fig. 2). As a result, unique green has high consistency when controlling for the variation of sensitivity. At the same time, Bosten and Lawrance-Owen (2014) also accounted for sensitivity, but did not obtain exactly the same consistencies across hues. They found highest consistencies for yellow and blue, and lowest consistencies for red and blue-red. Differences in stimulus sampling might explain differences across studies. Measurements of unique and binary hues may be affected by 9

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pronounced local maxima and minima. This implies that along the hue continuum there are abrupt changes in discriminable color differences, suggesting that hues in the JND troughs are perceived as more different than other adjacent hues. In particular, this was the case for green–blue (180 deg), blue-red (270 deg) and red hues (∼10 deg). These abrupt changes of sensitivity across hue suggest that hues are perceived categorically and there are perceptual categories across hues in DKL-space. When accounting for global variation of JNDs, a small fourth JND trough appeared at yellow-green (Fig. 4). As a result, the local JND patterns (Fig. 4) showed more overlaps with binary and unique hues than the JNDs in DKL-space (Fig. 2). This observation suggests that binary and unique hues tend to coincide with local rather than global variations of sensitivity. Overall, sensitivity maxima coincided with yellow-green, green–blue, blue-red, and sensitivity minima with unique blue. Unique yellow and green also tended to coincide with sensitivity minima, but these tendencies were not reliable across all tests. In contrast, unique red and binary red-yellow contradicted a relationship with the JND pattern. Unique red was closer to the sensitivity maximum than red-yellow, contrary to any category effect. At the same time, unique red differed from the other unique hues in several ways. Unique yellow, green, and blue were close to the centers between the respective binary hues. In contrast, unique red was not located at the center between binary blue-red and red-yellow. In addition, some previous studies reported unique red to be closer to blue than in our study, which also shifts unique red closer to the center between binary hues, which coincides with the JND maximum at 320 deg. Additional center tests showed that unique red would have yielded clear prototype effects if it coincided with the center. Above (Section 4.1) we discussed the possibility that our measurements of unique red were shifted towards a more yellowish hue because our instructions lead to confusions between unique red and the typical red of the linguistic category. If unique red was more bluish than our measurements indicate, red-yellow should also be shifted towards blue and might coincide with the sensitivity maximum at 10 deg. We wonder whether tasks that do not recur to linguistic descriptions of unique hues would yield a more bluish unique red. One such task might be partial hue matching (Logvinenko & Beattie, 2011; Logvinenko & Geithner, 2015). At the same time, partial hue matching (Logvinenko & Geithner, 2015) identifies Munsell Hues as unique red (R5 and R7.5) that are the same as the prototypes of the linguistic red category (cf. Fig. 8 in Olkkonen et al., 2010). Furthermore, JNDs were different for dark colors, i.e. when the luminance of the background was twice as high as the luminance of the hue circle (Fig. 5). At the same time, unique and binary hues varied only slightly across lightness. As a result, there was no evidence for a relationship between sensitivity and unique and binary hues. Considering all this, we conclude that unique and binary hues partially coincide with the variation of sensitivity. However, due to the contradictory results for unique red and for dark colors the link between sensitivity and unique and binary hues is ambiguous.

(Witzel & Franklin, 2014) previously observed that the prototype of the linguistic red category is adjusted to be more yellowish than unique hues. Some tasks and instructions might lead observers to confuse adjustments of typical and unique hues more than others. At the same time, this explanation cannot account for the effects of lightness on green–blue and the effect of chroma on blue and blue-red. In sum, the average binary and unique hue measurements in this study generally agree across DKL- and CIELUV stimulus samples. They also largely agree with the measurements in previous studies, though some studies report unique red to be closer to blue than observed in our study. Chroma had only an effect on blue and blue-red and mainly at lightness L∗ = 50. Lightness affected some of the unique and binary hues. However, the variations of the exact locations of unique and binary hues were small compared to the pronounced peaks and troughs we observed for JNDs. Hence, the majority of the observed variations in unique and binary hue measurements do not seem to affect the observed relationship between unique hues and JNDs. 4.2. Categorical sensitivity and perceptual categories As shown previously (Witzel & Gegenfurtner, 2013), JNDs in our first dataset varied systematically across hues, and the profile of JNDs was stable across observers. Our second dataset of JNDs (dotted line in Figs. 2–4) confirms the observed profile of JNDs for isoluminant colors in DKL-space (cf. Witzel & Gegenfurtner, 2015). Moreover, these measurements of JNDs are in line with most of the previous measurements. In particular, the JNDs for hues measured in our study correspond to JNDs in directions perpendicular to the radius of the hue circle. These JNDs are illustrated by the widths of the ellipses in previous studies (Fig. 4 in Giesel et al., 2009; Fig. 10 in Hansen, Giesel, & Gegenfurtner, 2008; Fig. 14 in Krauskopf & Gegenfurtner, 1992). Ellipses in those studies tend to be particularly “narrow” (i.e. have a small minor axis) at the +M pole of the L-M axis (blue-green, cf. Fig. 1.c), between the +L pole of the L-M axis and the diagonal in the –S/(M-L) quadrant (between unique red and red-yellow in Fig. 1.c), and at the +S pole of the S-(L + M) axis (blue-red in Fig. 1.c). Those hue directions also yielded local minima of JNDs in our study (cf. 180 deg, 0–45 deg, and 270 deg in Fig. 2). At the same time, ellipses in those studies were comparatively wide for colors on the –S/(M-L) diagonal. This is in line with our local maxima of JNDs at 135 deg (peak close to unique green) and 320 deg (peak in red area in Fig. 2). However, the JNDs measured in the present study seem to disagree with those obtained by Danilova and Mollon (2010, 2012, 2016). They measured JNDs in MacLeod-Boynton space, which is equivalent to the isoluminant plane of DKL-space apart from the scaling of the axes. Their results implied that the sensitivity to color differences is increased at unique yellow and blue (Danilova & Mollon, 2010; Danilova & Mollon, 2012). In contrast, our observations contradicted an increase of sensitivity around unique yellow and blue. Our results rather suggested that sensitivity decreases towards blue. A possible explanation of this difference may be a difference in stimulus sampling. The colors in our study were sampled along a color circle, implying that all colors had the same difference from the adaptation point (i.e. the origin of the DKL-space used here). In contrast, Danilova and Mollon sampled colors along a line that was perpendicular (Danilova & Mollon, 2010, 2012) to the cerulean line. The cerulean line goes through the adaptation point implying that colors on the perpendicular line that are closer to the cerulean line are also closer to the adaptation point. Since JNDs generally increase with the distance to the adaptation point (e.g. Fig. 10 in Giesel et al., 2009; Fig. 10 in Krauskopf & Gegenfurtner, 1992; Witzel et al., under revision), this might explain why Danilova and Mollon (2010, 2012) obtained a decrease in JNDs towards the cerulean line and we don’t. The JNDs obtained in the present study seem to be representative for measurements that control for the distance to the adaptation point. According to the profile of these JNDs, sensitivity shows three

4.3. Perceptual mechanisms As observed previously (Witzel & Gegenfurtner, 2013), the local variation of JNDs as represented by the residuals of the ellipse fit, coarsely coincide with the poles of the axes in DKL-space at 0, 90, 180, and 270 degree (cf. Fig. 4.a). These poles represent the 4 chromatic second-stage mechanisms (L-M, M-L, (L + M)-S, and S-(L + M)). Since JNDs in DKL-space follow Weber’s law, they increase with radius along the axes (Krauskopf & Gegenfurtner, 1992; Witzel et al., under revision). However, when test colors fall on one of the axes, no adaptation occurs along the perpendicular axis, and hue discrimination is maximal (see also Giesel et al., 2009; Hansen et al., 2008). In this way, the second-stage mechanisms may explain peaks of sensitivity for test colors close to the axes of DKL-space. Slight shifts of the peaks in sensitivity away from the DKL-axes 10

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5. Conclusion

might be explained through the incomplete control of isoluminance. Isoluminance across the chromatic axes varies across individuals, and isoluminance in DKL-space only coarsely controls average isoluminance. Luminance artifacts help to discriminate test and comparison and may slightly modulate the profile of JNDs. Binary yellow-green, green–blue, and blue-red roughly coincide with the cardinal axes. Hence, the increase in sensitivity close to the axes may account for categorical perception at those binary hues. In this way, the second-stage mechanisms may partly explain the emergence of perceptual categories that correspond to the subjective appearance of red, yellow, green, and blue. The absence of categorical patterns for dark colors and for unique red and red-yellow might be due to complex interactions between luminance and chromaticity. If we assume that unique hues are related to linguistic color categorization genuine red only exists at low and genuine yellow only at high lightness (see Section 4.1). In this case, binary red-yellow differs from other binary hues in that it involves a steep transition in lightness. The impact of lightness on both JNDs and binary and unique hues might have blurred the relationship between secondstage mechanisms and color appearance in the present study. Although this is yet just a speculation understanding the role of lightness in unique hues and in the sensitivity to hue differences might clarify the link between color appearance and sensitivity. The global variation of JNDs cannot be explained by the secondstage mechanisms. Instead, the main variation of JNDs for both isoluminant and dark colors occurred along the –S/(M-L) diagonal of DKLspace (i.e. highest JNDs at about 135 and 315 deg in Figs. 2 and 5). This is captured by ellipses fitted to the JNDs (cf. Figs. 1.a and 5 and S5 in Witzel & Gegenfurtner, 2013 for isoluminant and dark colors, respectively). The global variation of JNDs roughly corresponds to the variation of chroma along the hue circle in DKL-space. This is illustrated by comparing JNDs to the estimation of perceived chroma along the DKLhue circle in CIELUV- and CIELAB-space (blue and red curves in Fig. 1.a). Weber’s law may not provide a simple explanation for the increase of JNDs with chroma because the small differences in azimuth that correspond to JNDs for hue are almost perpendicular to the radius (see also Fig. S4 in Witzel & Gegenfurtner, 2013). Considering that radius and azimuth in DKL-space do not fully disentangle hue and chroma there may be a more complicated interaction between perceived chroma and JNDs for azimuth in DKL-space. While the global variation of JNDs is related to chroma, the variation of chroma in DKL-space had only minor or no effects on binary and unique hues, as shown by the similarity of measurements in DKL- and CIELUV-space (Fig. 1.c). As a result, the effects of chroma might complicate the relationship between JNDs, and unique and binary hues. These observations further highlight the importance of clarifying the role of chroma in measurements of color discrimination and color appearance (see also Witzel, in press). Previous studies had questioned the special status of unique hues because the empirical evidence for the uniqueness of unique hues is questionable (Bosten & Boehm, 2014), because unique hues vary depending on the color terms used in the instructions (Bosten & Boehm, 2014), and because there is no evidence for unique hues to have particular perceptual salience (Witzel & Franklin, 2014; Wool et al., 2015), constancy (Weiss et al., 2017; Witzel, van Alphen, Godau, & O'Regan, 2016), or consistency (Bosten & Lawrance-Owen, 2014). The latter point about consistency was further supported by our findings that unique hues do not vary less than binary hues when variation was assessed in terms of discriminable colors. If second-stage mechanisms could account for binary and unique hues this would suggest that unique hues are inherent in early color processing and that they have indeed a special perceptual status. However, evidence for this idea is ambiguous and yet insufficient to rehabilitate the special status of unique hues in color appearance.

We investigated whether unique hues are perceptual categories that are defined by high sensitivity at the boundaries (binary hues) and low sensitivity at the unique hues. This idea implies that unique and binary hues would be inbuilt in the early stages of color processing. We found partial evidence for this idea. In particular, the binary hues around green, blue, and to some extent yellow coincided with high sensitivity when the luminance of the colors was the same as the adapting grey background and when we accounted for the global variation of sensitivity. In contrast, results for red and the variation of sensitivity for darker colors contradicted the idea that unique hues are perceptual categories that can be related to the second-stage mechanisms. Our extensive JND data also allowed us to assess the consistency of unique and binary hues in terms of discriminable colors. Our results contradicted the idea that unique hues are adjusted more consistently than binary hues. This finding confirms previous observations using a slightly different approach (Bosten & Lawrance-Owen, 2014). Taken together, our findings suggest that some of the binary hues correspond to the boundaries of perceptual categories at the early stages of color processing. At the same time, our observations also raised important questions about the role of lightness, chroma, and color naming in the measurement of unique hues and their relationship to sensitivity. Clarifying these questions might help establishing a clearer link between unique hues and the sensitivity at the early stages of color processing. Acknowledgments This research was supported by project SFB/TRR 135 from the German Research Foundation (DFG), a European Research Council funded project (“Categories”, Ref. 283605), and a German Academic Exchange Service (DAAD) postdoctoral fellowship to CW. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.visres.2018.04.002. References Abramov, I., & Gordon, J. (1994). Color appearance: On seeing red–or yellow, or green, or blue. Annual Review of Psychology, 45, 451–485. http://dx.doi.org/10.1146/annurev. ps.45.020194.002315. Bohon, K. S., Hermann, K. L., Hansen, T., & Conway, B. R. (2016). Representation of Perceptual Color Space in Macaque Posterior Inferior Temporal Cortex (the V4 Complex). eNeuro, 3(4). doi:10.1523/eneuro.0039-16.2016. Bornstein, M. H., & Korda, N. O. (1984). Discrimination and matching within and between hues measured by reaction times: Some implications for categorical perception and levels of information processing. Psychological Research Psychologische Forschung, 46(3), 207–222. Bosten, J. M., & Lawrance-Owen, A. J. (2014). No difference in variability of unique hue selections and binary hue selections. Journal of the Optical Society of America. A, Optics, image science, and vision, 31(4), A357–A364. doi:10.1364/JOSAA.31.00A357. Bosten, J. M., & Boehm, A. E. (2014). Empirical evidence for unique hues? Journal of the Optical Society of America. A, Optics, image science, and vision, 31(4), A385–393. http://dx.doi.org/10.1364/JOSAA.31.00A385. Broackes, J. (2011). Where do the unique hues come from? Review of Philosophy and Psychology, 2(4), 601–628. http://dx.doi.org/10.1007/s13164-011-0050-7. Brown, A. M., Lindsey, D. T., & Guckes, K. M. (2011). Color names, color categories, and color-cued visual search: Sometimes, color perception is not categorical. Journal of Vision, 11(12). Danilova, M. V., & Mollon, J. D. (2010). Parafoveal color discrimination: A chromaticity locus of enhanced discrimination. Journal of Vision, 10(1), 1–9. Danilova, M. V., & Mollon, J. D. (2012). Foveal color perception: minimal thresholds at a boundary between perceptual categories. Vision Research, 62, 162–172. http://dx.doi. org/10.1016/j.visres.2012.04.006. Danilova, M. V., & Mollon, J. D. (2014). Is discrimination enhanced at the boundaries of perceptual categories? A negative case. Proceedings. Biological Sciences/The Royal Society, 281(1785), 20140367. http://dx.doi.org/10.1098/rspb.2014.0367. Danilova, M. V., & Mollon, J. D. (2016). Is discrimination enhanced at a category boundary? The case of unique red. Journal of the Optical Society of America A, 33(3), A260–A266. http://dx.doi.org/10.1364/JOSAA.33.00A260.

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