**Despite the importance of the appearance of human skin for theoretical and practical purposes, little is known about visual sensitivity to subtle skin-tone changes, and whether the human visual system is indeed optimized to discern skin-color changes that confer some evolutionary advantage. Here, we report discrimination thresholds in a three-dimensional chromatic-luminance color space for natural skin and skinlike textures, and compare these to thresholds for uniform stimuli of the same mean color. We find no evidence that discrimination performance is superior along evolutionarily relevant color directions. Instead, discriminability is primarily determined by the prevailing illumination, and discrimination ellipses are aligned with the daylight locus. More specifically, the area and orientation of discrimination ellipses are governed by the chromatic distance between the stimulus and the illumination. Since this is true for both uniform and textured stimuli, it is likely to be driven by adaptation to mean stimulus color. Natural skin texture itself does not confer any advantage for discrimination performance. Furthermore, we find that discrimination boundaries for skin, skinlike, and scrambled skin stimuli are consistently larger than those for uniform stimuli, suggesting a possible adaptation to higher order color statistics of skin. This is in line with findings by Hansen, Giesel, and Gegenfurtner (2008) for other natural stimuli (fruit and vegetables). Human observers are also more sensitive to skin-color changes under simulated daylight as opposed to fluorescent light. The reduced sensitivity is driven by a decline in sensitivity along the luminance axis, which is qualitatively consistent with predictions from a Von Kries adaptation model.**

*E*

_{LAB}and Δ

*E*

_{CAM02}. The aim of these color spaces is to propose a description of color based on appearance, where equal distances traversed in the color space correspond to roughly equal perceived differences in appearance. Although these theories offer critical insights into the early mechanisms of human color vision, such as color opponency, they do not provide a convincing framework to study natural polychromatic stimuli. The response of the visual system to these stimuli is more complex, and relatively less understood. For instance, Webster and Mollon (1997) showed that the human visual system adapts to color distributions in natural scenes. In particular, when natural (or naturallike) stimuli are presented to observers, their color perception has been shown to be affected by factors such as the object's textural properties (Vurro, Ling, & Hurlbert, 2013) and the observer's memory of the object (Olkkonen, Hansen, & Gegenfurtner, 2008). Consequently, attempts to define and estimate discrimination surfaces for polychromatic stimuli have been relatively fewer and more recent. Montag and Berns (2000) compared luminance thresholds for textures and uniform patches and found the luminance thresholds for textures to be higher by a factor of 2. Hansen, Giesel, and Gegenfurtner (2008) and Giesel, Hansen, and Gegenfurtner (2009) estimated chromatic thresholds in an isoluminant plane for uniform patches, natural objects, and polychromatic textures with color distributions similar to natural stimuli.

*reference patch*, while one—the

*test patch*—differed in color (Figure 1d). The observer's task was to indicate the odd one out by pressing the corresponding button on a response box. The test patch was generated by adding a

*test vector*in 3-D CIELAB color space (CIE, 2004) to each pixel of the reference patch. The process is illustrated in Figure 1c.

*xyY*coordinates (CIE, 2004) of [0.28 0.30 106.1445]

^{T}. The thresholds were estimated along 14 directions such that the CIELAB space was sampled evenly. Six of these coincided with the cardinal ±

*L*

^{*}, ±

*a*

^{*}, and ±

*b*

^{*}directions, while the other eight directions were along the centroids of the eight octants. During the experiment, the length of the test vector in each direction was controlled by the QUEST adaptive algorithm (Watson & Pelli, 1983), leading to 14 interleaved staircases. Theoretically, the measured threshold corresponded to an 86% score on the psychometric function. In the best-case scenario, each staircase lasted approximately 40 trials, although if observers made frequent errors, some lasted for as many as 90 trials.

*object mode*of stimulus presentation (Tangkijviwat, Rattanakasamsuk, & Shinoda, 2010). We think this is a more ecologically valid method of presenting stimuli such as natural or known textures and surfaces on a computer screen.

*x*= 0.32,

*y*= 0.34) at 20 cd/m

^{2}. This chromaticity was chosen in order to avoid arbitrary adaptation to the textured self-luminous stimuli while also ensuring that the dark condition remained comparable to the luminaire-illuminated D65 condition.

*E*

_{LAB}≥ 5) which were not part of the main experiment; the objective was to facilitate adaptation to the ambient illumination while at the same time making sure that the observers understood and remembered the task. After the test run, the observers remained in the lightproof chamber for another minute for further adaptation, before a long beep signaled the start of the main experiment. At this point, the observers pressed a button to start the presentation of the trials. Each trial consisted of on-screen display of the stimulus corresponding to a randomly chosen staircase, which timed out after a maximum of 5 s (the stimulus was displayed throughout the duration of the trial). If the observer failed to respond within 5 s in a given trial, the experiment advanced to the next randomly chosen staircase while the state of the original staircase (for which the observer did not register a response) was not changed. A response or time-out was signaled by a beep, after which the experiment moved on to the next trial.

*L*

^{*}for the lightness and

*a*

^{*}and

*b*

^{*}for the green–red and blue–yellow chromatic components. CIELAB includes a von Kries–type adaptation constant to account for appearance changes due to illumination changes. CIE 1976 UCS, on the other hand (whose axes are commonly labeled as

*u*′ and

*v*′), is a uniform chromaticity-scale diagram. It is a projective transformation of the CIE xy chromaticity diagram (CIE, 2004) designed to yield a more uniform perceptual color spacing. Its axes roughly denote the red–green and yellow–blue colors. Both spaces are attempts to improve perceptual uniformity of the standard tristimulus CIE XYZ space, but CIE 1976 UCS does not make any assumptions about the adaptational state of the visual system.

*u*′

*v*′

*Y*′ space, where

*Y*′ is the scaled version of the CIE luminance coordinate

*Y*.

*u*′

*v*′

*Y*′ space and averaged over the three repetitions. For each set of 14 average thresholds (along each of the 14 directions of measurement), an ellipsoid centered at the mean stimulus color was fitted by minimizing the total least-squared distance of the points from the ellipsoid surface. This resulted in one fitted ellipsoid per observer per condition. A detailed mathematical description of the ellipsoid fitting is provided in Appendix 1.

*spectral images*allowed for the simulation of the color of each pixel under any given illuminant using the simple illuminant-reflectance-sensor equation for each pixel:

*λ*is the wavelength in the visible spectrum,

*(*

**L***λ*) is the spectrum of the illuminant,

*i*th CIE 1931

*XYZ*color-matching function, and

*is the*

**X**_{i}*i*th tristimulus coordinate corresponding to

*(*

**L***λ*) correspond to the spectral power distribution curves shown in Figure 1. The color gamuts of the patches simulated using both overhead illuminants are shown in Figure 3a, while the luminance and chromatic projections of these distributions are shown in Figure 3b. The first row shows plots of luminance (ordinate) against the

*u*′ coordinate (abscissa), while the second row shows

*u*′

*v*′ chromaticity plots (

*v*′ ordinate,

*u*′ abscissa).

*u*′ axis in both illumination conditions, the Chinese patch showed variation along an inclined axis, with the inclination changing markedly with the illuminant.

*reference images*were the skin patches described under Skin images: Acquisition and simulation. In addition, discrimination thresholds for two uniform color patches were also measured using the same procedure as the skin patches. These two uniform color patches corresponded to the mean CIELAB colors of the two skin patches (Caucasian and Chinese), respectively.

*u*′

*v*′ chromaticity plane (for details, see Data analysis and Appendix 1). The length of the luminance projection (a line segment) and the area of the chromaticity projection (an ellipse) are shown in Figure 5b and 5c, respectively. Both luminance and chromatic thresholds are higher for skin stimuli than for uniform patches. Furthermore, the luminance projections for skin images are, on average, larger in TL84 than the other two illumination conditions.

*u*′

*v*′ chromaticity plane. The chromatic ellipses for skin images (solid lines) are larger than those for the corresponding uniform patches (dashed lines). It is also interesting to note that while the area of these chromatic ellipses changes between the two ethnicities (being higher for the Chinese skin patch), there is little variation within the illumination conditions. Besides the area, the orientation of these ellipses (Figure 5d) also shows an interesting trend: The ellipses for the TL84 illumination condition differ markedly in their orientation from the dark and D65 conditions. These effects are also reflected in the individual observer data (Supplementary File S1).

^{2}simulated daylight from an overhead luminaire in D65 vs. ≈20 cd/m

^{2}simulated daylight from the surround in the dark condition). Bearing this in mind, we observe that the chromatic projections of the discrimination ellipsoids under these two conditions display remarkably similar orientations (Figure 5d), whereas the discrimination ellipsoids themselves differ in overall volume (Figure 5a). This could suggest that while the chromatic mechanisms which respond to the skin stimulus depend on the spectrum of the foveal stimulus (which is the same in both dark and D65 conditions), the relative activations of these mechanisms are influenced by the adaptation conditions (which differ markedly between the two conditions).

*u*′ and

*v*′ axes.

*u*′

*v*′ are around 0.005), and the

*v*′ thresholds are about 0.7 times the

*u*′ thresholds. Thus, to a first approximation under a daylight illuminant, the commonly used

*u*′

*v*′ space can indeed be quite useful to predict whether two skin patches will look the same.

*reference stimuli*were color-accurate renderings of skin patches such that their appearance was consistent with the ambient illumination (D65 or TL84). In Experiment 2, the reference stimuli were obtained by translating the color distribution of simulated skin under one illuminant (say D65) such that its mean moved to the mean color of simulated skin under the other illuminant (in this case, TL84). Note that this manipulation, while swapping the means of the stimuli under the two illuminants, maintains their original relative color distributions (Figure 8a). Since the swap involved colors measured under different illuminants, it was carried out in the CIELAB space, which has some degree of inbuilt adaptation. To reduce the testing time per participant, only stimuli based on the original Caucasian patch were tested, and the ecologically inconsistent dark condition was dropped. Thresholds for uniform patches derived from the mean CIELAB colors of the stimuli were also measured.

*N*= 6) from Experiment 1 were recruited. In total, 168 thresholds (2 illuminants × 2 stimulus types: uniform and textures × 3 repetitions × 14 measurement directions) were measured, amounting to about 6 hr of testing per participant.

*u*′ axis than the D65 ellipses for both polychromatic and uniform stimuli.

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*Optics Express*^{3}space (

*u*′

*v*′

*Y*′ space in our case) be denoted by

*E*. The threshold boundary of this ellipsoid

*E*can be written as

_{}

^{3}is a color on the threshold boundary,

**Σ**is a diagonal matrix

*is an orthogonal matrix with each column representing a unit vector along one of the ellipsoid axes, and*

**U***is the center of the ellipsoid (defined as the average color of the tested stimulus in this study). Here,*

**c***is essentially a rotation matrix in three dimensions, and thus can be decomposed into a set of Tait–Bryan angles or rotation angles. The Tait–Bryan angles of an ellipsoid describe the sequence of rotations one must perform on the cardinal axes of the color space such that they are aligned with the ellipsoid axes. Although the mapping from*

**U**^{T}*to Tait–Bryan angles is not bijective (it is many–one), a branch of the solution suffices to cover all real 3-D cases computationally. If*

**U**^{T}*x*,

*y*) represents the four-quadrant arctangent (which takes two arguments and has a range different from that of the standard arctangent, which is denoted in this appendix as tan

^{−1}

*x*), a sufficient mapping for

**Θ**is given by

_{.}

*is fixed as the mean CIELAB color of the stimulus, the optimization was performed for only for the entries of*

**c****Σ**and

**Θ**—that is, six parameters. Suppose the estimated thresholds for a given condition and a given observer are given by the set {

**x**_{1},

**x**_{2}, …,

**x**_{14}}, such that each of

**x**_{1}through

**x**_{14}represents the threshold along one of the 14 measured directions. Furthermore, let

*E*(

**Σ**,

**Θ**) be an ellipsoid defined by the parameters {

**Σ**,

**Θ**}. Let us also define a metric

*d*(

*,*

**x***E*) which denotes the distance (Euclidean in our case) between a point

*and an ellipsoid*

**x***E*. The optimization problem to be solved for fitting an ellipsoid with optimized parameters

**Θ**are not a very intuitive parameter for a discrimination ellipsoid. For this reason, after optimization it was transformed back to the more easily interpretable orthogonal matrix

*of unit vectors along the axes of the ellipsoid. From these optimal estimates, the elevations (*

**U***θ*) and azimuths (

_{i}*φ*) for each column

_{i}*were derived simply by converting them to polar coordinates using*

**U***L*defined by

*is any point on the plane,*

**d***is the set of basis vectors defining the plane, and*

**T***is the vector of weights for each of the basis vectors—that is, the local coordinates of the point*

**t***on the plane*

**x***L*. With

*= 0 and*

**d***L*to represent the zero-luminance chromaticity plane in the

*u*

*v*′

*Y*′ color space. The parallel projection

*P*of an ellipsoid

_{E}*E*(as defined in Equation A1) on this plane

*L*can be calculated to be

*P*,

_{E}

**T**^{T}

**U****Σ**

^{−1}. The matrices

*and*

**U****Σ**in a 3-D space—that is,

*P*, and

_{E}_{,}which denotes a unit vector along the major axis of

*P*:

_{E}*u*′ and

*v*′ projections of chromatic ellipses for skin stimuli from Experiment 1 (Figure A2). These plots can be used to assess how the

*u*′

*v*′ chromaticity plane describes skin appearance. The artificial lighting (TL84, fluorescent) produces a large difference in thresholds along the two axes, whereas simulated daylight (D65) produces thresholds which are similar. The thresholds are 0.005–0.01 unit along either axis.