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Article  |   March 2017
Perceptual dimensions underlying lightness perception in homogeneous center-surround displays
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Journal of Vision March 2017, Vol.17, 6. doi:10.1167/17.2.6
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      Alexandra C. Schmid, Barton L. Anderson; Perceptual dimensions underlying lightness perception in homogeneous center-surround displays. Journal of Vision 2017;17(2):6. doi: 10.1167/17.2.6.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Lightness judgments of targets embedded in a homogeneous surround exhibit abrupt steps in perceived lightness at points at which the targets transition from being increments to decrements. This “crispening effect” and the general difficulty of matching low-contrast targets embedded in homogeneous surrounds suggest that a second perceptual dimension in addition to lightness may contribute to the appearance of test patches in these displays. The present study explicitly tested whether two dimensions (lightness and transmittance) could lead to more satisfactory matches than lightness alone in an asymmetric matching task. We also examined whether transmittance matches were more strongly associated with task instructions that had observers match perceived transparency or the perceived edge contrast of the target relative to the surround. We found that matching target lightness in a homogeneous display to that in a textured or rocky display required varying both lightness and transmittance of the test patch on the textured display to obtain the most satisfactory matches. However, observers primarily varied transmittance when instructed to match the perceived contrast of targets against homogeneous surrounds, but not when instructed to match the amount of transparency perceived in the displays. The results suggest that perceived target–surround edge contrast differs between homogeneous and textured displays. Varying the midlevel property of transparency in textured displays provides a natural means for equating both target lightness and the unique appearance of the edge contrast in homogeneous displays.

Introduction
When viewing a scene, we experience structure in the image as being caused by different physical sources, such as object shape, surface reflectance properties (e.g. lightness, color, gloss, and transparency), and the prevailing illumination. The perception of surface reflectance properties has been a main focus of vision research because they are “intrinsic” to objects and surfaces, and such properties seem to form the basis of our visual experience of the world. An extensively studied problem is how the visual system generates our experience of surface albedo or lightness, which is defined as the proportion of light a surface reflects diffusely. Determining how the visual system computes lightness is not straightforward because lightness, illumination, and surface pose are conflated in the image. 
The experience of surface lightness is known to depend on the context in which a surface is embedded. One of the most investigated forms of context dependence is the simultaneous contrast display similar to the example in Figure 1. Despite decades of research, there remains extensive debate on how to understand the context dependencies exhibited in these displays. Takasaki (1966) reported that target patches surrounded by a homogeneous background exhibit an abrupt “step” in perceived lightness between low-contrast decrements (targets slightly darker than the surround) and low-contrast increments (targets slightly lighter than the surround). For the same veridical difference in albedo, the perceived difference between two increments or two decrements is smaller than the perceived difference between a low-contrast increment and a low-contrast decrement. Takasaki (1966) called this effect “crispening.” Whittle (1992) observed that adding a black ring around the target reduced the size of the crispening effect, leading to a smoother relationship between simulated and perceived brightness. Schmid and Anderson (2014) found that the crispening effect was eliminated when a uniform target patch was surrounded by surfaces with complex “mesostructure” (small-scale three-dimensional relief); perceived lightness of the patch exhibited a smooth, monotonic relationship as a function of test patch albedo. The crispening effect has also been observed with colored center-surround displays (Ekroll & Faul, 2009, 2012a, 2012b, 2013; Ekroll, Faul, & Niederée, 2004; Ekroll, Faul, & Wendt, 2011). As with lightness studies, adding a black ring around the target or making the surround variegated greatly reduces or eliminates crispening (Ekroll & Faul, 2009, 2012a). Thus it appears that the crispening effect in lightness and color displays is a phenomenon that only occurs with homogeneous center-surround displays. 
Figure 1
 
Simultaneous contrast display. The gray patch on the black background looks lighter than the same gray patch on the white background.
Figure 1
 
Simultaneous contrast display. The gray patch on the black background looks lighter than the same gray patch on the white background.
An additional problem that arises in assessing the perception of lightness in homogenous center-surround displays is the inability to make satisfactory lightness or color matches with asymmetric matching (Ekroll et al., 2004; Faul, Ekroll, Wendt, 2008; Gelb, 1929; Vladusich, Lucassen, & Cornelissen, 2007). A number of researchers have suggested that an extra perceptual dimension in addition to lightness is required to capture the appearance of ostensibly “simple” lightness displays (Brainard, Brunt, & Speigle, 1997; Katz, 1935; Logvinenko & Maloney, 2006; Maloney, Wuerger, & Krauskopf, 1995; Vladusich, 2012, 2013; Vladusich et al., 2007; Wuerger, Maloney, & Krauskopf, 1995). Ekroll, Faul, and colleagues (Ekroll & Faul, 2009, 2012a, 2012b, 2013; Ekroll et al., 2004, 2011) suggest that impressions of transparency contribute to the appearance of the central patch especially at low chromatic contrasts, which is putatively responsible for the crispening effect. A significant body of work in both perceived lightness and color has shown that layered image decompositions can induce large lightness and color induction effects (Anderson, 1997; Anderson & Khang, 2010; Anderson & Winawer, 2005, 2008; Wollschläger & Anderson, 2009). In a study by Ekroll and Faul (2013), observers varied the transmittance and color of an adjustable patch on a variegated surround to match a target on a homogeneous surround. The variegated and homogeneous surrounds had the same average (mean) chromaticity, which the authors suggest is the most appropriate choice to equate temporal adaptation effects, such as those due to von Kries scaling. They found that targets embedded in uniform surrounds were better matched when observers were allowed to vary both the physical color and transmittance of the adjustable patch on the variegated surround. Furthermore, transmittance and saturation settings were inversely related to the chromatic contrast between the target patch and its surround; at low chromatic contrasts, homogeneous center-surround stimuli appeared to trigger impressions of transparency with the target region being perceptually divided into a saturated, transparent filter layer and a background layer the same color and saturation as the surround. 
Ekroll & Faul's (2013) suggestion that transparency is responsible for the appearance of low contrast targets in chromatic displays is consistent with the flimsy or wispy appearance of low contrast test patches embedded in lightness displays that use homogeneous surrounds such as those in Schmid and Anderson (2014; see Figure 2). However, there are also low-level image differences between homogeneous and textured/variegated stimuli that may contribute to differences in the appearance of test patches in homogenous and variegated displays. The perceived contrast of test patches against the surround also differs between homogeneous and textured displays (see Figure 2). Varying test patch reflectance also changes the apparent contrast of the test patch against the surround in the homogeneous displays (Figure 2A), but to a lesser extent in the textured (rocky) displays (Figure 2B). Whittle (1992) suggested that neural signals are enhanced for low contrast center-surround displays, leading to enhanced discrimination of test patches close in reflectance to their surround. Thus adding structure to the surround could potentially reduce crispening via gain control mechanisms (Chubb, Sperling, & Solomon, 1989; Rudd & Popa, 2007; Spehar, DeBonet, & Zaidi, 1996), or contrast within the surround might mask contrast effects between the central patch and the surround. Varying transmittance of a target also changes the contrast of the adjustable patch relative to its adjacent surround, so the improved matches obtained using the transmittance setting may arise because it allowed observers to better match the chromatic contrast of the test patch against the surround, rather than because the target on the homogeneous surround induces a sense of transparency. 
Figure 2
 
Examples of test patches and surrounds used in Schmid and Anderson (2014). The same test patches are embedded in the flat matte surround (A), and the rocky matte surround (B). Test patches increase in lightness from left to right and from top to bottom. The green square indicates the test patch that has the same albedo as the surround.
Figure 2
 
Examples of test patches and surrounds used in Schmid and Anderson (2014). The same test patches are embedded in the flat matte surround (A), and the rocky matte surround (B). Test patches increase in lightness from left to right and from top to bottom. The green square indicates the test patch that has the same albedo as the surround.
The aim of the present study is to determine whether achromatic homogeneous center-surround displays can be better matched using a transparent matching pattern, and whether any such advantage is due to the transparent appearance of the target on the homogenous surround and or its perceived contrast. To anticipate our results, we find that observers do obtain perceptually better matches when the adjustable match pattern has both a transmittance and lightness dimension, but that their use of this additional dimension is most effective when they are instructed to match contrast and lightness, rather than transparency explicitly. 
Experiment 1: Effect of instructions on a two-dimensional matching task
In Experiment 1, observers varied both the lightness and transmittance of an adjustable patch overlaying a rocky surround to match a test patch embedded in a homogeneous surround. Participants were divided into different instructional conditions (see Methods section) in an attempt to explore which mechanisms might be responsible for lightness effects in homogeneous center-surround displays. If the appearance of test patches embedded in homogeneous surrounds can be captured by lightness and an additional dimension (contrast or transparency), then observers should utilize the transmittance setting when matching that particular dimension. If crispening in lightness displays is caused by scission of the display into a transparent test patch overlaying an opaque background, then perceived test patch transparency should increase as the achromatic contrast between the center and surround is reduced, i.e., where the crispening effect occurs. Figure 3 illustrates how this inverse relationship between center-surround contrast and perceptual transparency would influence test patch lightness. If perceptual transparency increases as the test patch becomes lower in contrast against the surround, more of the background would become visible through the test patch. For increments (Figure 3A), this means more of the “blackness” in the test patch would be attributed to the darker background layer, causing the filter layer (the test patch) to appear lighter. For decrements (Figure 3B), as transparency increases, more of the “whiteness” in the test patch would be attributed to the lighter background layer, causing the test patch to appear darker. 
Figure 3
 
Illustration of perceptual decomposition (scission) of homogeneous center-surround displays. (A) Displays with increment test patches are divided into a light colored transparent test patch layer and an opaque continuous gray surround layer. (B) Displays with decrement test patches are divided into a dark colored transparent test patch layer and an opaque continuous gray surround layer.
Figure 3
 
Illustration of perceptual decomposition (scission) of homogeneous center-surround displays. (A) Displays with increment test patches are divided into a light colored transparent test patch layer and an opaque continuous gray surround layer. (B) Displays with decrement test patches are divided into a dark colored transparent test patch layer and an opaque continuous gray surround layer.
Methods
Observers
Sixty first-year psychology students participated in Experiment 1. Twenty observers were assigned to a transparency instructions condition, 20 observers were assigned to a contrast instructions condition, and the remaining 20 observers were assigned to a no-transmittance control condition (see Procedure). 
Apparatus and stimuli
Stimuli were presented on a LaCie Electron 22 Blue IV monitor (LaCie, Ltd.) running at a refresh rate of 75 Hz with a resolution of 1,280 × 1,024 pixels controlled by a Mac Pro computer (Apple) running Mac OX S 10, at the University of Sydney, Australia. Stimulus presentation and data collection were controlled by a MATLAB script (R2010a; MathWorks) using the Psychophysics Toolbox (Brainard, 1997). Stimuli were viewed in a dark room at a viewing distance of approximately 70 cm. The carpet and walls of the room were black and the only source of light was the monitor that displayed the stimuli. 
The stimuli were modelled in the open-source software Blender (v. 2.6). The test stimuli were matte homogeneous center-surround displays used in Schmid and Anderson (2014; see Figure 2A & Figure 4, left). The adjustable display was a rocky surface overlayed with a circular central disk that could vary in simulated albedo and transmittance (Figure 4, right). The surfaces were generated in the same way as the stimuli in Schmid and Anderson (2014). The rocky surface was generated with the displace modifier, a tool in Blender that displaces vertices in a mesh based on the intensity of a texture. Various textures were used to deform the surface (the inbuilt cloud, marble, and stucci textures as well as textures from images of rocks and rough surfaces (for more details, see 1). 
Figure 4
 
Example of test (left) and adjustable (right) displays used in Experiment 1. Both images have been cropped in this figure but were presented in full size during the experiment. The distance between the test and adjustable surfaces are also not to scale.
Figure 4
 
Example of test (left) and adjustable (right) displays used in Experiment 1. Both images have been cropped in this figure but were presented in full size during the experiment. The distance between the test and adjustable surfaces are also not to scale.
Stimuli were rendered using the RADIANCE rendering software (Ward, 1994), which simulates physical interactions between illuminants and surfaces. The surfaces were rendered using the Ward BRDF model. This model has five parameters: diffuse components R, G, and B, specularity (PS, the proportion of light reflected by the specular component, uncolored) and microroughness (α, which determines the amount of specular scatter). Central patches in the homogeneous test displays were embedded in the surrounds and rendered as part of the same scene. Gray shades were assigned to the center and surround regions by adjusting the diffuse reflectance parameters, keeping relative RGB values equal. For the rocky displays, matte surfaces were assigned a specularity value of 0 and a roughness value of 0, whereas glossy surrounds were assigned a specularity value of 0.05 (5% of the light reflected from the surface is specular) and a roughness value of 0.01. Surfaces were rendered frontoparallel to the observer, with two ambient reflections. 
All surfaces were illuminated by a gray-scale version of the “grove” light field from the Debevec Light Probe Image Gallery (Debevec, 1998) and were rendered 10 times larger than required and antialiased, resulting in high dynamic range (HDR) images with dimensions of 900 × 900 pixels. The HDR images were tone-mapped to fit the luminance range of the monitor. This was achieved by linearly compressing the diffuse component and nonlinearly compressing the specular component of the images (see 2 for details). 
Most aspects of the rocky matching surfaces were rendered in exactly the same way as the rocky test stimuli in Schmid and Anderson (2014; see previous material). However, they were not rendered with a flat match patch. Rather, the rocky centers were a continuation of the surround texture with the same level of surface relief, gloss, and albedo. The central disk in the adjustable display was created in MATLAB using Metelli's episcotister model to calculate the luminance of each pixel in the location of the central disk on the monitor (see Beck, Prazdny, & Ivry, 1984; Metelli, 1970, 1974a, 1974b; Singh & Anderson, 2002). For a given albedo and transmittance, each pixel in the adjustable patch was calculated using Metelli's formula:  where p is the luminance value of the pixel in the region of overlay, α is the transmittance value of the disk (the fraction of light passing through the foreground disk), b is the luminance of the background pixel, and t is the amount of light reflected by the disk (i.e. the luminance of the disk if it were opaque).1 The transmittance value α was bound between 0 (completely opaque) and 1 (completely transparent), inclusive. In the no-transmittance control condition (see procedure) the central disk had a fixed transmittance value of 0 (completely opaque) and could only vary in albedo.  
Procedure
In each trial, a homogeneous center-surround test surface (14.88°) was presented on the left side of the computer screen. The right side of the screen contained a matching surface (also 14.88°) with a rocky surround and adjustable central patch. Observers could adjust the lightness of the adjustable patch by moving the mouse left and right, and could also adjust its transmittance by moving the mouse up and down. The test and adjustable surfaces were separated by 15.25° of visual angle (center to center) and were presented against a black background. There were three instruction conditions. In all conditions, observers were instructed to first change the lightness of the adjustable patch until it looked like it was the same lightness or painted with the same paint as the test patch. Moving the mouse left made the patch darker, and moving it right made the patch lighter. Once observers matched the lightness of the test and adjustable patches, they were instructed to set the transmittance of the adjustable patch by moving the mouse down to make the patch more transparent, or up to make the patch more opaque. Observers given transparency instructions were told that if they perceived the test patch to be transparent they should adjust the transparency of the adjustable patch until it appeared equally transparent as the test patch. Observers given the contrast instructions were instructed to adjust the transmittance of the adjustable patch until the edge had the same contrast with the background, or same visibility against the background, as the test patch. In the no-transmittance control condition observers could not vary the transmittance of the adjustable patch, so were only asked to match the lightness of the test patch. The word “transmittance” was not used in any of the instructional conditions; we use this term here to refer to the vertical mouse adjustment. Once observers had made the transmittance adjustment, they were instructed to fine tune the lightness and transmittance settings by making minor adjustments until a satisfactory match was reached. They pressed the space bar to record their match settings. 
The test surface was always a homogeneous center-surround display. There were six surround albedo conditions (Munsell 1.95, 3.5, 5, 6.5, 8, 9.5), and 13 to 15 test patch albedo conditions (ranging from Munsell 1.95 to 9.5; see Table A2 in 3). The surround albedo of the matching surface varied from trial to trial, and was the same as the test surface's surround albedo. There were also two reflectance conditions (matte or glossy) for the background of the matching surface. This resulted in a total of 172 trials for each observer. 
Results and discussion
The results of Experiment 1 are presented in Figures 5 and 7. Figure 5 shows the test patch lightness settings for each instruction condition plotted in Munsell values. Figure 7 plots the transmittance settings for the contrast and transparency instruction conditions. The crispening effect was observed in all three instruction conditions, i.e., there was a “step” in lightness settings as the test patch albedo passed through that of the surround (Figure 5). To compare the size of the crispening effect in each instruction condition, difference scores were obtained by subtracting the lowest contrast (against the surround) decrement settings from the lowest contrast increment settings. These difference scores are plotted in Figure 6. The actual (simulated) increment–decrement Munsell difference was 0.3 (horizontal dotted line in Figure 6). A lower score indicates a smaller step and therefore less crispening. The darkest (Munsell value: 1.95) and lightest (Munsell value: 9.5) surround conditions were omitted because they contained only increments or only decrements, respectively. 
Figure 5
 
Lightness settings for Experiment 1, plotted in Munsell values. (A) Lightness settings for the matte adjustable surface condition. (B) Lightness settings for the glossy adjustable surface condition. Each column shows the settings for different instruction conditions (contrast, transparency, and no-transmittance). Each row shows the settings for different surround-albedo conditions (Munsell 1.95, 3.5, 5, 6.5, 8, and 9.5). Error bars are standard error of the mean, and represent the interobserver variability for a particular condition. In a number of conditions, error bars are smaller than the data points, so are not visible.
Figure 5
 
Lightness settings for Experiment 1, plotted in Munsell values. (A) Lightness settings for the matte adjustable surface condition. (B) Lightness settings for the glossy adjustable surface condition. Each column shows the settings for different instruction conditions (contrast, transparency, and no-transmittance). Each row shows the settings for different surround-albedo conditions (Munsell 1.95, 3.5, 5, 6.5, 8, and 9.5). Error bars are standard error of the mean, and represent the interobserver variability for a particular condition. In a number of conditions, error bars are smaller than the data points, so are not visible.
Figure 6
 
Increment minus decrement settings for the matte (A) and glossy (B) adjustable surfaces in Experiment 1. The horizontal dotted line represents the actual difference between increments and decrements. The solid bars represent the increment-decrement difference scores for each surround Munsell condition (3.5, 5, 6.5 and 8). The mean of these surround Munsell conditions was taken for each instruction condition and plotted as striped bars. Error bars are standard error of the mean, and represent the interobserver variability for a particular condition.
Figure 6
 
Increment minus decrement settings for the matte (A) and glossy (B) adjustable surfaces in Experiment 1. The horizontal dotted line represents the actual difference between increments and decrements. The solid bars represent the increment-decrement difference scores for each surround Munsell condition (3.5, 5, 6.5 and 8). The mean of these surround Munsell conditions was taken for each instruction condition and plotted as striped bars. Error bars are standard error of the mean, and represent the interobserver variability for a particular condition.
Figure 7
 
Transmittance settings from Experiment 1, for the matte (A) and glossy (B) condition. Closed square data points are settings from the contrast instructions condition, and open circle data points are settings from the transparency instructions condition. Each color represents the settings for a different surround albedo condition. The vertical dotted lines indicate the surround Munsell value. Error bars are standard error of the mean, and represent the interobserver variability for a particular condition.
Figure 7
 
Transmittance settings from Experiment 1, for the matte (A) and glossy (B) condition. Closed square data points are settings from the contrast instructions condition, and open circle data points are settings from the transparency instructions condition. Each color represents the settings for a different surround albedo condition. The vertical dotted lines indicate the surround Munsell value. Error bars are standard error of the mean, and represent the interobserver variability for a particular condition.
In all conditions, the increment–decrement difference scores were greater than the actual (simulated) increment–decrement Munsell difference of 0.3 (horizontal dotted lines in Figure 6). The crispening effect was visually largest when observers were instructed to match the center patches on lightness and apparent contrast against the background (Figure 6, dark-gray bars). In this condition, the immediate increments appeared, on average, about 1.7 Munsell values lighter than the immediate decrements. The crispening effect was smaller when observers were instructed to match the center patches on lightness and transparency or lightness alone when compared to the contrast instruction matches (Figure 6, mid-gray and light-gray bars, respectively). In the transparency instructions condition, the immediate increments appeared, on average, about 1.3 Munsell values lighter than the immediate decrements. In the no-transmittance control condition, the immediate increments appeared, on average, about 1 Munsell value lighter than the immediate decrements. 
The increment–decrement difference scores were subjected to a between-subjects one-way analysis of variance (ANOVA) to determine whether there were any statistically reliable differences in the crispening effect between the different instruction conditions. Since the pattern of results was identical for each gloss condition and each surround Munsell condition (see Figure 6A and B), observers' difference scores were averaged across these conditions (Figure 6C). The one-way ANOVA on these average difference scores revealed that there were differences between the conditions, F(2, 57) = 3.42, p = 0.0394. Follow-up t tests using Sidak-corrected alpha values of 0.0170 per test2 indicated that the perceived difference between immediate increments and decrements was larger for contrast instructions compared to the no-transmittance control, t(57) = 2.60, p = 0.0119. However, the perceived difference between increments and decrements did not reliably differ for the contrast instructions and the transparency instructions, t(57) = 1.56, p = 0.124, nor between the transparency instructions and no-transmittance conditions, t(57) = 1.04, p = 0.303. The aforementioned findings suggest that the crispening effect was largest when observers were instructed to match the central patches on lightness and apparent contrast against the background, at least compared to when observers were only allowed to match lightness. There was no clear difference in crispening between the contrast and transparency instruction conditions, even with the increased power gained by averaging each observer's score over all conditions. 
There were, however, substantial and highly significant differences between the contrast and transparency instruction conditions in the transmittance data. Figure 7 plots the transmittance settings for the contrast instructions and transparency instructions conditions. Each graph plots the transmittance data for each gloss condition of the matching display (Figure 7A & 7B for matte and glossy, respectively) and each surround Munsell condition. Within each graph, closed square data points represent transmittance settings for the contrast instructions condition, and open circular data points represent transmittance settings for the transparency instructions condition. These data revealed that transmittance settings strongly depended on task instructions. Observers varied the transmittance settings much more when they were instructed to match the central patches on contrast against the surround compared to when they were asked to match the central patches on perceived transparency. Transmittance settings increased as test patch reflectance became closer to the surround value in both conditions (vertical dotted lines in Figure 7). This effect was much more pronounced in the contrast instructions condition, where transmittance peaked at about 0.6 for most surround Munsell conditions3 whereas transmittance peaked at about 0.1 for most surround Munsell conditions in the transparency instruction condition. These observations were statistically verified by subjecting the transmittance settings to independent t test using Sidak-corrected alpha values of 0.00366 per test4 comparing transmittance settings in the contrast and transparency instructions conditions (see Tables A3 and A4 for t values, df, and p values). The asterisks in Figure 7 indicate a significant difference in transmittance settings between the two instruction conditions. As can be seen in these figures, most of the transmittance settings were significantly higher for the contrast (closed square data points) compared with the transparency (open circle data points) instructions condition (44 out of 80 for the matte match display; 41 out of 80 for the glossy match display). The transmittance settings that reliably differed are clustered around the test patches that were low in physical contrast against the surround. Thus, observers used transmittance to match the central patches on perceived contrast by increasing transmittance to lower the contrast of the adjustable patch. Observers did not to vary transmittance very much when asked to match the central patches on perceived transparency, which suggests that they may not have perceived transparency in the homogeneous center-surround displays, or had no clear means of equating the transmittance in the test and match patterns. 
Experiment 2: Which instructions lead to better matches?
In Experiment 1, transmittance settings were vastly different between the contrast and transparency instruction conditions. When observers were able to vary transmittance, they tended to use this setting to match the contrast of the center patches, but not when they matched the patches on transparency. However, the pattern of lightness matches was very similar, and the crispening effect did not reliably differ between these conditions. Experiment 1 shows that different instructions changed observers' use of the transmittance setting, but it does not provide insight into whether one set of instructions led to better or more satisfactory lightness matches. Experiment 2 investigates which adjustable patch settings in Experiment 1 were “best” matched to test patches embedded in homogeneous surrounds. In Experiment 2, a new set of observers directly compared the settings made by observers in Experiment 1 and judged which settings were considered to be better matched in lightness to the test patches in the homogeneous displays. If satisfactory lightness matches can be made by adjusting the reflectance of the adjustable patch alone, then observers should choose the settings from the no-transmittance control condition as being better matched in lightness to the homogeneous displays. If an additional dimension such as contrast or transparency is required to make satisfactory lightness matches, then observers should choose the settings from either the contrast or transparency instructions condition as being better matched in lightness to the homogeneous displays. (Remember that observers predominantly varied transmittance in the contrast condition.) 
Methods
Observers
Twenty first-year psychology students participated in Experiment 2. None had participated in Experiment 1
Apparatus and stimuli
The homogeneous center-surround stimuli were the same as in Experiment 1. The comparison rocky displays were the same as the adjustable displays in Experiment 1, containing a rocky surface overlayed with a circular central disk that varied in simulated albedo and transmittance. On each trial, the albedo (t in Equation 1) and transmittance value (α in Equation 1) were the average albedo and transmittance settings made by observers in Experiment 1, respectively. The surrounds of the displays were cropped by 2.49° on each side so that four displays could fit on the computer monitor on each trial. 
Procedure
Observers judged which instruction condition in Experiment 1 led to better lightness matches with the homogeneous display using a paired comparison task. In each trial, two pairs of displays (9.95° each) were presented on the computer screen. One pair was presented at the top of the screen, and one pair was presented on the bottom of the screen (see Figure 8). The surfaces of each pair were separated horizontally by 10.71° (center to center) and the pairs were separated vertically by 14.25° (center to center). Each pair consisted of a homogeneous center-surround display and the corresponding rocky matching display overlayed by a filter with the average reflectance and transmittance settings obtained for their respective conditions in Experiment 1. The matching displays in each pair compared two of the three instruction conditions in Experiment 1. The homogeneous display was the same in the top and bottom pair. Observers were instructed to choose in which pair (top or bottom) the central patches appeared more similar in lightness. For the displays with transparent central patches, observers were instructed to only pay attention to the apparent lightness of the filter, and not the background that showed through. They made their decision by pressing the up or down arrow key for the top and bottom pair, respectively. After the stimuli were displayed, there was a five second delay before observers could make a response. Observers were told to use this time to carefully consider which pair was better matched, as the lightness of the central patches in each pair were extremely similar. 
Figure 8
 
Representation of the layout of a trial in Experiment 2. The surfaces are cropped more in this display compared to in the experiment, and the instructions text was not displayed on the screen; observers were given the instructions at the beginning of the experiment.
Figure 8
 
Representation of the layout of a trial in Experiment 2. The surfaces are cropped more in this display compared to in the experiment, and the instructions text was not displayed on the screen; observers were given the instructions at the beginning of the experiment.
There were three comparison conditions: (1) the contrast condition compared to the transparency condition; (2) the contrast condition compared to the no-transmittance condition; and (3) the transparency condition compared to the no-transmittance condition. The position on the screen (top or bottom) that each instruction condition pair was presented was randomized. The position (left or right) of the homogeneous and rocky displays within each pair was also randomized. For each comparison condition there were two gloss levels (matte and glossy), and six surround Munsell conditions (1.95, 3.5, 5, 6.5, 8, and 9.5). Eight test patches that were the lowest in contrast against the homogeneous surround were chosen for each surround Munsell condition (four increments and four decrements), except for surround Munsell 1.95 and 9.5, which only had increment or decrement test patches, respectively. This led to a total of 240 trials for each participant. 
Results and discussion
The results of Experiment 2 are presented in Figure 9, which plots the number of times (out of 60) each instruction condition was chosen to have a match patch that was better matched in lightness to the homogeneous display. Each graph plots the preference for each test patch Munsell value for a particular surround Munsell value. Figure 9A shows the results for when the rocky displays were matte, and Figure 9B shows the results for when the rocky displays were glossy. The results showed that as the test patches became closer in albedo to the surround, the matching patches from the contrast instruction condition were chosen to be more similar in lightness to the homogeneous display compared to the other two conditions. Note that the contrast condition displays had the highest transmittance settings. There was no clear preference for test patches further away from the surround albedo. Figure 10 shows the data averaged across test patch Munsell value, plotted as percentage of times chosen (because surround Munsell 1.95 and 9.5 had fewer data points to average across). It is clear from this figure that, on average, observers perceived the stimuli generated from the contrast instructions condition to be better lightness matches to the homogeneous displays. The data for each surround Munsell condition were subjected to paired t tests that compared the percentage of times the contrast instructions condition was chosen over the no transmittance control condition. These two conditions were chosen because they correspond to the stimuli containing the highest transmittance settings (contrast instructions) to the no transmittance control. The t tests revealed that stimuli from the contrast instructions condition were chosen reliably more often in all matte surround albedo conditions, and the last five (out of six) glossy surround albedo conditions (see Table A5 for t values, df and p values).5 
Figure 9
 
Results of Experiment 2 for the matte condition (A) and the glossy condition (B). Each graph shows the results for a particular surround Munsell value, and plots the number of times (out of 60) each instruction condition was chosen to best match the lightness of the test patch embedded in the homogeneous display. The vertical dotted lines indicate the surround Munsell value.
Figure 9
 
Results of Experiment 2 for the matte condition (A) and the glossy condition (B). Each graph shows the results for a particular surround Munsell value, and plots the number of times (out of 60) each instruction condition was chosen to best match the lightness of the test patch embedded in the homogeneous display. The vertical dotted lines indicate the surround Munsell value.
Figure 10
 
Results of Experiment 2, averaged across test patch Munsell. Each panel shows the percentage of times each instruction condition was chosen for each surround Munsell condition, for the matte condition (left) and the glossy condition (right). Error bars are standard error of the mean, and indicate interobserver variability. Significance stars indicate when the contrast instructions condition was chosen reliably more than the no transmittance control.
Figure 10
 
Results of Experiment 2, averaged across test patch Munsell. Each panel shows the percentage of times each instruction condition was chosen for each surround Munsell condition, for the matte condition (left) and the glossy condition (right). Error bars are standard error of the mean, and indicate interobserver variability. Significance stars indicate when the contrast instructions condition was chosen reliably more than the no transmittance control.
The aforementioned results show that a transparent match display on a textured surround that varies in transmittance generates the best matches to a homogeneous center-surround display for low contrast targets that exhibit the greatest amount of crispening, and that the best matches arise when observers are instructed to match the contrast of the match to the contrast of the target rather than to explicitly match targets on their perceived transparency. 
General discussion
Summary of experimental results
The present study investigated whether a second perceptual dimension (contrast or transparency) in addition to lightness contributes to the crispening effect observed in homogeneous center-surround lightness displays, and whether allowing observers to manipulate this second dimension would lead to better overall lightness matches for low-contrast test patches. In Experiment 1, observers matched test patches embedded in homogeneous surrounds by varying the lightness and transmittance of an adjustable patch overlaying a rocky matching display. When instructed to match the centers on lightness and transparency, observers tended not to use the transmittance settings. However, when instructed to match the centers on lightness and perceived contrast against the surround, observers utilized the transmittance settings, making the adjustable patch more transparent to match the perceived contrast of the target's edge relative to the surround. The results of Experiment 2 revealed that the lightness of low contrast homogeneous displays were better matched when observers matched both the perceived lightness and contrast of the target by manipulating the transmittance and lightness of the matching pattern, when compared to either the transparency instructions or the no-transparency condition. 
Possible explanations for matching behavior
The role of instructions in one-dimensional lightness and color matching tasks has been well documented. For example, under some circumstances (e.g., when illumination is inhomogeneous) observers matches vary depending on whether they are instructed to match two test patches on their brightness (the apparent amounts of light coming from the patches), lightness (their apparent reflectances) or brightness contrast (the brightness difference between the patches and their surrounds; Arend & Spehar 1993a, b; Blakeslee, Reetz, & McCourt, 2008; Rudd, 2010). It is often reported that lightness judgments are closer to reflectance matches whereas brightness judgments are closer to luminance matches (Arend & Goldstein, 1987; Arend & Reeves, 1986; Arend, Reeves, Schirillo, & Goldstein, 1991; see also Bauml, 1999; Cornelissen & Brenner, 1995; Troost & de Weert, 1991). However, subsequent work has shown that the size of these instructional effects (or whether there is an effect of instructions) depends on the class of stimuli (simple versus complex/natural scenes), the task (asymmetric matching, achromatic adjustment, palette matching, or color selection task; Delahunt & Brainard, 2004; Logvinenko & Tokunaga, 2011; Madigan & Brainard, 2014; Ripamonti et al., 2004), and whether a within- or between-subjects design was implemented (for further discussion, see Radonjić & Brainard, 2016). In our study, all stimuli were rendered under the same illumination, so reflectance and intensity matches would have been identical. Additionally, all observers were instructed to match lightness, so it is not possible for us to distinguish between lightness and brightness matches. Nevertheless, our crispening results are not consistent with observers purely matching luminance or reflectance, and the effect of our instructional manipulation was not on the lightness matches, but rather on settings of the transmittance dimension. 
It is difficult to exactly determine why our instructions led to different transmittance settings, and what strategies observers might have been using in each condition. Previous lightness and color studies have offered a number of possible explanations for the effects of lightness instructions. One possibility is that the different instructions may tap into different aspects of a fixed perceptual representation; another suggestion is that they could reflect different types of processes or “perceptual modes;” and another possibility is that different instructions may prompt explicit reasoning leading to “inferred” color or lightness judgments (for discussion, see Radonjić & Brainard, 2016). We cannot say which of these might apply to observers in our experiments, although it is possible that instructing observers to match contrast led them to focus on the difference of the patches relative to their backgrounds, whereas the transparency instructions could have prompted them to focus on differences between the textures within the patches themselves (i.e., how well they can see the background through the patch). 
Regardless of the representations, modes, inferences, or strategies used by the observers, results of the present study show that giving observers the ability to vary transmittance allows them to better match edge contrast. To make more satisfactory lightness matches observers seem to require the ability to adjust a midlevel dimension (transparency) to match a low-level construct (contrast) as well as lightness. This suggests that the efficacy of using transparent match displays may have been a result of transparency providing a natural means for equating both the contrast of the edges and the lightness of the target. 
It is also plausible that midlevel perceptual mechanisms caused the lightness shifts in low-contrast center-surround displays without observers being explicitly aware of this. There are a number of possible reasons why observers did not vary transmittance when asked to match transparency. First, when transmittance was varied, the central adjustable patch became textured because the rocky background was visible through the filter. Observers may have been unwilling to match a textured patch to a uniform patch, and hence failed to use the transmittance variable altogether. Another possible explanation is that they did not explicitly perceive transparency in the homogeneous center-surround display. The perceptual outcome may be reminiscent of transparency (low contrast test patches look insubstantial or “wispy”), but perhaps observers did not have direct access to this impression, or they could not quantify it using a matching task. 
The fact that transmittance was slightly varied in the transparency instructions condition suggests that observers may have perceived transparency, but were unable or hesitant to quantify this percept. Our own explorations revealed that it was very difficult to judge how transparency should be matched in the adjustable patch even for observers who reported perceiving the test patch as transparent. In contradistinction, matching the contrast of the edges of the two displays seemed much more intuitive and comparatively easy. The ability to directly measure impressions of transparency in homogeneous center-surround displays may be akin to judging the level of illumination in a scene. Research has shown that observers can perceive differences in illumination between two rooms, but are quite poor at explicitly matching the illumination level (Rutherford & Brainard, 2002). A possible reason for why observers varied transmittance when asked to match the contrast of the central patches is that varying the midlevel property of transparency acted as a proxy to allow observers to match a low-level property such as edge contrast, and this is something that observers could explicitly match. 
Relation to previous work
The finding that observers did not substantially make use of the transmittance setting when asked to match transparency in Experiment 1 differs from the results reported by Ekroll and Faul (2013) using colored stimuli. We currently do not have any principled explanation for the differences in our results. The colored center-surround displays used in Ekroll and Faul's study may evoke a more compelling percept of transparency compared with achromatic displays, or the extra dimension of saturation may provide additional cues that observers could use to adjust transmittance. However, it should be noted that Ekroll and Faul (2013) only measured the effects of a fixed achromatic surround on targets where the hue was varied, whereas we varied both the surround and the target colors. It is currently unknown whether our results would generalize to colored surrounds. 
Other researchers have suggested that multiple perceptual dimensions are needed to capture the full perceptual experience of achromatic surfaces due to the different perceptual qualities of homogeneous center-surround displays (Logvinenko & Maloney, 2006; Vladusich, 2012, 2013; Vladusich et al., 2007) and the inability to satisfactorily match such displays by varying lightness or luminance alone (Brainard et al., 1997; Katz, 1935; Maloney et al., 1995; Wuerger et al., 1995). Vladusich et al. (2007) showed that observers were progressively less able to produce perfect achromatic matches as the contrast difference between test and matching displays increased, when measured with a 10-point scale that rated the possibility of making a perfect match. Vladusich and colleagues have suggested that blackness and whiteness form the perceptual dimensions involved in the appearance of achromatic surfaces. However, they pointed out that their model incorrectly predicted the quality of match ratings in low-contrast center-surround displays, and suggested that this may have to do with perceptual transparency. Similar to Vladusich, Logvinenko, and colleagues (Logvinenko & Maloney, 2006; Logvinenko, Petrini, & Maloney, 2008; Logvinenko & Tokunaga, 2011; Tokunaga & Logvinenko, 2010a, 2010b) have argued that asymmetric matching can never lead to an exact match; observers can only set the minimum subjective difference between stimuli. In one experiment, Logvinenko and Maloney (2006) discarded the asymmetric matching method altogether, and had observers rate the dissimilarity of pairs of stimuli under different levels of illumination. They used a multidimensional scaling technique to plot and compare the similarity of each stimulus in a two-dimensional space. They found that within an illuminant, achromatic colors fell along a single locus, forming a one-dimensional space. However, two distinct perceptual dimensions were needed to represent all of achromatic surface color, and the second dimension (which they termed “brightness”) was associated with changes in illumination. Logvinenko and Maloney (2006) accounted for perceptual differences when surfaces were illuminated differently. However, they did not compare the appearance of achromatic surfaces in cases of transparency, where luminance values are perceptually divided into a background layer and transparent foreground layer. Our results, along with those of Ekroll and Faul (2013), suggest that asymmetric matching can lead to better matches when observers are able to vary the dimensions of lightness and transmittance. 
The present findings demonstrate that it is difficult to tease apart low-level (e.g., contrast) and midlevel (e.g., transparency) contributions to lightness phenomena in simple displays. If perceptual transparency does affect the lightness of test patches embedded in homogeneous surrounds, then we suggest that representations of transparency need not be directly measurable or quantifiable, similar to observers' difficulty when matching illumination level (e.g., Rutherford & Brainard, 2002). Anderson and colleagues (Anderson, 1997, 1999, 2003a, 2003b; Anderson & Winawer, 2005, 2008) showed that geometric continuity of targets and surrounds, and consistent polarity relationships of the borders separating targets from the surrounds, determine how (or whether) scission is initiated and luminance values are separated into a foreground (see-through) and background layer. This in turn determines how (or if) luminance is partitioned between the different layers. Homogeneous center-surround displays meet the conditions for this perceptual image decomposition. There is a “continuity” of the homogeneous surround and center, although the distinct lack of geometry makes it ambiguous how luminance should be partitioned between the different layers. This ambiguity might be reflected in perception: Homogeneous displays may evoke a weaker sense of transparency, and or observers may not have perceptual access to this representation. 
One clear result from this study was that observers used transparent match displays to equate both the contrast between the center and surround and the lightness of the target in the homogeneous displays. Furthermore, observers preferred the matches made to these homogeneous center-surround displays using transparent displays over opaque matching displays. This suggests that observers require the ability to manipulate a midlevel property like transparency to obtain more satisfactory matches to homogeneous center-surround displays, which may occur even in the absence of any explicit impressions of perceived transparency. A low-level feature such as edge contrast co-varies with lightness and is something to which observers appear to have explicit perceptual access. Thus, observers may have been more effectively able to (and willing) to vary transmittance to match the contrast of the homogeneous center-surround displays. 
Conclusions
Our results suggest that homogeneous targets embedded in homogeneous surrounds cannot be perfectly matched to targets embedded on a textured surround by varying lightness alone; a second perceptual dimension is required. Giving observers access to midlevel dimensions such as transparency provides a natural means for equating the contrast between the center and surround and the lightness of the target in homogeneous center-surround displays. Dissociating midlevel transparency explanations from low-level contrast explanations of the crispening effect will always be problematic, as by definition information is processed by “low-level” mechanisms before higher visual processing areas responsible for the midlevel segmentation of surfaces. Our results suggest that the addition of the mid-level dimension of transmittance may be a powerful methodological tool that can be used to assess the dimensionality of the perceptual mechanisms underlying the perception of perceived lightness. 
Acknowledgments
This research was supported by grants from the ARC to B. L. Anderson. 
Commercial relationships: none. 
Corresponding authors: Alexandra C. Schmid; Barton L. Anderson. 
Address: Department of Psychology, Justus-Liebig-Universität Gießen, Germany; School of Psychology, University of Sydney, New South Wales, Australia. 
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Footnotes
1  Note that t was converted to reflectance or Munsell values, given that we knew the average luminance of an opaque test patch with a given reflectance illuminated by the “grove” light field (Debevec, 1998; see Schmid & Anderson, 2014).
Footnotes
2  Sidak-corrected alpha values were calculated as α1 = 1 − (1 − α)1/n = 1 − (1 − 0.05)1/3 = 0.0170.
Footnotes
3  The lowest contrast test patch against surround 1.95 was set close to 1 because this test patch was actually invisible against the surround, as explained in Schmid and Anderson (2014). Thus it would have been perceived as having zero contrast, leading observers to set the adjustable patch to be invisible.
Footnotes
4  Sidak-corrected alpha values were calculated as α1 = 1 − (1 − α)1/n = 1 − (1 − 0.05)1/14 = 0.00366.
Footnotes
5  Note that we could only validly compare two groups due to correlated measures (the percentage of times one group is chosen depends on the percentage of times the other two groups are chosen). If we compared the contrast instructions condition to the transmittance instructions conditions, the results are similar. For both matte and glossy conditions, stimuli from the contrast instructions condition were chosen reliably more often than stimuli from the transparency instructions condition, for the first five out of six surround albedo conditions, p < 0.05.
Appendix A: Creation of homogeneous and rocky surfaces
The surfaces were created in the same way as Schmid and Anderson (2014), and the details are repeated here. Each surface was created in Blender using an 800 × 800 mesh. The textures in each surround were generated with the displace modifier, a tool in Blender that displaces vertices in a mesh based on the intensity of a texture. Various textures were used to deform the surfaces: the inbuilt cloud, marble, and stucci textures as well as textures from images of rocks and rough paper. The image of rough paper used is displayed in Figure A1. The rocky texture image can be found at: http://junk-paris-stock.deviantart.com/art/macro-rock-texture-13-119245673. Table A1 shows the modifiers that were used for test (homogeneous) and match (rocky) surfaces and the order they were applied. Note that although the rough paper texture was used to displace vertices in the test surrounds, this effect was extremely subtle so the rendered images were essentially homogeneous. Also note that, although multiple textures were used to deform the match surfaces, we refer to them as “rocky” because of their rocky appearance after rendering.
Figure A1
 
Paper texture used to deform test surfaces.
Figure A1
 
Paper texture used to deform test surfaces.
Table A1
 
Modifiers used to create the effects in the test and match surfaces. The order the modifiers are displayed is the order they were applied (left column, top to bottom).
Table A1
 
Modifiers used to create the effects in the test and match surfaces. The order the modifiers are displayed is the order they were applied (left column, top to bottom).
 
Appendix B: Tone-mapping of RADIANCE HDR images
The procedure used to tone-map each HDR image is as follows: The diffuse component was linearly compressed by transforming luminance values below 140 cd/m2 with the equation:  where Display FormulaImage not available is the transformed luminance associated with the diffuse component for each pixel i, Display FormulaImage not available is the original HDR luminance associated with the diffuse component for each pixel i, Display FormulaImage not available is the maximum HDR luminance attributed to diffuse reflectance, and Display FormulaImage not available is the maximum luminance assigned to diffuse reflectance in the tone-mapped (transformed) image. Display FormulaImage not available was constant for all images and was equal to 140. Display FormulaImage not available was constant for all images and was equal to 53.59. Thus, the brightest regions of diffuse shading in the tone-mapped image had a luminance of approximately 53.59 cd/m2.  
The specular component (HDR luminance values above 140 cd/m2) was compressed non-linearly to create a smooth falloff of luminance values that started at Display FormulaImage not available (53.59 cd/m2) and peaked at Display FormulaImage not available, the luminance assigned to the brightest specular highlight and also the brightest luminance of the monitor (64.98cd/m2; see Figure A2). We achieved this by first subtracting Display FormulaImage not available (140 cd/m2) from each pixel and then transforming these values with the equation:  where Display FormulaImage not available is the transformed luminance associated with the specular component for each pixel i, R is the luminance range of the specular highlights and is equal to Display FormulaImage not available , S is the slope of the straight line from the linear transformation of the diffuse component and is equal to Display FormulaImage not available, and Display FormulaImage not available is the HDR luminance associated with the specular component for each pixel i. Finally, we added Display FormulaImage not available to these specular values and the result was a tone-mapped image with linearly transformed diffuse shading and non-linearly transformed specular highlights (Figure A2).  
The last step was to display the images using the 8-bit pixel values of the monitor. For this we made a color look-up table (CLUT) of luminance values corresponding to each 8-bit pixel value (0–255). Each luminance value in the tone-mapped image was transformed into its corresponding CLUT value.
Figure A2
 
Transformation of HDR luminance values (x axis) to tone-mapped luminance values (y axis).
Figure A2
 
Transformation of HDR luminance values (x axis) to tone-mapped luminance values (y axis).
 
Appendix C: Tables
Table A2
 
Surround and center patch reflectance and luminance values. The first row shows the test patch values that were common to all surrounds. The fifth, sixth, and seventh columns show this in % reflectance, Munsell values, and luminance values, respectively. For all remaining rows, the first column contains the six surround reflectance values (% reflectance). The second column shows the values in column 1 transformed to the Munsell scale. The third and fourth column shows the luminance range of the rocky matching surfaces (M = matte, G = glossy). The fifth column contains the extra two to four reflectance values (% reflectance) of the center patches that were very close in lightness and unique to each surround. Two of these values were increments and two were decrements, except for the black surround (3% reflectance), which contained only two extra increments, and the white surround (90% reflectance), which contained only two extra decrements. The sixth column shows the values in column 5 transformed to the Munsell scale, and the seventh column displays the luminance values of the test patches.
Table A2
 
Surround and center patch reflectance and luminance values. The first row shows the test patch values that were common to all surrounds. The fifth, sixth, and seventh columns show this in % reflectance, Munsell values, and luminance values, respectively. For all remaining rows, the first column contains the six surround reflectance values (% reflectance). The second column shows the values in column 1 transformed to the Munsell scale. The third and fourth column shows the luminance range of the rocky matching surfaces (M = matte, G = glossy). The fifth column contains the extra two to four reflectance values (% reflectance) of the center patches that were very close in lightness and unique to each surround. Two of these values were increments and two were decrements, except for the black surround (3% reflectance), which contained only two extra increments, and the white surround (90% reflectance), which contained only two extra decrements. The sixth column shows the values in column 5 transformed to the Munsell scale, and the seventh column displays the luminance values of the test patches.
Table A3
 
Experiment 1, matte matching display: t values and p values comparing transmittance settings between the contrast and transparency instruction conditions, for each surround albedo and test patch albedo condition. The comparison numbers 1–14 correspond to the test patches being compared in each graph in Figure 7A from left to right. * p < 0.00366; df = 38 for all comparisons.
Table A3
 
Experiment 1, matte matching display: t values and p values comparing transmittance settings between the contrast and transparency instruction conditions, for each surround albedo and test patch albedo condition. The comparison numbers 1–14 correspond to the test patches being compared in each graph in Figure 7A from left to right. * p < 0.00366; df = 38 for all comparisons.
Table A4
 
Experiment 1, glossy matching display: t values and p values comparing transmittance settings between the contrast and transparency instruction conditions, for each surround albedo and test patch albedo condition. The comparison numbers 1–14 correspond to the test patches being compared in each graph in Figure 7B from left to right. * p < 0.00366; df = 38 for all comparisons.
Table A4
 
Experiment 1, glossy matching display: t values and p values comparing transmittance settings between the contrast and transparency instruction conditions, for each surround albedo and test patch albedo condition. The comparison numbers 1–14 correspond to the test patches being compared in each graph in Figure 7B from left to right. * p < 0.00366; df = 38 for all comparisons.
Table A5
 
t values and p values comparing preferences in Experiment 2 for the contrast instructions condition over the no transmittance control condition, for each surround Munsell condition and gloss level. * p < 0.05; df = 19 for all comparisons.
Table A5
 
t values and p values comparing preferences in Experiment 2 for the contrast instructions condition over the no transmittance control condition, for each surround Munsell condition and gloss level. * p < 0.05; df = 19 for all comparisons.
 
Figure 1
 
Simultaneous contrast display. The gray patch on the black background looks lighter than the same gray patch on the white background.
Figure 1
 
Simultaneous contrast display. The gray patch on the black background looks lighter than the same gray patch on the white background.
Figure 2
 
Examples of test patches and surrounds used in Schmid and Anderson (2014). The same test patches are embedded in the flat matte surround (A), and the rocky matte surround (B). Test patches increase in lightness from left to right and from top to bottom. The green square indicates the test patch that has the same albedo as the surround.
Figure 2
 
Examples of test patches and surrounds used in Schmid and Anderson (2014). The same test patches are embedded in the flat matte surround (A), and the rocky matte surround (B). Test patches increase in lightness from left to right and from top to bottom. The green square indicates the test patch that has the same albedo as the surround.
Figure 3
 
Illustration of perceptual decomposition (scission) of homogeneous center-surround displays. (A) Displays with increment test patches are divided into a light colored transparent test patch layer and an opaque continuous gray surround layer. (B) Displays with decrement test patches are divided into a dark colored transparent test patch layer and an opaque continuous gray surround layer.
Figure 3
 
Illustration of perceptual decomposition (scission) of homogeneous center-surround displays. (A) Displays with increment test patches are divided into a light colored transparent test patch layer and an opaque continuous gray surround layer. (B) Displays with decrement test patches are divided into a dark colored transparent test patch layer and an opaque continuous gray surround layer.
Figure 4
 
Example of test (left) and adjustable (right) displays used in Experiment 1. Both images have been cropped in this figure but were presented in full size during the experiment. The distance between the test and adjustable surfaces are also not to scale.
Figure 4
 
Example of test (left) and adjustable (right) displays used in Experiment 1. Both images have been cropped in this figure but were presented in full size during the experiment. The distance between the test and adjustable surfaces are also not to scale.
Figure 5
 
Lightness settings for Experiment 1, plotted in Munsell values. (A) Lightness settings for the matte adjustable surface condition. (B) Lightness settings for the glossy adjustable surface condition. Each column shows the settings for different instruction conditions (contrast, transparency, and no-transmittance). Each row shows the settings for different surround-albedo conditions (Munsell 1.95, 3.5, 5, 6.5, 8, and 9.5). Error bars are standard error of the mean, and represent the interobserver variability for a particular condition. In a number of conditions, error bars are smaller than the data points, so are not visible.
Figure 5
 
Lightness settings for Experiment 1, plotted in Munsell values. (A) Lightness settings for the matte adjustable surface condition. (B) Lightness settings for the glossy adjustable surface condition. Each column shows the settings for different instruction conditions (contrast, transparency, and no-transmittance). Each row shows the settings for different surround-albedo conditions (Munsell 1.95, 3.5, 5, 6.5, 8, and 9.5). Error bars are standard error of the mean, and represent the interobserver variability for a particular condition. In a number of conditions, error bars are smaller than the data points, so are not visible.
Figure 6
 
Increment minus decrement settings for the matte (A) and glossy (B) adjustable surfaces in Experiment 1. The horizontal dotted line represents the actual difference between increments and decrements. The solid bars represent the increment-decrement difference scores for each surround Munsell condition (3.5, 5, 6.5 and 8). The mean of these surround Munsell conditions was taken for each instruction condition and plotted as striped bars. Error bars are standard error of the mean, and represent the interobserver variability for a particular condition.
Figure 6
 
Increment minus decrement settings for the matte (A) and glossy (B) adjustable surfaces in Experiment 1. The horizontal dotted line represents the actual difference between increments and decrements. The solid bars represent the increment-decrement difference scores for each surround Munsell condition (3.5, 5, 6.5 and 8). The mean of these surround Munsell conditions was taken for each instruction condition and plotted as striped bars. Error bars are standard error of the mean, and represent the interobserver variability for a particular condition.
Figure 7
 
Transmittance settings from Experiment 1, for the matte (A) and glossy (B) condition. Closed square data points are settings from the contrast instructions condition, and open circle data points are settings from the transparency instructions condition. Each color represents the settings for a different surround albedo condition. The vertical dotted lines indicate the surround Munsell value. Error bars are standard error of the mean, and represent the interobserver variability for a particular condition.
Figure 7
 
Transmittance settings from Experiment 1, for the matte (A) and glossy (B) condition. Closed square data points are settings from the contrast instructions condition, and open circle data points are settings from the transparency instructions condition. Each color represents the settings for a different surround albedo condition. The vertical dotted lines indicate the surround Munsell value. Error bars are standard error of the mean, and represent the interobserver variability for a particular condition.
Figure 8
 
Representation of the layout of a trial in Experiment 2. The surfaces are cropped more in this display compared to in the experiment, and the instructions text was not displayed on the screen; observers were given the instructions at the beginning of the experiment.
Figure 8
 
Representation of the layout of a trial in Experiment 2. The surfaces are cropped more in this display compared to in the experiment, and the instructions text was not displayed on the screen; observers were given the instructions at the beginning of the experiment.
Figure 9
 
Results of Experiment 2 for the matte condition (A) and the glossy condition (B). Each graph shows the results for a particular surround Munsell value, and plots the number of times (out of 60) each instruction condition was chosen to best match the lightness of the test patch embedded in the homogeneous display. The vertical dotted lines indicate the surround Munsell value.
Figure 9
 
Results of Experiment 2 for the matte condition (A) and the glossy condition (B). Each graph shows the results for a particular surround Munsell value, and plots the number of times (out of 60) each instruction condition was chosen to best match the lightness of the test patch embedded in the homogeneous display. The vertical dotted lines indicate the surround Munsell value.
Figure 10
 
Results of Experiment 2, averaged across test patch Munsell. Each panel shows the percentage of times each instruction condition was chosen for each surround Munsell condition, for the matte condition (left) and the glossy condition (right). Error bars are standard error of the mean, and indicate interobserver variability. Significance stars indicate when the contrast instructions condition was chosen reliably more than the no transmittance control.
Figure 10
 
Results of Experiment 2, averaged across test patch Munsell. Each panel shows the percentage of times each instruction condition was chosen for each surround Munsell condition, for the matte condition (left) and the glossy condition (right). Error bars are standard error of the mean, and indicate interobserver variability. Significance stars indicate when the contrast instructions condition was chosen reliably more than the no transmittance control.
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