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Paradoxical effect of spatially homogenous transparent fields on simultaneous contrast illusions Erica Dixon and Arthur G. Shapiro* Department of Psychology and Center for Behavioral Neuroscience, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016, USA *Corresponding author: [email protected] Received October 3, 2013; revised January 7, 2014; accepted January 10, 2014; posted January 13, 2014 (Doc. ID 198767); published February 27, 2014 In simultaneous brightness contrast (SBC) demonstrations, identical mid-luminance disks appear different from each other when one is placed on a black background while the other is placed on a white background. The strength of SBC effects can be enhanced by placing a semi-transparent layer on top of the display (Meyer’s effect). Here, we try to separate the causes of Meyer’s effect by placing a spatially homogenous transparent layer over a standard SBC display, and systematically varying the transmission level (alpha 0, clear; alpha 1, opaque) and color (black, gray, white) of the semi-transparent layer. Spatially homogenous transparent layers, which lack spatial cues, cannot be unambiguously interpreted as transparent fields. We measure SBC strength with both matching and ranking procedures. Paradoxically, with black layers, increasing alpha level weakens SBC when measured with a ranking procedure (no Meyer’s effect) and strengthens SBC when measured with a matching procedure (Meyer’s effect). With white and gray layers, neither procedure produces Meyer’s effect. We account for the differences between white and black layers by positing that the visual system separates luminance from contrast. The results suggest that observers attend to different information in the matching and ranking procedures. © 2014 Optical Society of America OCIS codes: (330.1720) Color vision; (330.5020) Perception psychology; (330.5510) Psychophysics; (330.6110) Spatial filtering. http://dx.doi.org/10.1364/JOSAA.31.00A307
1. INTRODUCTION Simultaneous brightness contrast (SBC) is a visual phenomenon in which two identical targets appear different from each other due to the spatial contexts in which the targets are placed. For instance, in Figs. 1(a)–1(e), the first disk is placed on a white background, and the second on a black background; the two disks do not appear identical, even though they have identical pixel values. Such phenomena have been studied extensively because understanding how context affects appearance can give insight into the visual system’s computational strategies [1–5]. A curious aspect of brightness contrast is that the effect becomes stronger if a semi-transparent surface (such as tissue paper) is placed over the display. The tissue-paper phenomenon has been known for generations and has also been referred to as Florkontrast, Gauzkontrast, or Meyer’s effect [6–12]; some popular books on illusions were packaged with tissue papers to illustrate the effect (see also Ekroll and Faul [13] for a description). von Helmholtz and Southall [14] famously noted that observers perceived this effect when viewing contrast demonstrations through a green transparent surface, and even standard psychology laboratory textbooks instruct students to perform experiments with tissue paper in front of brightness illusions (for instance, Sanford [15]). We have simulated the effect of transparency in Figs. 1(a)–1(e) by placing a digital layer over the image and adjusting the transparency (i.e., the alpha level in Adobe Photoshop), so that the disks are visible: an alpha value of 0 makes the layer clear; an alpha value of 1 makes the layer 1084-7529/14/04A307-07$15.00/0
opaque. The alpha value linearly changes transparency by the equation alpha * X 1-alpha * Y, where X is the transparency color and Y is the object color. For example, a white (pixel value 255) overlay with an alpha value 0.2 placed over a mid-luminance (pixel value 128) disk on a white background yields a disk value of 230 0.2 × 128 0.8 × 255 and a surround value of 255. In the discussion, we plot the values of the disks and the contrast values of the disks relative to their backgrounds. Anderson and Winawer recently presented demonstrations of the tissue-paper phenomenon, in which they placed a semitransparent layer of clouds on top of a standard simultaneous contrast display [16,17]. Their effects create a remarkably strong difference between the two patches, and seem to provide evidence that the visual system distributes luminance or chromaticity across perceptual layers perceived in a scene. Some researchers have pointed out that the strength of these phenomena is related to perceptual grouping [18,19]; that is, the lightness of the test patches does not change as dramatically as at first it would seem; instead, the image is grouped so that, on a black background, the test patch is organized out of the bright parts of the image, and on a white background the test patch is organized out of the black parts of the image; observers, therefore, mistake which parts of the patches they are actually comparing. Anderson and colleagues mentioned this aspect of the displays repeatedly [16,20,21]. The perceptual organization account, however, only deepens the mystery of the Anderson and Winawer displays and the mystery of the effect of transparency on brightness. © 2014 Optical Society of America
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images. As Wittgenstein [22] observed, “The impression that the transparent medium makes is that something lies behind the medium. If the visual image is thoroughly monochromatic it cannot be transparent.” In Figs. 1(d) and 1(e), the perception of transparency seems to have been removed, i.e., the top layer is thoroughly monochromatic, yet the strength of the brightness effect is still remarkably strong. In this paper, we manipulate the extent of the transmission in the transparent layer (the alpha level) and measure the difference between the test patches. The aim is to discover what aspect of transparency produces the experienced change in brightness, and how the strength or alpha level of the transparency contributes to this perception. Our main finding is that the result depends on the techniques used for measurement: if the observer makes a standard brightness match, increasing the level of transparency decreases the difference between the test patches; however, if the observer judges the difference between the test patches directly, then the effect is strongest for intermediate levels of transparency. We can account for brightness matching data through a simple filter model [23,24], but not the difference judgment data. We also attempt to account for the paradox in terms of the separation of luminance and contrast information present in the stimulus as a function of alpha level [25]; although such an analysis suggests a possible solution, it does not provide a satisfactory explanation of both results.
2. EXPERIMENT 1 Fig. 1. Transparent layers over SBC. The first column demonstrates the placement of transparent layers on top of traditional SBC demos (i.e., two identical test patches, one on a black background and one on a white background). The second column shows the final image construction. (a) and (b) Textured abstract multicolor layers. (c) Cloud layer, with Anderson and Winawer’s modification of a simultaneous contrast illusion as model. (d) Textureless green layer. (e) Textureless white layer.
Attempts to reduce these phenomena to simple figure-ground groupings overlook the fact that these effects can be created even if the image is devoid of local edges; that is, the same texture that creates a white object with black dots can also be interpreted as a black object with white dots. Clearly, the different colors are attaching themselves to different layers/objects, but it is not certain that the layering directly creates the change in brightness. Therefore, the effect of a transparent layer on SBC may, in part, be due to spatial organization and also to more traditional mechanisms, such as lateral inhibition and contrast adaptation (which, it seems, is the main thrust of the Anderson and Winawer papers). Here, we are directly concerned with determining which aspects of the transparency control the change of the brightness (like those changes produced by Meyer’s/Florkontrast/ Gauzkontrast effects). To address this issue, we examine what happens when the transparent layer is completely spatially homogenous; that is, instead of clouds or other displays with texture, what happens if the layer contains no indication that layering is present? For example, no physical cues indicate the presence of a transparent layer (a uniform green field) in Fig. 1(d) and the presence of a transparent layer (a uniform white field) in Fig. 1(e); therefore, both of these displays are indistinguishable from standard simultaneous contrast
Here, we manipulated the transmission (alpha level) of the transparency layer and evaluated the appearance of the test spot with a simple matching task. The test spot was placed either on a black (i.e., r, g, b 0, 0, 0) background, or a white (i.e., r, g, b 255, 255, 255) background; a white, gray (i.e., r, g, b 128, 128, 128), or black layer was placed over the entire field. Figure 2 shows examples of presented stimuli—the first column with a black overlay, the second with a white, and the third with gray. In each column, the alpha in row (a) is 0 (completely transparent), (b) is 0.2, (c) is 0.6, and (d) is 0.8 (closest to opaque).
Fig. 2. Sample stimuli for experiment 1. On each trial, a single disk on a black or white background was presented in isolation. The first column shows stimuli with a black overlay, the second with a white overlay, and the third with a gray overlay. Each row shows a different transparency (i.e., alpha) level; (a) alpha 0; (b) alpha 0.2; (c) alpha 0.6; (d) alpha 0.8.
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A. Methods 1. Observers There were two female university students between the ages of 20 and 27, the author (E.D.), and an observer naïve to the aims of the study; both observers had normal or corrected-tonormal vision. 2. Procedure The stimuli were presented on a CRT monitor (Sony Trinitron Multiscan G520) using a computer running Windows 7. The luminance levels of the monitor were measured using a Spectrascan 650 and gamma corrected using the driver software packaged with the computer graphics card (Catalyst Control Center on ATI Radeon HD 5970). The stimuli for the experiment were generated in Adobe Flash CS6, which was also the program used to run the experiment. Observers matched the appearance of the test patch to a selection of eleven comparison disks equally spaced on a gray strip set below the stimulus configuration at the bottom of the monitor screen. The observer made two matches: first from a coarse-scale selection, and second from a fine-scale selection. That is, at the beginning of each trial, the eleven disks had equal steps set from black (r, g, b 0, 0, 0) to white (r, g, b 255, 255, 255); the observer used a mouse to click on the disk closest in appearance to the test patch. After the click, the levels of the eleven patches changed to a finer scale, centered around the selected disk, and moving in steps of 3 away in either direction; i.e., if the selected disk was r, g, b 50, 50, 50, then the disks would range from r, g, b 38, 38, 38 to r; g; b 71, 71, 71. The observer selected again from the second finer array to make the final choice for each stimuli. There were 600 total trials, 300 per black background and 300 for white, with 10 trials for each overlay condition (black, white, or gray) of ten alpha levels (0–0.9 in steps of 0.1); e.g., the condition with a black background with a gray overlay of alpha 0.5 was repeated 10 times. Trial blocks were randomized, and 1200 total responses were made, as each trial had two selections—coarse scale and fine scale. The results for each condition (e.g., black background, gray overlay, alpha 0.5) are taken as the average of the fine scale response across the ten trials. The results were collected by the computer program and stored on the hard disk. B. Results and Conclusion The averages of the observer rankings as a function of the transmission level are presented in Fig. 3. Figure 3(a) shows the results for a black transparent layer; Fig. 3(b) for a gray transparent layer; and Fig. 3(c), for a white transparent layer. The lines represent the pixel values of the matches made for the test patch across the alpha levels. The difference between the lines indicates the effect produced by the background; that is, if the background did not change the appearance of the disks, then the two lines would fall on top of each other. As would be expected, when the transparent layer was clear (alpha 0), the match for the disk with the black background was of a higher pixel value than the match for the disk against the white background; these values are similar for all three conditions due to the stimuli being identical when the layer is clear (black transparent layer: 0.61 versus 0.38; gray background: 0.61 versus 0.36; and white background: 0.6 versus 0.38). As the transparent level became more opaque, the
Fig. 3. Results of Experiment 1. (a)–(c) The average of the observer settings as a function of the transmission level of the transparency layer. Triangles show matches for black surround; squares, for white surround. The panels indicate the color of the transparency layer: (a) black; (b) gray; and (c) white. (d) The difference between the white and black backgrounds for each transparency layer in Panels (a)–(c). High values indicate strong SBC; low values, weak SBC. For each condition, increasing the alpha level of the transparent layer decreases the perceived difference between disks.
appearance of the disk against the white background and the disk against the black background became more similar in appearance to the transparent layer. That is, against the black overlay, the disks became darker (values for alpha 0.9: 0.25 and 0.13); against a gray background, the disks converged toward gray (values for alpha 0.9: 0.53 and 0.47); and against a white background, the disks became brighter (values for alpha 0.9: 0.86 and 0.77). The result indicates that the effect of transparency is to decrease the strength of simultaneous contrast—that is, a test patch against a white background becomes more similar to a test patch against a black background as the transparent layer becomes more opaque. This contrasts with the usual finding that transparency increases SBC; here, no level of transparency produced this result. This relationship is depicted in Fig. 3(d), which shows the difference between test patches as a function of alpha level. As can be seen, for all three conditions, increasing alpha level produces a monotonic decrease in the differences between the disks. As we will mention in the discussion, a lower amount of induction may be expected since, as the alpha level increases as the contrast decreases, the surrounding values and the center values become more similar to each other.
3. EXPERIMENT 2 Experiment 1 indicates that transparency decreases the strength of SBC differences. This result seems to go against the observations that SBC illusions are stronger when viewed through a transparent layer, even when the transparent layer is spatially homogeneous. In experiment 2, therefore, we tested whether transparency does, in fact, strengthen SBC by having observers rank the strength of the SBC illusion for displays with differing alpha levels. A. Methods 1. Observers Eight graduate students enrolled at American University participated; the observers were between the ages of 22–28 years and all had normal or corrected-to-normal vision.
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2. Procedure Stimuli were presented on a gamma-corrected 2700 iMac LCD screen with a maximum luminance of 1. The stimuli consisted of a traditional SBC display using a rectangular background, half-black and half-white, with a width of 250 pixels and a height of 125 pixels. Both sides had a mid-luminance gray disk of diameter 75 pixels placed in the center. There are seven different overlay fields shown in Figure 4. For each overlay there were four alpha conditions: low (0–0.1), low-medium (0.2–0.4), medium (0.4–0.6), and high (0.7–0.9). In each trial, observers were presented with four SBC displays from a single overlay condition (i.e., one set of four SBC displays from any column in Fig. 4). The task was to rank the four conditions from 1 (strongest difference between the test disks) to 4 (weakest distance between the test patches). Each set of stimuli was presented twice in randomized order. In each presentation, the ordering of the disks on the screen was also randomized. Results from the two conditions were averaged. 3. Results Figure 5 plots the average ranking versus the alpha level of the transparent layer. The star indicates that there is a significant difference (p < 0.01) between the strongest (lowest value) and weakest (highest value) conditions, as marked by the bar; we performed a Tukey’s posthoc test to account for multiple comparisons. For instance, the results for the black transparent layer Fig. 5(a) show that the strongest SBC was found when the alpha level was 0.5 (average ranking value 2.13) and weakest when the alpha level was zero (average ranking value 3.06). The results for the red and green homogenous layers [Figs. 5(d) and 5(e)], and the two textured layers [Figs. 5(f) and 5(g)] also show that the strongest SBC effects occur for intermediate alpha levels. The two exceptions are the results for the gray transparent layer [Fig. 5(b)], which shows no significant effect between strongest and weakest conditions, and the white transparent layer [Fig. 5(c)], which shows the SBC effect to be strongest when alpha 0. For most images, the results are, therefore, consistent with Florkontrast, Gauzkontrast, or Meyer’s effect; i.e., the addition of a transparent layer increases the strength of SBC. These results were found for the black background condition, the red and green homogenous background conditions, and the textured background conditions. It is particularly striking that, in the textureless conditions—black, red, and green— there are no spatial cues to indicate the presence of layers, such as the clouds in the Anderson and Winawer display; that
Fig. 5. Average rankings of the SBC pairs shown in Fig. 4. Each panel shows the results for a different type of transparency layer. The average rankings are plotted versus the alpha level (as with Fig. 4, a: alpha low; b: alpha medium; c: alpha medium-high; d: alpha high; specific alpha values for each condition are listed on graph bars. Significant differences (p < 0.01) between strongest (lowest value) and weakest (highest value) conditions are marked with a star. For black, red, green, red tissue, and newsprint conditions in (a) and (d)–(g), addition of a transparency increased the reported difference between disks. For the white transparency (c) the difference was diminished by the transparency, and for gray transparency (b) there was no significant difference between any rankings.
is, the conditions could look like a standard simultaneous contrast display. The strength of the effect, therefore, seems to be due to something that does not require higher-order estimates about scene illumination. The white transparent layer, however, is consistent with the results from experiment 1. That is, in this condition, the strongest effect is seen when the transparent layer is not visible. The effect for the black background condition is directly at odds with the results from experiment 1, which showed that increasing the alpha level decreases the difference between the two patches; here, we see that increasing the alpha increases the perceived difference between test patches.
4. DISCUSSION
Fig. 4. Stimuli for Experiment 2. SBC with seven transparent layers—black, gray, white, red, green, red tissue paper, or newsprint. Each row shows a different transparency (i.e., alpha) level; (a) low; (b) alpha low-medium; (c) alpha medium; and (d) alpha high. On each trial, all four of the pairs within each column were presented. The observer’s task was to rank the four pairs according to the strength of the perceived SBC (1 strongest, 4 weakest).
Placing a semi-transparent surface on top of an SBC display has long been known to enhance the strength of SBC illusions (Meyer’s effect) [6–12]. Here, we investigated what happens when the semi-transparent layer is spatially homogenous, so that the observer cannot tell that the layer is present. We were hoping to be able to use this technique to separate effects due to perceptual transparency from effects due to standard (i.e., low-level) contrast. However, what we found
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was that, for black overlays, the strength of SBC depends upon the observer’s task. That is, an increase in the alpha level made the disks look more similar when observers matched the appearance of the disk. From this result, it would seem that increasing alpha would make SBC become weaker; however, when tested directly with a ranking procedure, we found that an SBC with a black overlay of alpha 0.5 was rated significantly stronger than an SBC with no overlay. The paradox, then, is that a black overlay does not produce a Meyer’s effect when observers perform the matching task, where the test patches are presented one at a time instead of in pairs, but does produce a Meyer’s effect when observers perform the ranking task. The paradox does not occur with a white overlay since, for both matching and ranking tasks, a Meyer’s effect does not occur. Additionally, we found a Meyer’s effect for both textured and colored overlays when observers performed a ranking task. We have not yet tested a matching task with these conditions. There are three questions that we address from our data. (1) Why does increasing alpha decrease the strength of SBC in experiment 1? (2) Why is there a difference between the white and black overlay conditions? (3) Why does Meyer’s effect occur for intermediate alphas? There are many possible explanations for such phenomena; historically, these explanations are based on inferences about the illuminant (an explanation associated with Helmholtz) or on low-level interactions (an explanation associated with Hering). The many recent explanations for brightness/lightness perception are also potentially informative about these data [17,26–30]. For this report, we are taking a physical approach; that is, we want to find out what aspects of the stimulus correspond to the judgments that were made; our strategy is to understand what physical characteristics of the stimulus produce each perceptual response. A. Why Does Increasing Alpha Decrease the Strength of SBC in Experiment 1? Experiment 1 shows that, as alpha increases, the two test disks become more similar in appearance. Shapiro and Lu [23] have shown that the relative values of an SBC display can be accounted for simply by removing low spatial frequency content. That is, once the “appropriate amount” of low spatial frequency content has been removed from the image, a disk with a pixel value of 128 against a black background will produce more luminance than a disk with a pixel value of 128 against a white background. Dixon et al. [24] have shown that the “appropriate amount” corresponds to the relative size of the target in the image, not the projected size of the target on the retina. These results suggest that operations that remove blur to efficiently represent an object also create the conditions that produce most brightness illusions. We implemented this idea by removing low spatial frequency content from images in experiment 1 and then measuring the resultant pixel values. To remove the low spatial frequency content, we simply placed the images in Adobe Photoshop and used the high-pass filter function with a filter diameter of 250 pixels. The resultant images are shown in Fig. 6. Figure 6(a) shows the four filtered images for the black overlay condition, and Fig. 6(c) shows the four filtered conditions for the white overlay condition. Unlike the unfiltered versions of the image in Fig. 4, the disks in the filtered versions
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Fig. 6. Relative luminance of filtered disks. (a) Four high-pass filtered images for the black overlay condition. (b) Pixel values of filtered disks as a function of alpha value. The diamonds show the pixel values for the disks against the black background while the squares show the pixel values of the disks against the white background. (c) Four high-pass filtered conditions for the white overlay condition. (d) Same as b, but for white overlay.
of the image are no longer physically equal to each other. Figures 6(b) and 6(d) show the pixels of the disks as a function of alpha value. The diamonds show the pixel values for the disks against the black background, while the squares show the pixel values of the disks against the white background. As would be expected from Shapiro and Lu [23], the pixel values for the disks against the dark background are physically higher than the disks against the white background. When alpha equals zero, the difference between the two pixel values is greatest, and as the alpha level increases, the difference between the two pixel values decreases. Thus, it seems as if the effect of alpha level on SBC corresponds to the relative difference in high spatial frequency content. Any low-level model that decreases the response to low spatial frequency content, or any inferential model that discounts the illuminant through some type of shadow-reducing spatial filter would, therefore, predict such an effect. B. Why Is There a Difference between the White and Black Overlay Conditions? In experiment 2, the white overlay follows the results from experiment 1 (i.e., as alpha increases, the difference between test patches decreases), and the black overlay elicits the opposite effect. A disk against a background can be considered both in terms of its luminance and in terms of its contrast with the background [11,25,31,32]. That is, a disk can be white and have high contrast with the background, or be white and have low contrast with the background; the contrast with the background, then, is a physical difference. Measuring this physical difference may provide valuable information indicative of the strength of a transparency. Figure 7 plots the physical values of the luminance levels of the disks and the contrast between disk and background as a
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measured between black and white overlay conditions correspond to physical differences present in the image.
Fig. 7. Relative luminance and Michelson contrast of disks to background. (a) The physical values of the pixels (luminance) in the black overlay condition are plotted against the alpha level for the black and white backgrounds. Lines overlap because values are identical. (b) The Michelson contrast of the disks to the background is plotted against the alpha level for the black and white backgrounds; black background is represented by diamonds, white is represented by squares. (c) Same as Panel (a), but for white overlay. (d) Same as Panel (b), but for white overlay.
function of the alpha level. Panels (a) and (b) show these values for the black overlay. One line shows the values for the disk against the black background, and the other line shows the values for the disk against the white background. As would be expected, in Panel (a) the pixel values of the disks decrease as the overlay becomes more opaque. In Panel (b), the Michelson contrast against the black background is high (1.0), while the Michelson contrast against the white background is lower (0.33). The contrast remains constant as a function of alpha. This means that, in the black overlay condition, a parametric change in alpha leads to changes in the luminance levels of the disks, but not in the contrast of the disks relative to the background. The luminance and contrast relationships, therefore, are the same as would be derived if the luminance levels of the disk were to change. Panel (c) shows the pixel value of the disks against the white background; as would be expected, the pixel values increase as a function of alpha, and only one line is visible because the test spots are equal to each other. The contrast values follow a completely different trend than in the black overlay condition. The contrast values are different when the alpha equals zero: (contrast equals 0.5 for the white background and 1.0 for the black background), but both contrast values converge to 0.0 as the alpha level increases. The difference between the white and black overlay conditions, therefore, corresponds to the contrast information available in the image. That is, in the black overlay condition, parametric changes to alpha correspond to a constant level of contrast—similar to changing the illumination on a disk and ring with fixed reflectance values. In the white overlay condition, the contrast diminishes with alpha level. If the judgment of strength of the SBC in experiment 2 corresponds in some way to the contrast between the two disks and their backgrounds, then it would be expected that the white overlay condition would not produce a Meyer’s effect. Again, we are not making claims about the processes, inferences, or judgments underlying this response; we simply note that the differences
C. Why Does Meyer’s Effect Occur for Intermediate Alphas? Experiment 2 shows that the strongest values of SBC are always for an intermediate level of alpha. This is expected since, at the highest values of alpha, the overlays become completely opaque, and the test spots are no longer visible. However, why should certain levels of transparency conditions be stronger than conditions with no transparency, and what would make a particular alpha level produce the strongest SBC? At this time, we cannot satisfactorily describe our results in terms of a simple physical attribute of the display. Instead, the results from the above experiments suggest processes that combine responses to luminance and contrast information. The combination could be accomplished in numerous ways. For instance, Whittle [33] suggested that brightness levels follow a nonlinearity. It is, indeed, possible that the contrast information also acts as a gain control to mediate the brightness levels of the disks. Models of this sort have been used to determine when textures are separable from each other (for instance, Sutter and Graham [34]). On the other hand, it could be that observers are attending to luminance and contrast information to make different judgments. For instance, observers have been shown to give different matches for the same stimulus, depending on whether they are told to match the apparent amounts of light coming from the patches (brightness) or their apparent reflectance (lightness) [35,36]. It is possible that the two tasks in our experiments tap into different interpretations of the stimulus.
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26. D. Purves, S. M. Williams, S. Nundy, and R. B. Lotto, “Perceiving the intensity of light,” Psychol. Rev. 111, 142–158 (2004). 27. S. C. Dakin and P. J. Bex, “Natural image statistics mediate brightness ‘filling in’,” P. R. Soc. Lond. Ser. B 270, 2341–2348 (2003). 28. A. L. Gilchrist and A. Radonjić, “Functional frameworks of illumination revealed by probe disk technique,” J. Vis. 10(5):6 (2010). 29. B. Blakeslee and M. E. McCourt, “When is spatial filtering enough? Investigation of brightness and lightness perception in stimuli containing a visible illumination component,” Vis. Res. 60, 40–50 (2012). 30. A. E. Robinson and V. R. De Sa, “Brief presentations reveal the temporal dynamics of brightness induction and White’s illusion,” Vis. Res. 48, 2370–2381 (2008). 31. A. G. Shapiro, A. D. D. Antona, J. P. Charles, L. A. Belano, J. B. Smith, and M. Shear-Heyman, “Induced contrast asynchronies,” J. Vis. 4(6):5 (2004). 32. T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, “Do cortical neurons process luminance or contrast to encode surface properties?” J. Neurophysiol. 95, 2638–2649 (2005). 33. P. Whittle, “The psychophysics of contrast brightness,” in Lightness, Brightness, and Transparency, A. L. Gilchrist, ed. (Lawrence Erlbaum, 1994), pp. 35–110. 34. A. Sutter and N. Graham, “Investigating simple and complex mechanisms in texture segregation using the speed-accuracy tradeoff method,” Vis. Res. 35, 2825–2843 (1995). 35. L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast; 2. reflectance variation,” Percept. Psychophys. 54, 457–468 (1993). 36. L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 1. illuminance variation,” Percept. Psychophys. 54, 446–456 (1993).
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Paradoxical effect of spatially homogenous transparent fields on simultaneous contrast illusions Erica Dixon and Arthur G. Shapiro* Department of Psychology and Center for Behavioral Neuroscience, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016, USA *Corresponding author: [email protected] Received October 3, 2013; revised January 7, 2014; accepted January 10, 2014; posted January 13, 2014 (Doc. ID 198767); published February 27, 2014 In simultaneous brightness contrast (SBC) demonstrations, identical mid-luminance disks appear different from each other when one is placed on a black background while the other is placed on a white background. The strength of SBC effects can be enhanced by placing a semi-transparent layer on top of the display (Meyer’s effect). Here, we try to separate the causes of Meyer’s effect by placing a spatially homogenous transparent layer over a standard SBC display, and systematically varying the transmission level (alpha 0, clear; alpha 1, opaque) and color (black, gray, white) of the semi-transparent layer. Spatially homogenous transparent layers, which lack spatial cues, cannot be unambiguously interpreted as transparent fields. We measure SBC strength with both matching and ranking procedures. Paradoxically, with black layers, increasing alpha level weakens SBC when measured with a ranking procedure (no Meyer’s effect) and strengthens SBC when measured with a matching procedure (Meyer’s effect). With white and gray layers, neither procedure produces Meyer’s effect. We account for the differences between white and black layers by positing that the visual system separates luminance from contrast. The results suggest that observers attend to different information in the matching and ranking procedures. © 2014 Optical Society of America OCIS codes: (330.1720) Color vision; (330.5020) Perception psychology; (330.5510) Psychophysics; (330.6110) Spatial filtering. http://dx.doi.org/10.1364/JOSAA.31.00A307
1. INTRODUCTION Simultaneous brightness contrast (SBC) is a visual phenomenon in which two identical targets appear different from each other due to the spatial contexts in which the targets are placed. For instance, in Figs. 1(a)–1(e), the first disk is placed on a white background, and the second on a black background; the two disks do not appear identical, even though they have identical pixel values. Such phenomena have been studied extensively because understanding how context affects appearance can give insight into the visual system’s computational strategies [1–5]. A curious aspect of brightness contrast is that the effect becomes stronger if a semi-transparent surface (such as tissue paper) is placed over the display. The tissue-paper phenomenon has been known for generations and has also been referred to as Florkontrast, Gauzkontrast, or Meyer’s effect [6–12]; some popular books on illusions were packaged with tissue papers to illustrate the effect (see also Ekroll and Faul [13] for a description). von Helmholtz and Southall [14] famously noted that observers perceived this effect when viewing contrast demonstrations through a green transparent surface, and even standard psychology laboratory textbooks instruct students to perform experiments with tissue paper in front of brightness illusions (for instance, Sanford [15]). We have simulated the effect of transparency in Figs. 1(a)–1(e) by placing a digital layer over the image and adjusting the transparency (i.e., the alpha level in Adobe Photoshop), so that the disks are visible: an alpha value of 0 makes the layer clear; an alpha value of 1 makes the layer 1084-7529/14/04A307-07$15.00/0
opaque. The alpha value linearly changes transparency by the equation alpha * X 1-alpha * Y, where X is the transparency color and Y is the object color. For example, a white (pixel value 255) overlay with an alpha value 0.2 placed over a mid-luminance (pixel value 128) disk on a white background yields a disk value of 230 0.2 × 128 0.8 × 255 and a surround value of 255. In the discussion, we plot the values of the disks and the contrast values of the disks relative to their backgrounds. Anderson and Winawer recently presented demonstrations of the tissue-paper phenomenon, in which they placed a semitransparent layer of clouds on top of a standard simultaneous contrast display [16,17]. Their effects create a remarkably strong difference between the two patches, and seem to provide evidence that the visual system distributes luminance or chromaticity across perceptual layers perceived in a scene. Some researchers have pointed out that the strength of these phenomena is related to perceptual grouping [18,19]; that is, the lightness of the test patches does not change as dramatically as at first it would seem; instead, the image is grouped so that, on a black background, the test patch is organized out of the bright parts of the image, and on a white background the test patch is organized out of the black parts of the image; observers, therefore, mistake which parts of the patches they are actually comparing. Anderson and colleagues mentioned this aspect of the displays repeatedly [16,20,21]. The perceptual organization account, however, only deepens the mystery of the Anderson and Winawer displays and the mystery of the effect of transparency on brightness. © 2014 Optical Society of America
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images. As Wittgenstein [22] observed, “The impression that the transparent medium makes is that something lies behind the medium. If the visual image is thoroughly monochromatic it cannot be transparent.” In Figs. 1(d) and 1(e), the perception of transparency seems to have been removed, i.e., the top layer is thoroughly monochromatic, yet the strength of the brightness effect is still remarkably strong. In this paper, we manipulate the extent of the transmission in the transparent layer (the alpha level) and measure the difference between the test patches. The aim is to discover what aspect of transparency produces the experienced change in brightness, and how the strength or alpha level of the transparency contributes to this perception. Our main finding is that the result depends on the techniques used for measurement: if the observer makes a standard brightness match, increasing the level of transparency decreases the difference between the test patches; however, if the observer judges the difference between the test patches directly, then the effect is strongest for intermediate levels of transparency. We can account for brightness matching data through a simple filter model [23,24], but not the difference judgment data. We also attempt to account for the paradox in terms of the separation of luminance and contrast information present in the stimulus as a function of alpha level [25]; although such an analysis suggests a possible solution, it does not provide a satisfactory explanation of both results.
2. EXPERIMENT 1 Fig. 1. Transparent layers over SBC. The first column demonstrates the placement of transparent layers on top of traditional SBC demos (i.e., two identical test patches, one on a black background and one on a white background). The second column shows the final image construction. (a) and (b) Textured abstract multicolor layers. (c) Cloud layer, with Anderson and Winawer’s modification of a simultaneous contrast illusion as model. (d) Textureless green layer. (e) Textureless white layer.
Attempts to reduce these phenomena to simple figure-ground groupings overlook the fact that these effects can be created even if the image is devoid of local edges; that is, the same texture that creates a white object with black dots can also be interpreted as a black object with white dots. Clearly, the different colors are attaching themselves to different layers/objects, but it is not certain that the layering directly creates the change in brightness. Therefore, the effect of a transparent layer on SBC may, in part, be due to spatial organization and also to more traditional mechanisms, such as lateral inhibition and contrast adaptation (which, it seems, is the main thrust of the Anderson and Winawer papers). Here, we are directly concerned with determining which aspects of the transparency control the change of the brightness (like those changes produced by Meyer’s/Florkontrast/ Gauzkontrast effects). To address this issue, we examine what happens when the transparent layer is completely spatially homogenous; that is, instead of clouds or other displays with texture, what happens if the layer contains no indication that layering is present? For example, no physical cues indicate the presence of a transparent layer (a uniform green field) in Fig. 1(d) and the presence of a transparent layer (a uniform white field) in Fig. 1(e); therefore, both of these displays are indistinguishable from standard simultaneous contrast
Here, we manipulated the transmission (alpha level) of the transparency layer and evaluated the appearance of the test spot with a simple matching task. The test spot was placed either on a black (i.e., r, g, b 0, 0, 0) background, or a white (i.e., r, g, b 255, 255, 255) background; a white, gray (i.e., r, g, b 128, 128, 128), or black layer was placed over the entire field. Figure 2 shows examples of presented stimuli—the first column with a black overlay, the second with a white, and the third with gray. In each column, the alpha in row (a) is 0 (completely transparent), (b) is 0.2, (c) is 0.6, and (d) is 0.8 (closest to opaque).
Fig. 2. Sample stimuli for experiment 1. On each trial, a single disk on a black or white background was presented in isolation. The first column shows stimuli with a black overlay, the second with a white overlay, and the third with a gray overlay. Each row shows a different transparency (i.e., alpha) level; (a) alpha 0; (b) alpha 0.2; (c) alpha 0.6; (d) alpha 0.8.
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A. Methods 1. Observers There were two female university students between the ages of 20 and 27, the author (E.D.), and an observer naïve to the aims of the study; both observers had normal or corrected-tonormal vision. 2. Procedure The stimuli were presented on a CRT monitor (Sony Trinitron Multiscan G520) using a computer running Windows 7. The luminance levels of the monitor were measured using a Spectrascan 650 and gamma corrected using the driver software packaged with the computer graphics card (Catalyst Control Center on ATI Radeon HD 5970). The stimuli for the experiment were generated in Adobe Flash CS6, which was also the program used to run the experiment. Observers matched the appearance of the test patch to a selection of eleven comparison disks equally spaced on a gray strip set below the stimulus configuration at the bottom of the monitor screen. The observer made two matches: first from a coarse-scale selection, and second from a fine-scale selection. That is, at the beginning of each trial, the eleven disks had equal steps set from black (r, g, b 0, 0, 0) to white (r, g, b 255, 255, 255); the observer used a mouse to click on the disk closest in appearance to the test patch. After the click, the levels of the eleven patches changed to a finer scale, centered around the selected disk, and moving in steps of 3 away in either direction; i.e., if the selected disk was r, g, b 50, 50, 50, then the disks would range from r, g, b 38, 38, 38 to r; g; b 71, 71, 71. The observer selected again from the second finer array to make the final choice for each stimuli. There were 600 total trials, 300 per black background and 300 for white, with 10 trials for each overlay condition (black, white, or gray) of ten alpha levels (0–0.9 in steps of 0.1); e.g., the condition with a black background with a gray overlay of alpha 0.5 was repeated 10 times. Trial blocks were randomized, and 1200 total responses were made, as each trial had two selections—coarse scale and fine scale. The results for each condition (e.g., black background, gray overlay, alpha 0.5) are taken as the average of the fine scale response across the ten trials. The results were collected by the computer program and stored on the hard disk. B. Results and Conclusion The averages of the observer rankings as a function of the transmission level are presented in Fig. 3. Figure 3(a) shows the results for a black transparent layer; Fig. 3(b) for a gray transparent layer; and Fig. 3(c), for a white transparent layer. The lines represent the pixel values of the matches made for the test patch across the alpha levels. The difference between the lines indicates the effect produced by the background; that is, if the background did not change the appearance of the disks, then the two lines would fall on top of each other. As would be expected, when the transparent layer was clear (alpha 0), the match for the disk with the black background was of a higher pixel value than the match for the disk against the white background; these values are similar for all three conditions due to the stimuli being identical when the layer is clear (black transparent layer: 0.61 versus 0.38; gray background: 0.61 versus 0.36; and white background: 0.6 versus 0.38). As the transparent level became more opaque, the
Fig. 3. Results of Experiment 1. (a)–(c) The average of the observer settings as a function of the transmission level of the transparency layer. Triangles show matches for black surround; squares, for white surround. The panels indicate the color of the transparency layer: (a) black; (b) gray; and (c) white. (d) The difference between the white and black backgrounds for each transparency layer in Panels (a)–(c). High values indicate strong SBC; low values, weak SBC. For each condition, increasing the alpha level of the transparent layer decreases the perceived difference between disks.
appearance of the disk against the white background and the disk against the black background became more similar in appearance to the transparent layer. That is, against the black overlay, the disks became darker (values for alpha 0.9: 0.25 and 0.13); against a gray background, the disks converged toward gray (values for alpha 0.9: 0.53 and 0.47); and against a white background, the disks became brighter (values for alpha 0.9: 0.86 and 0.77). The result indicates that the effect of transparency is to decrease the strength of simultaneous contrast—that is, a test patch against a white background becomes more similar to a test patch against a black background as the transparent layer becomes more opaque. This contrasts with the usual finding that transparency increases SBC; here, no level of transparency produced this result. This relationship is depicted in Fig. 3(d), which shows the difference between test patches as a function of alpha level. As can be seen, for all three conditions, increasing alpha level produces a monotonic decrease in the differences between the disks. As we will mention in the discussion, a lower amount of induction may be expected since, as the alpha level increases as the contrast decreases, the surrounding values and the center values become more similar to each other.
3. EXPERIMENT 2 Experiment 1 indicates that transparency decreases the strength of SBC differences. This result seems to go against the observations that SBC illusions are stronger when viewed through a transparent layer, even when the transparent layer is spatially homogeneous. In experiment 2, therefore, we tested whether transparency does, in fact, strengthen SBC by having observers rank the strength of the SBC illusion for displays with differing alpha levels. A. Methods 1. Observers Eight graduate students enrolled at American University participated; the observers were between the ages of 22–28 years and all had normal or corrected-to-normal vision.
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2. Procedure Stimuli were presented on a gamma-corrected 2700 iMac LCD screen with a maximum luminance of 1. The stimuli consisted of a traditional SBC display using a rectangular background, half-black and half-white, with a width of 250 pixels and a height of 125 pixels. Both sides had a mid-luminance gray disk of diameter 75 pixels placed in the center. There are seven different overlay fields shown in Figure 4. For each overlay there were four alpha conditions: low (0–0.1), low-medium (0.2–0.4), medium (0.4–0.6), and high (0.7–0.9). In each trial, observers were presented with four SBC displays from a single overlay condition (i.e., one set of four SBC displays from any column in Fig. 4). The task was to rank the four conditions from 1 (strongest difference between the test disks) to 4 (weakest distance between the test patches). Each set of stimuli was presented twice in randomized order. In each presentation, the ordering of the disks on the screen was also randomized. Results from the two conditions were averaged. 3. Results Figure 5 plots the average ranking versus the alpha level of the transparent layer. The star indicates that there is a significant difference (p < 0.01) between the strongest (lowest value) and weakest (highest value) conditions, as marked by the bar; we performed a Tukey’s posthoc test to account for multiple comparisons. For instance, the results for the black transparent layer Fig. 5(a) show that the strongest SBC was found when the alpha level was 0.5 (average ranking value 2.13) and weakest when the alpha level was zero (average ranking value 3.06). The results for the red and green homogenous layers [Figs. 5(d) and 5(e)], and the two textured layers [Figs. 5(f) and 5(g)] also show that the strongest SBC effects occur for intermediate alpha levels. The two exceptions are the results for the gray transparent layer [Fig. 5(b)], which shows no significant effect between strongest and weakest conditions, and the white transparent layer [Fig. 5(c)], which shows the SBC effect to be strongest when alpha 0. For most images, the results are, therefore, consistent with Florkontrast, Gauzkontrast, or Meyer’s effect; i.e., the addition of a transparent layer increases the strength of SBC. These results were found for the black background condition, the red and green homogenous background conditions, and the textured background conditions. It is particularly striking that, in the textureless conditions—black, red, and green— there are no spatial cues to indicate the presence of layers, such as the clouds in the Anderson and Winawer display; that
Fig. 5. Average rankings of the SBC pairs shown in Fig. 4. Each panel shows the results for a different type of transparency layer. The average rankings are plotted versus the alpha level (as with Fig. 4, a: alpha low; b: alpha medium; c: alpha medium-high; d: alpha high; specific alpha values for each condition are listed on graph bars. Significant differences (p < 0.01) between strongest (lowest value) and weakest (highest value) conditions are marked with a star. For black, red, green, red tissue, and newsprint conditions in (a) and (d)–(g), addition of a transparency increased the reported difference between disks. For the white transparency (c) the difference was diminished by the transparency, and for gray transparency (b) there was no significant difference between any rankings.
is, the conditions could look like a standard simultaneous contrast display. The strength of the effect, therefore, seems to be due to something that does not require higher-order estimates about scene illumination. The white transparent layer, however, is consistent with the results from experiment 1. That is, in this condition, the strongest effect is seen when the transparent layer is not visible. The effect for the black background condition is directly at odds with the results from experiment 1, which showed that increasing the alpha level decreases the difference between the two patches; here, we see that increasing the alpha increases the perceived difference between test patches.
4. DISCUSSION
Fig. 4. Stimuli for Experiment 2. SBC with seven transparent layers—black, gray, white, red, green, red tissue paper, or newsprint. Each row shows a different transparency (i.e., alpha) level; (a) low; (b) alpha low-medium; (c) alpha medium; and (d) alpha high. On each trial, all four of the pairs within each column were presented. The observer’s task was to rank the four pairs according to the strength of the perceived SBC (1 strongest, 4 weakest).
Placing a semi-transparent surface on top of an SBC display has long been known to enhance the strength of SBC illusions (Meyer’s effect) [6–12]. Here, we investigated what happens when the semi-transparent layer is spatially homogenous, so that the observer cannot tell that the layer is present. We were hoping to be able to use this technique to separate effects due to perceptual transparency from effects due to standard (i.e., low-level) contrast. However, what we found
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was that, for black overlays, the strength of SBC depends upon the observer’s task. That is, an increase in the alpha level made the disks look more similar when observers matched the appearance of the disk. From this result, it would seem that increasing alpha would make SBC become weaker; however, when tested directly with a ranking procedure, we found that an SBC with a black overlay of alpha 0.5 was rated significantly stronger than an SBC with no overlay. The paradox, then, is that a black overlay does not produce a Meyer’s effect when observers perform the matching task, where the test patches are presented one at a time instead of in pairs, but does produce a Meyer’s effect when observers perform the ranking task. The paradox does not occur with a white overlay since, for both matching and ranking tasks, a Meyer’s effect does not occur. Additionally, we found a Meyer’s effect for both textured and colored overlays when observers performed a ranking task. We have not yet tested a matching task with these conditions. There are three questions that we address from our data. (1) Why does increasing alpha decrease the strength of SBC in experiment 1? (2) Why is there a difference between the white and black overlay conditions? (3) Why does Meyer’s effect occur for intermediate alphas? There are many possible explanations for such phenomena; historically, these explanations are based on inferences about the illuminant (an explanation associated with Helmholtz) or on low-level interactions (an explanation associated with Hering). The many recent explanations for brightness/lightness perception are also potentially informative about these data [17,26–30]. For this report, we are taking a physical approach; that is, we want to find out what aspects of the stimulus correspond to the judgments that were made; our strategy is to understand what physical characteristics of the stimulus produce each perceptual response. A. Why Does Increasing Alpha Decrease the Strength of SBC in Experiment 1? Experiment 1 shows that, as alpha increases, the two test disks become more similar in appearance. Shapiro and Lu [23] have shown that the relative values of an SBC display can be accounted for simply by removing low spatial frequency content. That is, once the “appropriate amount” of low spatial frequency content has been removed from the image, a disk with a pixel value of 128 against a black background will produce more luminance than a disk with a pixel value of 128 against a white background. Dixon et al. [24] have shown that the “appropriate amount” corresponds to the relative size of the target in the image, not the projected size of the target on the retina. These results suggest that operations that remove blur to efficiently represent an object also create the conditions that produce most brightness illusions. We implemented this idea by removing low spatial frequency content from images in experiment 1 and then measuring the resultant pixel values. To remove the low spatial frequency content, we simply placed the images in Adobe Photoshop and used the high-pass filter function with a filter diameter of 250 pixels. The resultant images are shown in Fig. 6. Figure 6(a) shows the four filtered images for the black overlay condition, and Fig. 6(c) shows the four filtered conditions for the white overlay condition. Unlike the unfiltered versions of the image in Fig. 4, the disks in the filtered versions
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Fig. 6. Relative luminance of filtered disks. (a) Four high-pass filtered images for the black overlay condition. (b) Pixel values of filtered disks as a function of alpha value. The diamonds show the pixel values for the disks against the black background while the squares show the pixel values of the disks against the white background. (c) Four high-pass filtered conditions for the white overlay condition. (d) Same as b, but for white overlay.
of the image are no longer physically equal to each other. Figures 6(b) and 6(d) show the pixels of the disks as a function of alpha value. The diamonds show the pixel values for the disks against the black background, while the squares show the pixel values of the disks against the white background. As would be expected from Shapiro and Lu [23], the pixel values for the disks against the dark background are physically higher than the disks against the white background. When alpha equals zero, the difference between the two pixel values is greatest, and as the alpha level increases, the difference between the two pixel values decreases. Thus, it seems as if the effect of alpha level on SBC corresponds to the relative difference in high spatial frequency content. Any low-level model that decreases the response to low spatial frequency content, or any inferential model that discounts the illuminant through some type of shadow-reducing spatial filter would, therefore, predict such an effect. B. Why Is There a Difference between the White and Black Overlay Conditions? In experiment 2, the white overlay follows the results from experiment 1 (i.e., as alpha increases, the difference between test patches decreases), and the black overlay elicits the opposite effect. A disk against a background can be considered both in terms of its luminance and in terms of its contrast with the background [11,25,31,32]. That is, a disk can be white and have high contrast with the background, or be white and have low contrast with the background; the contrast with the background, then, is a physical difference. Measuring this physical difference may provide valuable information indicative of the strength of a transparency. Figure 7 plots the physical values of the luminance levels of the disks and the contrast between disk and background as a
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measured between black and white overlay conditions correspond to physical differences present in the image.
Fig. 7. Relative luminance and Michelson contrast of disks to background. (a) The physical values of the pixels (luminance) in the black overlay condition are plotted against the alpha level for the black and white backgrounds. Lines overlap because values are identical. (b) The Michelson contrast of the disks to the background is plotted against the alpha level for the black and white backgrounds; black background is represented by diamonds, white is represented by squares. (c) Same as Panel (a), but for white overlay. (d) Same as Panel (b), but for white overlay.
function of the alpha level. Panels (a) and (b) show these values for the black overlay. One line shows the values for the disk against the black background, and the other line shows the values for the disk against the white background. As would be expected, in Panel (a) the pixel values of the disks decrease as the overlay becomes more opaque. In Panel (b), the Michelson contrast against the black background is high (1.0), while the Michelson contrast against the white background is lower (0.33). The contrast remains constant as a function of alpha. This means that, in the black overlay condition, a parametric change in alpha leads to changes in the luminance levels of the disks, but not in the contrast of the disks relative to the background. The luminance and contrast relationships, therefore, are the same as would be derived if the luminance levels of the disk were to change. Panel (c) shows the pixel value of the disks against the white background; as would be expected, the pixel values increase as a function of alpha, and only one line is visible because the test spots are equal to each other. The contrast values follow a completely different trend than in the black overlay condition. The contrast values are different when the alpha equals zero: (contrast equals 0.5 for the white background and 1.0 for the black background), but both contrast values converge to 0.0 as the alpha level increases. The difference between the white and black overlay conditions, therefore, corresponds to the contrast information available in the image. That is, in the black overlay condition, parametric changes to alpha correspond to a constant level of contrast—similar to changing the illumination on a disk and ring with fixed reflectance values. In the white overlay condition, the contrast diminishes with alpha level. If the judgment of strength of the SBC in experiment 2 corresponds in some way to the contrast between the two disks and their backgrounds, then it would be expected that the white overlay condition would not produce a Meyer’s effect. Again, we are not making claims about the processes, inferences, or judgments underlying this response; we simply note that the differences
C. Why Does Meyer’s Effect Occur for Intermediate Alphas? Experiment 2 shows that the strongest values of SBC are always for an intermediate level of alpha. This is expected since, at the highest values of alpha, the overlays become completely opaque, and the test spots are no longer visible. However, why should certain levels of transparency conditions be stronger than conditions with no transparency, and what would make a particular alpha level produce the strongest SBC? At this time, we cannot satisfactorily describe our results in terms of a simple physical attribute of the display. Instead, the results from the above experiments suggest processes that combine responses to luminance and contrast information. The combination could be accomplished in numerous ways. For instance, Whittle [33] suggested that brightness levels follow a nonlinearity. It is, indeed, possible that the contrast information also acts as a gain control to mediate the brightness levels of the disks. Models of this sort have been used to determine when textures are separable from each other (for instance, Sutter and Graham [34]). On the other hand, it could be that observers are attending to luminance and contrast information to make different judgments. For instance, observers have been shown to give different matches for the same stimulus, depending on whether they are told to match the apparent amounts of light coming from the patches (brightness) or their apparent reflectance (lightness) [35,36]. It is possible that the two tasks in our experiments tap into different interpretations of the stimulus.
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