The role of local framework luminance range in the Simultaneous Lightness Contrast illusion with double increments

In double increment Simultaneous Lightness Contrast two equiluminant squares rest on darker backgrounds that differ in luminance. Research on such displays has produced conflicting results as to whether an illusion is observed. Anchoring theory of lightness predicts no illusion with double increment displays. Here we test the hypothesis that an illusion can be predicted if the framework containing the target and the darkest background carries more weight in lightness computations. We tested two displays, one with a general white and one with a general black background. An illusion was obtained only in the first display. These results suggest that an illusion can occur with double increment displays when the global value of the targets differs from their local value, as these conditions allow different local framework weighting to affect the targets’ final lightness. We propose that this parameter be added to the Anchoring Theory.

Lightness theories aim to explain two major phenomena: lightness constancy and lightness illusions.Constancy refers to the ability of the visual system to retain a relatively constant percept of a surface's shade of gray, despite changes in illumination and background intensity.Lightness illusions on the other hand are phenomena showing that surfaces with equal luminance do not necessarily appear to have the same color.The most celebrated lightness illusion is called Simultaneous Lightness Contrast (SLC).A typical SLC illusion consists of two adjacent backgrounds with different luminance values (Figure 1).Two smaller squares of equal luminance rest on each of the backgrounds.Although the two squares are identical in terms of luminance, they appear to have different shades of gray.The target on the dark background appears lighter than the one on the bright background.
Three major factors have been proposed to cause the illusion: low-level mechanisms, illumination miscalculations and perceptual grouping.These have Corresponding author: eliaseconomou@uoc.grbeen championed by three major theoretical approaches: low-level or contrast theories, high-level or cognitive theories and gestalt theories (for a full review see Gilchrist, 2006).
Low-level models have always felt at home with this illusion because its direction matched predictions made based on the lateral inhibition mechanism (Cornsweet, 1970;Jameson & Hurvich, 1964).The target resting on the bright background is strongly inhibited and so appears darker than the target resting on the dark background.High-level theories on the other hand, centered their explanations on the notion of "taking the illumination into account" following the classical Helmholtzian approach.In their view the illusion observed in SLC reflects the system's failure to accurately compute the illumination at the two sides of the illusion.The darker background (and its target) is considered to lie in a lower illumination than the brighter one, so the target on the bright background is perceived to have a darker shade of gray.Gestaltists demonstrated the importance of context in the illusion by creating variations in which changes in perceptual grouping alter the size and the direction of the effect (Benary, 1924;Benussi, 1916).Despite the efforts of both high-level and gestalt models to cast a shadow on the explanation of SLC offered by contrast theories, it is safe to say that the illusion has by large remained the best example of the effect of low level mechanisms on lightness perception.
A qualitative shift in the study of SLC occurred upon the publication of the "Anchoring theory of lightness" (AT) by Gilchrist and his colleagues in 1999.This new gestalt theory not only presented a rigorous model that accounted for lightness constancy phenomena, but also used the same principles to explain lightness illusions including SLC.It was essentially the first time that a viable alternative explanation of the illusion was offered.This account was based on a totally different set of factors than those used by both traditional and modern contrast theories.Having two theoretical approaches that predicted the same outcome in SLC led proponents of AT to turn their attention to the overall pattern of errors observed in SLC and not merely its direction.Economou, Zdravkovic, and Gilchrist (2007) created a series of tests in which predictions of AT and contrast models were pitted against each other.They argued that the overall pattern of their results fitted predictions made by AT.Contrast theorists responded by presenting a series of experiments in which the data were shown to fit the output of a new generation of contrast models, multi-scale filter models (Blakeslee, Reetz, & McCourt, 2009).In one of those experiments, Blakeslee and her colleagues reported an illusion in SLC with targets that were both increments relative to their backgrounds, contrary to the reports by Economou et al.(2009).This is a crucial point, given the fact that AT is the only lightness theory that predicts no illusion between incremental targets in SLC.
Testing the illusion produced by a double increment setup in SLC is not a new endeavor.A host of studies have employed SLC displays with double increments and a review of those studies reveals some inconsistency in the data.While most of the studies report little or no illusion (Agostini & Bruno, 1996;Arend & Spehar, 1993;Diamond, 1953;Gilchrist, 1988;Jacobsen & Gilchrist, 1988), a number of studies have found a small to moderate illusion (Bressan & Actis-Grosso, 2001;Blakeslee et al., 2009;Flock & Noguchi, 1973;Rudd & Zemach, 2005).The work presented here aims to provide some insight into this discrepancy and to propose the addition of a new component in AT that can account for some small illusions with double increments under certain conditions.
The only theory that does not predict an illusion with double increment SLC displays is AT.According to the anchoring account the lightness of the two targets in SLC is a compromise between two values; one with respect to the target and its background (local value) and one with respect to the target and the whole display (global value).Both values are computed using the highest luminance rule; that is the surface with the highest intensity in each framework is computed to be white (anchor) and the rest of the surfaces in the framework get a value proportional to their luminance ratio with the luminance of the anchor.According to AT the illusion is the product of anchoring in the local frameworks.These computations produce illusions with increment/decrement and double decrement displays, but not with double increments.In Figure 1 one can see the computations in a standard increment/decrement versus a double increment display.The incremental targets are both assigned a value of white in their local frameworks, both being the areas with the highest luminance.The global computations also come out equal between the two targets as they are the highest luminance in the whole display.Thus AT in its current form predicts no illusion with double increment SLC displays.Here we entertain a hypothesis that the two local values in double increment SLC displays do not have equal weights in the lightness computations.We propose that the framework with the highest luminance range has a larger weight in the computation.In the discussion section we explain why this is an intuitive hypothesis, but for the time being let us examine how this would affect the computations in double increment displays.
If the two targets are computed to be white both in the local and global frameworks, then just adding more weight to one of the local values, would still lead to the same result; no illusion.However, we argue that some times the global value of the two targets is not white, as it is possible to have other surfaces in the visual field with a higher intensity than that of the targets.Some researchers run experiments like these in dark rooms, with all white surfaces covered so that the highest luminance in the field is indeed that of the two targets.This need not be the case in all setups however.The white frame of the computer screen might not be masked, the matching stimulus might have a white surface visible on the screen close to the display, or the experiment might be ran with lights on in a regular room with plenty of white surfaces in the observer's view.In those cases the global value of the two targets is not white, but something between middle and light gray as they will be anchored to a higher intensity.In these situations the difference in weight between the local computations will affect the final lightness of the targets.In Figure 2 one can see the computations produced by two setups, one in which the display is surrounded by a general black background and one in which the display is surrounded by a general white background.In the setup with the general black background assigning more weight to the framework with the higher range has no impact.Both targets come out equal, so no illusion is predicted.In the setup with the white general background however, the larger weight of the local framework with the darker background, produces a small illusion, making the target on the darker background to come out slightly lighter than the target on the light background.
We tested this idea using similar displays with those presented in Figure 2. The hypothesis was that if the luminance range of a framework affects its weight, then a small illusion should be obtained in the display with the general white background (full range display) but not in the display with the general black background (partial range display).If on the other hand, luminance range does not alter the weight of the local frameworks then no illusion should be obtained in either display.The third possible outcome is in accordance with low and high-level accounts.In that case, an illusion should be obtained in both displays.

Method Participants
Two different groups of observers (12 and 13 participants) took part in two experimental conditions.Observers were first year psychology students at the Psychology Department, University of Crete and naïve to the purpose of the experiment.They received course credit in exchange for their participation in the experiment.All observers had normal or corrected to normal vision.

Stimuli
Diagrams of the two displays used in the experiment are shown in Figure 3. Photometric and size properties of the stimuli are indicated on the diagram.
Both displays were presented on an LG 23 inch calibrated computer screen.Luminance measures taken with a Conica Minolta LS-110 photometer ensured that there were no "hot spots" on the screen.The outer rim of the screen was glossy black.
The room lights were turned off but the room remained dimly illuminated due to the light coming from the screen and the illumination box of the matching chart.

Scale
The matching chart consisted of a standard 16 step Munsell scale placed on a white background and was independently illuminated.The luminance of the white chip on the chart was 10.2 cd/m 2 and that of the black chip was 0.41 cd/m 2 .The chart was off to the side with respect to the viewer's head position, so that it was not visible while the display was viewed.

Procedure
Observers were randomly assigned to one of the two conditions: general black background or general white background.
The setup was prepared prior to their arrival.After signing the consent form, each participant was instructed to match the color of the target with the chip from the chart that best fitted its appearance.The head position of the observer was maintained by a chin rest, 75 cm away from the screen.When performing the match, observers turned their head to see the chart and to select the chip that matched their percept.
It was noted that there were no right or wrong answers and that their perceptual impression was important for the purpose of the experiment.There was no time limit for the matches, and observers called out the number of the chip when they felt they had a satisfactory match.
For both experimental conditions, the order of matching between the targets was counterbalanced.

Re sults
Figure 4 shows the data obtained in both conditions.Munsell matches were transformed to log reflectance values, and the differences between the means of the two targets were analyzed by a paired T-test.In the partial range condition, the lightness matches between the targets did not differ significantly (T(12)= -1,56, p. = 0.14, two-tailed).Actually the absolute difference between the two targets tends to go towards assimilation instead of a contrast direction (target on dark gray = 1,762, target on middle gray = 1,789).In the full range display a statistically significant illusion was obtained (T(11) = 2,54, p. = 0,027, twotailed).The target on the dark gray background (1,623) was seen as lighter than the target on the middle gray background (1,557).The difference between the two targets gives the magnitude of the illusion.This is a much smaller illusion than what is observed with standard SLC displays (about 0.15 log units in Economou et al., 2007 compared   The percentage of observers that perceived a contrast illusion (the target on the darker background appeared lighter) in the full range condition was 67%, while in the partial range condition only 23% of the observers reported a contrast illusion.Reversed contrast illusions (the target on the darker background appeared darker) were reported by 8% of the observers in the full range condition and by 54% of the observers in the partial range condition.
These results are consistent with our hypothesis that a contrast illusion can be obtained with double increment displays, if a brighter area is present in the visual field to serve as a global anchor.

Discussion
The data obtained in this experiment can shed some light on the inconsistent reports on the illusions obtained (or not) with double increments in SLC.We interpret the data to mean that it is possible to obtain an illusion under conditions in which a brighter surface than the targets is visible in the field of the observer.This could account for most of the data obtained by Flock & Noguchi (1973) and by Blakeslee et al. (2009), as they used a general background with higher intensity than half of their backgrounds and targets.However, we failed to obtain an effect between incremental targets when there was no brighter surface visible in the visual field.These data are inconsistent with the data obtained by Bressan & Actis-Grosso (2001) and Rudd & Zemach (2005).Our hypothesis can also be applied to the data obtained in the so-called inverted White's illusion (Spehar, Clifford, & Agostini, 2002).When the targets in White's illusion have a higher luminance than the stripes Spehar et al report two illusions; in their "landscape" display an inverted White's illusion and in their "portrait" display a regular White's illusion.Our range hypothesis can account for the latter result but not the former suggesting that additional factors might be involved in White's illusion with double increments as suggested by Spehar et al.
A host of additional factors have been proposed to account for the inconsistencies observed in double increment SLC studies, including the matching method, the expertise of the observers, the luminance difference between the targets and the backgrounds and the absolute luminance of the targets.In our view none of these can account fully for the different results obtained in different experiments but could theoretically contribute individually to the discrepancy.For example it might be entirely possible that some of the discrepancy is due to different matching scales used in different experiments (for a review of the effect of different scales on lightness matches see Jando, Agostini, Galmonte, & Bruno, 2003) however we can offer no intuitive explanation of the discrepancy between the data obtained by Economou et al., 2007 andBressan &Actis-Grosso, 2001 based on differences on the scales alone.In that sense the range hypothesis stated here can provide some insight but it is definitely not the final answer.
Qualitative relations between the targets and their backgrounds in SLC do not seem to constrain the output of low-level theories of lightness perception.If one target sits on a lower luminance background than the other one, then it should always be seen as lighter.This claim is very explicit in both Hering's (1874Hering's ( /1964, p.125, p.125) and Cornsweet's (1970, p.279) books and is shared by modern contrast models as well (Blakeslee & McCourt, 2004;Pessoa, Mingolla, & Neumann 1995).In the standard version of SLC one of the targets has a lower luminance than its background (decrement) and the other has a higher luminance than its background (increment).The main factor that determines the illusion with respect to inhibitory forces, is the luminance difference between the backgrounds.In double increment and double decrement displays a smaller illusion would be predicted usually because the luminance difference between the backgrounds is decreased relative to the standard increment/decrement displays.A contrast illusion should still be obtained however, because the backgrounds differ in intensity.
The same logic can be applied to both the Helmholtzian account and the partial classified edge integration models (Gilchrist, 1988;Ross & Pessoa, 2000).If some of the difference in intensity between the two backgrounds is erroneously computed as an illumination difference, this should lead to illusions with all variations of SLC (increments/decrements, double decrements and double increments).Bressan's double anchoring theory also explicitly predicts an illusion with double increments due to the effect of its second anchor (Bressan, 2006).That essentially leaves AT alone to distinguish between the increment/ decrement relations of targets and backgrounds in SLC by predicting no illusion with double increment displays.
A simple demonstration of the role of the qualitative relations of the surfaces in SLC creates a problem for both the low and high-level accounts.In Figure 5 one can see two versions of the illusion.In the top row an increment/ decrement version is shown and in the bottom row a double increment version is depicted.The background luminance difference in the increment/decrement version is smaller than the luminance difference in the double increment display.It follows that inhibition or illumination calculation errors should be greater on the latter display.However it's clear that the illusion is more pronounced in the increment/decrement display.The hypothesis presented and tested here is not simply a "computational" correction to AT's failure to account for some data.On the contrary, adding the component of luminance range of a framework to the factors that affect its weight in lightness computations is quite an intuitive idea.The whole concept of assigning different weights to the frameworks in AT revolves around two functional attributes of frameworks: "coherence" of the framework and "number of lightness statistics" it contains (Economou, 2010).Coherence works toward identifying fields of common illumination.The more coherent a framework is, the more probable it is that its surfaces will lie in the same illumination field.Factors that affect the coherence of a group are co-planarity, proximity, type of luminance edges, common orientation, etc.Thus, frameworks that include coplanar surfaces should have a greater weight in the computation than frameworks that include non-coplanar surfaces, as has been shown in a dramatic fashion by Gilchrist's experiments in 1977and 1980(Gilchrist, 1977, 1980).Framework coherence serves to "correct" the mistakes produced by global anchoring, especially in cases where different fields of illumination are present in the visual field.The number of lightness statistics a framework contains serves a different goal: it increases the probability that the anchor in a framework is a real white.The most important factor under this category is articulation (the number of surfaces a framework contains).Increasing the number of surfaces in a framework also increases the probability that a real white is present and that local anchoring would be veridical.. Luminance range is proposed to add to the statistics of a framework as well.As the luminance range of a framework increases and approaches the physical range of black to white, it becomes almost certain that a real white is present in that framework.This should drive the system to assign a larger weight to frameworks with higher luminance ranges compared to those with low luminance ranges.While this is true for ranges up to the black/ white range, we propose that when the luminance range of a framework is extended beyond the black/white range, the weighting of this framework should decrease.This is because such a range should signal a change in illumination, thus subtracting weight from that specific framework.It seems then, that the luminance range of a framework can provide crucial information for both the presence of a real white in a group of surfaces and the presence of different illumination fields.This is a hypothesis that requires additional research.

Figure 1 .
Figure 1.Lightness computations for the two targets in an increment/decrement SLC display (top) versus a double increment display (bottom).In the top display the illusion is produced by the local value of the target on the black background.In the bottom display, no illusion is produced as both targets have equal local and global values.

Figure 2 .
Figure 2. Two double increment displays.In the top display with the black general background, no illusion is predicted because the local and global values of both targets are equal.In the bottom display with the white general background, the global values of the two targets differ from the their local values.Adding weight to the local value of the target with the highest luminance range (target on dark gray background) produces a larger lightening of this target with respect to the target sitting on the middle gray background.

Figure 3 .
Figure 3.A diagram of the display used in the experiment.Two different backgrounds were used to create two conditions: the full range condition and the partial range condition.
to 0.063 log units in the present experiment).

Figure 4 .
Figure 4. Target's perceived reflectance.A graph of the data obtained in the two conditions.Dark gray bars show the lightness of the targets on the dark gray background and light gray bars show the lightness of the targets on the middle gray background.A contrast effect was obtained only in the full range condition.

Figure 5 .
Figure 5.An increment/decrement display (top) versus a double increment display(bottom).The luminance difference between the backgrounds is larger in the double increment display, however the illusion is much more pronounced in the increment/ decrement display.