In the disk/ganzfeld experiment, the figure/ground distinction was confounded with relative area. Li and Gilchrist (in press) conducted a series of experiments to separate relative area from figure/ground. To create a stimulus pattern that fills the entire visual field, the observer's head was placed inside a large acrylic hemisphere. A simple two-part pattern was painted on its opaque interior. Relative area was varied while figure/ground arrangements were held constant. Schematic representations of these stimuli are shown in Figure 5, along with the results, given in Munsell values.
The net result is that the surround rule was completely undermined. In the incremental large oval condition, illustrated in Figure 5f, the background appeared middle gray (Munsell 6.0/), not white, as it should according to the surround rule. What had appeared to be a matter of figure/ground turns out to be a matter of relative area. This is seen clearly in the split dome conditions, shown in Figure 5a and 5b. As the darker region increases its area from half the visual field (Figure 5a) to most of the visual field (Figure 5b), its lightness moves from Munsell 4.5/ to 7.8/. This finding brings to mind Helson's (1964, p. 292) comment that: "...we need assume only that within certain limits area acts like luminance, that is, increase in area has the same effect as increase in luminance."
4.2. Highest luminance plus area
The highest luminance rule was rescued but combined with a tendency for the largest area to appear white. Thus anchoring under minimal conditions (two regions in the visual field) appears to depend upon both photometric and geometric factors. We can say that the larger a surface, the lighter it appears, or "the larger the lighter" for short. But "the larger the lighter" does not apply under all conditions. It applies only when there is a conflict between the tendency for the highest luminance to appear white and the tendency for the largest area to appear white. As long as the highest luminance has the largest area, there is no conflict and that region becomes a very stable anchor. Darker surfaces are seen relative to that anchor simply according to the ratio principle, and "the larger the lighter" does not apply.
By comparing our results with others in the literature we were able to formalize a rule governing the effects of relative area on perceived lightness that had not been previously recognized. The rule, which we call the Area Rule, describes how relative area and relative luminance combine to anchor lightness perception. The rule is this: In a simple display, when the darker of the two regions has the greater relative area, as the darker region grows in area, its lightness value goes up in direct proportion. At the same time the lighter region first appears white, then a fluorent white and finally, self-luminous.
The term "in direct proportion" here has the following meaning. When the darker region occupies 50% or less of the total area, its perceived lightness is determined simply by its luminance ratio with the lighter region according to Wallach's ratio principle and the highest luminance rule (the lighter region taken to be white). As the area of the darker region grows from 50% to 100% of total area, its lightness grows proportionately from this value toward white. We have empirical data supporting this claim regarding the lightness value at 50% and 100%, but we are making an assumption that the transition in lightness is smooth between these values.
Strictly speaking the rule applies to visual fields composed of only two regions of non-zero luminance. Application of the rule to more complex images remains to be studied.
There are at least ten other papers in the literature concerning the influence of area on lightness or brightness. We will see that a great deal of order is brought to this part of the literature when these results are analyzed in terms of anchoring in general, and the Area Rule in particular.
Wallach (1948) tested three annulus-to-disk area ratios in his experiments with decremental disks: 4:1, 1:1, and 1:4. The first two of these yielded identical results. Relative area had an effect on perceived lightness only in the third case. When the disk, which was the darker of the two, had an area four times greater than that of the annulus, the disk appeared lighter than it would otherwise appear. The Area Rule predicts no difference between the 4:1 and 1:1 area ratios because the darker region (the disk) does not have the largest area. But the rule does predict a difference between the 1:1 and 1:4 area ratios because the darker region does have the larger area. The darker region is predicted to lighten and this is what Wallach reported.
Using lighting conditions similar to those used by Gelb, Newson (1958) spotlighted a display consisting of a square target surrounded by a brighter square annular region. Holding both center and surround luminances constant, Newson tested perception of the center square while he varied the area of the surround from zero to an area roughly equal to that of the center square. This range is just the range within which the Area Rule applies. He obtained a pronounced effect on the lightness of the square. Moreover, his curve (Newson, 1958, Figure 4, p. 94) reaches an asymptote just where the areas of the center and surround become equal, suggesting that additional increases in the area of the surround would have no further effect on the lightness of the center.
Kozaki (1963) tested brightness using a haploscopic technique and a square center-surround display embedded in darkness. Because the area of the surround was always greater than the area of the test field, the Area Rule would apply under the conditions in which her test field was an increment. With increments, she obtained an area effect like that we obtained, consistent with our Area Rule. But she also obtained a weak area effect when the test field was a decrement.
Helson and his associates (Helson, 1963, 1964; Helson & Joy 1962; Helson & Rohles, 1959) varied the relative area of either white or black stripes on a gray rectangle in an attempt to resolve the paradox of lightness contrast versus lightness assimilation, as in the classic von Bezold (1874) spreading effect. Their results are not consistent with the Area Rule. We are unable to resolve this discrepancy beyond the observation that the von Bezold effect may involve a relatively low level kind of space averaged luminance.
Burgh and Grindley (1962) reported no effect of area on perceived lightness using the traditional simultaneous lightness contrast display. However, it is crucial to note that they achieved their area changes by magnifying or minifying the entire display. As a consequence, the relative area between each gray target and its background was never changed, so this outcome does not contradict the Area Rule.
Yund and Armington (1975) also tested the dependence of brightness on relative area in a disk/annulus display. But, contrary to all the other studies, they tested the effect of the darker region on the brighter, an effect known to be either tiny or nonexistent (Heinemann, 1971; Freeman, 1967, p. 173).
We will not comment on two studies (Diamond, 1962; Whipple, Wallach, & Marshall, 1988) in which effects of area were studied because area was confounded with separation between test and inducing fields in those studies.
Four additional studies of brightness and area by Heinemann (1955), Diamond (1955), Stevens (1967), and Stewart (1959) are consistent with the Area Rule. These studies were part of the brightness induction literature and will be considered in Section 10 as part of a general review of that literature.
4.4. Luminosity and the Area Rule
The surround rule had been proposed as a resolution of the apparent contradiction between the highest luminance rule and the perception of luminosity. If the surround rule must be abandoned, can the Area Rule resolve this contradiction and explain both surface lightness perception and luminosity? After all, Li and Gilchrist did obtain luminosity perception in several of their domes experiments even though their stimuli were nothing more than opaque surfaces. The Area Rule does appear to greatly illuminate the relationship between opaque surface lightness and self-luminosity. In general we can say that luminosity perception occurs at one extreme end of the zone to which the Area Rule applies; that is, when a given surface is high in relative luminance but at the same time low in relative area.
When the luminance difference between two regions of the visual field is increased, two basic outcomes (or some combination) are possible. The darker region might remain perceptually constant while the lighter region moves toward and into a self-luminous appearance. This might be called luminosity induction; it occurred in Gilchrist and Bonato's disk/ganzfeld experiments when the disk was an increment. Alternatively, the lighter region might remain perceptually constant while the darker region becomes darker and darker gray. This occurs in disk/annulus experiments (Heinemann, 1955; Wallach, 1948) when the disk is a decrement. Heinemann calls this brightness induction, but we will use the term grayness induction to distinguish it from luminosity induction, and to capture the notion of two opposing directions, grayness and luminosity.
The question then becomes, when the luminance difference between two regions is increased, what determines whether this increased difference is experienced as an induction of luminosity into the brighter region or grayness into the darker region? This, of course, is another way of stating the anchoring problem. Indeed Schouten and Blommaert (1995a) have put the problem in this way.
In short the answer appears to lie in relative area. When the darker region is large relative to the lighter region, most of the effect is expressed as luminosity induction in the lighter region, with only a small amount of grayness induction. But when the area of the darker region is small relative to the lighter region, there is very little luminosity induction; most of the effect is expressed as grayness induction in the darker region.
Figure 6 represents what is currently our best understanding of the appearance of the two regions in a simple framework as the relative area shifts from the lighter region to the darker. Typically a figure of this kind would plot perceived lightness and luminosity as a function of luminance ratio, with relative area held constant. Note that in this figure we have plotted lightness and perceived luminosity as a function of relative area, with luminance ratio held constant! We can understand this graph by walking through it, moving from left to right as the x-axis shows increasing relative area of the darker region. Beginning with the dark/light border at the extreme left eccentric position; the darker region is very small relative to the lighter region. In this case the lighter region will appear white and the lightness of the darker region will depend simply on its luminance ratio with the lighter region. Now, as the border shifts from the extreme left eccentric position to the center position, no change will occur in the perception of either region because all of these stimuli lie outside the zone of applicability of the Area Rule. Only when the border crosses the midpoint and begins to move toward the right hand eccentric position does the Area Rule apply and begin to produce perceptual changes.
As the border passes the midpoint, the darker region begins to grow lighter and lighter. The lighter region continues to appear white, gradually becoming a more fluorent white (Evans, 1959, 1964, 1974), despite the constant luminance ratio. But the lightening of the darker region is a stronger effect than the brightening of the lighter region. For example, with a luminance ratio of 30:1, the lightness of the darker region can move all the way from black to white (the lightness of the darker region approaches white as its relative area approaches 100%), while the lighter region remains at white. This implies a perceptual compression. That is, the difference between the perceived lightness of the darker region and the perceived lightness of the lighter region is reduced even though the physical difference remains constant. The perceived lightness values seem literally to be squeezed between the tendency of the lighter region to appear white by the highest luminance rule and the tendency of the darker region to appear white because of its preponderant area.
Several additional effects are associated with this compression, or squeezing. One seems to be an enhancement of the lighter region, causing it to appear as a kind of pre-luminous super white (Heinemann, 1955; MacLeod, 1947). This twilight zone between white and luminosity has been termed fluorence by Evans (1959, 1974). We believe this may be the same enhancement phenomenon that Heinemann reported to occur in his test disk when the luminance of the annulus was increased while its luminance was still below that of the test disk. As the area of the darker, side approaches 100%, its perceived lightness approaches white, and as this happens, the lighter region is forced to relinquish its white appearance (with its opaque quality) and take on the appearance of self-luminosity.
Schouten and Blommaert (1995a, 1995b) have recently reported a phenomenon that they describe as a novel compression mechanism in the luminance-brightness mapping. They call it brightness indention. Using a display that consisted of two disks within a ganzfeld, Schouten and Blommaert found that when the disks are both brighter than the ganzfeld, the ganzfeld background does not appear homogeneous; it appears darker in the immediate vicinity of the disks, creating a kind of dark halo around each. Newson (1958, p. 87) described what appears to be the same phenomenon. This phenomenon occurs only in the zone to which our Area Rule applies, when the ganzfeld, with its large area, is darker than both of the disks. We believe this happens for the same reason as fluorence and the enhancement effect, namely because of the competition between the tendency for the ganzfeld to appear white because it has the greatest area and the tendency for the two disks to appear white because they have the highest luminance. Apparently in this case the conflict is resolved by sacrificing the perceived homogeneity of the ganzfeld.
Bonato and Gilchrist (1994) studied luminosity thresholds by measuring the luminance value at which a target surface begins to appear self-luminous. These experiments were subsequently replicated (Bonato and Gilchrist, in press) with larger targets. This produced higher thresholds. A 17-fold increase in the area of the target produced a 3-fold increase in the luminance required for luminosity perception. A corollary result is that as the luminance of the large target was increased, the increasing luminance ratio between the target and its background showed up as a darkening of the perceived surface lightness of the background. These results are consistent with the Area Rule.
In view of the role of relative area in anchoring it seems no longer appropriate to use the terms anchor and highest luminance interchangeably. The anchor in a given framework is the luminance value that appears white, and because of the area effect, the luminance value that appears white is not necessarily the highest luminance. The highest luminance is the same thing as the anchor only when the Area Rule does not apply.
It should be further noted that the anchor, or luminance value that appears white, need not appear in a framework as an actual surface. For example, if a small white disk is placed in the center of a dome painted black, the disk will appear luminous and the black dome will appear light gray. Perceived white lies between these two perceived levels but is not represented by a physical surface. Within a framework, the lightness of a target surface is given by the ratio between the target surface luminance and the luminance of the anchor whether or not the anchor has the highest luminance and whether or not the anchor luminance is actually represented by a surface.
4.5. Anchoring rules for simple images: A summary
For simple images, the rules of anchoring can be stated very concretely. Except when the Area Rule is engaged, anchoring is straightforward: The brightest region appears white, and the appearance of each darker region depends on its relationship to that, according to the formula:
PR = Lt/Lh x 90% (1)
where PR is perceived reflectance, Lt is the luminance of the target, Lh is the highest luminance in the framework, and 90% is the reflectance of white.
For conditions to which the Area Rule applies the formula must be modified. Although greater precision will have to come from additional research, the evidence we have as of now, which has been expressed in graphic form in Figure 6, can be summarized algebraically as follows:
PR = (100-Ad)/50 * (Lt/Lh x 90%) + (Ad-50)/50 * (90%) (2)
where Ad is the area of the darker region, as a percentage of the total area in the field. The formula simply says that if Ad is 50% of the total area, the perceived reflectance of the darker region is just as it is given in Formula (1) above. As Ad approaches 100%, its perceived reflectance approaches 90%. Between these two endpoints there is a smooth transition. The lighter region has no lightness value other than white, but as Ad grows, the lighter region takes on additional qualities, first fluorence, and finally, self-luminosity. This qualitative change, not surprisingly, is difficult to capture mathematically.
