The place of white in a world of grays: a double-anchoring theory of lightness perception

The specific gray shades in a visual scene can be derived from relative luminance values only when an anchoring rule is followed. The double-anchoring theory I propose in this article, as a development of the anchoring theory of Gilchrist et al. (1999), assumes that any given region (a) belongs to one or more frameworks, created by Gestalt grouping principles, and (b) is independently anchored, within each framework, to both the highest luminance and the surround luminance. The region's final lightness is a weighted average of the values computed, relative to both anchors, in all frameworks. The new model accounts not only for all lightness illusions that are qualitatively explained by the anchoring theory but also for a number of additional effects, and it does so quantitatively, with the support of mathematical simulations.     

Lightness, equivalent backgrounds, and anchoring

Observers compared two center/surround configurations haploscopically. One configuration consisted of a standard surface surrounded by two, three, or four surfaces, each with a different luminance. The other configuration consisted of a comparison surface surrounded by a single annulus that varied in luminance. Center surfaces always had the same luminance but only appeared to have the same lightness with certain annuli (equivalent backgrounds). For most displays, the luminance needed to obtain an equivalent background was close to the highest luminance in the standard surround configuration. Models based on the space-average luminance or the space-average contrast of the standard surround configuration yielded poorer fits. Implications for computational models of lightness and for candidate solutions to the anchoring problem are discussed.     

Relative area and relative luminance combine to anchor surface lightness values

The anchoring of lightness perception was tested in simple visual fields composed of only two regions by placing observers inside opaque acrylic hemispheres. Both side-by-side and center/surround configurations were tested. The results, which undermine Gilchrist and Bonato’s (1995) recent claim that surrounds tend to appear white, indicate that anchoring involves both relative luminance and relative area. As long as the area of the darker region is equal to or smaller than the area of the lighter region, relative area plays no role in anchoring. Only relative luminance controls anchoring: The lighter region appears white, and the darker region is perceived relative to that value. When the area of the darker region becomes greater than that of the lighter region, relative area begins to playa role. As the darker region becomes larger and relative area shifts from the lighter region to the darker region, the appearance of the darker region moves toward white and the appearance of lighter region moves toward luminosity. This hitherto unrecognized rule is consistent with almost all of the many previous reports of area effects in lightness and brightness. This in turn suggests that a wide range of earlier work on area effects in brightness induction, lightness contrast, lightness assimilation, and luminosity perception can be understood in terms of a few simple rules of anchoring.     

Relative area and relative luminance combine to anchor surface lightness values.

The anchoring of lightness perception was tested in simple visual fields composed of only two regions by placing observes inside opaque acrylic hemispheres. Both side-by-side and center/surround configurations were tested. The results, which undermine Gilchrist and Bonato's (1995) recent claim that surrounds tend to appear white, indicate that anchoring involves both relative luminance and relative area. As long as the area of the darker region is equal to or smaller than the area of the lighter region, relative area plays no role in anchoring. Only relative luminance controls anchoring: The lighter region appears white, and the darker region is perceived relative to that value. When the area of the darker region becomes greater than that of the lighter region, relative area begins to play a role. As the darker region becomes larger and relative area shifts from the lighter region to the darker region, the appearance of the darker region moves toward white and the appearance of lighter region moves toward luminosity. This hitherto unrecognized rule is consistent with almost all of the many previous reports of area effects in lightness and brightness. This in turn suggests that a wide range of earlier work on area effects in brightness induction, lightness contrast, lightness assimilation, and luminosity perception can be understood in terms of a few simple rules of anchoring.     

Perceived area and the luminosity threshold.

Observers made forced-choice opaque/luminous responses to targets of varying luminance and varying size presented (1) on the wall of a laboratory, (2) as a disk within an annulus, and (3) embedded within a Mondrian array presented within a vision tunnel. Lightness matches were also made for nearby opaque surfaces. The results show that the threshold luminance value at which a target begins to appear self-luminous increases with its size, defined as perceived size, not retinal size. More generally, the larger the target, the more an increase in its luminance induces grayness/blackness into the surround and the less it induces luminosity into the target, and vice versa. Corresponding to this luminosity/grayness tradeoff, there appears to be an invariant: Across a wide variety of conditions, a target begins to appear luminous when its luminance is about 1.7 times that of a surface that would appear white in the same illumination. These results show that the luminosity threshold behaves like a surface lightness value--the maximum lightness value, in fact--and is subject to the same laws of anchoring (such as the area rule proposed by Li & Gilchrist, 1999) as surface lightness.     

Perceived area and the luminosity threshold

Observers made forced-choice opaque/luminous responses to targets of varying luminance and varying size presented (1) on the wall of a laboratory, (2) as a disk within an annulus, and (3) embedded within a Mondrian array presented within a vision tunnel. Lightness matches were also made for nearby opaque surfaces. The results show that the threshold luminance value at which a target begins to appear self-luminous increases with its size, defined as perceived size, not retinal size. More generally, the larger the target, the more an increase in its luminance induces grayness/blackness into the surround and the less it induces luminosity into the target, and vice versa. Corresponding to this luminosity/grayness tradeoff, there appears to be an invariant: Across a wide variety of conditions, a target begins to appear luminous when its luminance is about 1.7 times that of a surface that would appear white in the same illumination. These results show that the luminosity threshold behaves like a surface lightness value—the maximum lightness value, in fact—and is subject to the same laws of anchoring (such as the area rule proposed by Li & Gilchrist, 1999) as surface lightness.     

Local and global processes in surface lightness perception

Various demonstrations show that a target of constant luminance can be made to appear darker in perceived lightness merely by introducing an adjacent region of higher luminance. This has often been interpreted as a manifestation of contrast effects produced by lateral inhibition, a relatively local process. An alternative interpretation holds that the highest luminance in such a display serves as an anchor that defines the white level. This interpretation is global in the sense that the anchor need not be located near any particular target in order to serve as its standard. Edge integration processes have been postulated that would enable such remote comparisons, but there is controversy about the strength of these processes. We report a series of experiments in which local and global processes were assessed. Specifically, we tested whether the introduction of a higher luminance has a greater darkening effect on an adjacent target than on a remote target. We found no difference, suggesting that the darkening effect is a matter of anchoring, not contrast, and that edge integration processes required by anchoring are relatively strong.     

Hess and Pretori revisited: Resolution of some old contradictions

An early experiment by Hess and Pretori (1894) was replicated and modified in an attempt to determine why they failed to find the ratio principle later discovered by Wallach (1948). Separating the two surround-infield patterns by darkness made very little difference. However, allowing the observer to adjust the infield luminance (as in Wallach) rather than the surround luminance (as in Hess & Pretori) revealed some startling effects. At surround:infield luminance ratios greater than approximately 100∶1, there is no ratio effect; all infields appear equal and totally dark. Converging evidence is presented that Hess and Pretori’s data in this region actually represent surround-matching by the observers. Nor are ratio effects found with increments (infield brighter than surround). When free to match either infield luminances or ratios (by controlling infield luminance), observers match luminances. For decrements with ratios between 1∶1 and approximately 100∶1, lightness constancy and the ratio principle hold.     

Luminance gradient can break background-independent lightness constancy

A display with a luminance gradient was shown to induce a strong lightness illusion (Logvinenko, 1999 Perception 28 803-816). However, a 3-D cardboard model of this display was found to produce a much weaker illusion (less than half that in the pictorial version) despite the fact that its retinal image is practically the same. This is in line with the hypothesis that simultaneous lightness contrast is solely a phenomenon of pictorial perception (Logvinenko et al, 2002 Perception 31 73-82). The residual lightness illusion in the 3-D model can be accounted for by the fact that this model is a hybrid display. Specifically, while it is a real object, a pictorial representation (of the illumination gradient) is superimposed on it. Thus, lightness in the 3-D display is a compromise between two opposite tendencies: the background-independent lightness constancy and the lightness illusory shift induced by the luminance gradient.     

Lightness induction revisited

Lightness induction is the classical visual phenomenon whereby the lightness of an object is shown to depend on its immediate surround. Despite the long history of its study, lightness induction has not yet been coherently and satisfactorily explained in all its variety. The two main theories that compete to explain it descend (i) from H von Helmholtz, who believed that lightness induction originates from some central mechanisms that take into account the whole viewing situation, with particular stress upon the apparent illumination of the object; and (ii) E Hering who argued in favour of more peripheral sensory mechanisms based on local luminance contrast. The balance between these theories has recently been shifted towards Helmholtz's position by E H Adelson who has provided additional evidence that lightness induction depends on perceptual interpretation and, particularly, on apparent transparency. I challenge Adelson's conclusions by introducing modified versions of his tile pattern that use luminance gradients. In the first of these new demonstrations there is a strong lightness induction even though no apparent transparency is experienced. In the second there is a clear impression of transparent strips, yet no lightness induction is present. And the third shows that breaking up the Adelson tile pattern, while it affects neither the impression of transparency nor the type of grey-level junctions, makes the lightness-induction effect vanish. This implies that Adelson's illusion can be accounted for by neither local contrast, nor the apparent transparency, nor the type of grey-level junctions. Presented here is an alternative look at lightness induction as a phenomenon of the pictorial (as contrasted to natural) vision, which rests on the lightness-shadow invariance, much as Gregory's 'inappropriate constancy scaling' theory of geometrical illusions rests on the apparent size-distance invariance.     

Infant lightness perception: do 4-month-old infants follow Wallach's ratio rule?

When adults view a test disk embedded in a higher-luminance surround, the perceived lightness of the disk is largely determined by the surround-to-disk (S/D) luminance ratio (Wallach's ratio rule). Performance of 4-month-old infants tested with a forced-choice novelty-preference technique was consistent with predictions based on Wallach's ratio rule. This result suggests that the ability to extract and maintain information about local luminance ratios is present early in infancy. This ability is likely to contribute to the development of lightness constancy.     

Grouping based on phenomenal similarity of achromatic color.

It is widely acknowledged that a precondition for the perception of the world of objects and events is an early process of organization, and it has generally been assumed that such organization is based on the Gestalt laws of grouping. However, the stage at which such grouping occurs, whether early or late, is an empirical question. It is demonstrated in two experiments that grouping by similarity of neutral color is based not on similarity of absolute luminance at the level of the proximal stimulus, but on phenomenal similarity of lightness resulting from the achievement of lightness constancy. An alternative explanation of such grouping based on the equivalence of luminance ratios between elements and background is ruled out by appropriate control conditions.     

Lightness constancy through a veiling luminance

Observers were asked to select samples from a Munsell chart to match the lightness of seven identified surfaces in an outdoor scene they were shown. A separate group that was given the same task but viewed the same scene covered with a veiling luminance equal in intensity to the highest luminance in the scene selected almost the same matches. The same lightness constancy results were obtained using an abstract laboratory display to rule out memory color. These results challenge ratio and contrast theories because a veiling luminance, by adding a constant luminance to every poing in the image, dramatically alters luminance ratios. Lightness constancy was not obtained, however, when these three-dimensional real-world-type displays were replaced by a flat, Mondrian-type display consisting of surface grays from white to black, whether or not colored regions were present in the display; lightness matches were consistent with ratio predictions both with and without the veil.     

Lightness constancy: Ratio invariance and luminance profile

The term simultaneous lightness constancy describes the capacity of the visual system to perceive equal reflecting surfaces as having the same lightness despite lying in different illumination fields. In some cases, however, a lightness constancy failure occurs; that is, equal reflecting surfaces appear different in lightness when differently illuminated. An open question is whether the luminance profile of the illumination edges affects simultaneous lightness constancy even when the ratio invariance property of the illumination edges is preserved. To explore this issue, we ran two experiments by using bipartite illumination displays. Both the luminance profile of an illumination edge and the luminance ratio amplitude between the illumination fields were manipulated. Results revealed that the simultaneous lightness constancy increases when the luminance profile of the illumination edge is gradual (rather than sharp) and homogeneous (rather than inhomogeneous), whereas it decreases when the luminance ratio between the illumination fields is enlarged. The results are interpreted according to the layer decomposition schema, stating that the visual system splits the luminance into perceived lightness and apparent illumination components. We suggest that illumination edges having gradual and homogeneous luminance profiles facilitate the luminance decomposition process, whereas wide luminance ratios impede it.     

Lightness of an object under two illumination levels

Anchoring theory (Gilchrist et al, 1999 Psychological Review 106 795-834) predicts a wide range of lightness errors, including failures of constancy in multi-illumination scenes and a long list of well-known lightness illusions seen under homogeneous illumination. Lightness values are computed both locally and globally and then averaged together. Local values are computed within a given region of homogeneous illumination. Thus, for an object that extends through two different illumination levels, anchoring theory produces two values, one for the patch in brighter illumination and one for the patch in dimmer illumination. Observers can give matches for these patches separately, but they can also give a single match for the whole object. Anchoring theory in its current form is unable to predict these object matches. We report eight experiments in which we studied the relationship between patch matches and object matches. The results show that the object match represents a compromise between the match for the patch in the field of highest illumination and the patch in the largest field of illumination. These two principles are parallel to the rules found for anchoring lightness: highest luminance rule and area rule.     

The effects of figure/ground, perceived area, and target saliency on the luminosity threshold

Observers adjusted the luminance of a target region until it began to appear self-luminous, or glowing. In Experiment 1, the target was either a face-shaped region (figure) or a non-face-shaped region (ground) of identical area that appeared to be the face's background. In Experiment 2, the target was a square or a trapezoid of identical area that appeared as a tilted rectangle. In Experiment 3, the target was a square surrounded by square, circular, or diamond-shaped elements. Targets that (1) were perceived as figures, (2) were phenomenally small in area, or (3) did not group well with other elements in the array because of shape appeared self-luminous at significantly lower luminance levels. These results indicate that like lightness perception, the luminosity threshold is influenced by perceptual organization and is not based on low-level retinal processes alone.     

Dungeons, gratings, and black rooms: A defense of double-anchoring theory and a reply to Howe et al. (2007).

Replies to comments mad by Howe et al. on the current author's original article. The double-anchoring theory of lightness (P. Bressan, 2006b) assumes that any given region belongs to a set of frameworks, created by Gestalt grouping principles, and receives a provisional lightness within each of them; the region's final lightness is a weighted average of all these values. In their critique, P. D. L. Howe, H. Sagreiya, D. L. Curtis, C. Zheng, and M. S. Livingstone (2007) (a) show that the target's lightness in the dungeon illusion (P. Bressan, 2001) and in White's effect is not primarily determined by the region with which the target is perceived to group and (b) claim that this is a challenge to the theory. The author argues that Howe et al. misinterpret grouping for lightness by equating it with grouping for object formation and by ignoring that lightness is determined by frameworks' weights and not by what appears to group with what. The author shows that Howe et al.'s empirical findings, together with those on grating induction and all-black rooms that they cite as problematic, actually corroborate, rather than falsify, the double-anchoring theory. (PsycINFO Database Record (c) 2007 APA, all rights reserved).     

Lightness compression and hue changes

Two experiments were performed to relate the Bezold-Brücke (B-B) and lightness compression effects. The first used a calibrated screen to present an achromatic luminance staircase. In addition, it reproduced, the methodology and the essential aspects the lightness compression effect discovered by Cataliotti and Gilchrist (1995). That is, observers perceived a truncated grey scale (from white to medium grey) when the staircase was the only stimulation in the near background (Gelb condition), but not when presented on a Mondrian background, because of the high articulation level provided by this background. Experiment 1 design also included two other backgrounds that produced a partial compression effect. In Experiment 2, two chromatic staircases were used. Employing a naming task, changes in hue perception were only observed for the susceptible staircase. The observed changes were of two types. First, for the full staircase presentations, a Gelb background produced maximum lightness compression (more similarity in the lightness of the staircase stimuli) and, also, a minimum B-B effect (fewer differences in hue). Second, only for the Gelb condition, there were changes in the hue of the lowest luminance staircase stimuli depending on the staircase extension. Results are discussed in the framework of the anchoring theory of lightness perception.     

Simultaneous lightness contrast on plain and articulated surrounds

Simultaneous lightness contrast is stronger when the dark and light backgrounds of the classic display (where one of the targets is an increment and the other is a decrement) are replaced by articulated fields of equivalent average luminances. Although routinely attributed to articulation per se, this effect may simply result from the increase in highest luminance in the light articulated, vs plain, background; by locally darkening the decremental target, such an increase would amplify the difference between the targets. We disentangled the effects of highest luminance and articulation by measuring, separately, the magnitude of lightness contrast on dark and light plain and articulated backgrounds. We found that highest luminance and articulation contribute separately to the final illusion.