3. The Rules of Anchoring in Simple Displays

Our approach will be to consider the rules of anchoring under minimum conditions for the perception of a surface, and then to attempt to describe how the rules change as one moves systematically from simple images to complex images. We will find that, for simple images, anchoring depends on two dimensions of the stimulus: relative luminance and relative area.

3.1. What are minimal conditions?

Katz (1935) and Gelb (1929) were among the first to observe that the visual perception of a surface requires the presence of at least two adjacent regions of non-zero luminance. Wallach (1963 p. 112) noted: "Opaque colors which deserve to be called white or gray, in other words "surface colors," will make their appearance only when two regions of different light intensity are in contact with each other..." Ideally these minimal conditions would be met by a pair of surfaces that fill the entire visual field (Koffka, 1935, p. 111). One can, for instance, use the inside of a large hemisphere painted in two gray shades to cover an observer's entire visual field. Heinemann (1971, p. 146) has expressed a common view that the "simplest experimental arrangement for studying induction effects" consists of two surfaces presented within a void of total darkness. In our view, however, these conditions only approximate the simplest, because there are at least three regions in the visual field, including the dark surround, instead of two. There are two borders rather than the minimum of one.

3.2. Highest Luminance versus Average Luminance

Which rule is correct under such minimal conditions, Wallach's highest-luminance-as-white rule, or Helson's average-luminance-as-middle-gray rule? This question cannot be answered when the stimulus contains the entire gamut of gray shades from white to black because in that case the two rules make the same predictions. The most direct test of these two rules is to present an observer with a truncated gray scale; an array of luminances whose range is substantially less than the 30:1 range between white and black.

Combining a truncated gray scale with simple conditions, we placed observer's heads inside a large acrylic hemisphere, the inside surface of which was divided into two halves of equal size (Li and Gilchrist, in press). One half was painted completely matte black; the other half middle gray. The middle gray half was seen as fully white and the black half as a darkish middle gray. All observers reported this result and the variability was very low. This outcome decisively favors the highest luminance rule over the average luminance rule.

Other findings, using more complex stimuli, agree with this conclusion. In a separate line of work, Gilchrist and Cataliotti (1994) presented observers with a flat Mondrian containing 15 rectilinear pieces of gray paper, spanning only a 10:1 reflectance range (from black to middle gray). The Mondrian was illuminated by a special projector and presented within a relatively darkened laboratory and observers indicated their perceptions by making matches from a separately housed and lighted 16-step Munsell scale. In a further experiment (Cataliotti & Gilchrist, 1995), we placed observers heads inside a small trapezoidal shaped empty room, all the walls of which were covered with a Mondrian pattern spanning an even smaller range (4:1). In both of these Mondrian experiments, the highest luminance was perceived as white and no black surfaces were seen.

The results for all three tests are shown in Figure 4. Notice that in all cases the highest luminance is perceived as white, even if it is physically a dark gray surface. Notice further that the symmetry implicit in the average luminance rule is missing from these results. Although a perceived white is always present in the scene, it is not always the case that a perceived black is present in the scene, and the perceived values do not distribute themselves symmetrically about middle gray.

The two rules have been tested indirectly in several experiments on "equivalent surrounds." Bruno (1992) asked observers to make a brightness match between two target squares of equal luminance, one surrounded by a homogeneous region and one embedded in a checkerboard or Mondrian-like region. The luminance of the homogeneous surround that is chosen by the observers as having the same effect on a target as the checkerboard is a luminance value close to that of the highest luminance in the checkerboard not the average. Schirillo and Shevell (1996) presented a similar pair of displays to observers, but asked them to make a brightness match between a target square on a checkerboard and one on a uniform background of the same average luminance, as the checkerboard contrast is increased from 0% to 100%. Their results for increments (regions with a luminance higher than that of the surround) agree with those of Bruno, but their results for decrements show a different pattern (see also Bruno, Bernardis, and Schirillo, in press).

McCann (1994) has recently shown with chromatic Mondrians that, if the average color is held constant while the maximum excitation in a cone channel is varied, perceived colors in the Mondrian change. But if the maximum excitation in a cone channel is held constant while the average is varied, perceived colors change only slightly (see also Brown, 1994).

3.3. Luminosity Problem: Direct Contradiction to HLR

There is one phenomenon, however, that directly contradicts the highest luminance rule: the perception of self-luminous surfaces (Bonato & Gilchrist, 1994; Ullman, 1976). According to the highest luminance rule, white is a ceiling; nothing can appear to be brighter than white. But the fact is that we perceive various regions within the visual field to be self-luminous. This fact represents a serious challenge to the highest luminance rule.

To be fair to Wallach (1948, 1976), his support for the highest luminance rule was neither emphatic nor unambiguous. Wallach's systematic experiments were conducted only with decrements: disk/annulus displays in which the disk is darker than the annulus. Under these conditions it is an empirical fact that the higher luminance (the annulus) always appears white, regardless of its luminance. But Wallach reported informally that when the disk is an increment, that is brighter than the surrounding annulus, it appears luminous. The implication is that the highest luminance rule applies to decrements but not to increments. Here are his words: "We have seen that when two areas of different stimulus intensity exert their influence on each other, the area of lower intensity will be gray and the area of high intensity will be white. However, the correspondence between white and gray goes no further. When the difference in intensity is varied, the value of the gray changes; the gray may even turn black. If the spot is more intense, it will show no color other than white. An increase in the intensity difference will cause a different kind of quality, that is, luminosity, to appear in addition to the white and a further increase will merely cause luminosity to become stronger." (Wallach, 1976, p. 8) Thus, the luminosity that occurs with increments directly contradicts Wallach's Highest Luminance Rule.

If the highest luminance rule can be applied only to decrements, what rule could apply to both decrements and increments? The common denominator appears to be a geometric factor, not a photometric factor: it is always the annulus that appears white, both in decrements and in increments. So far, anchoring rules have been considered only in terms of luminance relations. This observation suggested that spatial relations play an important rule.

Wallach's disk/annulus stimuli lend themselves readily to a figure/ground analysis and Gilchrist and Bonato (1995) formulated the hypothesis that lightness values are anchored, not by any special luminance value, but by the surrounding or background region. The rule, which they called the surround rule says that for simple displays, lightness is anchored by the surround, which always appears white. Gilchrist and Bonato tested the surround rule against the highest luminance rule using both a disk/annulus configuration and a disk/ganzfeld configuration. The disk/annulus experiment produced data roughly consistent with the surround rule but with some influence of the highest luminance rule. The disk/ganzfeld data were completely consistent with the surround rule.