The Perception of Luminosity on Different ... - SAGE Journals

Perception, 1994, volume 23, pages 991-1006

The perception of luminosity on different backgrounds and in different illuminations Frederick Bonato Upsala College, East Orange, NJ 07019, USA Alan L GilchristH Institute for Cognitive Studies, Rutgers University, Newark, NJ 07102, USA Received 5 August 1992, in revised form 1 March 1994

Abstract. Observers were presented with target surfaces of varying luminance and asked to report whether they appeared luminous or opaque. In one experiment the targets were presented against three backgrounds, white, gray, and black. In another experiment the targets were presented within Mondrian patterns that were either brightly or dimly illuminated. The results indicate that, across a 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, whether or not a white surface is available in the visual field for comparison. Defined in this way the luminosity threshold exhibits the two main kinds of constancy characteristic of surface grays, constancy with respect to changes in the illumination level and constancy with respect to changes in the reflectance of the immediate background. This finding, while challenging a range of potential rules, places the problem of defining the conditions that produce luminosity squarely within the problem of lightness perception for opaque surfaces. 1 Introduction The perception of luminosity, of surfaces that appear to emit light, raises a very interesting problem. Glowing objects, such as light sources, stand out dramatically in perceptual experience. And yet very little is known as to how the visual system identifies glowing surfaces. The same problem confronts machine vision. Just as there is no program that can determine the whiteness or blackness of surfaces in a video image, so it is no more possible to distinguish luminous surfaces from opaque surfaces. This is remarkable given the qualitative difference between the appearance of luminous regions and the appearance of opaque surfaces. There is very little published research on perception of luminosity. One wonders whether this is because the problem seems so unchallenging, or because of the difficult challenge that it actually poses. In his 1976 book Wallach discusses the various geometric and photometric relations that he found, in his classic experiments (Wallach 1948) with disk/annuli patterns, would produce the appearance of luminosity. The simplest condition that produces a luminous appearance is also the simplest condition of visual stimulation, a completely homogenous visual field known as a ganzfeld. Wallach points out that a relationship between two different intensities of light is a necessary condition for the perception of an opaque surface lightness. Conditions that do not favor such a relationship tend to produce luminosity, specifically when (i) there is a strong difference in the area size of the two regions, (ii) the difference in intensity is too great, (iii) the length of border between the two regions is limited, or (iv) the regions are separated by a spatial interval of low intensity. According to Wallach, the perception of an opaque surface is the result of an 'interaction process' involving an unspecified neural interaction (not lateral inhibition) between activation produced by a surface and activation produced by its neighbor. He presents the hypothesis that "luminous appearance is the outcome of stimulation by neutral light U Author to whom requests for reprints should be addressed.

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whose effect on the nervous system does not participate in a surface color process" (page 10). This does not simply mean that surface color and luminosity are alternative outcomes. Even when two adjacent intensities produce the appearance of a surface color, there can be some light (or rather its neural correlate) that is left over and takes part in a 'residual process' that produces a luminous appearance. Wallach described conditions that can produce a curious appearance. When a disk is brighter than the annulus that surrounds it, the annulus takes on the appearance of translucent gray. The same dual appearance can occur in the disk if the area of the annulus is so reduced that it forms merely a thin ring around the disk, even if the annulus is brighter. Wallach's view that surface grays depend on differential stimulation whereas luminosity depends more simply on the light intensity per se makes sense, and it can arguably be applied to these cases of translucent gray. But Wallach reported another condition that does not seem consistent with his account: the disk will appear luminous when it is completely surrounded by light of lower intensity, that is, when the disk is an increment. This effect is independent of the area of the annulus. Luminous appearance under these conditions does not seem to flow from Wallach's analysis because (i) there is differential stimulation, (ii) the difference is not too large, (iii) the two regions are completely adjacent, and (iv) the outcome depends little on the relative areas. These conditions would seem to favor the surface-color process completely. Logically the disk should appear white and the surrounding region should appear some shade of gray. The luminous appearance of the disk in this case seems to require some factor not contained in Wallach's account. This is not to diminish Wallach's ground-breaking work in this area but rather to show the difficulty facing a theory of luminosity. Although the familiar experience of luminosity is produced by a wide range of circumstances, no one has yet been able to define what conditions of stimulation are common to all these cases. Lie (1977) has reported data on Wallach's case of an increment surrounded by an annular region. His study was concerned with, in his words, "the perception of local illumination, here called the colour/shadow discrimination, and its psychophysical basis" (page 251). By color/shadow discrimination, Lie is referring to what has been called edge classification—the discrimination of reflectance edges from illuminance edges (Gilchrist 1979; Gilchrist and Jacobsen 1984; Gilchrist et al 1983). After discussing factors that play a role in this discrimination in natural scenes, such as penumbra and luminance range, Lie reports two experiments that tested this discrimination under simple laboratory conditions, the first of which involves the same configuration, albeit with square regions, as Wallach's disk/annulus surrounded by darkness. Keeping the luminance of the annular region constant, Lie increased the luminance of the surrounded square until the observer felt sure that the two fields were differently illuminated. This produced a threshold that is closely related to what we are calling the luminosity threshold. His results will be compared with ours later in this paper. Evans (1959) has examined the problem of luminosity, especially in the context of chromatic color. He introduced the term fluorence as the perceptual equivalent of fluorescence, a term that is applied to surfaces that, although they do not appear to actually emit light, nevertheless appear to have a glowing quality. For achromatic surfaces, Evans applies the term fluorence to surfaces that have a luminance greater than white, but less than that at which they begin to appear to emit light. Imagine a middle-gray surface embedded in a rich context such as a Mondrian. If the luminance of that target is increased, without changes in any other part of the visual field, the target will first increase in apparent lightness until it comes to appear white. Then as its luminance increases slightly above that of white, the target appears fluorent.

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Finally, at a certain luminance, which we will call the luminosity threshold, the surface-color mode of appearance (Katz 1935) gives way to the illuminant mode, and the target begins either to appear to be a source of light or to have a level of illumination different from that of the surrounding context. Evans showed that chromatic surfaces, unlike achromatic, begin to appear fluorent at a luminance less than that of white, the more so as the purity of the target increases. Ullman (1976) has given a well-reasoned analysis of the problem of visual detection of light sources, particularly with regard to inadequacy of a number of intuitive models. He presents a mathematical model that, although not tested with humans, has been implemented on a computer system. Given the limited description that Ullman has provided of his methods, we have focused mainly on the strength of his logical arguments. He examines and rejects the following six possible rules for identifying a light source: (i) the highest intensity in the visual field, (ii) high absolute intensity value, (iii) local contrast, (iv) global contrast, (v) intensity compared with the average intensity of the scene, and (vi) lightness computation. The first of these factors, highest intensity in the field, is an obvious possibility, but it is neither necessary nor sufficient. A weak light source in a relatively shadowed part of the scene can appear to glow even though its intensity may be less than that of a white surface in bright illumination. Some scenes do not contain a visible light source at all, and the highest intensity does not appear to glow. It is interesting to note in this regard that the highest intensity has also been nominated (Horn 1974; Land and McCann 1971; Wallach 1963) as the white standard by which lesser shades of grey are defined. Clearly the highest intensity cannot be used to define both luminosity and white, and in fact it can define neither consistently. We provide evidence in experiment 3 that luminosity is perceived at intensity levels far below the highest in the field. There is certainly no absolute level of intensity at which an object begins to appear luminous. A disk of light seen against a totally dark background appears to glow at all intensity levels, even at very low intensities as long as it can be seen at all. Ullman's third candidate, local contrast, fails because it is just as much a product of the reflectance of the surround as of the intensity of the center itself. We confirm this in experiment 1. Global contrast, which refers to the overall luminance range within the field, fails for analogous reasons. As for intensity compared with the average intensity of the scene, Ullman points out that replacing all the papers in a Mondrian with darker-gray papers is not likely to lower the luminosity threshold. Ullman argues that the lightness algorithm of Land and McCann (1971) that separates sharp intensity changes from gradual ones does not help much. Given that light sources often have sharp boundaries, the problem of whether the highest luminance is white or glowing still remains. Ullman proposes the following method for detecting a light source: "Given two adjacent areas, compute both their intensity-ratio and their gradient ratio, and compare the two. If the ratios are not equal, one of the areas is a light source" (page 209). We will discuss Ullman's method in the context of our results, which suggest that perception of luminosity is closely associated with perception of surface color. In general, the goal in our work was to begin to establish a body of data concerning the perception of luminosity. Our method was to increase systematically the luminance of a target surface within a scene and measure the luminance at which it begins to appear luminous. We refer to this luminance as the luminosity threshold. We studied

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the effect on this threshold of two changes in the scene, a change in the level of illumination and a change in the background that surrounds the target surface. These are the two main challenges to constancy that have been studied in the perception of surface color. Together they provide an empirical test of every one of the potential rules discussed by Ullman. Our experiments were conducted with relatively naturalistic displays, both for ecological validity and because the distinction between luminosity and surface color is more ambiguous in simpler displays. In experiment 1 we tested the luminosity threshold on backgrounds of three different reflectances. This experiment was a test of the hypothesis that the luminosity threshold can be defined in terms of the local-contrast ratio of the target against the alternative hypothesis that the threshold exhibits a kind of constancy that takes into account the perceived lightness of the background. 2 Experiment 1 2.1 Method 2.1.1 Laboratory arrangements. Observers viewed one end of a laboratory room monocularly by looking through a pinhole mounted in the center of a large, rigid partition. They saw a square target surface (2.5 deg square) centered on a large black, white, or gray rectangle (7.2 deg by 9.5 deg) mounted on the far wall of the laboratory, as illustrated in figure 1. Although the square target appeared to be coplanar with the large rectangle, it was in fact much closer to the observer. It was 55 cm from the observer's eye, mounted in the center of a large (66 cm x 122 cm) sheet of clear glass. Figure 2 shows the laboratory arrangement. The glass was fixed in a position 7° away from parallel to the partition. This modest slant was necessary to prevent the right-hand edge of the target square from making a visible reflection in the glass and to move the reflection of the light source farther to the right, out of the way. Each target was a piece of Munsell paper, 2.5 cm square, mounted on a wedge of aluminium, 15.9 mm square.

Figure 1. The visual field as seen by observers in experiment 1. The luminance (in cd m 2) of various surfaces in the laboratory is indicated.


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The aluminum wedge, which compensated for the slant of the glass, was mounted in the center of the glass sheet by means of an aluminum peg that protruded from the rear and fitted snugly through a hole drilled in the glass sheet. This peg allowed targets to be changed quickly and without touching the glass. The background consisted of a 46 cm by 61 cm sheet of white, black, or gray Color-Aid paper cemented onto a piece of plywood 0.64 cm thick, 46 cm high by 61 cm wide, that was mounted on the rear wall of the laboratory, 3.6 m from the observer's eye. The only illumination was provided by a 250 W quartz bulb mounted behind and 25 cm to the right of the pinhole. The reflection of the light source in the glass was obscured by a metal baffle located between the pinhole and the bulb. The slant of the glass had the advantage of moving this reflection further to the right, allowing a wider field of view. Because the rectangular background was 5.5 times as far from the light source as the target, the intensity of illumination was 30 times greater on the target than on the background owing to the inverse-square law of illumination. These proportions were calibrated by placing a black (Munsell 2.0, reflectance 3.1%) target on the glass and a white (Munsell 9.5, reflectance 90%) background on the far wall. The glass was then moved closer to or farther away from the viewing pinhole until the target disappeared; that is, until the target and the background had the same luminance. At this point, of course, the illumination on the target was greater than the illumination on the background by exactly the same proportion as the reflectance of the background was greater than the reflectance of the target. Thus as the target reflectance moved up the Munsell scale from black, the target luminance moved above that of a white background.

Figure 2. Laboratory arrangements for experiment 1. See text for details.

2.1.2 Design. The seven targets had reflectances of 0.031, 0.046, 0.066, 0.090, 0.12, 0.156, and 0.198, with corresponding luminance values of 12.86, 17.22, 26.99, 38.07, 49.39, 64.14, and 75.46 cd m~2. The three backgrounds were black, gray, and white, with, respectively, reflectances of 0.031, 0.198, and 0.90, and luminances of 0.41, 1.99, and 11.52 cd m~2. Each of the seven targets appeared on all three backgrounds. This resulted in twenty-one possible stimuli, all of which were presented to each subject twice in random order.

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2.1.3 Procedure. The observer was escorted into the laboratory and seated in front of the viewing pinhole. The experimenter then set the lighting conditions and read the following instructions. "In this experiment you will be asked to make judgments about whether or not a surface appears to be glowing; I mean that the surface appears too bright to simply be a piece of white paper. When looking through the pinhole in front of you, you'll notice a rectangular shaped area on the far wall and underneath the clock. The target to be judged will always be the square patch which is embedded within this rectangle. After each presentation of the target you will tell me whether or not the square patch appears to be glowing or not glowing. Immediately following this procedure there will be a brief rest period during which nothing will be visible through the pinhole. After this rest period the previous sequence of events will be repeated until the end of the experiment. There will be 42 judgments in all. Are there any questions?" If the observers had no questions the experimenter opened an aluminum shutter and directed the observer to look through the pinhole, locate the target square, and make a forced-choice report. The experimenter then recorded the observer's response, closed the shutter, changed the target square, and opened the shutter, thus marking the beginning of the next trial. After all trials were completed, the experimenter interviewed the observer about his or her visual experience, and then revealed the actual setup. 2.1.4 Observers. Ten naive undergraduates served as observers, their participation being part of a course requirement. 2.2 Results and discussion The main results are shown in figures 3 and 4. In figure 3 the percentage of luminosity reports are plotted as a function of the local contrast, or luminance ratio. Defining the luminosity threshold in this way produces three separate ogive functions, with thresholds at target:background ratios of 2.2, 9.5, and 63 for the white, gray, and black backgrounds, respectively. This makes it clear that the luminosity threshold is not a simple function of local contrast. In figure 4 the percentage of luminosity reports are plotted as a function of the ratio between the luminance of the target and the luminance of a white background, whether or not the background happens to be white. Here we find that the three curves become dramatically coincidental, with a threshold ratio of 2.2. 100

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10 100 Luminance ratio Figure 3. Percentage of luminosity reports as a function of the ratio of the luminance of the target to that of the background.

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If it could be assumed that a white background in our display actually appears white then we could conclude that a surface begins to appear luminous when its luminance is 2.2 times that of a good white surface. But we know from other work that this assumption is not valid. When a target is presented against a background and the luminance of the target is increased, there are, logically, two possible effects. One is that the target moves up toward luminosity. The other is that the surround begins to move down into the gray range. Here we encounter what can be called the anchoring problem (Cataliotti and Gilchrist, in press; Gilchrist and Bonato, in press). If anchoring follows the widely invoked rule that the highest luminance in the scene appears white (Horn 1974; Land and McCann 1971; Wallach 1963) the target ought to continue to appear white as the surround becomes darker gray. But if the surround were to serve as the anchor, as it does in motion perception (Duncker 1929; Wallach 1959), then the lightness of the surround would appear to remain constant and the target would become increasingly luminous. We have recently shown (Gilchrist and Bonato in press) that both of these happen in the disk/annulus configuration, although the larger effect is the brightening of the center. The relative strength of these two effects probably depends on factors such as visual angle and the complexity of the scene in which it is embedded (Katz 1935). Although we did not measure the lightness of the surround in experiment 1, we did measure it under almost identical conditions in a subsequent experiment (Bonato and Gilchrist 1993). There we found that a white background with a reflectance of 90% is perceived as a light gray, with a reflectance of 65%. We used this value to calculate how much brighter than a perceived white (as opposed to physical white) a surface must be before it appears luminous. Our calculation was performed simply by dividing our obtained value of 2.2 by the ratio of the physical reflectance of the white background (90%) to its perceived reflectance (65%), which yielded a value of about 1.6. This means that our target began to appear luminous when its luminance value was 1.6 times as bright as a surface that appeared opaque white. This distance of 1.6 on the perceptual scale is the region that Evans characterized as exhibiting fluorence. We can now compare our results, obtained by using a relatively complex setting, with those of Lie (1977), who used a center/surround display in a dark environment. He found a threshold ratio of 4 : 1 . This threshold ratio is much higher than our ratio of 1.6, but there are two factors that resolve the discrepancy. First, we must perform 100

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3 4 Luminance ratio

Figure 4. Percentage of luminosity reports as a function of the ratio of the luminance of the target to that of a white background.

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the same kind of correction on Lie's threshold that we have just described for our own. Lie did not measure the perceived lightness of his surround region. We have done that (Bonato et al 1992) under the same simple conditions that Lie used, and found that at Lie's 4:1 threshold ratio the surround appears about 7.5 in Munsell value (reflectance 51%). Taking into account this perception of Lie's surrounding annulus, we can calculate that the threshold he obtained was approximately 2.3 times higher than perceived white. This value is still higher than our value of .1.6 and the remaining difference can be attributed to Lie's definition of the threshold. The observers were asked to report when a luminance level had been reached at which they felt sure that the two fields were differently illuminated. By comparison, we defined the threshold as the luminance at which the target was reported to be luminous 50% of the time. Lie's definition would probably correspond to a level of 75% or 80% reports of luminosity, and, as can be observed in figure 4, at that level our display also had a target:background ratio of about 4. Our results also seem to agree with those of Wallach (1976), who used a disk/ annulus display, although Wallach's report concerning luminosity is mainly qualitative. He reports that the disk begins to appear luminous when its luminance is at least two times that of the surrounding annulus. Our results seem to indicate a remarkable ability of the visual system to know the white level without a white surface nearby, and raises the very pregnant question of how the white level is determined. In a general sense, we can conclude that perception of luminosity, as perception of surface lightness, is not a local affair; it depends on global stimulus relations throughout a larger region of the visual field and it probably depends on temporal relationships among successive visual images. More specifically we can suggest two ways in which the luminosity threshold could be closely linked to the white level, even when the surround is not white. One possibility is that the target is linked to other white surfaces in the visual field via a process of edge integration. As Land and McCann (1971, page 1) have pointed out, "the eye cannot insert a comparison standard next to the object which it is regarding". However, their process of taking sequential products gives the visual system the capacity it would have if a comparison standard could be inserted next to any object of interest in the field. The local ratio required for a luminous appearance is directly tied to the perceived lightness of the background, which in turn depends, as has been amply shown (Gilchrist 1979; Krauskopf 1963; Wallach 1948), on the ratio at the border of the background. Thus the luminosity threshold depends on the integration of at least these two edges. This also implies that the abscissa in figure 4 could as well be labelled 'integrated ratio'. A second possible way to account for the results of experiment 1 involves temporal relations. In experiment 1 the luminance of the surrounding rectangle varied from trial to trial by a maximum factor of 30, as white, gray, and black backgrounds were presented in random order. One would expect those variations to be perceived as a change in the reflectance of the rectangle, not in the illumination level, given that luminances in the larger laboratory context did not also vary in this way. This in turn would imply that the surround with the highest luminance is white and that with the lowest is black, thus allowing the luminance of white to be extrapolated on trials in which the surround is either gray or black. A closely related hypothesis is that the luminosity threshold is defined by a constant luminance value (maintained in memory), given that the illumination level is perceived to remain constant. In any case, these results show that the luminosity threshold enjoys a kind of lightness constancy. The term lightness is appropriate here, even though it implies a surface quality, because the luminosity threshold defines the high end of the lightness dimension. The term constancy here refers to the stability of lightness in the face of


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changes in background reflectance, not the more usual changes in illumination level. This kind of constancy with respect to changes in the reflectance of the background has only recently been appreciated for surface colors. As long as the basic input to the lightness system was assumed to be absolute luminance values, the obvious constancy problem was how lightness could remain constant under changes in illumination that changed the luminance of a surface. As this 'photometer metaphor' began to give way to the view that relative luminance (ratios at borders) is the more important input, a new constancy came into focus. How can lightness remain constant when the background against which a surface is seen changes, thereby changing the luminance ratio at the border of the surface. Whittle and Challands (1969), who produced some of the clearest evidence for the basic nature of relative luminance, were among the first to discuss this second type of lightness constancy. Gilchrist (1988) measured this kind of constancy along with the traditional kind of constancy with respect to change in illumination level, finding an approximate parity in strength of the two kinds. 3 Experiment 2 It can be seen from the results of experiment 1 that observers behave as if they know the luminance value of white, even when the background of the target is gray or black. One way to account for these results is that other white surfaces in the field of view are being used as the standard, even if those surfaces are not adjacent to the target. There is plenty of evidence to indicate that the visual system is capable of comparing the luminance values of surfaces that are widely separated in the visual field, presumably by means of some kind of edge integration process (Arend et al 1971; Gilchrist et al 1983; Land and McCann 1971; Whittle and Challands 1969). In experiment 2 we tested the role of other remote white surfaces by eliminating all white or light gray surfaces from the observer's field of view. In a separate condition of experiment 2 we also eliminated all glossy highlights. Removal of the highlights was not motivated by any specific hypothesis as to their role. However, in the perception of chromatic surface color, it has been proposed that specular highlights are used by the visual system to determine the illuminant color (Healey and Binford 1987; Lee 1986; Shafer 1985), and it is at least plausible that such highlights could convey information about the intensity of the illumination (Beck 1964; Flock 1984). In that case the luminance of the target could be compared with the inferred intensity of illumination (or perhaps directly with the luminance of the highlight) to determine the maximum luminance value that an opaque (white) surface could have. 3.1 Method The method was identical to that of experiment 1, with four exceptions, (i) In condition 1 all surfaces with a reflectance value greater than 5 1 % (Munsell 7.5) were covered with either matte gray paper (reflectance 20%; Munsell 5.0) or black cloth. (ii) In condition 2, in addition to the light-gray surfaces, all non-Lambertian surfaces producing specular highlights were also covered, (iii) One group of ten observers served in condition 1 and a separate group of ten served in condition 2. (iv) Trials on which the white background was presented were not intermixed with trials on which the gray or the black backgrounds were presented. Instead, a block of trials was first presented that included all the trials involving either the gray or the black background. After this a separate block of trials was presented that included only the trials involving the white background. This was done so that white surfaces, in addition to being eliminated from the visual field, were also eliminated, at least in the gray and black background trials, from any preceding trials.

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3.2 Results and discussion The results were essentially the same as in experiment 1. That is, there were no significant differences among the luminosity thresholds obtained on the white, gray, or black backgrounds, defining the threshold in terms of the luminance of the target relative to the luminance of a perceived white. None of the thresholds obtained either in condition 1 or in condition 2 differed significantly either from each other or from those obtained in experiment 1. These results indicate that the presence of either white surfaces or specular highlights in the visual field is not necessary for the kind of constancy exhibited by the luminosity threshold in experiment 1. They demonstrate that results such as those of experiment 1 can be obtained even when the target cannot be related to a white surface through edge integration because there is no white surface in the field. Nor could those results be attributed to the memory of a previously presented white background because all the trials with gray and black backgrounds were presented before any of those with the white background. This does not rule out the possibility that either temporal or spatial integration of luminance relationships is exploited when it is available. It might be noted that the failure of removal of the highlights to influence our results is consistent with Hurlburt's (1989) findings that specular highlights are ineffective as indicators of the illuminant color. 4 Experiment 3 The results of experiments 1 and 2 can be interpreted in two different ways. Although, as we have noted, the luminosity threshold occurred at the same value relative to the lightness scale, namely a certain reliable distance above white, it also occurred at the same absolute luminance value for all three backgrounds. In experiment 3 we tested which of these two interpretations is correct by measuring the luminosity threshold in differently illuminated regions of a complex image. If the first of these interpretations is correct it would imply that the luminosity threshold is subject to both kinds of lightness constancy—that with respect to different backgrounds (type II) and that with respect to different levels of illumination (type I). This would also imply the interesting result that a target surface located in a shadowed part of the scene could appear luminous at a luminance value far below the highest within the scene. 4.1 Method \ 4.1.1 Apparatus. The stimulus consisted of a pair of achromatic Mondrians, joined to form a dihedral angle, and suspended in the center of a vision tunnel by means of a horizontal aluminum rod, as shown in figure 5. The aluminum rod, hidden to the observer by the Mondrians, was anchored to the center of a square translucent panel that served as the back wall of the tunnel. Rear illumination of the translucent panel by a 150 W light bulb produced a homogeneous background of 192 c d m " 2 for the Mondrians, with no shadow of the aluminum rod. Each Mondrian was illuminated by light coming through a window in its corresponding side wall of the tunnel, from a 150 W floodlight bulb controlled by a rheostat and located 48 cm from the Mondrian. In the 'highly illuminated' condition the Mondrian on the left received thirty times more illumination than the Mondrian on the right. In the 'dimly illuminated' condition these intensities were reversed. Each Mondrian was composed of a random distribution of twenty rectilinear pieces of matte paper, drawn approximately equally from six gray shades: 90%, 59%, 36%, 20%, 9%, and 3%. The target, although appearing as a surface coplanar to the other elements of the Mondrian, was actually an aperture 2.3 deg square in the left-hand Mondrian. The light that filled this aperture was the surface of a rectangular panel


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(8.9 cm by 6.4 cm) of Color-Aid paper mounted in a holder at 45° to the line of sight. This panel was illuminated, via slanted mirrors, by one (for the dimly illuminated condition) or two Kodak Carousel slide projectors located on top of the tunnel. Because, as Evans (1959) has shown, chromatic targets reach luminosity at lower levels of luminance and because we chose to restrict our study to the achromatic domain, it was necessary to equate the chromaticity of the projector light to that of the Mondrian. This was accomplished as follows. First the luminance of the target was equated to that of an opaque white surface in the same plane. It is well known that small chromatic differences become most salient at equal luminance. Gelatin filters were then placed in the path of the projector beams to nullify this chromatic difference. This in turn produced a small inequality in luminance, and the process was repeated until no differences in either luminance or chromaticity could be detected. The observer sat in a viewing booth at one end of the tunnel and viewed the display through a pair of circular aperatures 2.5 cm in diameter, each of which was mounted in a panel that could slide to adjust for interocular distance. Parallel sliding panels served as shutters. Figure 6 illustrates the display as seen by the observer. A line drawing corresponding to this display was located on a slanted shelf just above the observer's lap. The target region was indicated by an X on this diagram, along

translucent panel

illumination window

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8 -a > > target aperture

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^ (b) Figure 5. Vision tunnel used in experiment 3. (a) Side view, (b) top view. For explanation, see text.

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with six additional numbered regions (a white, a gray, and a black adjacent to the target, and one of each nonadjacent) that were also judged. This diagram and a sixteen-step Munsell chart on the same shift were both illuminated by a hidden 20 W fluorescent bulb located 25 cm above the shelf. The Munsell chart was composed of sixteen chips (1.3 cm by 2.5 cm) graded from 2.0 (3%) to 9.5 (90%), mounted on a piece of white cardboard 10 cm by 30 cm.

Figure 6. Visual field as seen by observers in experiment 3. The target area is indicated by an 'X' and the additional target panels are numbered 1-6.

4.1.2 Design. The six target panels had reflectance percentages of 16, 20, 30, 42, 68, and 90, producing, respectively, luminances (in cdm~ 2 ) of 1026, 1286, 1904, 2675, 4116, and 5797 in the highly illuminated condition and 34, 45, 65, 93, 141, and 196 in the dimly illuminated condition. The six target values were presented twice, in random order. 4.1.3 Procedure. The observer was escorted into the laboratory and seated in the viewing booth. The room lights were turned off and the following instructions were read. "In this experiment you will be asked to do two things. Your first task will be to make judgments about whether or not a surface appears to be glowing. By glowing, I mean that the surface appears too bright to simply be a piece of white paper; for example, it may appear to be emitting light from within. If you look down you will see a drawing of the display you are about to see through the eye holes in front of you. I want you to tell me whether or not the area marked with the 'X' is glowing or not. It will always be the same area from trial to trial; however, you can check back to the drawing at any time should you feel the need to do so. In addition to this task, three of the trials will entail a second task. On these trials I will ask you to judge the color of six other surfaces in the display. These are numbered from one to six on the drawing above your lap. When I ask you about these surfaces I want you to pick from the chart in front of you the color which most closely matches the color of the area of the display. Immediately following each trial there will be a brief rest period at which time nothing will be visible through the eyeholes. There will be twelve trials in all. Do you have any questions?" If there were no questions, the experimenter opened the shutters and began the first trial. On the first, third, and fifth trials the observer was asked to judge the six opaque surfaces (in random order) in addition to judging the luminosity of the target. This was done to compare the perceived gray levels, especially white, with the physical gray levels. After all trials were completed, the experimenter interviewed the observer about his or her visual experience, and then revealed the actual setup.

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4.1.4 Observers. Twenty naive undergraduates served, ten each in the highly illuminated and the dimly illuminated conditions. 4.2 Results and discussion It can be seen from figure 7 that when the luminosity judgments are plotted with respect to a single standard, such as absolute luminance, as in this case, or the highest luminance in the visual field, two distinct functions emerge, giving two different threshold values. In figure 8 these two functions become almost identical if we define the abscissa as the ratio between the luminance of the target and the luminance that appears white in the same plane. Note the two components in this revised definition. First, the threshold is defined relative to a white surface in the same plane (Gilchrist 1977, 1980). Second, the definition refers to perceived white, not physical white. Matches made to the various opaque papers in the Mondrian revealed that, as before, a physical white was not perceived as fully white, especially in the shadowed Mondrian. It appeared light gray, or about 8.25 on the Munsell scale. Therefore we applied the same correction as described for experiment 1. The resulting measure, target luminance relative to perceived white, gives threshold values of 1.7:1 on the shadowed side and 1.8:1 on the illuminated side, close to the 1.6 value obtained in experiment 1.

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5 General discussion The results of these experiments challenge every one of the rules criticized by Ullman (1976). (i)In experiments targets in the shadowed Mondrian appeared luminous at luminance levels far below the highest luminance in the field, which would have been a white surface in the illuminated Mondrian. (ii) The fact that the luminosity threshold in the illuminated Mondrian was about thirty times higher than that of the shadowed Mondrian demonstrates that the threshold is not associated with any absolute value, (iii) In experiment 1 luminosity thresholds were produced at local contrast ratios of 2.2:1, 9.5:1, and 6 3 : 1 , showing that the threshold is not uniquely associated with any level of local contrast, (iv) Ullman defined global contrast as the contrast between the light source and the darkest area in the field. It was shown in experiment 3 that luminosity cannot be defined this way because, relative to the lowest luminance in the visual field, the luminosity threshold was much higher on the illuminated Mondrian than on the shadowed Mondrian. (v) In experiment 1 we showed that the luminosity threshold cannot be defined as the luminance of the target relative to the average intensity in the scene because the absolute intensity at threshold remained constant despite substantial changes in the average scene intensity as the black background was substituted for the white background. The same conclusion can be drawn from experiment 2. There the removal of light grays and glossy highlights from the visual field substantially lowered the average intensity in the scene and yet thresholds were unaffected, (vi) It was demonstrated in experiments 1, 2, and 3 that the separation of sharp from gradual luminance changes, as proposed by Land and McCann (1971) and Horn (1974) does not help the detection of luminosity because the boundary of the target is sharp whether it is luminous or merely white. Our experiments have thus provided empirical support for Ullman's logical arguments. However, our results also present a challenge for Ullman's method of comparing the gradient ratio on the two sides of a boundary with the luminance ratio on the two sides. These ratios were essentially equal in all of our conditions, yet we did obtain the appearance of luminosity at certain luminance values. To be fair, Ullman does not claim that if the ratios are equal no luminosity will be perceived. He says only that if the ratios are not equal, one of the areas is a light source. A Mondrian element having a luminance somewhere in the middle of the range will never appear luminous, regardless of the gradient relations at its boundary. Ullman's insight is valuable nonetheless. It is derived from the observation that the luminance gradients across a set of neighboring opaque surfaces fit into a consistent pattern (although ironically this means the gradients are unequal as he defines them).(1) The gradient across a luminous surface is not likely to be consistent with the gradient across neighboring surfaces. But it remains to be seen whether a surface can be made to appear to glow merely by giving it a gradient that is inconsistent with the gradients of the surrounding illumination field. We suspect that other relationships would also have to be satisfied for this outcome to occur. Ourj~esults suggest that the most important relationship would be that between the luminance of the target surface and the luminance that would be perceived as white, in the local context. This is fully consistent with Hering's suggestion (1879, page 575) that a surface must be brighter than white under the same conditions of illumination if it is to be characterized as luminous. We have been able to establish just how much brighter than white the target must be. We have found that the luminosity threshold shows little variation, between 1.6 and 1.8, when it is defined as the ratio between the luminance of the target and the W These gradients are equal on a log scale but unequal on Ullman's linear scale, for gradients of adjacent opaque surfaces standing in common illumination.


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luminance in the same plane that appears white, despite important variations in the nature of the stimulus display. One might argue that this is a trivial point, one that is true almost by definition. For example, it would be somewhat trivial to observe that perceived white is always about four Munsell steps above perceived middle gray, regardless of stimulus display. One might say this is true by definition. The importance, however, of the observation that the luminosity threshold is always about 1.7 times higher than perceived white lies in showing that the distance between the luminosity threshold and perceived white can be treated just like any other distance between two values of perceived surface lightness. This in turn implies that the luminosity threshold behaves as if it were a value of surface lightness. We believe that the luminosity threshold behaves like a lightness value because it is part of the lightness scale, even if only the upper boundary of the scale. Once that boundary is crossed, however, a new mode of appearance emerges (Katz 1935). We believe that target regions in this mode do not show constancy (see Arend and Goldstein 1987; Jacobsen and Gilchrist 1988). This implies that the luminosity threshold is very different from a luminosity match. Imagine, for example, two target surfaces are embedded within different contexts, such as the brightly and dimly illuminated Mondrians used in experiment 3. Very different results will be obtained depending on whether observers are asked either to set both targets to the luminosity threshold or to make the two targets equal in luminosity. For a luminosity match observers will try to set the two targets to approximately the same absolute luminance. But as shown in experiment 3, if both targets are set to the luminosity threshold, they will be equal in relative luminance, not absolute. We are currently conducting work to clarify this point. These findings indicate an exquisite sense of the white level by the visual system. This ability is all the more remarkable in light of the results of experiment 2, which show that a sense of the white level survives even when there are no whites or nearwhites in the visual field and even when no whites have been seen in previous trials. A full understanding of this sense continues to elude us, reaching, as it does, to the heart of the lightness-constancy problem. But a fair conclusion from our results is that the ability to predict when a surface will appear luminous will come hand in hand with the ability to predict the perceived lightness value of opaque surfaces in general. Acknowledgement. The authors wish to acknowledge the support of the National Science Foundation (grant numbers BNS-8909182 and DBS-9222104). References Arend L E , Buehler J N, Lockhead G R, 1971 "Difference information in brightness perception" Perception &Psychophysics 9 3 6 7 - 3 7 0 Arend L, Goldstein R, 1987 "Simultaneous constancy, lightness and brightness" Journal of the Optical Society ofAmerica A 4 2281 - 2285 Beck J, 1964 "The effect of gloss on perceived lightness" American Journal of Psychology 11 54-63 Bonato F, Gilchrist A, 1993 "The effect of target size and number on luminosity perception" Investigative Ophthalmology and Visual Science 34 781 Bonato F, Gilchrist A, Li X, 1992 "The anchoring rule for lightness perception under minimal conditions" Investigative Ophthalmology and Visual Science 33 1258 Cataliotti J, Gilchrist A L, in press, "Local and global processes in lightness perception" Perception & Psychophysics Duncker D K, 1929 "Uber induzierte Bewegung (Ein Beitrag zur Theorie optisch wahrgenommener Bewegung)" PsychologischeForschung 1 2 1 8 0 - 2 5 9 Evans R, 1959 "Fluorescence and gray content of surface colors" Journal of the Optical Society of America 49 1049-1059 Flock H R, 1984 "Illumination: Inferred or observed?" Perception & Psychophysics 35 293 Gilchrist A L, 1977 "Perceived lightness depends on perceived spatial arrangement" Science 195 185-187

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Gilchrist A L, 1979 "The perception of surface blacks and whites" Scientific American 240 112-123 Gilchrist A L, 1980 "When does perceived lightness depend on perceived spatial arrangements" Perception &Psychophysics 28 527 - 538 Gilchrist A L, 1988 "Lightness contrast and failures of constancy: a common explanation" Perception & Psychophysics 43 415-424 Gilchrist A L, Bonato F, in press, "Anchoring of lightness values in center/surround displays" Journal of Experimental Psychology: Human Perception and Performance Gilchrist A, Delman S, Jacobsen A, 1983 "The classification and integration of edges as critical to the perception of reflectance and illumination" Perception & Psychophysics 33 425 - 436 Gilchrist A, Jacobsen A, 1984 "Perception of lightness and illumination in a world of one reflectance" Perception 13 5 - 1 9 Gilchrist A L, Jacobsen A, 1988 "Qualitiative relationships are decisive" Perception & Psychophysics 45(1) 9 2 - 9 4 Healey G, Binford T O, 1987 "The role and use of color in a general vision system", technical report, Artificial Intelligence Laboratory, Stanford University, Stanford, CA 94305 Hering E, 1879 "Der Raumsinn und die Bewegungen des Auges", in Handbuch der Physiologie Ed. L Hermann, Band 3, Teil 1 (Leipzig: Vogel) [English translation by C A Raddle Spatial Sense and Movement of the Eye (Baltimore, MD: American Academy of Optometry, 1942)] Horn B K P, 1974 "Determining lightness from an image" Computer Graphics and Image Processing 3 2 7 7 - 2 9 9 Hurlburt A, 1989 The Computation of Color technical report 1154, MIT Artificial Intelligence Laboratory, Cambridge MA 02139 Jacobsen A, Gilchrist A, 1988 "The ratio principle holds over a million-to-one range of illumination" Perception & Psychophysics 4 3 1 - 6 Katz D, 1935 The World of Colour (London: Kegan Paul, Trench, Trubner, & Co) Krauskopf J, 1963 "Effect of retinal image stabilization on the appearance of heterochromatic targets" Journal of the Optical Society ofAmerica 53 741 - 744 Land E H, McCann J J, 1971 "Lightness and retinex theory" Journal of the Optical Society of America 61 1-11 Lee H C, 1986 "Method for computing the scene-illuminant chromaticity from specular highlights" Journal of the Optical Society ofAmerica A 3 1 6 9 4 - 1 6 9 9 Lie 1,1977 "Perception of illumination" Scandinavian Journal of Psychology 1 8 2 5 1 - 2 5 5 Shafer S A, 1985 "Using color to separate reflection components" Color Research and Application 10 210-218 Ullman S, 1976 "On visual detection of light sources" Biological Cybernetics 21 205-212 WallachH, 1948 "Brightness constancy and the nature of achromatic colors" Journal of Experimental Psychology 38 310 - 324 Wallach H, 1959 "The perception of motion" Scientific American 201 5 6 - 6 0 Wallach H, 1963 "The perception of neutral colors" Scientific American 208 107 -116 Wallach H, 1976 On Perception (New York: Quadrangle/The New York Times Book Co) Whittle P, Challands P D C, 1969 "The effect of background luminance on the brightness of flashes" Vision Research 9 1 0 9 5 - 1 1 1 0

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