Lightness and illumination: comments on Kingdom and Blakeslee and McCourt

Dejan Todorovic, University of Toronto


Todorovic's comments on Kingdom's chapter

Kingdom suggests that some strong lightness/brightness illusions, such as those demonstrated by Adelson (1993), Logvinenko (1999), as well as his own figure 12, can be accounted for by a Helmholtzian illumination-interpretive mechanism. I have criticized Adelson's theory (Todorovic, 1997), and Logvinenko's account (Todorovic, 1999), by producing displays with similar luminance distributions inducing similar perceptual effects, but for which the illumination interpretation is unlikely. I will try here to question Kingdom's explanation with the same strategy. As he notes, the problem is to construct adequate control stimuli. My first argument involves a series of structurally related displays, presented in Figure 1, and the possible explanations of the effects demonstrated in them.


Figure 1. Four displays and their luminance distributions. The graphs depict schematic spatial luminance distributions corresponding to the levels of the two horizontal dotted lines in the displays; the lines are indicated by two arrows, the full line in the graph corresponding to arrow A in the display, and the double-dot-dashed line corresponding to arrow B. The luminance distributions were not actually measured, but are displayed as specified by the computer graphics program that generated the displays; it may be assumed that the luminances specified as identical are printed as approximately equal, and that the ordinal luminance relations are preserved in the printout. The diamonds that belong to the same column within a display have the same luminance distribution. As indicated by the vertical dashed lines, the heavier printed portions of the graphs depict the portions of luminance distributions corresponding to diamonds denoted as a and b. In each display they have identical luminances, but look different. (a) Monotonic distribution. Luminance increases from left to right both along level A and level B, but starts with a lower value for B. The luminance distributions are for simplicity depicted as linearly rising, as they were specified as such by the computer graphics program, and may be assumed to be monotonic. (b) Discretized monotonic distribution. The monotonic distribution is replaced by a series of small steps. All individual diamonds have uniform luminances. The step increases are specified as numerically equal by the computer graphics program, and are depicted as such. (c) Step distribution. The left-hand portion of the display involves diamonds of only two different luminance levels, low and medium, and the right-hand portion also contains only two luminance levels, medium and high. Along level A the luminance steps up from medium to high, whereas along level B it steps up from low to medium. (d) Semi-inverted distribution. The display is the same as in (c), except that in the right-hand portion of the display, the patches that had a high luminance level in (c) have medium luminance level in (d), and vice versa. In consequence, luminance along level A is medium throughout, and along level B it steps up from low to high.

The display in Figure 1a is a slight variation of Kingdom's Figure 12. The difference is only in that the overall luminance variation is not sinusoidal but monotonic. Such a luminance distribution could be produced by a simple black-and-white checker-board pattern, exposed to a monotonic horizontal gradient of illumination. As in Kingdom's figure, the luminance distributions are identical for diamonds a and b, but a looks appreciably lighter than b. According to a version of the Helmholtzian account, this is because the perceiver interprets the luminance gradient as a variation in illuminance, and concludes that diamond a is light but dimly lit, whereas diamond b is dark but well lit.

Figure 1b is a discrete version of Figure 1a. The luminances of diamonds a and b are flat and identical, but they again look appreciably different. The overall impression of the display is much the same as for Figure 1a, and the same Helmholtzian account applies, assuming that in assessing illumination distributions the visual system cares mainly about lower frequency components.

The luminance distribution in Figure 1c is a coarse version of Figure 1b, in that, for both level A and B, the many small luminance steps are replaced by a single big step. There are only three luminance levels in the display. The diamonds a and b have the same, medium level, but again a looks appreciably lighter. I will assume that a consistent Helmholtzian theoretician would readily adopt the same type of account as for Figures 1a and 1b. The difference is only that the presumed illumination distribution is not gradual, as in Figure 1a, or quasi-gradual, as in Figure 1b, but abrupt, as if a sharp shadow or illuminance border had fallen upon the checker-board. Accepting this, one can still maintain that, as in Figures 1a and 1b, diamond a is perceived as light but poorly lit, and diamond b as dark but well lit.

However, this line of reasoning is called into question by the display in Figure 1d. The left-hand portion is identical as in Figure 1c; in the right-hand portion the geometry has stayed the same but the photometry is switched, in that the medium-luminance patches have assumed high luminance, and vice versa. In particular, diamonds a and b are physically identical but look different. Informally, their difference in appearance seems to be much the same as for diamonds a and b in Figure 1c. The crucial point is that, in contrast to Figure 1c, the luminance distribution in Figure 1d could not have been produced by a uniform vertically oriented shadow (or a spotlight) falling upon a checker-board. Instead, it is not hard to adopt an interpretation involving a matrix of gray diamonds (the left-hand ones light, and the right-hand one dark) standing in front of a bipartite black-white background, all uniformly illuminated. I assume that Figure 1d fulfills Kingdom's criterion of an adequate control for Figure 1c.

A Helmholtzian account, based on the claim that the perception of achromatic color may be affected by the knowledge that the visual system has accumulated about the physical properties of luminance distributions and their possible decompositions into reflectance and illumination distributions, thus appears to be inapplicable for Figure 1d. I will not discuss alternative explanations here, but an obvious hint is the fact that diamond a is bordered by patches of lower luminances, whereas diamond b is bordered by patches of higher luminances.

Now, if the irrelevance of the illumination account is accepted for Figure 1d, then it does not make much sense to adopt this account for the highly similar Figure 1c. But, if this is acknowledged, then, I would claim, the illumination-interpretation account for Figure 1b also becomes doubtful. This is because the luminance structures of the surrounds of diamonds a and b in Figures 1b and 1c are similar and seem to require similar accounts. It is not parsimonious to propose very different explanations for the appearances of the two diamond pairs in these two figures; therefore, if the illumination account is discounted for figure 1c, then it does not look promising for Figure 1b either. By the same reasoning, this account fails for Figure 1a, and finally for Kingdom's Figure 12 as well.

I will now discuss and criticize another variant of the Helmholtzian account. There are two ways to interpret gradual or quasi-gradual luminance distributions such as those in Figure 1a and 1b. The interpretation discussed above involves gradually changing illumination upon a flat surface. The other possibility involves uniform illumination falling upon a curved or faceted surface. In such cases it is also possible to invoke a Helmholtzian account. For example, Adelson (1993) discussed such an interpretation for his corrugated mondrian display. In Figure 2, I present displays based on a luminance distribution similar to Figure 1b, and will try again to show that an illumination interpretation of the phenomena is untenable.



Figure 2. Lightness and illumination interpretations. (a) The faceted hemi-cylinder. The figure is composed of 36 quadrilaterals of various uniform luminances. The numerical values displayed in the bottom two rows are specified by the computer graphics program; they were chosen from a range between 0 (minimum luminance) and 100 (maximum luminance), and are presented here to convey the ordinal relations between the luminances of the patches. Note the zigzag arrangement of darker quadrilaterals, with left-to-right increasing luminances given as 10, 20, 30, 40, 50, and 60, and the complementary zigzag arrangement of lighter quadrilaterals, with increasing luminances given as 40, 50, 60, 70, 80, and 90. The other two pairs of rows repeat the luminance values of the first pair. In particular, diamond a has the same luminance as diamond b, but looks lighter. (b) Diamonds in isolation. The nominal luminance values are 50 each for diamonds a and b, 20 for diamond c, and 80 for diamond d. (c) A photometric variant. The figure is the result of a photometrical transformation of (a), related to transformations used by Adelson (1993) for the corrugated mondrian. Geometrically, the figure has stayed the same, but photometrically it is turned by 90 degrees. Note in the leftmost two rows the same specified luminances as in the bottom two rows in Figure 2a. Diamonds a and b have the same luminance, specified as 50. (d) A geometric variant. The figure is the result of a geometrical transformation of (a), similar to the one used for the corrugated mondrian by Todorovic (1997). The left-hand portion is the same as in (a), and the right-hand portion is the mirror image of the right-hand portion of (a). Diamonds a and b have the same luminance.


In Figure 2a the diamonds a and b have the same uniform luminance, but, similar as in the above examples, a looks lighter. The two diamonds are re-displayed in Figure 2b, isolated and surrounded by the same background luminance. For comparison, also presented in isolation are diamonds c and d, whose contrast, within Figure 2a, appears only slightly larger than the contrast between a and b, but which are in fact quite different in luminance.

A Helmholtzian account appears readily applicable to explain the difference between diamonds a and b. Note that Figure 2a conveys the appearance of a faceted hemi-cylindrical checker-board patterned surface, illuminated from right by a uniform light source. The gradual turning-away of the surface elements from the light source would account for the general decreasing luminance gradient from right to left. Therefore, one can argue that diamond a is perceived as light gray in weak, grazing illumination, whereas diamond b appears as dark gray in strong, direct illumination. The logic is similar to the Helmholtzian approach developed for the flat-appearing displays in Figure 1, but the argument may look even stronger in this case. This is because in Figure 1 the gradual variation of illumination is just assumed to be present, whereas in Figure 2a the physical origin of the luminance gradient can be plausibly accounted for by the geometry of the depicted object and its orientation to the light source.

Figures 2c and 2d present visual counterarguments to this version of the Helmholtzian account. Like Figure 2a, they contain two physically indentical diamonds, a and b, that look different. Informally, this difference appear similar in strength as in Figure 2a; however, it cannot be accounted for in the same way.

In particular, Figure 2c retains the shape of Figure 2a, but not its illumination interpretation, since the horizontal luminance gradient is replaced by a vertical one. Such a luminance gradient cannot be accounted for naturally by the geometrical relations between the orientations of the individual surface elements and a uniform light source. Figure 2d involves a simpler transformation of Figure 2a, produced by copying its left-hand portion and mirroring its right-hand portion. Thus each surface element has retained not only its luminance but also its intrinsic shape and the geometrical relations to its neighbors. However, the overall geometry of the surface has switched from being C-shaped to being S-shaped. In particular, diamonds a and b appear to have parallel spatial orientations, and thus should be equally illuminated by a uniform light source. This figure should fulfill Kingdom's criterion for a control for Figure 2a involving, in his words, 'a stimulus in which two test regions were surrounded by a near-identical pattern of luminance, but with very different perceived configurations'.

Compared with Figure 2a, both Figures 2c and 2d present cases in which the illumination interpretation is changed but lightness is not, showing the independence of perceptual assessments of lightness and illumination in these figures. Note that, although it cannot be accounted for 'naturally' as in Figure 2a, in both Figures 2c and 2d a sense of an illumination gradient is apparent, similar to Figures 1a and 1b. My argument here is not directed against the phenomenal presence of illumination gradients in the figures, but against their causal force in the account of the phenomena.


Todorovic's comments on Blakeslee and McCourt's chapter

Blakeslee and; McCourt discuss the usage of the terms brightness and lightness, issues that have been addressed a number of times in the achromatic perception literature, such as by Hering (1920/1964), Katz (1911/1935), Gelb (1929), Koffka (1935), Evans (1964), Lie (1969a), Heggelund (1974, 1992), Arend and Goldstein (1987), Whittle (1991), and in papers in Gilchrist (1994). Their proposal to regard brightness as a 'direct sensory quality' and lightness as an 'inferential judgment' is reminiscent of a long tradition, reaching back to Alhazen, Descartes, and the British empiricists, of dividing sensory awareness into two levels: the first level, often labeled 'sensation', would correspond to a more or less direct neural response to the incoming proximal stimulus, whereas the second level, often labeled 'perception', would correspond to judgments of object characteristics based on mental processing of the initial response, using assumptions, inferences, knowledge, and the like. Two influential general approaches to perception in the past century, Gestalt psychology and Gibson's ecological psychology, arose in strong opposition to this traditional account.

In discussing lightness and brightness it is quite helpful to broaden the view somewhat, and to take into consideration analogous problems raised in other perceptual domains. I (Todorovic, in press) have discussed these and related problems in six domains (size, shape, direction, orientation, achromatic, and chromatic color), but will only concentrate on the analogy with size perception here.

The projected, proximal size of an object depends on its physical, distal size (an intrinsic property of the object), and its distance from the observer (an extrinsic, accidental property). In the simplest case, proximal size is given as a function (more precisely, as the arctangent of the ratio) of distal size and distance. Corresponding to these three physical variables (distal size, proximal size, distance), there are three phenomenal or perceptual variables: in psychophysical experiments, one can ask subjects for their judgments of the physical size of an object (perceived distal size), of its visual angle (perceived proximal size), and of its distance (perceived distance).

These two triads of variables, one physical and the other phenomenal, have direct analogues in achromatic color perception. The luminance arriving at the eye from an object depends on the objects' reflectance (intrinsic property) and its illuminance (extrinsic property). In the simplest case, luminance is given as a function (more precisely, as the product) of illuminance and reflectance. Corresponding to the three physical variables (reflectance, luminance, illuminance) there are three phenomenal variables: subjects can be asked to judge the reflectance of an object (perceived reflectance, or lightness), its luminance (perceived luminance, or brightness), or its illuminance (perceived illuminance). Note that this account is in accord with the Trieste group definitions, and also with the analogous issues in size perception. Distal size corresponds to reflectance (both are intrinsic), proximal size to luminance (both are proximal), and distance to illuminance (both are extrinsic), and each of these comes both in a physical and in a phenomenal variant.

The above definitions of the perceived distal and proximal variables are in agreement with the tasks given to subjects in experiments. For example, in a size perception study one can present to subjects a standard stimulus in the distance and several nearby comparison stimuli, and give to them two differently focused tasks: the distal task is to identify a matching comparison stimulus that has the same distal size as the standard (meaning physically equal), whereas the proximal tasks is to identify the comparison stimulus with the same proximal size (meaning subtending the same visual angle). Quite analogously, in an achromatic color experiment one can present a standard stimulus in a shadow and several well illuminated comparison stimuli, and give two tasks: the distal, lightness task, is to locate the comparison stimulus with the same reflectance as the standard (meaning made from the same material, cut from the same piece of paper, painted with the same paint, and the like, see Arend and Goldstein, 1987), and the proximal, brightness task, is to locate the comparison stimulus with the same luminance (meaning of same intensity, sending the same amount of light towards the perceiver).

Note that the above account of the perceptual variables is nontheoretical, as it does not presuppose any mechanism or theory of these judgments; it is also more or less straightforward, in that it can be used to formulate understandable instructions to subjects. In comparison, the CIE definition of lightness, cited by Blakeslee and McCourt as being 'an attribute according to which a visual stimulus appears to emit more or less light in proportion to that emitted by a similarly illuminated area perceived as white', has several shortcomings. It is unnecessarily theoretical and relative, because whether perceived surface color does depend on white in this relative manner, and whether subjects indeed engage in judgments of emitted light when judging lightness, are theoretical and not definitional issues. Furthermore, this definition has not been used to formulate instructions: nobody has, to my knowledge, studied lightness by asking subjects to identify a stimulus which 'appears to emit more or less light in proportion to that emitted by a similarly illuminated area perceived as white'. Also, the definition does not seem to cover the possibilities in which a white may not be present in the scene but an achromatic gray may be perceived.

Blakeslee and McCourt claim that brightness is 'simply perceived intensity, which is a primary sensation and can be reliably measured', whereas lightness 'is always the outcome of a perceptual inference, ... a cognitive interpretation or appraisal of a stimulus property, rather than a primary sensory quality'. However, it is not easy to substantiate either claim, that is, to demonstrate, in general, the immediacy of brightness judgments, or the presence of cognitive interpretations in lightness judgments. In everyday, full-cue conditions, the perceptual output is geared towards assessments of intrinsic properties of objects under variable extrinsic conditions, rather than towards capturing the proximal variations. Contrary to the Blakeslee and McCourt proposal that 'reflectance is not directly given but must in all cases be assigned, based on either direct knowledge or assumptions (conscious or unconscious) about the illumination', lightness judgments may, at least in principle, be based on a 'direct' readout of a Gibsonian higher-order variable (the luminance ratio is a simple example), whereas conscious brightness judgment, being an unusual and novel task in everyday conditions, may involve indirect inferences based on perceived reflectance and illumination. Whatever the ultimate theoretical resolution, the basic concepts are certainly preferably defined in a nontheoretical manner, as described above.

In contrast to modern studies using computer generated displays, classical studies of lightness constancy used real stimuli of different reflectances exposed to various real illuminations. Although generally they found some degree of underconstancy, objects in shadow looking somewhat darker than under full illumination (Katz, 1911/1935; Jaensch and Müller, 1920; Helson, 1943), under optimal conditions involving many surfaces of many different reflectances, excellent lightness constancy (reflectance matching) is present (Burzlaff, 1930; see also Jacobsen and Gilchrist, 1988). Unfortunately, judgments of brightness in such conditions were studied only occasionally, but it was found that subjects do have some ability to match surfaces in terms of luminance (Katz, 1911/1935, Henneman 1935, Lie, 1969b).

Many achromatic color studies involve displays that are in fact homogeneously illuminated, so that luminance and reflectance are perfectly correlated. In such cases the distinction between lightness and brightness, although conceptually valid, may not make much of a difference, and a general, undifferentiated notion of perceived achromatic color may suffice. This is analogous to size perception studies in which all stimuli are presented at the same distance, such as in size illusions. In these cases distal and proximal size are perfectly correlated, and the distinction of perceived distal and perceived proximal size may not be very relevant. However, whether a distal or a proximal task is more natural, may depend on circumstances of stimulus presentation. When presenting size illusions on paper, performing judgments of distal size is probably more natural than judging proximal size. On the other hand, when achromatic stimuli are presented on luminous computer screens, asking for judgments of luminance may be more appropriate than asking for reflectance judgments.

What complicates these issues considerably is that whereas some displays are abstract, representing nothing beyond themselves, other displays are representational or pictorial. Although for stimuli described in the preceding paragraph the actually present extrinsic variables (distance, illumination) are held constant, variation of these variables may nevertheless be conveyed or represented by the display pattern. Thus an actually flat 2-D figure may represent a scene with objects at various distances, and an actually homogeneously illuminated figure may convey a variably illuminated scene (and both is usually the case in photographs). With such representational displays, whether the task is focused distally (reflectance judgments) or proximally (luminance judgments) may make a difference, but such a distinction appears to have rarely been made explicit in instructions. An important exception is work by Arend and; Goldstein (1987) and Arend and Spehar (1993a,b), in which both tasks were used. Furthermore, for some displays the subjects could relatively easily apply two different illumination interpretations, one involving uniform and the other involving variable represented illumination. Perhaps Blakeslee and McCourt, who cite this work, may have had primarily such displays in mind when they claimed that reflectance judgments are always interpretational and based on illumination assessments. However, in everyday conditions, whether a luminance difference is due to illumination or to reflectance is usually well specified, and a voluntary switching between two interpretations is rarely possible.

Closing comments

At the risk of introducing more complications into these conceptually somewhat intricate issues, it should be noted that representational displays, such as pictures, are very rarely completely convincing and realistic, and that usually the perceiver is not fooled but is aware of their dual nature. What this means is that in such cases one can in principle distinguish between, on the one hand, reflectance, luminance, and illumination of a patch as a physical object in the display image itself, and, on the other hand, reflectance, luminance, and illumination that the patch represents in the scene conveyed by the display. Consider a photograph of a sunny landscape containing a portion of snow in the shade: on the photograph itself, this may actually be a medium reflectance patch observed by the viewer under medium illumination, but it represents a high reflectance surface under low illumination.

Such distinctions between displayed image attributes and represented scene attributes may be of importance in assessing the nature of achromatic color phenomena. For example, Kingdom claims that the effect present in his Figure 12 is a brightness but not a lightness illusion, and a similar claim might be made for my Figure 2a. I agree that patch a looks more intense than patch b, although it is not, and would call that an error of judgment of displayed luminance, and hence a brightness illusion. However, I am also fooled into perceiving that the reflectance of patch a, as printed on the page, within the figure, is higher than the reflectance of patch b, although it is not, and would call that an error of judgment of displayed reflectance. Thus this display involves both a lightness and a brightness illusion. I suppose that what Kingdom had in mind are, in my terminology here, judgments concerning the represented reflectances. If the figure conveys to me the appearance of a differentially illuminated real patterned surface, and if I judge two particular represented surface patches, a and b, to have different reflectances, then no illusion is involved. However, such judgments involve achromatic attributes of the represented scene and not of the displayed image.

I have claimed that the proposed Helmholtzian theories involving illumination interpretations fail to account for some strong illusions in pictorial displays involving represented illumination, such as those by Adelson, Logvinenko, Kingdom, and myself. However, one could argue that the demonstrations in Figure 1d, 2c, and 2d, do not in fact invalidate this account: it could be claimed that what they show is at most that the illumination interpretation in these cases could be in logical trouble, but that the perceptual system might nevertheless use a dumb general illumination-based heuristic anyway, that does not care about niceties such as physical implausibility. My problem with this argument is that it then becomes unclear what it exactly means that the visual system 'takes illumination into account', and thus it gets hard to test whether the studied phenomena are indeed dependent on illumination assessments all.

On the other hand, these demonstrations cannot refute the illumination interpretation approach in general. There may be other cases, such as perhaps the one presented in Kingdom's Figure 13, in which such an account might be tenable. Furthermore, all these examples deal with 2-D displays involving represented illumination. In 3-D scenes involving real illumination distributions, the situation may well be quite different. Pioneering studies by Gelb (1929, 1932) and Kardos (1934) have shown that manipulations of illumination and depth cues in real scenes may lead to strong effects on perceived reflectance. More recently, impressive examples were provided by Gilchrist (1977, 1988). In contrast to the demonstrations presented here, in these studies changes of perceived reflectance strongly correlated with changes of perceived illumination.