Todorovic comments on Kingdom's reply

Dejan Todorovic

Kingdom describes the illumination-interpretation stage in achromatic color perception as a putative lightness constancy mechanism that discounts spatially varying illumination. I will call this process an illumination-interpretation mechanism (IIM). Such a mechanism is presumably based on the accumulated wisdom of the organism or the species about the interactions of illumination distributions, surface shapes, and reflectance patterns. There are several aspects of this interaction. Illumination distributions can be homogeneous, but can also involve more or less abrupt steps, such as in shadows, or more continuous gradients, such as due to variable distance from the light source. Surface 3-D shapes may be planar, or may involve abrupt orientation changes, such as in dihedral or trihedral edges, or continuous orientation changes, such as for spatially curved surfaces. Reflectance distributions on surfaces may be homogeneous, or involve abrupt reflectance edges, or more continuous gradations. Thus any particular luminance distribution could in principle result from an infinity of combinations of patterns of illuminance, 3-D shapes, and reflectance. Nevertheless, in everyday perception the separate sources generally appear to be successfully parsed out of the resulting luminance distributions, suggesting the existence of efficient recovery mechanisms.

The problem under discussion here is whether an IIM is at work in a particular class of achromatic color effects. Figure 2a in my preceding comment presents a case in which such a mechanism initially offers a plausible and natural explanation of a lightness illusion, based on the structure of interactions of illumination and curved patterned surfaces. However, Figures 2c and 2d present counterexamples, showing that the illusory effect persists even when the natural illumination interpretation is ruled out. From this I have concluded that an IIM account of the effect is unlikely. This has failed to convince Kingdom, who has concluded that an IIM may still be at work there, but one based only on impressions of illumination gradients, lacking sensitivity for the structure of interactions of light with curved surfaces. Such a move does immunize his version of the IIM from my criticism, but I do not find it compelling. What is the reason that an IIM should lack one particular type of sensitivity rather than some other? Is there any other supporting evidence that illumination interpretations win against competing surface shape interpretations? Why would an efficient constancy mechanism, the supposed basis of the effect, care only about illumination distributions but not about surface shapes, when both are essential for correct lightness assessments? Does such selective sensitivity follow from the general IIM idea, as described above? To the contrary, had I only produced my Figure 2a, I believe that IIM proponents would not have hesitated much to accept that display as another confirmation of the IIM approach, including sensitivity to surface 3-D shapes; it is only in conjunction with figures 2c and 2d that the problem is revealed.

Figure 3. Lightness and shadows. The left-hand portion of the figure conveys the appearance of a shadow, S, falling upon a checkered ground. The transition between the shaded and unshaded portion is characterized by a penumbra-like distribution. The luminance of square a1 inside the shadow is equal to the luminance of square b outside (and all other darker square outside the shadow as well). The right-hand portion of the figure contains a patch T, identical to S but displaced with respect to the checkered background. In particular, the luminance of square a2 is the same as the luminance of a1. The displacement of the 'shaded' region has violated several shadow-based regularities, but the lightness difference between a-squares and b-squares persists.

However, a proponent of the IIM approach could argue that such a mechanism might still be at work in both cases. For example the suggestion of a shaded region in both S and T might be triggered by heuristics responsive to the penumbra-like configuration, or to the decreased average luminance, but insensitive to the violent discontinuities that are inconsistent with the presence of a real shadow. This move would follow a logic similar to Kingdom's response concerning my Figure 2. Thus rather than constituting criticisms of the IIM approach to this class of effects, my attempted counterexamples might in fact be regarded as contributions to its development, helping to clarify what processes it is and is not based on.

In my judgment, however, such arguments would increase the flexibility of the IIM approach only at the cost of decreasing its plausibility and threatening its falsifiability. Instead, it would be desirable to formulate more precisely its predictions, so that it could be pinned down better and thus tested adequately. As noted above, one would also need a more convincing rationale both for the presence and for the absence of particular proposed heuristics in the putative IIM. In the preceding example, why would an IIM be sensitive to discontinuities of average illumination, but not to discontinuities of local geometry and photometry, rather than, say, the other way around? An IIM is supposed to be based on relevant environmental regularities concerning the interactions of light and matter. The plausibility of the existence of such a process is proportional to the extent that these regularities are manifested in its working. If the putative process fails to take into account some major illumination-related regularities in these images, such as those concerning shadows or 3-D shape, then it remains to be shown that such a mechanism is indeed an IIM, and that its origin really involves 'taking illumination into account'.

I have offered a similar argument in my previous contribution, involving my Figures 1c and 1d: according to the IIM account the effect present in Figure 1c should be due to an IIM, but its existence in Figure 1d shows that it isn't. In his reply, Kingdom claims that the lightness phenomena in these figures are weak or negligible, failing to reveal the illusory effects which are the signature of the putative IIM.

Figure 4. A transition between a continuous and an abrupt illumination distribution. The portion of the figure between the two top dashed lines is equivalent to Figure 1b, and the portion between the bottom two dashed lines is equivalent to Figure 1c. The transition portion in between is constructed as a linear interpolation between the top and the bottom pattern. Two vertical columns of diamonds are indicated by the arrows. The members of the left-hand column, containing the diamond labeled as 'a', and the members of the right-hand column, containing the diamond labeled as 'b', all have the same luminance.

I have several comments. First, Kingdom himself in his chapter accounts for a stereoscopic lightness phenomenon in terms of an IIM mechanism, but that effect is rather weak, which shows that not all putative IIM effects have to be strong. Furthermore, if the effect in Figure 1c were indeed nonexistent, this could be a problem for the IIM account itself, because the stimulus conditions there should invoke a shadow interpretation. Kingdom writes only that for 'some reason' the abrupt illumination transition fails to produce the same magnitude of illusion as the smooth transition. As for the strength of the phenomena in Figure 1, there appear to exist some individual differences and perhaps effects of viewing strategies, since to me it does not seem fair to describe the effects in Figures 1c and 1d as 'negligible', compared to the 'much larger' effects in Figures 1a and 1b, especially when I carefully scrutinize and directly compare all a-diamonds and b-diamonds in all four figures with each other. Clearly, the matter must be resolved experimentally. As a contribution to the clarification of this issue, consider Figure 4. The top portion of the figure corresponds to Figure 1b, the bottom portion to figure 1c, and the in-between region is an interpolation between them. The diamonds in the two columns indicated by the arrows all have identical luminance. Would it be appropriate to describe the a-b difference in the bottom pair as 'negligible', and in the top pair as 'much larger'? To my eyes, it is the lightness contrast in the bottom pair that appears, if anything, slightly larger. Inspecting the display from top to bottom, the diamonds in the a-column appear, if anything, to get slightly lighter, and those in the b-column slightly darker; this is consistent with the fact that, due to the construction of the interpolation between the top portion and the bottom portion, the luminances of the diamonds adjoining the target diamonds in the two columns decrease for the a-column and increase for the b-column.

Figure 5. Illumination and induction. Three stripes of identical homogeneous luminance are superimposed upon Figure 1b. The top one crosses the lighter diamonds, the bottom one the darker diamonds, and the middle one crosses both groups of diamonds. The stripes have the same luminance as diamonds a and b. Illusory gradients are induced in each stripe. The direction of the induced gradients is opposite to the direction of real stepwise luminance gradients present across both the darker and the lighter diamonds (see the graph corresponding to Figure 1b).

Finally, I agree with Kingdom that a valid interpretation in terms of an IIM, such as for his Figure 12a, must control for effects of contrast in a display (regardless of the theoretical account of contrast itself). I contribute to this discussion with my Figure 5. It is based on my Figure 1b, which is similar to Kingdom's Figure 12a. The new aspect is the introduction of three stripes of homogeneous luminance (same as for diamonds a and b in the figure). It can be seen that illusory gradients are generated in the stripes, similar in appearance to McCourt's (1982) grating induction effect. An interesting question for IIM proponents is whether this approach should be extended from accounting for the a-b difference, and applied to this version of grating induction as well, rather than explaining these two effects with different principles. To me, it appears logical and consistent with this approach to argue that the perceived gradients in the stripes, which have a homogeneous luminance distribution, are generated as a consequence of taking the inhomogeneous illumination distribution into account. In fact, one might even extend this explanation to the original grating induction displays as well. They involve simple sinusoidal induction gratings instead of the checkered variants in Figure 5, but if checkered distributions are supposed to be able to trigger the apparently gross heuristics of the putative IIM, then sinusoidal distributions might do it as well.

It is a different question, however, how plausible such an account would be. Induced gradient effects can in principle be accounted for without invoking an IIM, for example with mechanisms modeled by Blakeslee & McCourt (1999). These or some other non-illumination based mechanisms may account for the fancier version of grating induction in Figure 5. If so, it would remain to be shown that an IIM contribution needs to be invoked instead of or in addition to such mechanisms. Thus in order to bolster the presence of an IIM component for the a-b difference effect in my Figure 1b or Kingdom's Figure 12a, it should be shown that the strength of this effect goes beyond what can be expected from grating induction. This seems doubtful, since the strength of the effects in the a-diamond and the b-diamond in Figure 5 appears to be approximately as strong as the effects at the corresponding positions within the stripes.

I would like to reiterate that my arguments are not directed against sensitivity to illumination and its effects on lightness recovery in general 3-D environments involving real depth and illumination variations. I only share Kingdom's own concern that one should be cautions before accepting such processes as being responsible for effects arising in uniformly illuminated flat displays.