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Research Article  |   December 2004
Hering’s and Helmholtz’s types of simultaneous lightness contrast
Author Affiliations
  • A. D. Logvinenko
    Department of Vision Sciences, Glasgow Caledonian University, Glasgow, UK
  • John Kane
    School of Psychology, The Queen’s University of Belfast, Belfast, UK
Journal of Vision December 2004, Vol.4, 9. doi:10.1167/4.12.9
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      A. D. Logvinenko, John Kane; Hering’s and Helmholtz’s types of simultaneous lightness contrast. Journal of Vision 2004;4(12):9. doi: 10.1167/4.12.9.

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Abstract

Detaching of the test objects from the inducing background was found to reduce significantly Adelson’s “snake” lightness illusion but not grating induction. Moreover, the same grating induction effect was measured from 3D real cylinders and a 2D sinewave grating. We conclude that grating induction and Adelson’s snake lightness illusion are different types of simultaneous lightness contrast.

Introduction
Simultaneous lightness contrast is a textbook illusion, which demonstrates that the lightness of an object may depend on its immediate surround. There are two classical explanations of this illusion — a low level (physiological) one descending from Hering’s ideas of inhibitory processes in the visual system (Hering, 1874/1964; Cornsweet, 1970), and a high-level (psychological) one enunciated by Helmholtz (1867), who believed that simultaneous lightness contrast is a result of “misjudgement of illumination.” Hering’s approach has evolved into a number of low-level models (e.g., Kingdom & Moulden, 1992; Blakeslee & McCourt, 1999; Ross & Pessoa, 2000), which give an account of simultaneous lightness contrast and related illusions such as grating induction (McCourt, 1982). At the same time, a variety of impressive modifications of simultaneous lightness contrast have been presented over the last two decades — the tile and snake illusions (Adelson, 1993, 2000) to mention two — that challenge the low-level explanation and lend themselves to Helmholtzian explanation (Adelson & Pentland, 1996; Kingdom, 1997, 1999; Logvinenko, 1999, 2002a, 2000b). Eventually, a general opinion has been established that there are two different mechanisms — Hering-type and Helmholtz-type — and they both contribute into simultaneous lightness contrast (e.g., Kingdom, 2003a). Furthermore, it is widely believed that Hering-type mechanisms mainly contribute into classical simultaneous lightness contrast, grating induction, and some other related lightness illusions (such as Mach bands, Herman grid, and the like), whereas Helmholtz-type mechanisms are mostly responsible for illusions such as Adelson’s tile and snake lightness illusions. 
In this report, we raise the following question. Being very different in their nature, do Hering- and Helmholtz-type mechanisms cooperate to create the same lightness illusion or do they produce different illusions? In other words, are, say, grating induction, on the one hand, and Adelson’s tile and snake illusions, on the other, particular cases of the same lightness illusion (simultaneous lightness contrast), or are they different lightness phenomena? Below we present some evidence that these may be different phenomena. 
As shown recently, the tile illusion disappears when the wall of blocks depicted in the tile pattern is implemented as a real 3D object despite that the retinal image of this 3D wall of blocks is practically the same as that of the tile pattern (Logvinenko, Kane, & Ross, 2002). On the other hand, grating induction can be observed when the inducing patterns (cylinders) are presented stereoscopically (Kingdom, 2003b). We decided to ascertain whether grating induction can be produced by real 3D cylinders, illuminated to form a sinusoidal illuminance distribution on the retina, which usually invokes grating induction. 
Experiment 1: Grating induction from real cylinders
Method
Observers
Ten volunteers, unaware of the purpose of the experiment, were employed as observers. They all had normal or corrected-to-normal vision. 
Stimuli and apparatus
We presented to our observers both 3D and pictorial displays. The 3D display comprised three cylinders (20 cm × 9 cm) made from rolled up grey card (of 48% reflectance). These were placed side by side on top of a platform (21 cm × 40 cm) on a large table. A horizontal strip (5 cm × 35 cm) was suspended on thin wire 5 cm in front of the cylinders. The cylinders, platform, and strips were made from the same homogeneous grey card. Illumination was provided by a standard desktop lamp fitted with a 60-w bulb. The lamp was positioned on the same table at 45 deg to and 60 cm from the cylinders and strip. This display was at head height to the observer who sat 1 m away from it. The curvature of the cylinders and angle of illumination gave each cylinder a perceived lightness gradient. 
The pictorial display was a photograph of the cylinders with the strip, taken from the observer’s position (Figure 1). The photograph (21 cm × 29 cm) was placed on the same plane as the cylinders and to their immediate left. A Munsell 31-point neutral scale was positioned to the right of the picture and underneath the 3D display. 
Figure 1
 
A photograph of the 3D display of the cylinders and the test strip (see explanation in the text).
Figure 1
 
A photograph of the 3D display of the cylinders and the test strip (see explanation in the text).
The linear size of the pictorial cylinders (i.e., those in the photograph) and the test strip was the same as those in the 3D display. Thus, when projected on the retina, both the 3D and pictorial displays produce practically the same pattern, namely, a sinusoidal grating with a horizontal strip across it, as in Figure 1. The sinusoidal profile of the pattern was slightly asymmetrical because of the illumination gradient across the horizontal dimension. Michelson contrasts of the cylinders (left to right) were 0.736, 0.748, and 0.880, the average Michelson contrast being 0.786. The average mean luminance of the sinusoidal grating was 32.2 cd/m2. Its spatial frequency was 0.194 c/deg. The average luminance of the test strip was 26.5 cd/m2
Experimental design and procedure
The observer’s task was to evaluate the lightness of four different sections along the strip, which were identified by the experimenter using a laser pointer. These sections were immediately in front of an area perceived as either light or dark on the background cylinders. The Munsell 31-point neutral scale was used to measure lightness. Observers were instructed to select a Munsell chip, which they judged to be the same grey as that indicated by the experimenter. Four matches were made for the 3D display in every run, for the two apparently light and dark parts of the test strip. Analogous matches were also made for corresponding sections of the strip in the photograph. 
Each observer completed five sessions with two runs in each session. In all, each observer made 40 matches for each display, 20 matches for the apparent lightening, and 20 for the apparent darkening. The matches in each session were in a different order, and observers were instructed to not engage their memory of previous judgments. 
Results
The median Munsell matches for the apparently light (ML) and dark (MD) parts of the (physically homogeneous) test strip were 7.25 and 6.25, respectively. The corresponding median matches for the picture were 7.5 and 6.5. Thus, the difference in lightness between the apparently light and dark parts of the test strip was equal to one Munsell unit for both displays. Taken as a measure of the illusion, the Michelson contrast (ML + MD)/(ML + MD) averaged across the whole population of 200 measurements was 9.3% and 9.1% for the 3D and pictorial displays, respectively, with no significant difference (p = .56). Thus, the grating induction effect for the 3D display was found to be as strong as that for the picture. 
Discussion
Unlike Adelson’s tile illusion, the grating induction was found to be independent of the type of display. There were at least two reasons to expect that the grating induction effect produced by the 3D cylinders display would be smaller. First, the lightness gradient across the cylinders was reduced (in comparison to the luminance gradient) because of lightness constancy. (A white ball looks white despite the luminance gradient produced by its surface’s curvature. This is a sort of lightness constancy that should be distinguished from other well-known types, illumination-independent and background-independent lightness constancies [Whittle, 1994b]). 
In other words, the cylinders’ surface was perceived to be, by and large, homogeneous in lightness. This was hardly surprising as the cylinders were made from a homogeneous sheet of paper. If lightness constancy were perfect, there would be no lightness gradient at all. Second, the test object (strip) was detached from the cylinders, that is, it did not belong to the cylinders. However, it was well established by Gestalt psychologists that belongingness played an important role in producing lightness illusions. For instance, Gilchrist (1977) showed that coplanarity of the test object with the inducing background was a crucial factor in producing the simultaneous lightness contrast effect and similar lightness illusions. 
In contrast with Adelson’s tile illusion, which, as shown by Logvinenko et al. (2002), can be observed only in a pictorial display, the grating induction effect of the same magnitude can be equally produced by both 3D cylinders and the photographic picture of them. This supports the view that grating induction and Adelson’s tile demonstration are lightness illusions of different type. 
In the next experiment, we contrast grating induction with another Adelson lightness illusion, produced by the so-called “snake pattern” (Adelson, 2000). Specifically, we show that Adelson’s snake illusion can be significantly reduced by (i) detaching test objects from the inducing background, and (ii) using 3D cubes as test objects to reduce belongingness of the test objects to the background as much as possible. This is particularly pertinent because the manipulations of the test display made in the next experiment are quite similar to those made in Experiment 1, thus making these two experiments comparable. 
Experiment 2: Lightness illusion induced by Adelson’s snake pattern on detached test objects
Method
Observers
Ten new subjects (5 males and 5 females), all volunteers, with an age range of 17–40 years, undertook a lightness-matching task. They were unaware of the purpose of the experiment. All observers reported normal or corrected-to-normal vision. 
Stimuli and apparatus
The observers were presented with three displays. One was Adelson’s snake pattern, which produces a strong illusory difference in lightness between the two identical test squares inserted into dark and light strips (Figure 2). The second display was made up from Figure 2 by detaching the test squares and placing them between the snake pattern and the observer. The test squares were cut from paper of the same reflectance as those in Figure 2. They were stuck to thin metal needles that were inserted through the snake pattern. The needles were not visible to the observer. The angular size of the test squares was equal to that of the squares in the first display (i.e., Figure 2). Therefore, while the test squares in the second display were not coplanar with the snake pattern, the retinal images of the two displays were practically identical. The third display was the same as the second except that the 2D-test squares were replaced with 3D cubes made from the same paper and printed with the same ink. They were mounted in the same manner as in the second display. The angular size of the cubes was the same as that of the test squares in the previous displays. Thus, the retinal images of all the three displays were practically the same. Therefore, any theory of lightness perception based solely on the retinal luminance patterns would predict the same illusion, if any, for all the three displays. 
Figure 2
 
Adelson’s snake pattern. Two small grey squares are printed with the same ink. Nevertheless, they look different because of the strong illusory effect induced by their different surrounds.
Figure 2
 
Adelson’s snake pattern. Two small grey squares are printed with the same ink. Nevertheless, they look different because of the strong illusory effect induced by their different surrounds.
The displays were presented in a viewing booth, against a white cloth background (1 m × 1 m) at a distance of 1 m from the observer. The size of both snake patterns was 20 cm × 20 cm; the size of all test objects was 1 cm × 1 cm. Lightness evaluation of the test objects (squares or cubes) in each display was made using the Munsel1 31 step neutral value scale. The instruction given to observers was to pick out a Munsell chip that looked the same shade of grey as the test object to be evaluated. The participants looked into the booth through an aperture (150 cm × 20 cm) that allowed them to view the displays and the set of Munsell chips. The sidewalls of the booth were covered with the same white cloth material. An adjustable chinrest was used to insure that the observer’s line of sight was at a right angle to each display during matching. Observers were instructed to restrict their attention to the central (target) area of each display comprising the two test objects when evaluating their lightness. 
Illumination was produced inside the booth by four incandescent “natural daylight” lamps, which were attached two above and two below the inside of the viewing slot. The lamps were not directly visible to the observer. Luminance measurements were taken before the experiment started. Mean luminance for the test objects and mean luminance contrast, which the test objects made with their immediate surround, are presented in Table 1
Table 1
 
Mean luminance (cd/m2) of the test objects and the corresponding background strip and mean luminance contrast (test vs. background) in Experiments 2 and 3.
Table 1
 
Mean luminance (cd/m2) of the test objects and the corresponding background strip and mean luminance contrast (test vs. background) in Experiments 2 and 3.
Display Expt. 2 Background Test Contrast Expt. 3 Test
1 Light strip 1312 1220 −0.0392 1200
Dark strip 900 1213 0.1511 1187
2 Light strip 1320 1223 −0.0381 1245
Dark strip 902 1222 0.1508 1237
3 Light strip 1319 1219 −0.0394 1245
Dark strip 898 1217 0.1509 1232
Small though statistically significant differences in luminance were found between the test objects presented against different strips (i.e., light and dark) and between those in different displays. However, these differences had no impact on the luminance contrast between the test objects and the strips. Specifically, two-way ANOVA (strip x display) showed no statistically significant differences for luminance contrast. 
Experimental design and procedure
Each observer completed five sessions, with two runs in each session. During each run the lightness of a target in each display was evaluated twice, once in a light strip and once in a dark strip. The experimenter indicated (with a laser pointer) which target was to be evaluated. The order of the targets was changed for each run. All observers completed a total of 12 lightness matches during each of the five sessions (i.e., a target in a light strip and one in a dark strip in each of the three displays twice). One session lasted approximately 30 min. As a rule, one session per week was completed with each observer. 
Results
The results are presented in Figure 3 as a multiple box plot graph (comprising “extracted” histograms). As can be seen in this figure, for each display the matching distributions obtained for the light and dark strips are shifted relative to each other, thus manifesting the illusory lightness shift. We used the Hodges-Lehmann estimator for the shift (Hollander & Wolfe, 1973, p. 33) as a quantitative index of the snake lightness illusion (Table 2). 
Figure 3
 
Extracted histograms of the lightness matches obtained for the test objects presented against the light and dark strips in each of the three displays in Experiment 2. Munsell matches are along the vertical axis. The ends of the boxes are the first and third quartiles. Hence, the height of the boxes is the interquartile range. A horizontal line in the box is drawn at the median. An upper whisker is drawn at the largest match; a bottom whisker is drawn at the smallest match.
Figure 3
 
Extracted histograms of the lightness matches obtained for the test objects presented against the light and dark strips in each of the three displays in Experiment 2. Munsell matches are along the vertical axis. The ends of the boxes are the first and third quartiles. Hence, the height of the boxes is the interquartile range. A horizontal line in the box is drawn at the median. An upper whisker is drawn at the largest match; a bottom whisker is drawn at the smallest match.
Table 2
 
Mean, median, and the Hodges-Lehmann estimators (H-L E) of the Munsell matches obtained in Experiments 2 and 3.
Table 2
 
Mean, median, and the Hodges-Lehmann estimators (H-L E) of the Munsell matches obtained in Experiments 2 and 3.
Display Expt. 2
Mean Median H-LE
1 Light strip 5.91 6.00 2.65
Dark strip 8.62 8.75
2 Light strip 7.14 7.50 1.125
Dark strip 8.43 8.50
3 Light strip 7.47 7.50 0.875
Dark strip 8.33 8.50
Display Expt. 3
Mean Median H-L E
1 Light strip 6.14 6.25 2.25
Dark strip 8.38 8.50
2 Light strip 7.40 7.50 1.00
Dark strip 8.44 8.50
3 Light strip 7.49 7.75 0.875
Dark strip 8.43 8.50
The mean and median Munsell matches are also presented in Table 2. To be more exact, the lightness shift between the test squares in Figure 2 was found to be 2.65 Munsell units, which is significantly more than for grating induction (1 Munsell unit). When the test squares were detached from the snake pattern, the lightness shift was reduced to 1.125 Munsell units. The lightness shift registered for the 3D cubes as test objects was even less, viz 0.875 Munsell units. Therefore, the snake illusion for the third display (with 3D cubes as test objects) is reduced by a factor of 3 as compared to the first (pictorial) display. 
Discussion
We found that the same grey square presented against the same background (snake pattern) looks different depending on the spatial layout. When it is coplanar with the snake pattern, being a part of the picture, it is subject to strong simultaneous lightness contrast (2.65 Munsell units). When it is implemented as a side of a 3D cube, its appearance becomes much less dependent on the background, exhibiting a rather low simultaneous lightness contrast effect (0.875 Munsell units). 
In a sense, the results of this experiment are quite feasible, being in line with our everyday life experience. Indeed, we found that the appearance of a real thing — a 3D cube — does not depend too much on the remote background. This is a well-known visual phenomenon, usually referred to as lightness constancy with respect to the background (e.g., Whittle, 1994b). Note, however, that from this point of view we run into a problem with the results of Experiment 1. Why did lightness constancy with respect to the background not take place for the test strip presented against real cylinders? 
One might argue that lightness constancy with respect to the background did not take place in Experiment 1, that is, the grating induction effect was robust to the type of display because it was produced by a luminance gradient. Indeed, the tile pattern with a luminance gradient (Logvinenko, 1999) was found to be able to induce a residual lightness illusion even when it was implemented as a 3D wall of blocks (Logvinenko & Kane, 2002). If there is something special about a lightness illusion induced by a luminance gradient that makes it independent of whether the test objects are coplanar with the inducing pattern or not, then blurring the border between the horizontal strips in the snake pattern may make the snake illusion robust to detaching the test object from the pattern itself. We tested this hypothesis in the following experiment. 
Experiment 3: Lightness illusion induced on detached test objects by a snake pattern with a luminance gradient
Method
Observers
The same 10 observers as in Experiment 2 were employed. 
Stimuli and apparatus
Observers were presented with three displays as in Experiment 2. The first display was made up from Figure 2 by blurring the strips’ borders (Figure 4). The second display was produced from Figure 4 in the same way as the second display in Experiment 2 from Figure 2. Particularly, the test squares in the second display were located at the same distance (2 cm) between the blurred snake pattern and observer as in Experiment 2. The third display was the same as the second except that the 2D-test squares were replaced with 3D cubes made from the same paper and printed with the same ink. The angular size of the cubes was the same as that of the test squares in the previous displays. The illumination also was the same as in Experiment 2. Luminance of the test objects is presented in Table 1. As in Experiment 2, small significant differences for luminance were found for different strips and displays. Although luminance contrast could, obviously, not be measured because of the luminance gradient in the background pattern, by analogy with Experiment 2, we believe that these differences in luminance had a negligibly small effect, if any, on our results. 
Figure 4
 
The snake pattern with blurred horizontal borders between the strips. The sinusoidal luminance gradient arising from such blurring is very similar to that in the sinusoidal gratings bringing about the grating induction effect.
Figure 4
 
The snake pattern with blurred horizontal borders between the strips. The sinusoidal luminance gradient arising from such blurring is very similar to that in the sinusoidal gratings bringing about the grating induction effect.
Experimental design and procedure
Experimental design and procedure were exactly the same as in Experiment 2. In fact, both Experiment 2 and 3 were run concurrently for the purpose of convenience. 
Results
A multiple box plot graph in Figure 5 presents the results of Experiment 3. The mean and median Munsell matches can be found in Table 2 as well as the Hodges-Lehmann estimator for each of the three types of the display. As one can see, the results are quite similar to those obtained in Experiment 2. While the lightness shift for the blurred snake pattern (Figure 5) was found to be slightly smaller (2.25 Munsell units) than that for the original snake pattern (2.65 Munsell units), the lightness shift for the 3D cubes was exactly the same (0.875 Munsell units). 
Figure 5
 
The results of Experiment 3 (see explanation in the caption to Figure 3).
Figure 5
 
The results of Experiment 3 (see explanation in the caption to Figure 3).
Discussion
In contrast with the tile pattern (Adelson, 1993), whereby blurring the border between the strips only enhances the lightness illusion (Logvinenko, 1999), we found that blurring the border between the strips in the snake pattern reduces the illusion a little. Perhaps, this happens because, first, being stronger than the tile illusion, the strength of the snake illusion is very difficult to be increased. And second, as a matter of fact, the test targets in the snake pattern in this experiment were larger than in the blurred tile pattern used by Logvinenko (1999). The larger targets occupy more physical space in the display, which might have reduced the induction effect of the luminance gradient in this experiment. 
Because the 3D cubes presented against both snake patterns show the same (rather small) amount of the lightness illusion, one has to conclude that there is nothing special in a luminance gradient itself that secures the robustness of the grating induction to the type of the display (i.e., detaching the test strip from the cylinders). 
General discussion
Grating induction, on the one hand, and Adelson’s tile and snake demonstrations, on the other, were found to have different properties. Indeed, grating induction of equal magnitude was observed for both 2D and 3D displays (Experiment 1), whereas the tile illusion was not observed for a 3D display (Logvinenko et al., 2002). Furthermore, detaching the test strip from the inducing cylinders did not affect grating induction, whereas detaching the test objects from the snake pattern was shown to considerably affect the illusion. Specifically, the snake illusion was found to be reduced by a factor of 3 when the test objects (3D paper cubes) were positioned in front of the inducing snake pattern (Experiment 2). The same result was found for the snake pattern where the luminance borders between the strips were blurred to make a sinusoidal luminance gradient (Experiment 3). Therefore, robustness of grating induction to the test strip detachment cannot be explained just by the presence of sinusoidal luminance ramp in the inducing pattern. 
One might argue, however, that we found no difference between the 2D and 3D displays in Experiment 1 because the test strip did not look as if it belonged to the cylinders even in Figure 1. In other words, when apparent coplanarity takes place, as in the 2D displays in Experiments 2 and 3 (Figures 2 and 4), an illusion of large magnitude is observed. When, on the other hand, there is no apparent coplanarity, as in the 2D display in Experiment 1, and all the 3D displays, one observes a weak illusion. 
It should be pointed out, however, that, first, a much bigger grating induction effect can be observed for a pictorial display where the test strip undoubtedly belongs to the grating pattern (McCourt & Blakeslee, 1994). Second, coplanarity as such does not guarantee a strong illusion. (Otherwise, a question immediately arises: Why is the classical simultaneous contrast effect so weak despite that the tests and backgrounds are coplanar with each other?) Strength of the illusion is determined by an apparent illumination of a surface with which the test appears to be co-planar. For example, in his demonstrations, Gilchrist (1977) showed that lightness of a surface can be dramatically changed when the surface changed its apparent orientation to a direction of prevailing illumination. It is important in this context that illumination in the whole volume of the viewing booth was physically homogeneous. And in this experiment, it also looked homogeneous. Therefore, apparent illumination was the same in the plane of the tests and backgrounds. We believe that this rules out coplanarity as an explanatory principle for our results. 
All this leads us to suggest that grating induction is a lightness illusion of a different type than the tile and snake illusions. First of all, these illusions are, probably, brought about by different mechanisms. Grating induction is most likely to be produced by low-level mechanisms based on processing luminance contrast originally proposed by Hering (1874/1964). On the contrary, the tile and snake illusions seem to emerge from high-level mechanisms, first suggested by Helmholtz (1867) and probably the same mechanisms that secure lightness constancy with respect to illumination under the circumstances of natural vision (Logvinenko, 1999). However, the difference in mechanisms does not exhaust all the differences between these illusions. Different mechanisms may contribute into the same visual phenomenon. We claim more, that is, we suggest that grating induction, on the one hand, and Adelson’s tile and snake demonstrations, on the other, are different visual phenomena. In other words, they are different types of lightness illusion – Hering’s and Helmholtz’s types. A variety of lightness illusions of Helmholtz’s type can be found, for example, in Adelson (2000), Logvinenko (1999), Logvinenko and Ross (in press), and Logvinenko, Adelson, Ross, and Somers (in press). 
Modern low-level theories of simultaneous lightness contrast (e.g., Kingdom, & Moulden, 1992; Blakeslee, & McCourt, 1999, 2003) suggest that it arises as a result of functioning of a set of spatial-frequency filters at the early stage of the visual process. These filters constitute a sort of pre-processor through which all the retinal inputs have to come. Actually, the further parts of the visual system and the brain as a whole do not have an access to the proximal stimulus; they deal with its altered form — the pre-processor’s output. In other words, the luminance distribution in the proximal stimulus remains directly unavailable for the brain. Therefore, lightness can, strictly speaking, be derived only from the pre-processor’s output rather than from luminance (or relative luminance, or luminance contrast), as it is widely believed (e.g., Gilchrist, 1994; Gilchrist et al., 1999). 
For the sake of clarity and brevity, we are making the following terminological distinction. We shall use the term brightness to refer to luminance as transformed by the pre-processor. In other words, brightness is a pre-processed luminance in the present context. In the visual literature, brightness is usually defined as a subjective luminance, or subjective intensity of light (e.g., Wiszecki & Stiles, 1982). Because it is not clear yet what the stimulus correlate of brightness is (e.g., see Whittle,1994a), it is hard to say how our definition of brightness is related to the classical one. We believe that they are very close because there is every indication that brightness is determined at the earliest stages in the visual system (Whittle, 1994a, 1994b). 
As a rule, the pre-processor’s output does not differ significantly (at least with regard to lightness perception) from the luminance spatial distribution. However, there are some luminance patterns that are essentially altered by the pre-processor. At these rare occasions, when they differ, brightness illusions take place. We believe that Mach bands, Hermann grid, and grating induction can be considered examples of brightness illusions of this sort. It should be noted, however, that, resulting from discordance between the luminance distribution and the pre-processor’s output, these brightness illusions could hardly be called an illusion. At any rate, they must be distinguished from the other types of illusions. For example, according to Gregory’s classification, they would be referred to as physical illusions. 
Every brightness illusion results in a corresponding lightness illusion. However, the inverse is obviously not true. Not every lightness illusion is a result of discrepancy between the luminance and brightness distributions over space. We believe that, for instance, Adelson’s tile pattern induces a lightness illusion that is not a brightness illusion. Indeed, as mentioned above, the same luminance pattern, namely that produced by the 3D wall of blocks (Logvinenko et al., 2002), brings about no illusion at all. Thus, if the tile illusion were a brightness illusion, then the luminance pattern from the 3D wall of blocks would have to result in the same effect as the original 2D-tile pattern because pre-processing of the proximal stimulus, by definition, cannot depend on what type of distal stimulus has produced this proximal stimulus. 
One might argue, however, that, while essentially reduced, the snake illusion does not disappear completely in the displays with 3D cubes as test objects. There are residual illusory effects, which might indicate that, at least partly, there is a brightness component in the snake illusion. However, we believe that this is highly unlikely to be the case because there is an alternative explanation of this residual illusory effect that we believe to be more plausible. As claimed recently, some lightness illusions, including the classical simultaneous lightness contrast, may be a result of a so-called anchoring effect, which is visually nonspecific and can be observed in different modalities (Logvinenko, 2002b). Moreover, it was shown that isolated strips cut from the snake pattern could produce a lightness shift of the same magnitude as observed in Experiment 2 for the display with 3D cubes, even when the luminance contrast between the squares and the strips was equal for both strips (Logvinenko, 2002b). The conclusion was made that the hoops themselves in the snake pattern could produce the anchoring effect, which was experienced as a lightness shift of the same type as the classical simultaneous contrast. Hence, it is very likely that the residual illusory effect observed for the display with 3D cubes is nothing more than the anchoring effect. If this is the case, then this residual illusory effect does not undermine our claim that the snake pattern produces no brightness illusion. 
If the lightness shift induced by the tile and snake pattern is not a brightness illusion, then it has to emerge at the higher levels where brightness (or more generally, the pre-processor’s output) is transformed into lightness. Because there is no one-to-one relationship between luminance (thus, brightness) and lightness, that is, the same luminance (thus, brightness) may bring about different lightness (e.g., Wallach, 1963; Gilchrist, 1994), lightness cannot be simply computed (restored) from luminance (thus, brightness). There should be a special process reducing this ambiguity (redundancy) of luminance (thus, brightness), which after Gilchrist et al. (1999) is referred to as a process of anchoring luminance (thus, brightness). The tile and snake illusions are most likely to arise at the level of the anchoring process. 
We believe that apparent illumination plays an important role in the process of anchoring brightness (Logvinenko, 1997). Furthermore, we believe that the tile and snake illusions are pure pictorial phenomena resulted from improper functioning of the same mechanism, which underlies lightness constancy with respect to illumination changes (Logvinenko, 1999; Logvinenko & Ross, in press). It explains why the 3D wall of blocks produces no illusion at all (Logvinenko et al., 2002), and the third display (with 3D cubes as test objects) in Experiments 2 and 3 also induced almost no lightness shift at all. 
Conclusion
Although the Hering-Helmholtz controversy on simultaneous lightness contrast has been debated for a very long time (e.g., Turner, 1994), we are still as far from consensus as we were in the beginning. The reason for this is not only that there are many mechanisms contributing to simultaneous lightness contrast, but also that the very phenomenon of simultaneous lightness contrast is not unique. We argue that there are two types of simultaneous lightness contrast – Hering’s type (e.g., grating induction) and Helmholtz’s type (e.g., Adelson’s tile and snake lightness illusions). Hence, one can hardly expect to account for these different types of simultaneous lightness contrast by employing a single mechanism. Each type requires its own explanation. 
Acknowledgments
This work was supported by the Biotechnology and Biosciences Research Council Grant 81/S13175 (to ADL). 
Commercial relationships: none. 
Corresponding author: Alexander D. Logvinenko. 
Address: Department of Vision Sciences, Glasgow Caledonian University, Cowcaddens Road, Glasgow, G4 0BA, UK. 
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Figure 1
 
A photograph of the 3D display of the cylinders and the test strip (see explanation in the text).
Figure 1
 
A photograph of the 3D display of the cylinders and the test strip (see explanation in the text).
Figure 2
 
Adelson’s snake pattern. Two small grey squares are printed with the same ink. Nevertheless, they look different because of the strong illusory effect induced by their different surrounds.
Figure 2
 
Adelson’s snake pattern. Two small grey squares are printed with the same ink. Nevertheless, they look different because of the strong illusory effect induced by their different surrounds.
Figure 3
 
Extracted histograms of the lightness matches obtained for the test objects presented against the light and dark strips in each of the three displays in Experiment 2. Munsell matches are along the vertical axis. The ends of the boxes are the first and third quartiles. Hence, the height of the boxes is the interquartile range. A horizontal line in the box is drawn at the median. An upper whisker is drawn at the largest match; a bottom whisker is drawn at the smallest match.
Figure 3
 
Extracted histograms of the lightness matches obtained for the test objects presented against the light and dark strips in each of the three displays in Experiment 2. Munsell matches are along the vertical axis. The ends of the boxes are the first and third quartiles. Hence, the height of the boxes is the interquartile range. A horizontal line in the box is drawn at the median. An upper whisker is drawn at the largest match; a bottom whisker is drawn at the smallest match.
Figure 4
 
The snake pattern with blurred horizontal borders between the strips. The sinusoidal luminance gradient arising from such blurring is very similar to that in the sinusoidal gratings bringing about the grating induction effect.
Figure 4
 
The snake pattern with blurred horizontal borders between the strips. The sinusoidal luminance gradient arising from such blurring is very similar to that in the sinusoidal gratings bringing about the grating induction effect.
Figure 5
 
The results of Experiment 3 (see explanation in the caption to Figure 3).
Figure 5
 
The results of Experiment 3 (see explanation in the caption to Figure 3).
Table 1
 
Mean luminance (cd/m2) of the test objects and the corresponding background strip and mean luminance contrast (test vs. background) in Experiments 2 and 3.
Table 1
 
Mean luminance (cd/m2) of the test objects and the corresponding background strip and mean luminance contrast (test vs. background) in Experiments 2 and 3.
Display Expt. 2 Background Test Contrast Expt. 3 Test
1 Light strip 1312 1220 −0.0392 1200
Dark strip 900 1213 0.1511 1187
2 Light strip 1320 1223 −0.0381 1245
Dark strip 902 1222 0.1508 1237
3 Light strip 1319 1219 −0.0394 1245
Dark strip 898 1217 0.1509 1232
Table 2
 
Mean, median, and the Hodges-Lehmann estimators (H-L E) of the Munsell matches obtained in Experiments 2 and 3.
Table 2
 
Mean, median, and the Hodges-Lehmann estimators (H-L E) of the Munsell matches obtained in Experiments 2 and 3.
Display Expt. 2
Mean Median H-LE
1 Light strip 5.91 6.00 2.65
Dark strip 8.62 8.75
2 Light strip 7.14 7.50 1.125
Dark strip 8.43 8.50
3 Light strip 7.47 7.50 0.875
Dark strip 8.33 8.50
Display Expt. 3
Mean Median H-L E
1 Light strip 6.14 6.25 2.25
Dark strip 8.38 8.50
2 Light strip 7.40 7.50 1.00
Dark strip 8.44 8.50
3 Light strip 7.49 7.75 0.875
Dark strip 8.43 8.50
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