Spatial Vision, Vol. 18, No. 1, pp. 25 – 72 (2005) VSP 2005.
Also available online - www.vsppub.com
Adelson’s tile and snake illusions: A Helmholtzian type of simultaneous lightness contrast ALEXANDER D. LOGVINENKO 1,∗ and DEBORAH A. ROSS 2,∗∗ 1 Department of Vision Sciences, Glasgow Caledonian University, Glasgow, G4 0BA, 2 School of Psychology, The Queen’s University of Belfast, Belfast, BT7 1NN, UK
UK
Received 26 March 2004; accepted 28 April 2004 Abstract—Adelson’s tile, snake, and some other lightness illusions of the same type were measured with the Munsell neutral scale for twenty observers. It was shown that theories based on low-level luminance contrast processing could hardly explain these illusions. Neither can those based on luminance X-junctions. On the other hand, Helmholtz’s idea, that simultaneous lightness contrast originates from an error in judgement of apparent illumination, has been elaborated so as to account for the tile and snake illusions as well as other demonstrations presented in this report. Keywords: Lightness perception; anchoring effect; apparent illumination; apparent transparency; apparent illumination/lightness invariance; lightness constancy.
INTRODUCTION
A series of elegant lightness illusions produced by Adelson (1993) have had a farreaching impact on lightness perception studies in the last decade (e.g. Albright, 1994; Blakeslee and McCourt, 2003; Kingdom, 1999, 2002; Paradiso, 2000; Schirillo and Shevell, 2002). Although a number of attempts have been made to explain (Bressan, 2001; Gilchrist et al., 1999; Todorovic, 2003; Wishart et al., 1997) and/or to model them (e.g. Blakeslee and McCourt, 1999; Dakin and Bex, 2002; McCann, 2001; Ross and Pessoa, 2000), they still remain quite a challenge to visual scientists. For instance, we still do not know why the tile (Fig. 1a) and snake (Fig. 2) illusions are much stronger than the classical simultaneous lightness contrast effect (Fig. 3). Does it follow that Adelson’s illusions and classical simultaneous lightness * E-mail: ** E-mail:
[email protected] [email protected]
26
A. D. Logvinenko and D. A. Ross
(a) Light strip
(b)
Dark strip
Light strip
Dark strip
Reflectance
Median
Reflectance
Median
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 6.75 4.75
0.48 0.43 0.29
7.75 7.25 5.50
0.79 0.48 0.43
9.00 6.00 4.50
0.48 0.29 0.26
7.25 5.25 4.25
Figure 1. (a) Tile pattern (after Adelson, 1993). The original Adelson tile pattern is modified so that (i) there is a patch (with reflectance 0.48) that is included in both the ‘light’ and ‘dark’ strips; (ii) the reflectances of the patches in the ‘light’ and ‘dark’ strips are in approximately same proportions: 0.48 : 0.29, and 0.79 : 0.48. The diamonds in both strips have the same reflectance (0.43). However, they appear different in lightness. (b) The modified tile pattern. The diamonds in the ‘light’ strips have a reflectance of 0.43 while those in the ‘dark’ strips have a reflectance of 0.26, yet they look remarkably similar.
contrast are different visual phenomena? If not, which features of Adelson’s patterns strengthen the effect? There are, at least, four differing explanatory approaches to Adelson’s illusions: (i) the low-level explanation based on the local contrast around the target (diamond) borders (e.g. Cornsweet, 1970; Whittle, 1994a, b) and its recent modifications (e.g. Blakeslee and McCourt, 1999, 2003; McCann, 2001); (ii) a mid-level explanation emphasizing the role of the borders between strips or the type of the luminance junctions across the strips (Adelson, 1993, 2000; Anderson, 1997; Todorovic, 1997); (iii) the anchoring theory (Gilchrist et al., 1999); and (iv) a highlevel explanation enunciated by H. Helmholtz (1867) who thought that lightness illusions such as simultaneous lightness contrast resulted from a ‘misjudgement of illumination’ (Adelson, 1993; Adelson and Pentland, 1996; Kingdom, 2003; Logvinenko, 1999).
A Helmholtzian type of simultaneous lightness contrast
Light strip
27
Dark strip
Reflectance
Median
Reflectance
Median
0.73 0.61 0.52
8.75 7.00 5.50
0.52 0.37 0.31
8.75 6.25 5.50
Figure 2. Snake pattern (after Adelson, 2000). The snake pattern is also modified so that make the ratios of the abutting patches in the ‘light’ and ‘dark’ strips as close as possible (0.73 : 0.37 and 0.61 : 0.31). The diamonds in the ‘dark’ and ‘light’ strips have the same reflectance 0.52; however, they look different.
Figure 3. The classical simultaneous lightness contrast display. When presented against different backgrounds, the square targets of the same reflectance look slightly different in lightness.
It is easy to show that local luminance contrast plays a minor role, if any, in Adelson’s illusions. Indeed, the tile illusion is known to almost disappear after a slight rearrangement of the pattern (Adelson, 1993). For instance, the local contrast around diamonds borders in Figs 4 and 5 is the same as in Fig. 1a but
28
A. D. Logvinenko and D. A. Ross
Light strip
Dark strip
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 7.00 6.00
0.48 0.43 0.29
7.00 6.50 4.75
Figure 4. Ribbon pattern. It is made from the tile pattern (Fig. 1a) by shifting the ‘light’ strips to the right so as to align the patches with the reflectance 0.48.
the illusion is hardly observed in these pictures. A similar dependence on the spatial rearrangement which does not affect the local luminance contrast around the diamonds’ border was recently shown for the snake illusion too (Logvinenko et al., in press). On the other hand, the snake illusion may be observed, though in reduced form, even when the target diamonds have the same local contrast (Fig. 6). Likewise, the borders between strips and luminance junctions are not necessary for observing Adelson’s tile and snake illusions. Blurring the border between the strips, for instance, does not reduce the snake illusion despite the distortion of some of the luminance junctions and borders (Fig. 7). Furthermore, the tile illusion may even be enhanced by blurring the border between strips (Logvinenko, 1999, 2002b; Logvinenko and Kane, 2003). Figures 8 and 9 also show that the illusory lightness shift between the diamonds can be observed without borders between strips. Figure 8 is made up of only light strips of Fig. 1a whereas Fig. 9 consists of only dark strips of Fig. 1a. As one can see, the difference in the diamonds’ lightness in Figs 8 and 9 is quite large. A Helmholtzian type of explanation is essentially based on the assumption that lightness and apparent illumination are not independent; that is, they are locked in a certain relationship, such as an apparent illumination/lightness invariance (Logvinenko, 1997, 1999). It implies that if a misjudgement of illumination occurs,
A Helmholtzian type of simultaneous lightness contrast
Light strip
29
Dark strip
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 7.50 6.25
0.48 0.43 0.29
7.00 6.50 5.00
Figure 5. Hex pattern (after Adelson, 1993). It is made up from the patches of the same reflectance as the tile pattern (Fig. 1a).
it must affect lightness. For example, the tile pattern in Fig. 1a is perceived as a 3D wall of blocks viewed through a striped filter, implying that apparent illumination of the alternate strips is different. This difference in apparent illumination between the strips brings about the corresponding difference in lightness — the diamonds in the strips, which appear to have the lower illumination, look lighter in accord with the apparent illumination/lightness invariance. Since lightness constancy can be thought as a particular case of this invariance (Logvinenko, 1997), Adelson’s tile illusion and lightness constancy might have a common explanation. Fig. 1b provides a strong support for this conjecture, that is, that Adelson’s tile illusion and lightness constancy are two sides of the same coin — the apparent illumination/lightness invariance. It is the same pattern as Fig. 1a, where the luminance ratio across the horizontal borders is 1.65, except that the diamonds in the lighter strips have reflectivity 1.65 times that of the diamonds in the darker strips. If the visual system interprets the luminance ratio across the horizontal borders in Figs 1a and 1b as that of the strips’ illuminations, then Fig. 1b should produce no illusion at all, that is, the diamonds in alternate rows in Fig. 1b should look the same. Indeed, being physically different, the diamonds in the alternate rows in Fig. 1b look very similar, thus exhibiting a nearly perfect lightness constancy phenomenon.
30
A. D. Logvinenko and D. A. Ross
Light strip
Dark strip
Reflectance
Median
Reflectance
Median
0.43
5.00
0.43
7.25
Figure 6. Iso-contrast snake pattern. While a striped structure seems to be quite distinctive, it is an illusion. So is an apparent difference in lightness between the diamonds. Both diamonds are the same (reflectance 0.43); and they are surrounded by the surface of the same reflectance (0.50). Apparent strips emerge from horizontal arrays of dark (reflectance 0.23) and light (reflectance 0.77) hoops.
It is important for such an explanation to specify what sort of information the visual system uses to infer that the alternating strips in Figs 1 and 2 are differently illuminated. Adelson believes that it is luminance X-junctions that signal the difference in apparent illumination between the strips (Adelson, 1993, 2000). Also, it may be constancy of the luminance ratio across the borders (Logvinenko, 2002d). Both may contribute to the illusions since removing the borders (Figs 8 and 9) reduces the illusion. However, neither luminance X-junctions nor constancy of the luminance ratio are the only cues for apparent illumination in Figs 1 and 2, since the walls of blocks depicted in Figs 8 and 9 still look differently illuminated despite the fact that there is neither luminance X-junctions nor constancy of the luminance ratio in these pictures. This implies that the global pictorial content of Figs 8 and 9 can in itself bring about the difference between the apparent (pictorial) illuminations in these figures, thus inducing (in line with a Helmholtzian type prediction) the corresponding lightness shift. Still, the illusion can be experienced when the global pictorial content (i.e. the wall of blocks) is absent. Indeed, the illusion emerges even for isolated strips (Fig. 10). While there is neither 3D pictorial content nor luminance X-junctions in Fig. 10, the diamonds in the upper strip still look darker than those in the bottom strip. The fact that the isolation of the strips in Fig. 1a only reduces the illusion
A Helmholtzian type of simultaneous lightness contrast
Light strip
31
Dark strip
Reflectance
Median
Reflectance
Median
0.51
5.75
0.51
9.00
Figure 7. Blurred snake pattern. The horizontal borders of the snake pattern (Fig. 2) were blurred so that the luminance varies sinusoidally along the vertical dimension.
but does not completely eliminate it indicates that Helmholtzian misjudgement of illumination is not the only cause of the illusion. There should be some other, local rather than global, factors contributing to the effect. The present report is devoted to studying the contribution of various factors, local as well as global, to Adelson’s tile and snake illusions.
EXPERIMENT 1
The purpose of this experiment was (i) to measure the strength of the illusion for the pictures presented above; (ii) to study quantitatively the contribution of different configurational elements by breaking the tile and snake patterns into their parts — strips, tiles, and patches. The main experiment was preceded by a preliminary one during which the observers had been trained to evaluate the lightness of simple grey patches on a white background. Methods Observers. Twenty observers (8 males and 12 females, age range 20–41) took part in the experiment. All the observers were naïve as to the purpose of the experiment. All had normal or corrected to normal vision.
32
A. D. Logvinenko and D. A. Ross
Reflectance
Median
0.79 0.48 0.43
9.25 6.75 5.00
Figure 8. ‘Light’ wall of blocks pattern. It comprises only ‘light’ strips in Fig. 1a.
Stimuli and apparatus. In the preliminary experiment we used eight grey squares on the white background the reflectances of which were as follows: 0.79; 0.48; 0.43; 0.39; 0.31; 0.29; 0.23; and 0.16. This choice was motivated by the fact that the patches constituting the tile and snake patterns had these reflectances. In the main experiment the observers were presented with the patterns (13.4 × 13.4 cm) shown above (Figs 1–9) along with isolated strips for the tile (Fig. 10) and snake patterns (Figs 11 and 12), and isolated tiles for the tile pattern (Figs 13–15). Among these, eight classical simultaneous lightness contrast displays (Fig. 3), with different target squares, were used. The reflectance of the target square was one of the eight values that were used in the preliminary experiment. The rationale was to measure the classical simultaneous contrast effect for all the patches involved in the tile and snake patterns. Each pattern, printed on an A4 sheet of white paper, was mounted on the white wall in front of an observer who sat at a distance of 1 m in an experimental room with ordinary illumination. Two tungsten lamps were used to make an illumination of the test pictures as homogeneous across space as possible. Luminance measurements from eight different points across the display area showed that the illumination variation was statistically insignificant (p = 0.36). The mean luminance for the white background of the display area was 100 cd/m2 .
A Helmholtzian type of simultaneous lightness contrast
Reflectance
Median
0.48 0.43 0.29
7.50 7.00 5.25
33
Figure 9. ‘Dark’ wall of blocks pattern. It comprises only ‘dark’ strips in Fig. 1a.
The 31-point Munsell neutral scale was used to evaluate the lightness of the test patches. The Munsell chips (2 × 5 cm each) were attached to the same white wall next to the stimulus display. Procedure and experimental design. Each stimulus display was presented one at a time to an observer who was asked to select a Munsell chip that matched the test patch. (Since the diamond patches (reflectance 0.43) and the patches with reflectance 0.48 were included in both light and dark strips of the tile pattern, each of them counted as two different test patches tested independently.) Using a laser pointer, the experimenter pointed out (in random order) which particular patch was to be matched. Observers also used a laser pointer to indicate their match. After an observer completed the matches for all patches in the stimulus pattern, it was replaced by another pattern on a random basis. The whole set of stimulus patterns was divided into four groups, the pictures of just one group being presented in a random order during one experimental session lasting approximately half an hour. Not more than one session a day was conducted with each observer. Each session was repeated ten times in the preliminary experiment and five times in the main experiment with each observer so that in all two hundred matches were made for each test patch in the preliminary and one hundred in the main experiment1 .
34
A. D. Logvinenko and D. A. Ross
Light strip
Dark strip
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 6.50 5.75
0.48 0.43 0.29
7.50 7.00 5.375
Figure 10. Two separated strips of which the tile pattern (Fig. 1a) is made up.
Results The results of the preliminary experiment are presented in Table 1, and in Fig. 16 as a multiple boxplot graph (‘extracted’ histograms). Among other things, the graph shows the median matches and the interquartile ranges for all eight reflectances studied in the preliminary experiment2 . Table 2 and Fig. 17 show the classical simultaneous lightness contrast effect for various target squares (Fig. 3). To be more exact, Fig. 17 represents ‘extracted’ histograms of differences between Munsell matches made for the same target square on the white and black backgrounds. While the Friedman rank test showed the reflectance of the target square in Fig. 3 was significant (p = 0.04), as follows from Fig. 17, the simultaneous lightness contrast shift was approximately the same for all target squares irrespective of their reflectance. It should be mentioned that while the Munsell neutral scale is generally believed to be of the interval type, there is not sufficient evidence for this. On the contrary, it was argued that lightness matching was of the ordinal nature (Logvinenko, 2002d). So we chose to use non-parametric statistics in this study (with 5% level of significance). Specifically, we used the Wilcoxon signed-rank test to establish if there was a significant difference between lightness of the test objects in two different surroundings (e.g. in ‘light’ and ‘dark’ strips in the tile and snake patterns).
A Helmholtzian type of simultaneous lightness contrast
Light strip
35
Dark strip
Reflectance
Median
Reflectance
Median
0.73 0.61 0.52
8.75 7.75 6.25
0.52 0.37 0.31
8.75 6.00 4.75
Figure 11. Strips constituting the snake pattern (Fig. 2).
If this difference was statistically significant we claimed that a lightness illusion was observed. To evaluate the magnitude of the illusion, we used a non-parametric estimator of the shift between two distributions of the matches (i.e. obtained for ‘light’ and ‘dark’ strips in the tile and snake patterns) — the Hodges–Lehmann estimator3 associated with Wilcoxon’s signed rank statistic (Hollander and Wolfe, 1973, p. 33). As seen in Table 2, the simultaneous lightness contrast effect in terms of the Hodges–Lehmann estimator varied from 0.375 to 0.625 Munsell units4 . The median Munsell matches, obtained in the main experiment for each patch, are presented beneath each pattern (Figs 1–15). Table 3 presents the median and mean Munsell matches obtained for the diamonds (reflectance 0.43 for Figs 1, 2, 4–10, and 13–15; and 0.52 for Figs 11 and 12) in the ‘light’ and ‘dark’ surround. Fig. 18 shows the lightness shift between the diamonds in the ‘light’ and ‘dark’ surround. The Hodges–Lehmann estimator of the shift can be found in Table 3. As one can see, the ribbon (Fig. 4) and hex (Fig. 5) patterns produced the smallest, though statistically significant lightness shifts (Wilcoxon signed-rank normal statistic with correction Z = 5.18 and 5.22 respectively, p < 0.01). The Wilcoxon signed-rank test showed a significant difference between the simultaneous lightness contrast effect measured for the test patch of the same reflectance as the diamonds (i.e. 0.43), and the lightness shift obtained for the ribbon pattern (Z = 2.33, p = 0.02). Therefore, the illusion produced by the ribbon pattern
36
A. D. Logvinenko and D. A. Ross
Light strip
Dark strip
Reflectance
Median
Reflectance
Median
0.77 0.50 0.43
9.00 6.75 5.50
0.50 0.43 0.23
8.00 6.75 4.25
Figure 12. Strips constituting the iso-contrast snake pattern (Fig. 6).
(Fig. 4) is even weaker than the simultaneous lightness contrast effect (Fig. 3). While the Hodges–Lehmann estimator for the hex pattern (Fig. 5) was also found to be smaller than that for the simultaneous lightness contrast display, there was no significant difference between these two distributions (Wilcoxon signed-rank normal statistic with correction Z = 1.56, p = 0.12). The lightness shift observed for the isolated tiles was approximately of the same magnitude as the simultaneous lightness contrast effect. The Friedman rank test showed a non-significant difference between these patterns for both the diamond (p = 0.29) and the patch with reflectance 0.48 (p = 0.23). The lightness shifts produced by the isolated strips were significantly stronger than that produced by the isolated tiles. Specifically, the Friedman rank test showed a significant effect when the data registered for the isolated strips cut from the tile pattern were combined with those registered for isolated tiles (Friedman χ 2 = 47.5, df = 3, p < 0.01). In line with the previous studies, a remarkably strong lightness shift was obtained for the tile and snake patterns, the snake pattern producing the strongest illusion (Wilcoxon signed-rank normal statistic with correction Z = 6.70, p < 0.01). Moreover, the lightness shift observed for the isolated strips from the snake pattern (Fig. 11) was of the same strength as that observed for the tile pattern (Fig. 1a), there being no significant difference between them (Z = 0.34, p = 0.73). The blurred-
A Helmholtzian type of simultaneous lightness contrast
Light tile
37
Dark tile
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 6.50 5.75
0.48 0.43 0.29
7.25 6.50 5.125
Figure 13. Tiles from the Fig. 1a.
snake pattern (Fig. 7) produced as strong an illusion as the original snake pattern (Fig. 2). The Wilcoxon signed-rank test showed no significant differences between the lightness shifts for these two patterns (Z = 0.49, p = 0.63). While the illusion produced by the iso-contrast snake pattern (Fig. 6) was significantly smaller than that measured for the tile-pattern in Fig. 1a (Wilcoxon signed-rank normal statistic with correction Z = 4.41, p < 0.01), it was much higher than for the simultaneous lightness contrast effect (Fig. 3). The difference in lightness between the diamonds observed for the wall-of-block patterns (Figs 8 and 9) was significantly smaller than the lightness shift produced by the tile pattern in Fig. 1a (Wilcoxon rank-sum5 normal statistic with correction Z = 4.47, p < 0.01) but larger than that produced by isolated tile strips in Fig. 10 (Wilcoxon rank-sum normal statistic with correction Z = 2.05, p = 0.04). It should be pointed out that a significant lightness shift was observed not only for the diamonds but also for the patches with reflectance 0.48 (Table 4 and Fig. 19). While significantly less, it was in the same direction as the lightness shift for the diamonds with one exception (Fig. 20) — in Fig. 5 it looked significantly darker in the ‘dark’ surround and lighter in the ‘light’ (the Wilcoxon signed-rank test, p < 0.01). The darkest patch in the tile pattern (reflectance 0.29) also changed its appearance (Table 5 and Fig. 21). Specifically, it became significantly lighter in the tile pattern
38
A. D. Logvinenko and D. A. Ross
Light tile
Dark tile
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 6.50 5.75
0.48 0.43 0.29
7.25 6.50 5.00
Figure 14. The same tiles as in Fig. 13 except that the diamonds are separated from the other patches.
in Fig. 1a. For example, having considerably lower reflectance than the diamond it looked lighter than the diamond in the ‘light’ strip. Thus, we observe that in the tile pattern (Fig. 1a) all the patches in the ‘dark’ strips appeared lighter, and those in the ‘light’ strips darker, except for the lightest patch with reflectance 0.79, the median Munsell match for which was the same (9.25) for all of the patterns6 . A similar ‘lightness shift’ between alternating strips was observed in Fig. 1b too. Note that the magnitude of this shift was approximately as much as to make the diamonds in the alternating strips in Fig. 1b look nearly the same. Indeed, the median difference between the Munsell matches (as well as the Hodges–Lehmann estimator) for the diamonds in the light and dark strips for Fig. 1b was 0.25. While being statistically significant (the signed rank Wilcoxon test, p < 0.01), the illusion in the modified tile pattern (Fig. 1b) was reduced by a factor of 10 as compared to that in Fig. 1a. Discussion These results provide strong evidence against any low-level explanation of the tile and snake illusions based on the local luminance contrast between the diamonds and their immediate surround. Indeed, the diamonds in the tile (Fig. 1a), ribbon
A Helmholtzian type of simultaneous lightness contrast
Light tile
39
Dark tile
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 6.75 5.75
0.48 0.43 0.29
7.375 6.75 5.00
Figure 15. Another set of tiles from Fig. 1a.
(Fig. 4), and hex (Fig. 5) patterns, as well as in the isolated strips (Fig. 10) and tiles (Figs 13–15) patterns, have the same local contrast. However, the illusion observed for these patterns varies in strength across a rather wide range — from 0.25 Munsell units (the ribbon pattern) to 2.375 Munsell units (the tile pattern). There should be some other factor, which reduces the tile and snake illusions by nearly a factor of 10. Furthermore, as shown recently, the tile illusion completely disappears when the tile pattern is implemented as a real 3D wall of blocks with the same diamond/surround local contrast (Logvinenko et al., 2002). On the other hand, the iso-contrast snake pattern (Fig. 6) produces the illusion which is much stronger than the ribbon (Fig. 4) and hex (Fig. 5) patterns. While the diamond/surround local contrast is equal for all the strips in this pattern, it yields almost as strong an illusion as that produced by the tile pattern. Hence, the difference in local contrast is neither necessary nor sufficient to experience the illusion. The mid-level explanation based on the luminance junctions and constancy of the luminance ratio only has not been supported by the data either. Really, removing the borders between the strips in the snake pattern (Fig. 7) was not shown to affect the illusion. Also, quite large differences between the corresponding diamonds’ lightness was found in Figs 8–10 where there was no striped structure.
40
A. D. Logvinenko and D. A. Ross
Figure 16. The results of the preliminary experiment. Reflectance of the target is on the horizontal axis. Munsell match is 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 that is less than or equal to the third quartile plus 1.5 times the interquartile range. Likewise, a bottom whisker is drawn at the smallest match that is greater than or equal to the first quartile plus 1.5 times the interquartile range. All the matches which fall outsides of the range marked by the whiskers are indicated by individual lines. Table 1. Median and mean Munsell matches obtained in the preliminary experiment Target reflectance
Median
Mean
0.16 0.23 0.29 0.31 0.39 0.43 0.48 0.79
4.00 5.00 5.75 5.75 6.50 6.75 7.00 9.00
4.15 5.04 5.68 5.83 6.49 6.76 7.01 8.86
Therefore, the luminance junctions and sharp luminance borders are not necessary for observing the illusion. Still, the illusion produced by the plain walls (Figs 8 and 9) as well as the isolated strips (Fig. 10) is significantly smaller than for the tile pattern (Fig. 1a). The obvious
A Helmholtzian type of simultaneous lightness contrast
41
Figure 17. Classical simultaneous lightness contrast effect. The horizontal axis is reflectance of the target square in Fig. 3. The difference between Munsell matches for the black and white backgrounds is on the vertical axis. Table 2. Median and mean Munsell matches, and the Hodges–Lehmann estimator, obtained for the classical simultaneous contrast display (Fig. 3) Target reflectance
Light surround
Dark surround
Median
Mean
Median
Mean
Hodges–Lehmann estimator
0.16 0.23 0.29 0.31 0.39 0.43 0.48 0.79
4.00 5.00 5.75 6.00 6.50 7.00 7.25 9.00
4.03 5.10 5.78 5.97 6.51 6.90 7.21 8.86
4.75 5.75 6.25 6.50 7.00 7.25 7.75 9.25
4.66 5.71 6.37 6.63 7.12 7.40 7.76 9.25
0.50 0.50 0.50 0.625 0.625 0.50 0.625 0.375
difference between these patterns is that Fig. 1a contains the luminance border with a constant luminance ratio across it (and the X-luminance junctions) whereas Figs 8–10 do not. Hence, the luminance junctions and constancy of the luminance ratio may have an enhancing effect on the illusion. This issue will be looked at in more detail in the next section (Experiment 2).
42
A. D. Logvinenko and D. A. Ross
Figure 18. Lightness illusory shift observed for the diamonds (reflectance 0.43) in various displays.
Table 3. Median and mean Munsell matches, and the Hodges–Lehmann estimator, obtained for the diamonds in Figs 1a, 1b, 2, and 4–15 Figure number
Reflectance
1a 1b 2 4 5 6 7 8/9 10 11 12 13 14 15
0.43 0.43/0.26 0.52 0.43 0.43 0.43 0.51 0.43 0.43 0.52 0.43 0.43 0.43 0.43
Light strip Median
Mean
Dark strip Median
Mean
Hodges–Lehmann estimator
4.75 4.50 5.50 6.00 6.25 5.00 5.75 5.00 5.75 6.25 5.50 5.75 5.75 5.75
4.87 4.36 5.27 5.96 6.11 5.16 5.52 5.13 5.45 6.05 5.32 5.59 5.53 5.54
7.25 4.25 8.75 6.50 6.50 7.25 9.00 7.00 7.00 8.75 6.75 6.50 6.50 6.75
7.35 4.29 8.70 6.40 6.50 7.19 8.86 6.75 6.85 8.53 6.63 6.54 6.49 6.59
2.375 0.25 3.375 0.25 0.25 2.125 3.375 1.75 1.375 2.50 1.25 0.875 1.00 0.875
A Helmholtzian type of simultaneous lightness contrast
43
Figure 19. Lightness illusory shift observed for the patch with reflectance 0.48 in various displays. Table 4. Median and mean Munsell matches, and the Hodges–Lehmann estimator for the patch with reflectance 0.48 Figure number
Light strip
Dark strip
Median
Mean
Median
Mean
Hodges–Lehmann estimator
1a 1b 4 5 8/9 10 13 14 15
6.75 6.00 7.00 7.50 6.75 6.50 6.50 6.50 6.75
6.56 5.91 6.98 7.47 6.68 6.53 6.50 6.45 6.63
7.75 7.25 7.00 7.00 7.50 7.50 7.25 7.25 7.375
7.67 7.28 6.90 7.02 7.39 7.43 7.09 7.11 7.31
1.00 1.25 0.00 −0.25 0.75 0.75 0.375 0.50 0.50
At the same time, the data testify unequivocally in favour of the Helmholtzian type of explanation based on the idea of misjudgement of illumination. According to this idea the black half of the background in the classical simultaneous lightness contrast display might be perceived as if it is less illuminated than the white half (Fig. 3). If this is the case, then the luminance edge dividing the background into the black and white halves gives rise to not only a lightness edge but to an apparent illumination edge as well. However, it remains unclear in Helmholtzian
44
A. D. Logvinenko and D. A. Ross
Figure 20. The Hodges–Lehmann estimator of the illusory lightness shift for the diamonds (reflectance 0.43) and the patch with reflectance 0.48 in various displays.
writings why such a ‘misjudgement’ of the illumination of the black half of the background should affect the lightness. We believe that this is because the apparent illumination and lightness are interlocked into the apparent illumination/lightness invariance (Logvinenko, 1997, 1999). Furthermore, a luminance edge determines a reciprocal pair of lightness and apparent illumination edges. As a result, given a particular contrast of the luminance border, if the apparent illumination of the black background is underestimated it entails a corresponding overestimation of the lightness of the target on this background and of the background itself. While it is not clear whether such an explanation is valid for the classical simultaneous lightness contrast, it certainly works for the tile and snake illusions. Consider, for instance, the original and modified tile patterns (Figs 1a and 1b). At first glance we seem to have obtained a paradoxical result. When the diamonds in the alternated rows in Fig. 1a are physically the same they appear very different, but when they are different (Fig. 1b) they look quite similar in lightness. However, this is exactly what would be expected if the tile illusion and lightness constancy have a common root (the apparent illumination/lightness invariance). If the visual system interprets the alternative strips in Fig. 1b as being differently illuminated, and takes into account this difference when assigning the same lightness to the diamonds in different rows, then it is more than likely that the same taking-into-account will occur for Fig. 1a as well. It should be pointed out, however, that the idea of ‘misjudgement of illumination’ is not specific enough to be a genuine explanation. It requires further elaboration. First of all, one has to specify what illumination is supposed to be subject to ‘misjudgement’. In the present context it is worth distinguishing between an absolute (ambient) and relative illuminations (Kingdom, 2002; Logvinenko, 1997). An increase of the intensity of the only light source in the scene results in a change
A Helmholtzian type of simultaneous lightness contrast
45
Figure 21. Lightness illusory shift observed for the patch with reflectance 0.29 in various displays. Table 5. Median and mean Munsell matches for the patch with reflectance 0.29 Figure number
Median
Mean
1a 1b 4 5 9 10 13 14 15
5.50 5.25 4.75 5.00 5.25 5.375 5.125 5.00 5.00
5.41 5.18 4.89 5.17 4.99 5.34 5.16 5.20 5.24
in only the absolute, not relative illumination. A difference in relative illumination can be observed between shadowed and non-shadowed (highlighted) areas7 . The luminance ratio between the shadowed and non-shadowed areas remains constant when the ambient illumination changes (Logvinenko, 2002d; Marr, 1982, p. 90). As known, there are two types of shadows, namely, cast and attached ones. The former are caused by the spatial layout of the scene. The latter arise due to the spatial relief of a particular object. Accordingly, we shall distinguish between the
46
A. D. Logvinenko and D. A. Ross
relative illumination of the cast-shadow type and the relative illumination of the attached shadow type. The difference in illumination of all the three types can be observed in our pictures8 . For instance, the difference in the apparent ambient illumination is seen between Figs 8 and 9. The difference in the apparent relative illumination of the cast-shadow type is clearly observed between the horizontal strips in Figs 1 and 2. The lateral sides of the cubes in Fig. 5 differ in the apparent relative illumination of the attached-shadow type. It is easy to see that every picture presented above is readily segmented into areas of equal apparent illumination. We shall call them equi-illuminated frames9 . According to the three types of apparent illumination, there are three levels of equiilluminated frames. These levels are hierarchally subordinated. More specifically, a pictorial fragment can belong to only one equi-illuminated frame of the same level, but it can belong to different equi-illuminated frames of different levels. For instance, in Fig. 5 there is just one equi-illuminated frame at the level of ambient illumination and at the level of cast shadow (i.e. the pattern as a whole); and there are three equi-illuminated frames at the level of attached shadow (the sides of the blocks). Likewise, Fig. 1a contains the same three equi-illuminated frames at the level of attached shadow and one equi-illuminated frame at the level of ambient illumination, but in this picture there are two different equi-illuminated frames at the level of cast shadow (i.e. the horizontal strips). In Fig. 10 there are two different equi-illuminated frames at the level of ambient illumination (the strips), one equiilluminated frame at the level of cast shadow, and three equi-illuminated frames at the level of attached shadow. The apparent illumination/lightness invariance predicts that two equiluminant (i.e. of the same luminance) patches belonging to different equi-illuminated frames will be perceived as being of a different lightness. More specifically, the equiluminant patch belonging to the darker equi-illuminated frame will appear lighter, and the equiluminant patch belonging to the brighter equi-illuminated frame will look darker. It accounts for why the diamonds in the dark strips of the tile pattern appear lighter than the same diamonds in the light strips — these alternating strips belong to the different equi-illuminated frames at the level of cast shadow. Furthermore, it also explains why the patch with the reflectance 0.48 in the hex pattern (Fig. 5) appeared darker in the dark strip contrary to what is observed in the tile pattern (Fig. 1a) where it appeared lighter in the dark strip. In Fig. 5 this patch belongs to different equi-illuminated frames only at one level (attached shadow). On the contrary, in Fig. 1a this patch belongs to different equi-illuminated frames at two levels (attached and cast shadow). At the level of attached shadow it belongs to the more illuminated frame. This explains why in Fig. 5 it looks darker10 . However, at the level of cast shadow it belongs to the less illuminated frame, thus it has to look lighter. As we can see in Fig. 1a, this apparent perceptual conflict is resolved in favour of the equi-illuminated frame at the level of cast shadow, that is, the patch in question looks lighter. Nevertheless, the lightness shift observed for the patch with
A Helmholtzian type of simultaneous lightness contrast
47
reflectance 0.48 is generally lower as compared to that for the diamonds (Fig. 20). Such a reduction of the illusory shift is a consequence of the perceptual conflict in which this patch is involved. A further problem is how the visual system carries out the segmentation of the whole scene into equi-illuminated frames. In other words, what cues does the visual system use to infer differences in illumination? It is clear that such cues might be different at different levels of illumination. For example, a distribution of luminances in the whole scene may be an important source of information about the ambient illumination (Adelson, 2000). If it is shifted towards the darker (respectively, lighter) end in one scene as compared to another it may indicate that the ambient illumination in this scene is lower (respectively, higher) than in the other. Perhaps, this is why Fig. 8 looks more illuminated than Fig. 9. As mentioned above, the type of luminance junctions and the constancy of the luminance ratio across the luminance border may play an important role in the segmentation into equi-illuminated frames at the level of cast shadow. Indeed, splitting the tile pattern into separate strips where there are neither luminance junctions nor luminance borders considerably reduces the illusion. As the segmentation into equi-illuminated frames at the level of attached shadow is intimately connected with the perception of 3D shape, the classical depth cues may contribute to it, thus affecting lightness perception. While the role of depth cues in lightness perception is well-known (Bloj and Hurlbert, 2002; Freeman et al., 1993; Gilchrist, 1977; Knill and Kersten, 1991; Logvinenko and Menshikova, 1994; Mach, 1959), it has not always been realised that their effect on lightness is mediated by that they, first of all, affect the apparent illumination and as a result of this — lightness. This explains why the tile illusion is so sensitive to spatial rearrangements of the pictorial content. For example, the ribbon pattern (Fig. 4) differs from the original tile pattern (Fig. 1a) only by a small horizontal shift of the alternating strips (the patches with reflectance 0.48 are abutting in Fig. 4, whereas they are shifted relative to each other in Fig. 1a). However, the illusion in Fig. 4 nearly disappears. It happens because the 3D pictorial content in Fig. 4 is rather different (a ribbon against the black-white striped background). A new pictorial content invokes a new segmentation into equi-illuminated frames. In contrast with Fig. 1a, where there are two different equi-illuminated frames at the level of cast shadow, Fig. 4 contains only one equi-illuminated frame at the level of cast shadow. As all the diamonds belong to the same equi-illuminated frame at the level of cast shadow, they look nearly the same. The segmentation into equi-illuminated frames must be followed by evaluation of how frames differ from each other in terms of the illumination magnitude. Having claimed this we do not necessarily mean that such evaluation takes place in terms of ratio or interval scale. It might be the case that the visual system only decides which frame is lighter, and which is darker. In other words, the segmentation may take place only in ordinal terms.
48
A. D. Logvinenko and D. A. Ross
If the apparent illumination/lightness holds true, then assignment of a particular illumination to different frames has to be accompanied by assigning a corresponding lightness to any luminance in a frame. In other words, we suggest that the apparent illumination of a frame plays the role of the lightness anchor within the frame. In the anchoring theory of lightness perception the maximal luminance in a frame is claimed to serve as an anchor (Gilchrist, 2003; Gilchrist et al., 1999). To be more exact, the region of the maximal luminance in a frame is supposed to be assigned white in this frame. Such anchoring is equivalent to the suggestion that apparent illumination is assigned to equi-illuminated frames in the same proportion as that of maximal illuminations in these frames. It is easy to show that this predicts 100% lightness constancy and huge simultaneous lightness contrast effect (Gilchrist, 1988), both predictions being obviously wrong11 . The authors of the anchoring theory resort to weighting the lightness values assigned to a given luminance in different frames, so as to reconcile their predictions with the experimental data. However, the lack of a strict definition of frame and weighting process itself makes the anchoring theory unclear on this subject. The results suggest that the assigned apparent illuminations are not in the same relation as the maximal luminances in the frames. In other words, the range of the assigned apparent illuminations is a great deal narrower than that of the maximal luminances in the equi-illuminated frames. Such a compression of this range can be accounted for if one assumes that it is maximal brightness rather than maximal luminance that underlies assigning the apparent illuminations12 . Specifically, if the apparent illuminations are assigned in direct proportion to the maximal brightnesses in the frames, then the range of the assigned apparent illuminations will undergo the same compressive transformation as that relating brightness to luminance. For example, both Weber–Fechner and Stevens laws would predict such a compression of the apparent illumination range. While we have not measured the apparent illumination in the pictures, it is easy to see that it is in line with the Helmholtzian account of the illusion presented above. The impression of the apparent illumination in the pictures generally correlates with the strength of the illusion; that is, the greater the difference in the apparent illumination, the greater the difference in the lightness. Really, the difference in the apparent illumination between alternating strips in Fig. 1a is bigger than that of the isolated strips in Fig. 10. This is in line with the fact that the illusion as measured for Fig. 1a is stronger than that for Fig. 10. On the other hand, the difference in the apparent illumination between walls in Figs 8 and 9 is clearly larger than that between the isolated strips in Fig. 10, which is in line with the reduction of the illusion in Fig. 10 as compared to that in Figs 8 and 9. However, the statistically significant difference in lightness between the diamonds was also found for isolated tiles (Figs 13–15) where a difference in apparent illumination can hardly be seen. Therefore, the Helmholtzian account is unlikely to be appropriate here. Moreover, as shown elsewhere, the patches may be separated from the diamonds for quite a distance with the same result — the diamond
A Helmholtzian type of simultaneous lightness contrast
49
accompanied by the patch with reflectance 0.29 looks lighter than that accompanied by the patch with reflectance 0.79 (Logvinenko, 2002c). It was argued that such an illusion might be a result of the so-called anchoring effect well established in the psychophysical literature (Luce and Galanter, 1965).
EXPERIMENT 2
As pointed out above, when the isolated strips (Fig. 10) are combined so as to make up the tile pattern (Fig. 1a) the illusion considerably increases. It occurs because such combining gives rise to, at least, two cues which may signal that the luminance border between the strips is produced by an illumination edge. One of these cues is the X-luminance junction (Adelson, 1993), the other is luminance-ratio invariance across the border (Marr, 1982, p. 90). Specifically, the patches with the reflectance 0.79 and 0.48 in the light strips make the same luminance ratio (1.65) with the patches with the reflectance 0.48 and 0.29 in the dark strip, respectively. It was shown recently that, although luminance-ratio invariance is not necessary to produce the illusion, the illusion might disappear when it is significantly violated (Logvinenko, 2002d). In this experiment we studied more systematically the effect of violation of the luminance-ratio invariance on the tile illusion using more observers than in previous study (Logvinenko, 2002d). Methods Altering the patch with reflectance 0.48 in the light strip of the tile pattern (Fig. 1a) the luminance ratio (between this and the abutting patch with reflectance 0.29) was varied at the following levels: 1.34; 1.06; 0.79; and 0.66 (Figs 22–25). As shown before, the illusion could be reduced even by reversing the contrast polarity in just one column (Logvinenko, 2002d). To study this effect in more detail, we prepared three more patterns where the contrast polarity was reversed in the same way as for Fig. 25 but only for one (Fig. 26), two (Fig. 27), or three (Fig. 28) of the five columns. The modified tile patterns (Figs 22–28) were presented to the same twenty observers who took part in Experiment 1. The procedure and experimental design were also the same as in Experiment 1. Observers were asked to match the lightness of the indicated patches with a chip from the 31-point Munsell neutral scale. Lightness of all patches with different reflectance in each strip was measured five times for each observer. Measurements in altered and unaltered columns were done separately13 . Results As above, the table beneath each figure presents the median Munsell matches for all the patches measured in experiment. Figure 29 and Table 6 show how the strength
50
A. D. Logvinenko and D. A. Ross
Light strip
Dark strip
Reflectance
Median
Reflectance
Median
0.79 0.43 0.39
9.25 5.75 5.00
0.48 0.43 0.29
7.50 7.25 4.75
Figure 22. An altered version of Fig. 1a. The patches with reflectance 0.48 in the light strips in Fig. 1a are replaced with those having reflectance 0.39, thus decreasing the luminance ratio from 1.60 to 1.34 for these tiles.
of the illusions varies with the luminance ratio at the border between the strips. When luminance ratio becomes less than 1 the contrast polarity at the strip border for this patch become reversed as compared to an unaltered pair. As can be seen in Fig. 29, the illusion decreases gradually when the luminance ratio decreases, being completely reduced for the lowest ratio 0.66 (Fig. 25). The Wilcoxon signedrank test showed no significant difference between the diamonds’ lightness in the alternating strips in Fig. 25 (Z = 1.86, p = 0.06), this difference being significant in all the other pictures (Figs 22–24). While the effect of the luminance ratio on the diamonds’ lightness in the ‘dark’ strips was found to be significant (Friedman χ 2 = 96.9, df = 4, p < 0.01), it was relatively small. As seen in Fig. 29, it is the diamonds’ lightness in the ‘light’ strips (where the alternation was made) that mainly changed with the luminance ratio. Figure 30 and Table 7 show how the median lightness match measured in the altered as well as unaltered columns depends on the number of columns altered. The Munsell matches for the diamonds in the ‘dark’ strips and unaltered columns was the same for all Figs 26–28 (7.25 Munsell units), being equal to that for the original tile pattern (Friedman χ 2 = 2.90, df = 3, p = 0.41). While the match for the diamonds in the ‘dark’ strips and altered columns significantly decreased
A Helmholtzian type of simultaneous lightness contrast
Light strip
51
Dark strip
Reflectance
Median
Reflectance
Median
0.79 0.43 0.31
9.25 6.00 4.75
0.48 0.43 0.29
7.00 6.75 4.75
Figure 23. An altered version of Fig. 1a. The patches with reflectance 0.48 in the light strips in Fig. 1a are replaced with those having reflectance 0.31, thus decreasing the luminance ratio from 1.60 to 1.06 for these tiles.
with the number of altered columns (Friedman χ 2 = 46.76, df = 3, p < 0.01), the decrease was relatively small. Once again, the illusory change of lightness was mainly observed in the ‘light’ strips. Discussion Decreasing the luminance ratio at the strip borders for one of two tiles in Adelson tile pattern was found to drastically reduce the illusion. Such a gradual decrease of the illusion strength in Figs 22–25 as compared to Fig. 1a, challenges both the account based on the luminance X-junctions and that based on the luminance ratio invariance. Indeed, the luminance X-junctions of the same sort are present in both Figs 1a and 23. However, being rather large in Fig. 1a (2.375 Munsell units), the illusion in Fig. 23 is reduced to the level observed for the classical simultaneous lightness contrast effect (0.625 Munsell units). Such a reduction cannot be accounted for by a theory based on the luminance X-junctions since being ordinal in nature luminance junctions can only indicate a difference in the strips’ illumination but not the magnitude of this difference. Moreover, as pointed out by Kersten (1992, Fig. 15.5, p. 215), one luminance X-junction is not enough to induce a difference
52
A. D. Logvinenko and D. A. Ross
Light strip
Dark strip
Reflectance
Median
Reflectance
Median
0.79 0.43 0.23
9.25 6.50 4.25
0.48 0.43 0.29
7.25 6.875 5.00
Figure 24. An altered version of Fig. 1a. The patches with reflectance 0.48 in the light strips in Fig. 1a are replaced with those having reflectance 0.23, thus decreasing the luminance ratio from 1.60 to 0.79 for these tiles.
in apparent illumination between the regions making the junction. A series of the luminance X-junctions is necessary for an apparent illumination difference to emerge. However, when the luminances X-junctions of different types are arranged together as in Figs 26–28 they become ambiguous. For instance, in Figs 26–28 the type of luminance X-junctions is different for the unaltered and altered columns. It is double-contrast preserving in unaltered columns, and single-contrast preserving in altered columns. Single-contrast preserving X-junctions were found to produce a very small illusion, (0.3125 Munsell units) for Fig. 24 and no illusion for Fig. 25. So the theory based on X-junctions would predict no illusion in altered columns and a full illusion in unaltered columns in Figs 26–28. Quite the contrary, the diamonds in the unaltered and altered columns in Figs 26–28 look much the same (Fig. 30). It means that the visual system shows a tendency towards global interpretation of the luminance distribution across strips borders. Being local by definition, the concept of a luminance X-junction does not seem to be relevant to this tendency. The notion of the luminance ratio invariance fails to account for the results either. Indeed, Figs 22 and 23 induce a rather strong illusion despite that there is no such invariance in these figures. Strictly speaking, none of the Figs 22–25
A Helmholtzian type of simultaneous lightness contrast
Light strip
53
Dark strip
Reflectance
Median
Reflectance
Median
0.73 0.43 0.16
9.25 7.00 3.875
0.48 0.43 0.29
7.375 7.00 4.75
Figure 25. An altered version of Fig. 1a. The patches with reflectance 0.48 in the light strips in Fig. 1a are replaced with those having reflectance 0.16, thus decreasing the luminance ratio from 1.60 to 0.66 for these tiles.
should produce an illusion since the luminance ratio is not constant across the strips borders. However, it is only Fig. 25 that induces no illusion, the rest of these figures exhibiting a significant difference between the lightness of the diamonds in the ‘light’ and ‘dark’ strips contrary to this prediction. Moreover, we observe a gradual decrease in the illusion strength from Fig. 22 to Fig. 25. What causes this gradual deterioration of the illusion? It is unlikely that the illusion in Figs 22–25 is reduced because of the difference in the local contrast around the diamonds. Truly, the altered patch in Figs 22– 25 becomes physically darker as the luminance ratio gets smaller. Hence, one might argue that it is a result of this progressive reduction that leads to the apparent darkening of the diamonds in the ‘light’ strips (Fig. 29). However, as follows from Fig. 30, a similar (only slightly less) reduction was observed for the diamonds in the unaltered columns in Figs 26–28 where the local contrast around the diamonds remained unchanged. Therefore, it is hardly the local contrast that gradually reduces the illusion in Figs 22–25. Still, the notion of luminance ratio invariance can be further elaborated so as to be applicable to Figs 22–25 too. So far, it was implicitly assumed that the optical media represented in the pictures is perfect, that is, completely transparent. When
54
A. D. Logvinenko and D. A. Ross
Light strip — unaltered column
Dark strip — unaltered column
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 7.00 6.375
0.48 0.43 0.29
7.75 7.25 5.75
Light strip — altered column
Dark strip — altered column
Reflectance
Median
Reflectance
Median
0.79 0.43 0.16
9.25 6.75 3.75
0.48 0.43 0.29
7.75 7.375 4.75
Figure 26. An altered version of Fig. 1a. The patches with reflectance 0.48 in the light strips in Fig. 1a are replaced with those having reflectance 0.16 but only in one column.
it is not perfect (e.g. as in the presence of fog, haze, etc.), the light coming through to the eyes can be, at least in the first approximation, represented as a sum of two components: l = I r + a, where l is the intensity of the light entering the eyes; r is reflectance; I and a are multiplicative and additive constants, which depend on the intensity of the incident light and the transmittance of the optical media, respectively, the latter emerging due to scattering light. Such a relationship between the luminance and reflectance was called the atmosphere transfer function by Adelson (2000, pp. 346–348). When the optical media (atmosphere, in Adelson’s terms) is completely clean the additive compo-
A Helmholtzian type of simultaneous lightness contrast
Light strip — unaltered column
Dark strip — unaltered column
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 7.25 6.50
0.48 0.43 0.29
7.875 7.25 6.00
Light strip — altered column
Dark strip — altered column
Reflectance
Median
Reflectance
Median
0.79 0.43 0.16
9.25 7.00 3.75
0.48 0.43 0.29
7.875 7.25 4.75
55
Figure 27. Same as Fig. 26 except that an alteration was made in two columns.
nent is zero, and we have a perfect transmittance when the intensity of light coming to the eyes is multiplicatively related to the intensity of incident light and the surface reflectance. In this case the luminance ratio across the illumination border is constant (Logvinenko, 2002d). Figure 1a as well as Fig. 2 simulates a situation when the atmosphere transfer functions for the alternating strips differ only in multiplicative component, both having zero additive components. On the other hand, Fig. 6 simulates the opposite case when the atmosphere transfer functions for the alternating strips differ only in additive component, the multiplicative component being the same. Indeed, in Fig. 6 the reflectance of the strips, the lighter and darker hoops were 0.50, 0.77, and 0.23, respectively. Given a homogeneous illumination of the whole pattern, say, with the intensity I , we have the following four intensities of the reflected light (Fig. 31):
56
A. D. Logvinenko and D. A. Ross
Light strip — unaltered column
Dark strip — unaltered column
Reflectance
Median
Reflectance
Median
0.79 0.48 0.43
9.25 7.25 6.75
0.48 0.43 0.29
7.875 7.25 6.00
Light strip — altered column
Dark strip — altered column
Reflectance
Median
Reflectance
Median
0.79 0.43 0.16
9.25 7.00 3.75
0.48 0.43 0.29
8.00 7.25 4.75
Figure 28. Same as Fig. 26 except that an alteration was made in three columns.
l1 = 0.50I ; l2 = 0.23I ; l1 = 0.77I ; l2 = 0.50I . It is easy to see that l1 = l1 + a and l2 = l2 + a where a = 0.17I . It follows, first, that the atmospheric function for the strips with the darker hoops can be represented as l = I r. Second, the atmospheric function for the strips with the lighter hoops differs only in an additive constant: l = I r + a . Such a difference between the strips in additive component simulates a haze; and indeed, a sort of an apparent haze14 over the strips with the lighter hoops is experienced in Fig. 6. Note that an additive component brings about not only an apparent haze but it induces quite a strong (2.25 Munsell units) lightness illusion15 . Adelson recently demonstrated a similar haze illusion (Adelson, 2000, Fig. 24–17, p. 348). The haze illusion can be well understood within the same explanatory framework as the tile illusion. Indeed, if one of two regions of the same luminance looks hazy whereas the other clear, it would mean that the surface viewed through the murky
A Helmholtzian type of simultaneous lightness contrast
57
Figure 29. Match data as a function of luminance ratio across the horizontal border in Figs 1 and 22– 25. Table 6. Median and mean Munsell matches, and the Hodges–Lehmann estimator, obtained for the diamonds in Figs 22–25 Figure number
Light strip
Dark strip
Median
Mean
Median
Mean
Hodges–Lehmann estimator
22 23 24 25
5.75 6.00 6.50 7.00
5.43 5.96 6.50 6.89
7.25 6.75 6.875 7.00
7.17 6.74 6.81 6.97
1.625 0.625 0.3125 0.125
atmosphere should have less reflectivity to reflect the same amount of light. Thus, apparent haze reduces lightness16 . When the optical transmittance is reduced, thus, the additive component is not zero; the luminance ratio across the illumination border is not constant any longer. Indeed, let us consider a Mondrian-like pattern with reflectances r1 , . . . , rn , two parts of which is viewed through two different translucent filters (Fig. 33). Let l = I r + a and l = I r + a be the atmosphere transfer functions of these filters. Then, li / li = (I ri + a )/(I ri + a ) is obviously not equal to lj / lj = (I rj + a )/(I rj + a ). Nevertheless, the ratio of luminance differences (li − lj )/(li − lj ) is invariant of reflectance. Really, (li − lj )/(li − lj ) = ((I + a ) − (I rj + a ))/((I ri + a ) − (I rj + a )) = I (ri − rj )/I (ri − rj ) = I /I .
58
A. D. Logvinenko and D. A. Ross
Figure 30. Match data for Figs 1 and 25–28.
Such luminance-difference ratio invariance can be used as a cue to segment the visual scene into frames with the same atmosphere transfer function. In other words, this ratio can be used to distinguish reflectance edges from atmosphere borders. Moreover, since the ratio of luminance differences is equal to the ratio of the multiplicative constants in the atmosphere transfer functions, this ratio can be used to infer reflectance from luminance. The haze illusion (Fig. 6) shows, however, that when assigning lightness to luminance, the visual system takes into account not only luminance-difference ratio but the additive constant too. Indeed, direct calculation shows that the luminancedifference ratio across the horizontal strips’ border in Fig. 6 is equal to 1. It means that there is no shadow difference between the strips. If lightness were assigned only according to the luminance-difference ratio, in this case the diamonds would appear equal in lightness, thus no illusion being predicted.
26 27 28
Figure number
6.75 7.00 7.00
6.69 6.89 6.90
7.375 7.25 7.25
Dark strip Median
Median
Mean
Light strip
Altered
7.35 7.27 7.22
Mean 0.625 0.375 0.375
Hodges– Lehmann estimator 6.375 6.50 6.75
Median
Light strip
Unaltered
6.25 6.49 6.67
Mean
Table 7. Median and mean Munsell matches, and the Hodges–Lehmann estimator, obtained for the diamonds in Figs 26–28
7.25 7.25 7.25
Median
Dark strip
7.36 7.26 7.31
Mean 1.125 0.75 0.625
Hodges– Lehmann estimator
A Helmholtzian type of simultaneous lightness contrast 59
60
A. D. Logvinenko and D. A. Ross
Figure 31. Luminancies constituting the iso-contrast snake pattern (Fig. 6) evaluated under assumption that the illumination border is linear, i.e. that between the strips (see explanation in the text).
Figure 32. Luminancies constituting the iso-contrast snake pattern (Fig. 6) evaluated under assumption that the illumination border is snake-shaped (see explanation in the text).
Figure 33. A Mondrian-like pattern viewed through two different atmospheres. The atmosphere border is a curvilinear line dividing the pattern into the upper and bottom halves (see explanation in the text).
A Helmholtzian type of simultaneous lightness contrast
61
Table 8. The luminance difference ratio as evaluated for Figs 1a and 22–25 Fig. 1a
Fig. 22
Fig. 23
Fig. 24
Fig. 25
1.63
2.11
2.53
2.95
3.32
Table 9. The additive component as evaluated for Figs 1a and 22–25 Fig. 1a
Fig. 22
Fig. 23
Fig. 24
Fig. 25
0.00
0.09
0.15
0.20
0.23
As distinct from figures 1a and 6, the atmosphere transfer functions for the alternating strips in Figs 22–25 differ in both multiplicative and additive components. The difference in the multiplicative component is experienced as a difference in apparent illumination (or shadow). The difference in the additive component is experienced as an apparent haze. The luminance-difference ratio in Figs 22–25 can be evaluated as follows: (0.79− x)/(0.48 − 0.29), where x is the reflectance of the altered patch in the ‘light’ strip. This ratio varies from 1.65 for Fig. 1a to 3.3 for Fig. 25 (Table 8). In other words, the multiplicative component for the ‘light’ strips becomes more than three times as much as that for the ‘dark’ strips for Fig. 25. Such an increase of the luminancedifference ratio signals an even larger difference in apparent lightness between the diamonds in the alternating strips. Hence, if the luminance-difference ratio were the only determinant of the illusion, it should have become stronger in Figs 22–25 as compared to Fig. 1a. To evaluate the additive component let us assume, for the sake of simplicity, that the additive component a is zero. This amounts to assuming no haze for the ‘light’ strips (where the alteration was made), which is in line with what we see in Figs 22–25. In this case one can use the episcotister luminance model17 (Gerbino, 1994, pp. 240–245) to evaluate the additive component a for the ‘dark’ strips in Figs 22–25. Direct calculation shows that the additive component a rapidly increases when the reflectance of the altered patch in Figs 22–25 decreases (Table 9), which is in agreement with the amount of apparent haze in Figs 22–25. Increasing the luminance-difference ratio and increasing the additive component are in apparent conflict since the former contributes towards enhancing whereas the latter towards diminishing the illusion. Since the illusion gradually reduces from Fig. 22 to Fig. 25, the additive component proves to be more effective than the multiplicative component. It should be noted, however, that while a conflict between the additive and multiplicative components explains the apparent difference in lightness between the diamonds in the different strips, it remains unclear why the diamonds in the ‘light’ strips come to look lighter, and the diamonds in the ‘dark’ strips undergo only little
62
A. D. Logvinenko and D. A. Ross
change becoming slightly darker. Note, however, that the same takes place also in the original Adelson tile pattern (Fig. 1a), that is, the diamonds in the ‘light’ strips undergo the main change in appearance. Indeed, the diamonds in the ‘dark’ strips in Fig. 1a become only slightly lighter as compared to how the patch with the same reflectance (0.43) looks in Figs 3 and 4.
GENERAL DISCUSSION
A distinctive feature of psychology is that it is full of long-standing controversies which look as if they will never be solved (e.g. nativism vs. empirism; nature vs. nurture). One such controversy is personified by the debate between H. von Helmholtz and E. Hering on lightness simultaneous contrast (Kingdom, 1997; Turner, 1994). Since these theories have generally been considered as mutually exclusive, the history of the issue is often thought of as an oscillation between these two extremes (e.g. Kingdom, 1997, 1999) with a shift towards the Helmholtzian stance for the last two decades (Adelson, 1993; Adelson and Pentland, 1996; Arend, 1994; Bergstrom, 1977; Gilchrist, 1977; Logvinenko, 1999; Williams et al., 1998a, b). That the Helmholtz–Hering controversy has not been resolved for more than a hundred years suggests that there might have been strong evidence in favour of both theories. Indeed, since then each side has developed their own class of lightness phenomena that the other side are hard pressed to account for. These may be called Helmholtzian and Hering types of simultaneous lightness contrast (Logvinenko, 2002c; Logvinenko and Kane, in press). Adelson’s tile and snake illusions certainly belong to the Helmholtzian type. Indeed, local luminance contrast was not shown to play a significant role in their production, thus challenging numerous low-level models of lightness perception based on local luminance contrast (Cornsweet, 1970; Hering, 1874, trans. 1964; Hurvich and Jameson, 1966; Ratliff, 1972; Wallach, 1963; Whittle, 1994a, b). Furthermore, even recent versions of low-level models based on a series of linear spatial filters (e.g. Blakeslee and McCourt, 1999; Kingdom and Moulden, 1992) cannot explain, for example, why the tile illusion, which is quite strong in Fig. 1a, disappears completely for a 3D implementation of Fig. 1a so that the retinal images of this 3D wall of blocks made of the same paper as Fig. 1a, and Fig. 1a itself are practically the same (Logvinenko et al., 2002). Indeed, as pointed out elsewhere (Logvinenko, 2002a), all these models, no matter how complicated processing takes place in them after the filter stage, predict the same output in response to the same input. Since the input (retinal pattern) is nearly the same, they should predict nearly the same effect for both Fig. 1a and its 3D implementation, which is in disagreement with what was observed in experiment (Logvinenko et al., 2002). On the other hand, as shown above, Adelson’s tile and snake illusions lend themselves readily to an account developing further Helmholtzian idea of misjudged illumination.
A Helmholtzian type of simultaneous lightness contrast
63
Still, there are some lightness illusions of Hering’s type — Mach bands, Hermann grid, grating induction to mention a few — which are hard to account for in terms of Helmholtzian ideas. We believe that these two types of illusions are rather different in their nature. Indeed, the tile illusion was shown to disappear when the same wall of blocks was made as a 3D object (Logvinenko et al., 2002) whereas grating induction can easily be observed from 3D cylinders (Logvinenko and Kane, in press). Such robustness of grating induction to the perceptual context (2D vs. 3D shape) shows that it is probably underlain by some mechanisms based on low-level luminance contrast processing. It is no surprise that low-level models have proved to be successful in accounting for grating induction (e.g. Blakeslee and McCourt, 1999, 2003; McCourt and Foley, 1985; McCourt and Blakeslee, 1994; McCourt and Kingdom, 1996; Moulden and Kingdom, 1991). Each of the two different types of simultaneous lightness contrast obviously requires its own account. Although the idea of a monistic explanation of simultaneous lightness contrast seems to be very attractive (e.g. Gilchrist, 2003), all attempts to extend either account onto the whole variety of lightness illusions have proved unsuccessful. For example, there is no doubt that luminance contrast (or luminance ratio) is more appropriate than absolute luminance as an input variable since it is well-established that due to light adaptation brightness (subjective intensity) of light correlates with luminance contrast rather than absolute luminance (e.g. Shapley and Enroth-Cugel, 1984; Whittle, 1994a). However, as pointed out by Gilchrist, luminance contrast (as well as luminance ratio) is ambiguous as a determinant of lightness; thus, it should be anchored (Gilchrist, 1994; Gilchrist et al., 1999). We believe that it is apparent illumination, or to be more exact, apparent atmosphere (i.e. apparent transmittance and apparent haze), that plays the role of such an anchor. For example, both diamonds in the iso-contrast snake pattern (Fig. 6) have the same luminance contrast with their immediate surrounds. Moreover, their immediate surrounds are the same. However, they look rather different. As claimed above, the difference in lightness in this figure is likely to be caused by the corresponding difference in apparent haze over the alternating strips. Admittedly, encoding contrast is an efficient sensory mechanism for discounting the ambient illumination that makes the sensory input independent of any possible change in the illuminant intensity across a range. However, being ecologically as valid as material changes (i.e. in reflectance), the illumination changes such as shadows are worth being perceived to the same extent as lightness. And we are as good at perceiving shadows as at perceiving lightness. Therefore, the question is not how the visual system discounts the illumination changes, but how it encodes them, and takes them into account when calculating lightness. One might argue, however, that taking apparent illumination into account, when calculating lightness, implies an evaluation of illumination that is a problem on its own. Hering was probably the first to point out this problem. However, first, he seemed to mean the physical illumination whereas we believe that it is an apparent rather than physical illumination that affects lightness. Second, we do
64
A. D. Logvinenko and D. A. Ross
not suggest that computing apparent illumination (and/or apparent transmittance) precedes computing lightness. Neither do we suggest the opposite (i.e. lightness precedes apparent illumination). They both appear together as a pair of perceptual dimensions of an object. In other words, the luminance ratio determines not a single dimension (lightness or apparent illumination) but a pair — apparent illumination and lightness. Of course, a particular luminance ratio can give rise to a number of apparent illumination/lightness pairs. However, not just any possible apparent illumination/lightness pair can emerge in response to a particular luminance ratio. Apparent illumination and lightness in a pair are bound by certain constraints. In other words, there is a sort of percept-percept coupling (Epstein, 1973, 1982; Hochberg, 1974) between these two perceptual dimensions — apparent illumination and lightness. The albedo hypothesis was probably the first quantitative formulation of the relationship between apparent illumination and lightness (Beck, 1972; Koffka, 1935; Kozaki and Noguchi, 1976; Noguchi and Kozaki, 1985). However, the albedo hypothesis in its original form was criticised from both the theoretical (Logvinenko, 1997) and experimental point of view (Beck, 1972). The experimental criticism was based on the fact that subjective estimates of the ambient illumination do not follow the relation with lightness that is predicted by the albedo hypothesis (Beck, 1961; Kozaki, 1973; MacLeod, 1940; Oyama, 1968; Rutherford and Brainard, 2002). However, as pointed out elsewhere (Logvinenko, 1997), the apparent illumination/lightness invariance implies that the apparent illumination is a perceptual dimension of an object rather than a characteristic of the illuminant. Indeed, the apparent illumination of a surface depends on the spatial orientation of this surface, the general spatial layout of the scene, etc. Altering the spatial orientation of the surface, for example, may change its apparent illumination even when the illuminant, and thus the ambient illumination, remains unchanged. There is abundant evidence that a change in an apparent slant may cause a change in apparent illumination, and this, in turn, may cause a corresponding change in lightness, while the retinal stimulation remains the same (e.g. Bloj and Hurlbert, 2002; Gilchrist, 1977; Knill and Kersten, 1991; Logvinenko and Menshikova, 1994; Mach, 1959; Wishart et al., 1997). It is also in line with our results. For instance, the apparent ambient illumination of the wall of blocks in Fig. 5 is perceived as being homogeneous. The patches with reflectance 0.48 have the same luminance. Why then do they look as though they have different lightness? The most likely reason for this is that they have different apparent slant. Surfaces having different slants cannot have the same apparent illumination under even ambient light falling onto these surfaces. Such a constraint is built in the apparent illumination/lightness invariance. Such apparent illumination/lightness invariance is a form in which the prior experience exists in our perception. To put it another way, this and other invariances of this sort (Epstein, 1982) are a way in which the prior experience affects perceiving. It should be kept in mind that the apparent illumination/lightness invariance discussed so far implies apparent illumination and lightness of real objects whereas,
A Helmholtzian type of simultaneous lightness contrast
65
as mentioned above, our explanation of the tile and snake illusion involves pictorial apparent illumination. However, it does not mean that we imply that pictorial apparent illumination is involved in the same sort of relationship with lightness as is apparent illumination in real scenes. Nor do we suggest that the tile and snake illusion require a conscious experience of an ‘erroneous’ illumination in the pictures. We believe that the lightness illusions in question result from an indirect effect of pictorial cues for illumination available in the pictures (Logvinenko, 1999). Although all these cues are effective in producing a pictorial impression of illumination, it is unlikely that they contribute to an apparent illumination of the picture as a real object embedded in the natural environment since there are also abundant cues for real illumination of the picture (at the level of natural vision) which provide veridical information about real illumination. So we are usually able to distinguish between real and pictorial illuminations, having no doubts in what the real illumination of the picture is. Nevertheless, we believe that the pictorial cues of illumination may trigger the hypothetical perceptual mechanism securing the invariant relationship between lightness and apparent illumination (and transmittance). Although veridical cues for real illumination of the picture (which is usually homogeneous) override a direct effect of these pictorial cues, an indirect effect (through the apparent illumination/lightness invariance mechanism) on the picture lightness may take place. Most displays presented in this report contain pictorial illumination cues which are in apparent conflict with real illumination cues. For example, pictorial illumination cues in Fig. 7 testify to an illumination gradient whereas real illumination cues tell us that the picture is homogeneously lit. The way such a conflict is resolved by the visual system probably depends on the relative strength of the illumination cues available. Also, it could be hypothesised that some process of weighting these cues may play a role in producing the resultant apparent illumination. However, whatever the perceptual mechanism of producing apparent illumination is, we suggest that original information concerning pictorial illumination cues is driven, in parallel and independently, into both mechanisms — the apparent illumination mechanism and the lightness mechanism. This information may be overridden in the former (thus producing no effect on apparent illumination), but it could be taken into account in the latter (producing the lightness induction effect). This line of reasoning is similar to that involved in Gregory’s ‘inappropriate constancy scaling’ theory of geometrical illusions resting on the apparent size-distance invariance (Gregory, 1974; Logvinenko, 1999), and it is very close to the stance of Gilchrist (1979) and Gilchrist, Delman and Jacobsen (1983). Such an account predicts that lightness illusions might depend on the relative strength of the available pictorial illumination cues; and if these cues are contradictory, on the result of some compromise resolving this contradiction (e.g. weighting, pooling, etc.). In other words, it is flexible enough to account, qualitatively, for the differences in the magnitude of the lightness induction effect in the different figures above.
66
A. D. Logvinenko and D. A. Ross
As to the classical simultaneous lightness contrast display, it is not clear what type of illusion it produces. Perhaps, both mechanisms partly contribute to it; and this explains why such a long dispute concerning the nature of simultaneous lightness contrast has not been resolved yet. One might argue, however, that the Helmholtzian explanation is hardly applicable to the classical simultaneous lightness contrast effect because of the difference in the magnitude between simultaneous lightness contrast, which is usually rather weak, and lightness constancy, which is much stronger (e.g. Gilchrist, 1988). Indeed, if the black background in the classical simultaneous lightness contrast display is mistakenly perceived as an area of reduced illumination, then the simultaneous lightness contrast effect should be much stronger than that which is usually observed. It should be kept in mind, however, that this would be true only if the trade-off between lightness and apparent illumination were complete. In other words, one can expect a much stronger contrast effect only if the black background is perceived as white paper (same as the white background) which is dimly illuminated. But this never happens. We always see black and white backgrounds. However, the question is: what shade of black is seen in the black part of the classical simultaneous lightness contrast display? As a matter of fact, a complete trade-off between lightness and apparent illumination did not take place even in the most favourable condition of classical Gelb’s display (Gelb, 1929). Actually, it is Gelb’s effect that Gilchrist (1988) measured in his first experiment under what he called ‘contrast condition’. To be more exact, he found that in spite of his observers seeing the shadowed part of the background as if it was made of a dark paper, the observers’ matches showed that the trade-off between shadow and lightness was not complete. Specifically, his observers were found to match the apparent lightness of the shadowed part of the background as being lighter than what was predicted by a complete trade-off between shadow and lightness. This result might have been in line with the apparent illumination/lightness invariance provided that his observers saw the shadowed part of the background as being slightly less illuminated than the highlighted part. Unfortunately, the apparent illumination was not measured in Gilchrist’s experiment. The Helmholtzian account of simultaneous lightness contrast is, therefore, equivalent to the claim that a luminance edge produced by the border between the black and white backgrounds is never perceived as a pure reflectance (lightness) edge. It is always accompanied by a coinciding apparent illumination edge, though of low contrast, which might cause the lightness shift in a classical simultaneous lightness contrast display. This is in line with a growing body of evidence that a border between shadowed and highlighted areas is also never perceived as a pure apparent illumination edge. Specifically, Gilchrist and his collaborators have recently shown that lightness matches for the same grey paper on two sides of a shadow border, are never evaluated as having the same lightness (Gilchrist and Zdravkovic, 2000; Zdravkovic and Gilchrist, 2000). The paper in the shadowed area is always underestimated (looks darker). Unfortunately, these authors have not reported on any measurements of apparent illumination, so it only remains to speculate if the ap-
A Helmholtzian type of simultaneous lightness contrast
67
parent illumination of the shadowed area was also underestimated (as follows from the shadow/lightness invariance) or not. However, when shadow along with lightness was measured it was found that they went hand in hand as predicted by the shadow/lightness invariance (Logvinenko and Menshikova, 1994). Thus, in spite of Gilchrist’s criticism, Helmholtz’s ‘misjudgement of illumination’ may prove to contribute to the classical simultaneous lightness contrast effect. Moreover, we believe that the anchoring effect also plays an important role in producing this effect (Logvinenko, 2002c). Therefore, there are, generally speaking, three types of mechanisms which might contribute into the classical simultaneous lightness contrast effect. However, it remains for the future investigation to ascertain in which proportions these contributions are made.
CONCLUSION
Adelson’s tile and snake illusions constitute a special, Helmholtzian type of simultaneous lightness contrast that lends itself to an explanation based on the apparent illumination/lightness invariance. Such an explanation implies an ability to classify luminance edges into reflectance and illumination ones. We suggest that the visual system uses the luminance-differences ratio invariance across a luminance border to distinguish between the reflectance and illumination edges. Acknowledgement This work was supported by a research grant from the BBSRC (Ref. 81/S13175) to A. Logvinenko.
NOTES
1. For technical reasons the data for Fig. 9 were collected from only 15 of 20 observers. So, only 75 matches are available for this picture. 2. Note that for some technical reasons the reflectances in Fig. 16 are equally spaced, so this graph does not give the right idea of how the median match varies with reflectance. 3. The Hodges–Lehmann estimator gives a shift value such that if we shift all the observations of one distribution by this value there will be no significant difference between the two distributions. 4. Note that the Hodges–Lehmann estimator proved to be equal to neither the difference of the medians nor the median difference of the matches. 5. Since the number of matches was unequal (75 for the Fig. 9 and 100 for Fig. 1), we used the Wilcoxon rank-sum, rather than signed-rank, test. 6. Still, there were significant differences in its appearance in different patterns (Friedman χ 2 = 19.1, df = 7, p < 0.01). Although it might be against the
68
A. D. Logvinenko and D. A. Ross
intuition that a significant difference can exist between two distributions with the same medians, there is no theoretical reason why it cannot happen. Moreover, the opposite may happen too. More specifically, two distributions with different medians can manifest no significant difference. For instance, the difference between the median matches for the patch with reflectance 0.29 in Figs 4 and 9 is 0.5 Munsell units, though it was found to be not significant (Wilcoxon rank-sum normal statistic with correction Z = 1.55, p = 0.12). In fact, the Wilcoxon signed-rank test tests the difference between the distributions as the whole rather than between the medians. 7. Apart from shadows the difference in relative illumination can be produced by a transparent media (e.g., transparent filter). 8. It should be mentioned that once we deal with pictures a distinction between an apparent and pictorial apparent illumination of a picture should also be made. It reflects a dual nature of a picture as an object to be perceived. As pointed out by Gibson (1979), on the one hand, a picture is just a surface contaminated with paint; on the other, there is a pictorial content which is rendered by this surface. Accordingly, there is an apparent illumination of a contaminated surface and an apparent illumination of a rendered (pictorial) object, which might be different. For example, an apparent illumination of the paper on which the patterns were depicted was always perceived as even and equal for all parts of the displays by all our observers. On the contrary, a pictorial apparent illumination was judged differently for different parts of the displays. In this discussion apparent illumination will mean pictorial apparent illumination unless it says otherwise. 9. Although frame is a key notion in the anchoring theory of lightness perception (Gilchrist et al., 1999), unfortunately, it was never clarified by its authors whether frame is supposed to be an area of equal illumination. 10. While the wall of blocks looks equally illuminated in Fig. 5, the lateral sides of the blocks have different slant. Because of this difference in the apparent slant one lateral side looks be more shadowed than the other, thus creating another difference in apparent illumination, namely, that of the lateral sides of the blocks. As a result, a patch with the reflectance 0.48 belonging to the side in shadow looks lighter than that belonging to the highlighted side, being in line with the prediction based on the apparent illumination/lightness invariance. In a sense, here we have an example of slant-independent lightness constancy that has recently been documented (Boyaci et al., 2003; Ripamonti et al., submitted). 11. If the maximal luminance in Figs 8 and 9 were the anchor, the diamonds in these figures would look similar, since in both figures the same white background is the area of maximum luminance; but they look rather different. 12. We understand brightness as a subjective intensity of light. It should be distinguished from lightness and apparent illumination which are both perceptual dimensions of object rather than light. For instance, a change in apparent depth may affect lightness but not brightness (Schirillo et al., 1990).
A Helmholtzian type of simultaneous lightness contrast
69
13. In fact, both experiments were run simultaneously with the same observers. They were divided into two only for the convenience of presentation. 14. In the visual literature apparent haze is often called apparent transparency (e.g. Gerbino, 1994; Kersten, 1992; Mettelli, 1974). We find such terminology in the present context rather misleading since apparent haze implies that the optical media is not transparent. For example, it would be strange to apply the term transparency to translucency, that is, the limiting case of haze when the additive component dominates. 15. It should be noted that Fig. 6 is ambiguous in the sense that the snake-shaped luminance border can also be interpreted as an atmospheric boundary with the same atmospheric functions. In order to show this one has simply to swap the designations of identical patches with reflectance 0.50 (Fig. 32). 16. Note that if the snake-shaped luminance border is interpreted as an atmospheric boundary then the lightness shift should be in the opposite direction. Indeed, in this case the lower diamond in Fig. 6 would belong to a hazy snake. Hence, the lower diamond should look darker than the upper one when the atmospheric boundary is snake-shaped. The fact, that all our observers saw the upper rather than lower diamond darker, indicates that the visual system is reluctant to treat the snake-shaped luminance border as an atmospheric boundary. Perhaps, as claimed elsewhere (Adelson and Somers, 2000; Logvinenko et al., in press), it is a general rule built in somewhere in the visual system that for a luminance border to be interpreted as an atmospheric boundary it should be straight rather than curved. 17. The filter model (Gerbino, 1994) yields similar results.
REFERENCES Adelson, E. H. (1993). Perceptual organization and the judgment of brightness, Science 262, 2042– 2044. Adelson, E. H. (2000). Lightness perception and lightness illusions, in: The New Cognitive Neurosciences, 2nd edn, M. Gazzaniga (Ed.), pp. 339–351. MIT Press, Cambridge, MA, USA. Adelson, E. H. and Pentland, A. P. (1996). The perception of shading and reflectance, in: Perception as Bayesian Inference, D. Knill and W. Richards (Eds), pp. 409–423. Cambridge University Press, New York. Adelson, E. H. and Somers, D. (2000). Shadows are fuzzy and straight; paint is sharp and crooked, Perception 29 (Suppl.), 46. Albright, D. (1994). Why do things look as they do? Trends In Neuroscience 17, 175–177. Anderson, B. L. (1997). A theory of illusory lightness and transparency in monocular and binocular images: The role of contour junctions, Perception 26, 419–453. Arend, L. E. (1994). Surface colours, illumination, and surface geometry: Intrinsic-image models of human colour perception, in: Lightness, Brightness, and Transparency, A. Gilchrist (Ed.), pp. 159–213. Lawrence Erlbaum Associates, Hillsdale, NJ, USA. Beck, J. (1961). Judgments of surface illumination and lightness, J. Exper. Psychol. 61, 368–375. Beck, J. (1972). Surface Colour Perception. Cornell University Press, Ithaca, NewYork. Bergstrom, S. S. (1977). Common and relative components of reflected light as information about the illumination, colour, and three-dimensional form of objects, Scand. J. Psychol. 18, 180–186.
70
A. D. Logvinenko and D. A. Ross
Blakeslee, B. and McCourt, M. E. (1999). A multiscale spatial filtering account of the White effect, simultaneous brightness contrast and grating induction, Vision Research 39, 4361–4377. Blakeslee, B. and McCourt, M. E. (2003). A multiscale spatial filtering account of brightness phenomena, in: Levels of Perception, L. Harris and M. Jenkin (Eds). Springer-Verlag, Berlin. Bloj, M. G. and Hurlbert, A. C. (2002). An empirical study of the traditional Mach card effect, Perception 31, 233–246. Boyaci, H., Maloney, L. T. and Hersh, S. (2003). The effect of perceived surface orientation on perceived surface albedo in three-dimensional scenes, J. Vision 3, 541–553. Brainard, D. H. and Maloney, S. I. (2002). The effect of object shape and pose on perceived lightness, in: Vision Sciences Society, Sarasota, Florida (Proc. pp. 191). Bressan, P. (2001). Explaining lightness illusions, Perception 30, 1031–1046. Cornsweet, T. (1970). Visual Perception. Academic Press, New York. Dakin, S. C. and Bex, P. J. (2002). 1/f channel reweighting predicts many aspects of lightness perception, Perception 31 (Suppl.), 149. Epstein, W. (1982). Percept–percept couplings, Perception 11, 75–83. Gelb, A. (1929). Die farbenkonstanz’ der sehdinge, in: Handbuch der Normalen und Patologischen Physiologie, A. Bethe (Ed.), pp. 594–678. Springer, Berlin. Gerbino, W. (1994). Achromatic transparency, in: Lightness, Brightness, and Transparency, A. L. Gilchrist (Ed.), pp. 215–255. Lawrence Erlbaum Associates, Hillsdale, NJ, USA. Gibson, J. J. (1979). The Ecological Approach to Visual Perception. Houghton Mifflin, Boston MA, USA. Gilchrist, A. L. (1977). Perceived lightness depends on perceived spatial arrangement, Science 195, 185–187. Gilchrist, A. L. (1979). The perception of surface blacks and whites, Scientific American 240, 112– 123. Gilchrist, A. (1988). Lightness contrast and failures of lightness constancy: a common explanation, Perception and Psychophysics 43, 415–424. Gilchrist, A. L. (1994). Absolute versus relative theories of lightness perception, in: Lightness, Brightness, and Transparency, Gilchrist, A. L. (Ed.), pp. 1–31. Lawrence Erlbaum Associates, Hillsdale, NJ, USA. Gilchrist, A. (2003). Dualistic versus monistic accounts of lightness perception, in: Levels of Perception, L. Harris and M. Jenkin (Eds). Springer-Verlag, Berlin. Gilchrist, A. L. and Zdravkovic, S. (2000). Mining lightness errors, Investigative Ophthalmology and Visual Science Supplement 41, 226. Gilchrist, A. L., Delman, S. and Jacobsen, A. (1983). The classification and integration of edges as critical to the perception of reflectance and illumination, Perception and Psychophysics 33, 425– 436. Gilchrist, A., Kossyfidis, C., Bonato, F., Agostini, T., Cataliotti, J., Li, X., Spehar, B., Annan, V. and Economou, E. (1999). An anchoring theory of lightness perception, Psychol. Rev. 106, 795–834. Gregory, R. L. (1974). Distortion of visual space as inappropriate constancy scaling, in: Concepts and Mechanisms of Perception, pp. 342–349. Duckworth, London. Helmholtz, H. von (1867). Handbuch der Physiologischen Optik. Voss, Leipzig. Hering, E. (1964). Outlines of a Theory of the Light Sense (original work published in 1874). L. M. Hurvich and D. Jameson (trans.). Harvard University Press, Cambridge MA, USA. Hochberg, J. (1974). Higher-order stimuli and inter-response coupling in the perception of the visual world, in: Perception Essays in Honour of James J. Gibson, R. B. McLeod and H. L. Pick, Jr. (Eds), pp. 17–39. Cornell University Press, Ithaca, New York. Hollander, M. and Wolfe, D. A. (1973). Nonparametric Statistical Methods. John Wiley, New York. Kersten, D. (1992). Transparency and the co-operative computation of scene attributes, in: Computational Models of Visual Processing, M. S. Landy and J. A. Movshon (Eds), pp. 209–228. MIT Press, Cambridge MA, USA.
A Helmholtzian type of simultaneous lightness contrast
71
Kingdom, F. A. A. (1997). Simultaneous contrast: the legacies of Hering and Helmholtz, Perception 26, 673–677. Kingdom, F. A. A. (1999). Old wine in new bottles? Some thoughts on Logvinenko’s “Lightness induction revisited”, Perception 28, 929–934. Kingdom, F. A. A. (2003). Levels of brightness perception, in: Levels of Perception, L. Harris and M. Jenkin (Eds). Springer-Verlag, Berlin. Kingdom, F. and Moulden, B. (1992). A multi-channel approach to brightness coding, Vision Research 32, 1565–1582. Knill, D. C. and Kersten, D. (1991). Apparent surface curvature affects lightness perception, Nature 351, 228–230. Koffka, K. (1935). Principles of Gestalt Psychology. Harcourt, Brace, New York. Kozaki, A. (1973). Perception of lightness and brightness of achromatic surface color and impression of illumination, Japanese Psychol. Res. 15, 194–203. Kozaki, A. and Noguchi K. (1976). The relationship between perceived surface-lightness and perceived illumination, Psychol. Res. 39, 1–16. Logvinenko, A. D. (1997). Invariant relationship between achromatic colour, apparent illumination, and shape of surface: Implications for the colour perception theories, in: John Dalton’s Colour Vision Legacy, C. M. Dickinson, I. J. Murray and D. Carden (Eds). Taylor and Francis, London. Logvinenko, A. D. (1999). Lightness induction revisited, Perception 28, 803–816. Logvinenko, A. D. (2002a). Does bandpass linear filter response predict gradient induction? A reply to Fred Kingdom, Perception 32 (5), 621–626. Logvinenko, A. D. (2002b). A fair test of the effect of a shadow-incompatible luminance gradient on the simultaneous lightness contrast, Perception 32, 717–720. Logvinenko, A. D. (2002c). The anchoring effect in lightness perception, Neuroscience Letters 334, 5–8. Logvinenko, A. D. (2002d). Articulation in the context of edge classification, Perception 31, 201–207. Logvinenko, A. D. and Kane, J. (2003). Luminance gradient can break background-independent lightness constancy, Perception 32, 263–268. Logvinenko A. D. and Kane, J. (2004). Hering’s and Helmholtzian types of simultaneous lightness contrast, Journal of Vision (in press). Logvinenko, A. D. and Menshikova, G. (1994). Trade-off between achromatic colour and perceived illumination as revealed by the use of pseudoscopic inversion of apparent depth, Perception 23, 1007–1023. Logvinenko, A. D., Kane, J. and Ross, D. A. (2002). Is lightness induction a pictorial illusion?, Perception 31, 73–82. Logvinenko, A. D., Adelson, E., Ross, D. A. and Somers, D. (2004). Linearity as a cue for luminance edge classification, Perception and Psychophysics (in press). Luce, R. D. and Galanter, E. (1965). Psychophysical scaling, in: Handbook of Mathematical Psychology, Vol. I, R. D. Luce, R. R. Bush and E. Galanter (Eds), pp. 245–307. John Wiley, New York. MacLeod, R. B. (1940). Brightness constancy in unrecognised shadows, J. Exper. Psychol. 27, 1–22. Mach, E. (1959). The Analysis of Sensations, translated from the 5th German edition by S. Waterlow. Dover Publications, New York. Maloney, L. T., Boyaci, H. and Hersh, S. (2002). Human observers do not correct perceived lightness for perceived orientation, in: Proc.Vision Sciences Society, Sarasota, Florida, p. 192. Marr, D. (1982). Vision. W. H. Freeman, San Francisco. McCann, J. (2001). Calculating lightnesses in a single depth plane, J. Electronic Imaging 10, 110–122. McCourt, M. E. (1982). A spatial frequency dependent grating-induction effect, Vision Research 22, 119–134. McCourt, M. E. and Blakeslee, B. (1994). Contrast-matching analysis of grating induction and suprathreshold contrast perception, J. Opt. Soc. Amer. A 11, 14–24.
72
A. D. Logvinenko and D. A. Ross
McCourt, M. E. and Foley, J. M. (1985). Spatial frequency interference on grating-induction, Vision Research 25, 1507–1515. McCourt, M. E. and Kingdom, F. A. A. (1996). Facilitation of luminance grating detection by induced gratings, Vision Research 36, 2563–2575. Mettelli, F. (1974). Achromatic colour conditions in the perception of transparency, in: Perception Essays in Honour of James J. Gibson, R. B. McLeod and H. L. Pick, Jr. (Eds), pp. 95–116. Cornell University Press, Ithaca, New York. Moulden, B. and Kingdom, F. (1991). The local border mechanism in grating induction, Vision Research 31, 1999–2008. Noguchi, K. and Kozaki, A. (1985). Perceptual scission of surface-lightness and illumination: An examination of the Gelb effect, Psychol. Res. 47, 19–25. Oyama, T. (1968). Stimulus determination of brightness constancy and the perception of illumination, Japanese Psychol. Res. 10, 146–155. Paradiso, M. A. (2000). Visual neuroscience: Illuminating the dark corners, Current Biology 10, R15– R18. Ratliff, F. (1972). Contour and contrast, Scientific American 226, 91–101. Ripamonti, C., Bloj, M., Hauck, R., Mitha, K., Greenwald, S., Maloney, S. I. and Brainard, D. H. Measurements of the effect of surface slant on perceived lightness, Journal of Vision 4, 735–746. Ross, W. D. and Pessoa, L. (2000). Lightness from contrast: A selective integration model, Perception and Psychophysics 62, 1160–1181. Rutherford, M. D. and Brainard, D. H. (2002). Lightness constancy: a direct test of the illumination estimation hypothesis, Psychological Science 13, 142–149. Schirillo, J. A. and Shevell, S. K. (2002). Articulation: brightness, apparent illumination, and contrast ratios, Perception 31, 161–169. Schirillo, J., Reeves, A. and Arend, L. (1990). Perceived lightness, but not brightness, of achromatic surfaces depends on perceived depth information, Perception and Psychophysics 48, 82–90. Shapely, R. M. and Enroth-Cugell, C. (1984).Visual adaptation and retinal gain controls, in: Progress in Retinal Research, Vol. 3, N. N. Osborne and G. J. Chader (Eds), pp. 263–343. Pergamon Press, Oxford. Todorovic, D. (1997). Lightness and junctions, Perception 26, 379–394. Todorovic, D. (2003). Lightness and illumination: comments on Kingdom, Blakeslee and McCourt, in: Levels of Perception, L. Harris and M. Jenkin (Eds). Springer-Verlag, Berlin. Turner, R. S. (1994). In the Eye’s Mind Vision and the Helmholtz-Hering Controversy. Princeton University Press, Princeton NJ, USA. Wallach, H. (1963). The perception of neutral colours, Scientific American 208, 107–116. Whittle, P. (1994a). The psychophysics of contrast brightness, in: Lightness, Brightness, and Transparency, A. L. Gilchrist (Ed.), pp. 35–110. Lawrence Erlbaum Associates, Hillsdale NJ, USA. Whittle, P. (1994b). Contrast brightness and ordinary seeing, in: Lightness, Brightness, and Transparency, A. L. Gilchrist (Ed.), pp. 111–157. Lawrence Erlbaum Associates, Hillsdale NJ, USA. Williams, S. M., McCoy, A. N. and Purves, D. (1998a).The influence of depicted illumination on brightness, Proc. Natl Acad. Sci. USA 95, 13296–13300. Williams, S. M., McCoy, A. N. and Purves, D. (1998b). An empirical explanation of brightness, Proc. Natl Acad. Sci. USA 95, 13301–13306. Wishart, K. A., Frisby, J. P. and Buckley, D. (1997). The role of 3-D surface slope in a lightness/brightness effect, Vision Research 37, 467–473. Zdravkovic, S. and Gilchrist, A. L. (2000). Lightness determination for an object under two illuminations, Perception 29 (Suppl.), 73.
