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:
a.logvinenko@gcal.ac.uk
d.ross@qub.ac.uk
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.
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