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Measurements of the effect of surface slant on perceived lightness
Abstract
When a planar object is rotated with respect to a
directional light source, the reflected luminance changes. If surface lightness
is to be a reliable guide to surface identity, observers must compensate for
such changes. To the extent they do, observers are said to be lightness
constant. We report data from a lightness matching task that assesses lightness
constancy with respect to changes in object slant. On each trial, observers
viewed an achromatic standard object and indicated the best match from a palette
of 36 grayscale samples. The standard object and the palette were visible
simultaneously within an experimental chamber. The chamber illumination was
provided from above by a theater stage lamp. The standard objects were
uniformly-painted flat cards. Different groups of naïve observers made
matches under two sets of instructions. In the
Neutral Instructions, observers were
asked to match the appearance of the standard and palette sample. In the
Paint Instructions, observers were
asked to choose the palette sample that was painted the same as the standard.
Several broad conclusions may be drawn from the results. First, data for most
observers were neither luminance matches nor lightness constant matches. Second,
there were large and reliable individual differences. To characterize these, a
constancy index was obtained for each observer by comparing how well the data
were accounted for by both luminance matching and lightness constancy. The index
could take on values between 0 (luminance matching) and 1 (lightness constancy).
Individual observer indices ranged between 0.17 and 0.63 with mean 0.40 and
median 0.40. An auxiliary slant-matching experiment rules out variation in
perceived slant as the source of the individual variability. Third, the effect
of instructions was small compared to the inter-observer variability.
Implications of the data for models of lightness perception are discussed.
History
Received March 5, 2004; published September 8, 2004
Citation
Ripamonti, C., Bloj, M., Hauck, R., Kiran, K., Greenwald, S., Maloney, S. I., & Brainard, D. H. (2004). Measurements of the effect of surface slant on perceived lightness.
Journal of Vision, 4(9):7, 747-763,
Keywords
lightness, lightness constancy, scene geometry, surface slant, real objects
The perceived lightness of an object provides useful
information about the object only if it is stable across the variety of scenes
in which the object could appear. A visual system that achieves such invariance
is said to exhibit lightness constancy.
Lightness constancy is difficult to achieve because the light reflected to the
observer from an object depends both on the material properties of the object
and on the illumination.
Many empirical studies of lightness constancy have
investigated how perceived lightness changes with variation in the intensity of
a light source (e.g., Henneman, 1935;
Wallach, 1948; Arend & Goldstein, 1987), and this is the situation considered in
most textbook treatments. It is also possible to manipulate the illumination
incident on an object in other ways. Figure 1
shows pictures of the same (planar) object oriented at two different slants with
respect to a directional light source. The luminance of the reflected light
changes considerably with the change in slant, even though the intensity of the
physical light source is
unchanged. Figure 1. The
image shows the same object displayed in two different poses with respect to a
light source. The light source is located to the upper left of the object. The
luminance reflected from the object to the eye varies with slant.
Mach (Mach, 1886/1959; see Bloj & Hurlbert, 2002) demonstrated that the perceived
configuration of a folded card could affect its perceived lightness.
Subsequently, a number of studies have demonstrated that perceived geometry
interacts with perceived lightness in a manner consistent with lightness
constancy (Hochberg & Beck, 1954;
Flock & Freedberg, 1970; Gilchrist, 1980; Knill & Kersten, 1991; Pessoa, Mingolla, & Arend, 1996; Williams, McCoy, & Purves, 1998; also Bloj, Kersten, & Hurlbert, 1999; but see Epstein, 1961). These studies are generally qualitative
in nature and, although they demonstrate that geometry affects perceived
lightness, the range of stimulus configurations where such effects occur and the
mechanisms that mediate them are not well understood.
In a recent study, Boyaci, Maloney, and Hersh (2003) report parametric measurements of the
dependence of lightness on perceived surface slant in computer-simulated scenes.
They argue that the data can be understood within a computational framework,
wherein observers estimate and discount the illuminant as a function of the
scene geometry. Gilchrist et al. (1999),
on the other hand, suggest that effects of geometry are best modeled as arising
from (mostly) separate processing within distinct frameworks. Geometry enters
the calculation through its effect on how the frameworks are segmented from each
other. Adelson (1999) has articulated a
similar theoretical perspective.
The present work reports new measurements of how
perceived lightness depends on surface slant, and draws some qualitative
conclusions. Observers were asked to match the lightness of flat cards displayed
at different slants with respect to a single light source. In the companion
study (Bloj et al., 2004), we develop a
quantitative model of the data.
It is well established that under some viewing
conditions different instructions yield different outcomes in matching
experiments (e.g., Arend & Reeves, 1986;
Bauml, 1999; Bloj & Hurlbert, 2002). Experiments
1 and 2 differed only in the instructions
given to observers. In Experiment 1, observers
were instructed to match the appearance of the objects. In Experiment 2, observers were instructed to match
the paint on the objects.
The data show that for many observers the relation
between the luminance of the light reflected to the observer and perceived
lightness depends on surface slant, in a manner that tends toward but does not
achieve lightness constancy. There are large differences between observers,
however, and some observers’ data are well described as luminance matches.
The variability between observers was large compared to the mean difference
induced by our instructional manipulation.
Experiment 3 tested
whether inter-observer variability could be attributed to differences in the
perception of object slant. It cannot. This experiment also measures how the
judgments vary with a change in the position of the physical light
source.
The experimental apparatus consisted of an illuminated
booth (see Figure 2). The illumination was
provided by a theater stage lamp [SLD Lightning, 6-in. (15-cm) Fresnel #3053,
BTL 500-W bulb] placed at the upper left of the booth. Observers viewed stimuli
placed in the booth binocularly through a shutter (17 cm wide × 12 cm high)
that could be opened and closed under computer control. The observer was
positioned inside a separate viewing booth (not shown) that was dimly
illuminated by light entering from the back. The observer’s head position
was stabilized with a chin rest. Information about the light source direction
was available to the observer in the form of visible cast shadows (see Figure 2). Observers could not see the light
source directly, nor were they explicitly told anything about the illumination
in the apparatus. Light reached the stimuli both directly and after
inter-reflection within the booth. Information about the relative strength of
direct and indirect illumination was potentially available from the shadow
contrast.
Figure 2. Experimental apparatus. The top panel
shows a schematic drawing of the experimental apparatus that consisted of an
illuminated booth into which objects could be placed. The azimuth of the left
light source was 36° clockwise relative to a reference line normal to the
back wall of the booth, while the azimuth of the right light source was 23°
counterclockwise with respect to the same reference. The bottom panel
illustrates the observer’s view of the stimulus. On each trial, both the
standard object and the palette were changed through two doors on the sides of
the booth. The right light source and the flat-screen monitor seen in the
picture were used only in Experiment 3, and
were not present during Experiments 1 and 2.
On each trial of the experiment, observers viewed a
standard object. The standard object
was always a flat card (7 × 7 cm; 3° × 3°) painted matte
gray. The card was positioned on a computer-controlled rotatable stage. Eight
different standard objects were used. These differed only in the reflectance of
the paint. All paints were created by mixing black and white flat acrylic latex
house paints (Rich Lux Wal-Shield) in varying proportions. The eight
reflectances used were 0.362, 0.265, 0.186, 0.137, 0.114, 0.080, 0.064, and
0.046.1 The range of standard reflectances was limited to minimize ceiling
and floor effects in the
matches.
The observer’s task was to compare the lightness
of the standard object to that of 36 grayscale samples (4 × 4 cm;
1.63° × 1.63°) displayed on a palette that was simultaneously
visible in the light booth (Figure 2). The
samples were arranged on a 6 x 6 grid and the observer chose the palette sample
that was closest in lightness to the standard object. The instructions provided
to observers are described in more detail below.
The observer responded verbally by reporting the row
and column of the selected sample using a letter/number coordinate system (see
Figure 2). An experimenter recorded the
observer’s response on each trial. Observers were allowed to look back and
forth between the standard object and the palette for as long as they required.
If the observer was unable to find an acceptable match because of gamut
limitations on the palette (i.e., there was no surface light or dark enough), he
or she was asked to state this rather than choosing the best available sample.
This occurred rarely. Across all three experiments reported in this study, the
number of trials on which observers were unable to find matches, or on which
they chose either the highest or lowest palette reflectance, was less than 1% of
the total number of trials (33 trials out of 5460). Data from such trials were
excluded from the quantitative analyses described in the “Appendix.”
Each palette sample was matte gray, painted using the same technique as the standard objects. The lightest sample had a reflectance of 0.869, while the darkest sample had a reflectance of 0.029. The rest of the samples were selected by the authors to produce an approximately uniform lightness scale. Supplementary material (click on the link to view) tabulates the palette reflectances. All eight standard object reflectances were contained in the palette.
We constructed four separate palettes, each containing
the same 36 sample reflectances in a different random arrangement. On each trial
of the experiment, a randomly chosen palette was placed in the booth. Each
palette could be placed with a different edge at the top, so that there were
effectively 16 different random arrangements used in the experiment. We used
randomly arranged palettes to discourage observers from employing a strategy
where they attempted to produce consistent responses by classifying the standard
objects and remembering the palette location they had selected for a given
object on a previous trial.
The interior surfaces of the light booth were painted
gray using a mixture of the same black and white paints used to paint the
samples. The reflectance of these surfaces was 0.375. In addition to the
standard object and palette, other objects were visible in the apparatus. These
varied from experiment to experiment, but always included the stands that
supported the standard object and palettes. For Experiment 3, an LCD flat panel monitor was
mounted on the back wall of the booth to enable measurement of the perceived
slant of the standard objects. Although it is shown in Figure 2, this monitor was not present for Experiments 1 and 2.
Seven naïve observers with normal or
corrected-to-normal vision participated in the experiment. Observers were
screened using two visual tests: Keystone VisionScreener II to ascertain their
visual acuity and stereopsis and Ishihara’s test for color deficiency to
ascertain their color vision. Observers with corrected Snellen acuity less than
20/30 and/or a stereopsis of less than 75% on the Sheperd-Fry scale were
excluded from the study as were those that made any mistakes in the Ishihara
test.
The standard objects were displayed in five different
slants: +60°, +45°, +30°, 0°, and –45°. The
0° slant corresponds to the standard object displayed at an orientation
parallel to the back wall of the apparatus. Positive orientations correspond to
counter-clockwise rotations when the standard object is viewed from above. An
experimental session consisted of 40 trials presented in random order (eight
standard object reflectances crossed with five slants). At the start and finish
of each trial, the shutter was closed so that the observer could not see into
the booth.
Each observer participated in three experimental
sessions, for a total of 120 matches per observer.
At the end of the third session, observers were asked
to fill in an evaluation form consisting of questions about perceptual
strategies used to accomplish the task, comments on the stimuli,
etc.
Observers were told that during the experiment they
would see a series of cards displayed at different slants and that their task on
each trial was to identify the palette sample that appeared the same shade of
gray as the card. However, observers were allowed to interpret the word
“appearance” themselves: They were not explicitly instructed as to
whether they should try to match the reflectance of the card and sample or the
luminance of the reflected light. For this reason, we refer to these
instructions as the Neutral
Instructions.
The instructions were accompanied by a demonstration in
which the experimenter showed a card rotated with respect to a directional light
source.
In Experiment 2 below,
we used different instructions where observers were explicitly told to judge
card and sample reflectance (Paint
Instructions).
The independent stimulus variables in our experiment
are the reflectance and slant of the standard objects, while the dependent
variable is the palette sample reflectance. Slant was measured using a 1°
scale with an indicator needle, mounted permanently on the rotatable stage. The
needle was not visible to the observer. Standard and palette reflectances were
measured as described above.
In addition to these variables, the actual stimulus
seen by the observer depended on the intensity and location of the light source.
We were particularly interested in knowing how the luminance reflected from the
standard object varied with its slant. At the start of the experiment, this was
measured in situ for each standard object reflectance. For all slants except for
+60°, the reflected luminance was measured directly using a PhotoResearch
PR-650 spectral radiometer placed at the observer’s location. For the +60° slant, the visual angle subtended by the standard object was too small to be measured directly by the PR-650. To obtain luminances for this card, we used the PR-650 to calibrate the nominal pixel values of dark-corrected images acquired through a 550-nm interference filter using a high-quality digital CCD camera (Photometrics PXL). The calibration information was then used to infer the luminance of the standard objects at +60° from images taken at this slant. The reflectances, luminances, and chromaticities of the standards are tabulated in the supplementary material. Auxiliary measurements were made on a daily basis to monitor against apparatus drift.
The top panel of Figure
3 shows the matching data for two observers. The mean match reflectance
(averaged over the three sessions) is plotted as a function of the slant of the
standard object. The individual curves in each plot show data for one standard
object reflectance. The vertical shifts between the individual curves indicate
an increase of match reflectance with standard object reflectance, as one would
expect. It is also clear from the raw data that the observers’ reflectance
matches depend on the standard object slant.
Figure 3. The figure shows mean matching
data for two observers. The top panel illustrates the raw data and their
respective standard errors for the eight standard objects plotted as a function
of slant. The ticks next to the right top panel illustrate the 36 palette
samples reflectances; colored ticks illustrate the subset of palette
reflectances used for the standard. The bottom panels show the data for each
standard reflectance normalized to a mean of 1. Error bars are omitted from the
bottom panels for clarity.
The different magnitude of the matches for different
standards makes it difficult to compare the effect of slant on match reflectance
across the standards. In addition we found, consistent with Weber’s Law,
that the variability of the matches was roughly proportional to the value of the
raw match. This effect is illustrated in Figure
4. To visualize the effect of slant across standard reflectances, and to
plot the data from different standards on a scale that equalized the precision
of the matches across standards, we scaled the mean match reflectance 
for each standard reflectance  and slant 
to obtain normalized matches  :
where  is the mean of the
taken over . The normalized
matches for same two observers are plotted in the bottom panels of Figure
3.Figure 4. Average standard deviation of
matches plotted against corresponding mean match. We divided the range of mean
reflectance matches into 10 bins and obtained the standard deviations of the
matches (over the three sessions) for each mean match within the bin. We then
averaged the standard deviations for all matches within each bin. This average
standard deviation is plotted in the figure. The data were aggregated over all
standards, slants, and observers from Experiment
1.
The normalized matches show that the effect of slant is
similar for each standard reflectance and emphasizes the dependence of the
matches on the slant of the standard object. Also clear in the plots is that the
detailed dependence of the matches on slant differs between the two
observers.
Because our primary interest is in understanding how
the appearance of the standard objects varies with their slant, we aggregated
the data over standard object reflectance. This aggregation increases our
experimental power to address questions about the overall effect of slant. We
refer to the aggregated data for each observer at slant
as the normalized relative match reflectance  . The procedure used to
obtain the is described in the “Appendix.” A feature of the aggregation
procedure is that for each observer the has a mean over
of 1. As described in the “Appendix,” the procedure also removes from the
data of each observer the effect of sigmoidal nonlinearities in the relation
between standard and match reflectance.The differences between observers can be seen even more
clearly in Figure 5, where data aggregated over
reflectance are shown for all seven observers. The difference in the effect of
slant for observers BST and FGS remains quite clear, and the other observers
show results that, qualitatively, fall between those for BST and
FGS. Figure 5. The figure illustrates data for
all seven observers who were given Neutral Instructions. Observers’
normalized relative match reflectance (connected green symbols) has been plotted
versus the standard object slant. The red horizontal broken lines represent the
predictions of lightness constancy. The blue broken lines represent the
predictions for luminance matches. Error bars show 90% confidence intervals.
Observers are listed from top to bottom, roughly in order of increasing
constancy, as evaluated by the model-based constancy index developed in the
companion work (Bloj et al., 2004). The values
at the top left of each panel are the error-based constancy indices for each
observer.
The differences between the observers are not due to
measurement variability. The error bars in Figure
5 indicate 90% confidence intervals obtained using a resampling procedure.2 Where error bars are not visible, they are
smaller than the plotted points. The 90% confidence intervals are small compared
to the differences between observers. In addition, an ANOVA indicates that the
differences between observers are statistically significant. The main effect of
slant was significant at
p < .001, whereas the
slant by observer interaction was significant at
p < .01. Because the data
are normalized for each observer, there is no main effect of observer.
The supplementary material tabulates the raw data for Experiment 1, as
well as for Experiments 2 and 3
below.
The data shown in Figure
5 do not indicate lightness constancy. If the observers’ matches were
lightness constant, each standard would always be matched with the same palette
reflectance, leading to normalized relative match versus slant curves that
consisted of horizontal lines (i.e.,
 , red broken line in
each panel). None of the observers’ data are well described by a
horizontal line.Another useful comparison for observer performance is
the prediction obtained by assuming that observers make their matches in
proportion to the luminance reflected from the standard (luminance matching). In
this case, the data should be fit by a scaled version standard card luminance as
a function of slant. The predictions for luminance matching are shown in Figure 5 as blue, broken lines. For each observer,
the predicted curve has been scaled to provide the best fit to that
observer’s data.
Observer BST comes close to exhibiting luminance matching. The other observers all show deviations from luminance matching in the general direction of lightness constancy. The data from observers FGS and GYD come close to being constant over a range of standard object slants (–45° to +45°) but deviate substantially as the slant increases to +60°. Other observers exhibit behavior that varied between these extrema.
To provide a sense of how observers vary between
luminance matching and lightness constancy, we derived a simple error-based
constancy index. We found for each of the three sessions, the normalized
relative matches for that session. Let  represent the sum of
squared errors between the luminance matching prediction (blue broken lines in
Figure 5) and the individual session data for a
single observer. Similarly, let  be the sum of squared
errors for the constancy prediction (red broken lines in Figure 5).
Then
is a constancy index that takes on a value of 0
when the data are perfectly characterized as luminance matches and a value of 1
when the data reveal perfect constancy. For Experiment 1, the index ranges between 0.17 and
0.54, with a mean of 0.35 and median of 0.33. Table
1 provides the index values for all experiments reported in this paper.
Error-based constancy indices for each observer are provided in Figure 5. Interpretation of the index should be
tempered against the observation that the index definition is somewhat arbitrary
and that no single number can capture the richness of the data. In the companion
study, we present model-based summary measures of the individual
variation.
Table 1. Error-based constancy index. The
table provides the minimum, maximum, mean, and median values of the error-based
constancy index (Equation 2) for all
experiments reported in this work.
The mean data (across observers) from
Experiment 1 are plotted in Figure 7 below. This plot also reveals performance
that is intermediate between luminance matching and lightness constancy, but it
should again be emphasized that individual variation around the mean is
large.
We used the same apparatus and stimuli as in Experiment
1.
Seven naïve observers who did not participate in
Experiment 1 took part in Experiment 2. Observers were screened using the
same visual tests and exclusion criteria as in Experiment
1.
Experimental conditions were the same as for Experiment
1.
Observers were told that during the experiment they
would see a series of cards that had been painted using different paints. They
were also told that the cards would be displayed at different slants. These
instructions were accompanied by a demonstration that showed a card rotating
under a directional light source. The rotation of the card served to show that,
in the demonstration at least, the apparent lightness changed across slants.
Observers were then told that their task was to pick the sample from the palette
that had been painted with the same paint as the standard card, despite the fact
that the standard might appear different when seen under different lighting.
This is essentially the “paper match” task of Arend and Reeves (1986), and we refer to these instructions as
Paint
Instructions.
Experiments 1 and 2 were run concurrently, so that the measurements
of standard luminance and apparatus stability were common to the two
experiments.
Figure 6 illustrates
normalized relative match reflectances for all seven observers plotted versus
the standard object slant. Normalized relative match reflectances and 90%
confidence intervals were obtained using the same procedures described for Experiment 1, and constancy and luminance matching
predictions are again shown (cf., Figure
5).
Figure 6. The figure illustrates data for all
seven observers who were given Paint Instructions. Same format as Figure 5.
As with Experiment 1,
the data from Experiment 2 indicate substantial
variability among observers. In an ANOVA, the slant by observer interaction was
significant at p < .001.
Observer LEF’s data (Experiment 2) is
very close to the luminance matching prediction, just as with observer BST (Experiment 1). Several observers (e.g., JPL, KIR,
and NMR) in Experiment 2 performed similarly to
observer FGS from Experiment 1. Thus the range
of performance observed in Experiment 2 is
similar to that observed in Experiment 1.
Comparison of Figures 5 and 6, however, does give the impression that on the
whole more luminance matching behavior was seen in Experiment 1 and more lightness constant behavior
(at least over a range of slants) was seen in Experiment 2. Error-based constancy index values
are provided in Table 1.
Figure 7 shows the
mean data from both Experiments 1 and 2, obtained by averaging the individual normalized
matches from each experiment. The difference in means is small compared to the
range of performance observed in either experiment, although an ANOVA reveals
that it is statistically significant (slant by instructions interaction,
p <
.05).
Figure 7. Mean data from Experiments 1 and 2, obtained by averaging the data from individual
observers shown in Figure 5 (Experiment 1) and Figure 6 (Experiment
2). Error bars show +/- one SEM.
The predictions for lightness constancy and luminance matching (scaled to the
mean of the two plotted curves) are also shown.
Experiment 2 confirms
the essential conclusions of Experiment 1: Most
observers exhibit performance that lies somewhere between luminance matching and
lightness constancy, and there are large individual differences between
observers. The effect of instructions is small compared to the range of
performance within each instructional group.
One possible cause for the individual differences is
that they are indeed due to differences in strategy employed by individual
observers, but that our instructional manipulation was not powerful enough to
have a decisive influence on the strategy employed by any given observer.
Another possibility is that the individual differences have a different origin.
In Experiments 1 and 2, we did not independently assess how observers
perceived the slant of the standard object. Systematic differences in perceived
slant could produce differences in how perceived lightness depends on physical
slant, even if the basic mechanisms that integrate slant and lightness are
performing identically for all subjects. In Experiment 3, we added a slant-matching task to
our protocol to test this
idea.
As noted above, one aim of Experiment 3 was to investigate whether the
variability we found in Experiments 1 and 2 could be attributed to variation in the
perception of object slant. In addition, we wanted to explore the effect of
changing the light source position and to replicate the results of our
instructional
manipulation.
The experiment consisted of two parts. During the first
part, 14 naïve observers were asked to perform lightness matches, using
essentially the same procedure employed for Experiments 1 and 2. During the second part, the same observers were
asked to match the slant of the standard object. Seven observers were given the
Neutral Instructions and seven were given the Paint
Instructions.
We used the same apparatus as in Experiments 1 and 2. The illumination was provided by either of two
theater-stage lamps placed above the booth (Figure
2, top panel). One of the two light sources was located at the upper left of
the booth, whereas the other was located at the upper right. We set the
intensity of the two lamps such that when the standard object was displayed at
0° slant, its luminance would be the same under the two light
sources.
Observers were required to perform two tasks. The first
task was the lightness-matching task used in Experiments 1 and 2. The only change in this task was that rather
than reporting their responses verbally, observers used a joystick to control
the position of a small red indicator dot projected onto the palette. When the
dot was on their preferred palette samples, observers pressed a button to record
their choice. This modification eliminated the need for the experimenters to
manually enter the observers’ verbal responses.
After the lightness-matching task was completed (three sessions), observers performed a slant-matching task. We adopted the task described by Van Ee and Erkelens (1995). Observers adjusted the orientation of a
line displayed on an LCD flat panel monitor located on the back wall of the
viewing booth (see Figure 2). The image
displayed on the monitor provided a schematic representation of the experimental
chamber viewed from above (see Figure 8). The
image contained a rectangular frame (22 cm wide × 16.5 cm tall;
7.56° ×
5.68°)
representing the booth, with an aperture on the front which indicated
schematically the observer’s viewing position. Two lines (11.5 cm;
3.96°) were drawn
inside the rectangular frame: One represented a reference line parallel to the
back wall of the booth, while the other was the match line controlled by the
observers. The lines were drawn using an anti-aliasing algorithm. The
orientation of the match line was controlled through two game-pad push-buttons.
Observers could also control the angular step size of the rotation
(1° or
10°). Observers
were asked to adjust the match line so that it provided a top view of the slant
of the standard object. The starting orientation of the match line was selected
randomly on each trial. On a small number of trials, the observer accepted a
match before he or she meant to and indicated this to the experimenter before
the start of the next trial. Data from such trials were excluded from the
analysis. The raw slant-matching data are available in the supplementary material.
Figure 8. Schematic representation of the
slant-matching display. The rectangular frame represented the booth viewed from
above. The line parallel to the back wall was held fixed throughout the whole
experiment, while the oblique line was adjusted by the observer to match the
slant of the standard object. The spatial resolution of the monitor was 832 x
624 pixels. The distance between the monitor and the observer was 161.4
cm.
Two groups of seven naïve observers participated
in the experiment. None of them had participated in either Experiment 1 or Experiment 2. Observers were screened using the
same visual tests and exclusion criteria used in Experiments 1 and 2.
Lightness
matching. During the lightness-matching part, the standard objects were
displayed in nine different slants: –60°, –45°,
–30°, –15°, 0°, +15°, +30°, +45°, and
+60°. Five standard objects were used. As in Experiments 1 and 2, these were flat matte cards. The card
reflectances used in Experiment 3 were 0.265,
0.186, 0.137, 0.114, and 0.080.
On every trial, the light source position (left or
right) was randomly selected. While the shutter occluded the observer’s
view of the chamber, both light sources were turned on. Then one of the lights
was turned off, leaving the selected light on. Thus the lights cycled between
every trial, even if the selected light was the same for two or more consecutive
trials.
An experimental session consisted of 90 trials (five
standard object reflectances crossed with nine slants and two light sources.)
These trials were presented in random order. Each observer participated in three
lightness-matching sessions, for a total of 270 matches per observer.
Within a session, the 90 trials were run in two blocks
of 45 trials each. The same two blocks were used for all observers and sessions,
but the order of the trials within each block was randomly chosen for each
observer/session. Observers were allowed to take a 10-min break between
blocks.
Slant
matching. In the slant-matching part, only two of the five standard
object reflectances (reflectances 0.186 and 0.114) were used. The standard
objects were displayed in the same nine slants used for the lightness matches.
The same two light source positions were also used.
An experimental session consisted of 36 trials (two
standard object reflectances crossed with nine slants and two light sources).
These trials were presented in random order.
Each observer repeated the slant matches three times in
a single session, for a total of 108 matches per observer.
Debriefing.
At the end of the slant estimation session, observers were asked to fill in an
evaluation form consisting of questions about potential strategies used to
accomplish the two tasks, comments on the stimuli,
etc.
Lightness
matching. The 14 observers were divided in two groups. One group was
given Neutral Instructions (as in Experiment
1), and the other was given Paint Instructions (as in Experiment 2).
Slant
matching. All 14 observers were told that during this session they would
see a standard object displayed at various slants and that their task was to
adjust the slant of a line on a computer screen such that it matched the
standard object’s slant. Observers were told that the image displayed on
the screen represented a schematic view of the standard object seen from above
and that the horizontal reference line on the screen indicated a slant parallel
to the back of the
apparatus.
The same calibration procedures employed in Experiments 1 and 2 were used. Reflectances, luminances, and chromaticities are tabulated in the supplementary material.
Lightness
matches as a function of physical
slant. Figure 9 illustrates the data for the Neutral
Instructions and the left light source position. The plots in the left column
show the normalized relative match reflectance as a function of slant. As in Experiments 1 and 2, observers’ data exhibit performance that
varies from luminance matching (e.g., FGP) toward lightness constancy (e.g.,
ALR). The data are somewhat noisier than in Experiment 1, a point to which we return below.
Error-based constancy index values are provided in Table 1.
Figure 9. The figure plots normalized
relative match reflectances for the trials on which the standard objects were
illuminated from the left. These observers were given Neutral Instructions. Left
column: matches plotted against physical slant. The red horizontal broken lines
represent the predictions of lightness constancy. The blue broken lines
represent the predictions for luminance matches. The error-based constancy index
for each observer is provided at the top left of each panel. Right column:
matches for each observer plotted against the match slant obtained for that
observer. Prediction for luminance matches not shown as we did not measure card
luminances at observers’ matched slants. Error bars show 90% confidence
intervals, obtained as described for Experiment
1.
Figure 10 shows the
data for the same seven observers aggregated over trials where the light source
was on the right: generally speaking, the match reflectance decreases with slant
when the light is on the left but increases with slant when the light is on the
right. This qualitative dependence is what one would expect for observers who
perform luminance matches, as can be seen from how the luminance matching
prediction changes when the light source is moved. For observers whose
performance is approximately characterized as luminance matching for both light
source positions (e.g., FGP), it is possible that the effect of changing light
source position can be explained entirely in terms of the change in reflected
luminance.
Figure 10. Normalized relative matches for
trials on which the standard objects were illuminated from the right; same
observers, instructions, and format as Figure
9.
Figures 11 and 12 show the data for those observers who were
given Paint Instructions. Results for this group of observers are quite similar
to those obtained for the Neutral Instructions.
Figure 11.
Same as Figure 9 for observers who were given
Paint Instructions.
Figure 12.
Same as Figure 10 for observers who were given
Paint Instructions.
Lightness
matches as a function of matched slant.
One of the purposes of Experiment 3 was
to test whether differences between observers could be attributed to differences
in perception of slant. During the second part of Experiment 3, observers were asked to match the
slant of the standard
objects.
Figure 13 shows the
mean slant matches of those observers who were given Neutral Instructions,
separated by light source position. Figure 14
shows the same data for observers who were given Paint Instructions. Generally,
observers matched slant quite accurately, with only a small tendency for
underestimation of absolute slant for slants near 0°. The right columns of
Figures 9, 10,
11, and 12
replot individual observers’ match reflectances as a function of match,
rather than physical slant. This representation does little to reconcile the
large individual variation.
Figure 13. The
figure illustrates mean slant matches for observers given Neutral Instructions.
Left column: slant matches for illumination from left. Right column: slant
matches for illumination from right. Data were averaged over replications and
standard object reflectances. Error bars show +/–1
SEM.
Figure 14. The
figure illustrates mean slant matches for observers given Paint Instructions.
Same format as Figure 13.
Effect
of instructions. Figure 15 compares the mean data from each
instructional condition. As with the comparison between Experiments 1 and 2, any overall effect of instructions is small
compared to the range of performance shown by individual observers. ANOVAs
indicated no significant effect of
instructions (slant by instructions interaction
p = .87 for illuminant from
left; p = .75 for illuminant
from right).
Figure 15. Mean data from Experiment 3. The left panel shows data for trials
when the illumination was from the left, while the right panel shows the data
when the illumination was from the right. Each panel is in the same format as Figure 7.
Replication
of Experiments
1 and 2. The
left illuminant position trials of Experiment 3
provide a replication of Experiments 1 and 2, albeit with the right illuminant position
trials intermixed. In addition, Experiment 3
employed more slants and fewer standard object reflectances. Figure 16 compares the mean reflectance matches
across experiments. The differences are small. For the comparison between Experiments 1 and 3, an ANOVA indicated that the interaction between
experiment and slant was not significant
(p = 0.60), while for the
comparison between Experiments 2 and 3, the same interaction was significant at the
0.05 level (p = 0.052). The
small difference may arise because in Experiment
3 trials with the right illuminant position were intermixed with those with
the left illuminant position. Individual observer differences were significant
in all four (light source by instructions) conditions of Experiment 3
(p < .01).
Figure 16. Comparison across experiments.
The left panel compares the mean reflectance match obtained in Experiment 3 for the left illuminant position and
Neutral Instructions with the mean reflectance match from Experiment 1. The right panel compares the mean
reflectance match obtained in Experiment 3 for
the left illuminant position and Paint Instructions with the mean reflectance
match from Experiment 2. In each panel, the
data from Experiment 3 are scaled to have a
mean of 1 for the subset of slants for which data were obtained in Experiments 1 and 2. Error bars show +/-1
SEM.
Variability
in Experiment
3. The data from Experiment 3 appear somewhat noisier than the data
from Experiments 1 and 2. One possible reason for this is that fewer
points were collected for each slant. In Experiments 1 and 2, data for each slant are aggregated over eight
standard reflectances, while in Experiment 3,
only five standard reflectances were used. A second important difference is that
two light source positions were interleaved in Experiment 3. If observers failed to track (either
implicitly or explicitly) the change in illuminant position on some trials, this
would show up as noise in the data. We have not examined the difference in
variability in any formal way, but it may be advantageous to block trials by
illuminant position in future
experiments.
We report experiments that measure how perceived
lightness depends on slant. Consistent with most of the earlier literature
(Mach, 1886/1959; Hochberg & Beck, 1954; Flock & Freedberg, 1970; Gilchrist, 1980; Williams et al., 1998; Bloj et al., 1999; Boyaci et al., 2003), our data indicate that the visual system
takes the scene geometry into account as it computes object lightness. Most of
the earlier studies report only data averaged over observers, and certainly the
average observers in our experiments show performance that deviates
systematically from luminance matching toward lightness constancy (see Figures 7 and 15).
A striking feature of our data is the large and
reliable individual differences. Although the average observer clearly takes
geometry into account, some of our individual observers exhibit performance that
is close to that predicted by simple luminance matching, while others show a
considerable degree of lightness constancy. It is not possible to evaluate the
degree of individual observer differences from most previous reports. An
exception is a recent study by Boyaci et al. (2003). Our design was very similar to theirs,
with the important exception that they used synthetically generated stimuli
displayed on computer-controlled monitors. Figure
17 replots their individual observer data in the same general format as Figure 5. As with our observers, most of their
observers show performance that is intermediate between luminance matching and
lightness constancy, although by eye their data are closer to luminance matches
than ours. There also appear to be systematic differences between their
individual observers, although again these seem smaller than the ones we
measure. It is possible that differences between their experiments and ours are
due to effects of the use of synthetic versus real images.
Figure 17. Data replotted from Boyaci et al. (2003) in the same format as Figure 5. Data were normalized and averaged over
the two standard reflectances they used in the same manner as we aggregated our
data. Luminance matching and lightness constancy predictions were scaled to the
data using our normalization procedures. The figure was produced from tabulated
data kindly provided by H. Boyaci.
The slant-matching data in Experiment 3 rule out the possibility that the
individual differences arise because of individuals’ disparate perceptions
of slant. There was considerable consistency in the slant matches across
observers, and replotting the lightness data as a function of individually
matched slant did not reduce the variability.
It remains possible that different observers bring
different strategies to the lightness matching task, and that the differences
between observers result from different strategic choices. For example, some
observers may be trying to match standard object luminance while others attempt
to match standard object reflectance. Our instructional manipulation failed to
separate observers into two groups. This may be because our Neutral Instructions
were weaker than the appearance instructions that have been used previously
(e.g., Arend & Reeves, 1986; Bauml, 1999; Bloj & Hurlbert, 2002). It remains of interest to pursue this
issue further, perhaps by employing a wider range of instructions or by
developing other methods of distinguishing perceptual and strategic aspects of
lightness matching.
Some indication that observers explicitly employed
different strategies is provided by written answers they gave to questions
administered after they had completed the experiment. In response to the
question, “Can you describe in words what aspects of the stimuli you paid
more attention to when performing the matching task?,” observer IBO from
Experiment 2 wrote, “. . .I tried to keep
in mind that the orientation of the card will change the color.” This
observer’s data show considerable lightness constancy. Observer FGB from
Experiment 3, whose data are on the luminance
matching end of the spectrum, responded to the same question with “Not
sure – just matched the color.” Our overall impression is that
there is some correlation between observers’ responses as to what they
were doing and their measured performance, and that this correlation is stronger
than that between report and actual instructions given. It is difficult to
quantify these impressions. An important issue for future research is how to
assess and manipulate the strategies used by observers to perform lightness
matching in complex
scenes.
The evaluation forms of Experiment 3 also included questions that asked
about the light sources and standard objects used in the experiment. Only 3 of
14 observers reported the correct number and location of the two light sources
used. Six out of the remaining 11 observers reported that only one light source
position was used but did indicate that some aspect of the lighting (presumably
intensity) varied from trial to trial. Only 2 of 14 observers correctly reported
the number of standard object reflectances used in the experiment, which
indicates that observers were probably not explicitly memorizing standard object
reflectances.
Our experiments were conduced with real illuminated
objects, viewed binocularly. This is a feature they share with the early
experimental work (Hochberg & Beck, 1954; Flock & Freedberg, 1970; Epstein, 1961; Gilchrist, 1980; see also Bloj et al., 1999). More recently, the availability of
sophisticated computer graphics programs has made it possible to render
synthetic three-dimensional scenes, and stimuli created in this way have been
used to study the interaction of geometry and lightness (Knill & Kersten, 1991; Pessoa et al., 1996; Boyaci et al., 2003). Although synthetically generated stimuli
offer important advantages in terms of the range of stimulus manipulations that
can easily be implemented, it remains an open question as to how performance
measured with synthetic stimuli relates to performance measured with actual
objects.
We expect that over the next several years, this
question will receive increasing attention. We believe that the class of
experiments reported here, which combine the use of real stimuli and the type of
parametric manipulations that often motivate the use of synthetic stimuli, will
play an important role in improving our understanding of the relation between
results obtained with synthetic stimuli and performance for more natural
viewing.
Our data have a number of implications for models of
lightness perception in complex three-dimensional scenes. First, the individual
differences we measured require that any quantitative model contain parameters
that can account for these differences. A model that simply predicts lightness
as a function of the stimulus will not be able to account satisfactorily for our
data.
The classic account of lightness constancy emphasizes
the role of contrast coding, that is the luminance relation between a test
region and its local surround (e.g., Wallach, 1948) or some other reference region in the
scene (e.g., Land & McCann, 1971; see
Brainard & Wandell, 1986). Earlier
studies showing an interaction between perceived geometry and lightness
challenge the completeness of such accounts, because in these studies the
perceived lightness is often manipulated without any change to the luminance
relations in the scene (Mach, 1886/1959; Hochberg & Beck, 1954; Gilchrist, 1980; Gilchrist, Delman, & Jacobsen, 1983). Our results add to this challenge
– a contrast account of our data would predict a close approximation to
luminance matching, because the available references in the image change little
if at all with the slant of the test. It is also not clear how to model
individual differences within a contrast coding approach.
Gilchrist et al. (1999; see also, Adelson, 1999) advocate a theory of lightness
perception (anchoring theory) in which
geometry acts through its role in segmenting the scene. To apply these ideas to
our experiment, one would conjecture that changing the slant of the standard
card affects the set of objects in the scene with which it is grouped. For any
given grouping, the perceived lightness of the standard card would be determined
primarily by the relative luminances of the objects within the group, which
Gilchrist et al. (1999) would call the
standard card’s “framework.” It does seem clear that
grouping-like effects can have a large effect on the role of geometry in
perceived lightness (e.g., Gilchrist, 1980), and our experiments do not speak
directly to that question. On the other hand, because our standard card is
presented in isolation, it is not obvious how to determine which other objects
in the scene it might be grouped within an anchoring account. Indeed, we do not
find that the grouping rules of anchoring theory are currently sufficiently well
specified to allow quantitative (or even qualitative) prediction of our data. In
addition, for anchoring theory to account quantitatively for our data, the
grouping rules would have to be specified in a manner that allowed them to vary
between observers.
To develop a model that can account quantitatively for
individual variability requires a model containing a parametric description of
the effect of slant on perceived lightness. Brainard and colleagues (Speigle
& Brainard, 1996; Brainard, Brunt, &
Speigle, 1997) have suggested that one way
to parameterize the form of the transformation induced by context is through an
equivalent illuminant model. In such models, the observer is assumed to be
correctly performing a constancy computation, with the one exception that their
estimate of the illuminant deviates from the actual illuminant. Thus the
observer’s estimate of the illuminant parameterizes the transformation
induced by context. Boyaci et al. (2003) have
successfully employed an equivalent illuminant model to account for their
lightness matches as a function of slant. In the companion study (Bloj et al.,
2004), we formulate such a model and evaluate
how well it can account for our
data.
This “Appendix” describes the procedure we
used to aggregate the matches
over standard
reflectance to obtain the normalized relative matches .For each observer, we fit the matches
with a function of the form
where  is the reflectance of
the  standard,  is a constant that
depends on , and  and 
are constants that are independent of . This form has two
important features. First, it is separable in slant
and standard reflectance , so that the dependence of match
reflectance on is the same for each up to multiplicative
constant . Second, it can account for a fairly wide range of
monotonically increasing forms of the dependence of the
on reflectance when is held
fixed.Equation 3
was fit to each observer’s data using numerical search. The search
procedure found the values of parameters , ,
and that minimized the error  defined
by
In this expression, the index 
indicates replications of the measurement and the expression 
is an estimate of the measurement variance of matches  .
The estimate was obtained from the mean match
under the assumption of Weber’s Law behavior (see Figure 4). In fitting, any matches
that were at the minimum or maximum of the palette, or where the observer
indicated that a satisfactory match was not possible, were excluded from the
calculation of the fit error .Given the fit of Equation 3, normalized relative matches were obtained
through
where  is the average over
of . The choice of
as proportional to may be understood as follows. Suppose that
the form of the function relating the to standard object
reflectances were linear for each :  .
In this case, it is clear that for any fixed standard object reflectance, the
matches considered as a function of slant are proportional
. Equation 5 preserves
this interpretation in the face of a nonlinearity between perceived lightness
and palette match.The normalization by
in Equation 5 simply makes the mean of the
over equal to 1.
Normalization of the data seem sensible given that we have aggregated across
standard reflectance, and also because the palette provides a somewhat arbitrary
lightness standard. For example, one might expect a shift in the actual matches
had the palette samples been surrounded by a highly reflective surface rather
than the low-reflectance surround we employed. This shift would not be of
interest here, where the focus is on the dependence of lightness on standard
slant.This work was supported by National Institutes of
Health Grant EY 10016. John Andrews-Labenski, Mike Suplick, and Leigh Checcio
helped design and construct the apparatus. We thank B. Backus, J. Hillis, A.
Gilchrist, L. Maloney, H. Boyaci, J. Nachmias, and S. Sternberg for useful
discussions and comments. H. Boyaci provided us with the data from Boyaci et. al
(2003) in tabular
format. Commercialrelationships:
none.
Corresponding author: David H. Brainard.
Email: brainard@psych.upenn.edu.
Address: Department of Psychology, University
of Pennsylvania, Suite 302C, 3401Walnut Street, Philadelphia, PA 19104.
1The reflectance of each of the 36 paint
mixtures was obtained by comparing the light reflected from each card to that
reflected from a reflectance standard (PhotoResearch RS-2). Measurements were
between 380 and 780 nm at 4-nm steps (PhotoResearch PR-650), and reflectance was
obtained by averaging computed reflectance over the visual spectrum.
2Each datum shown in
Figure 3 is the mean of matches set in three
separate sessions. To resample each datum, we averaged a random draw of three
samples (with replacement) from the corresponding three matches. We then
aggregated the resampled data using the same procedure that we used to generate
the normalized relative matches shown in Figure
5. This resampling and aggregation were then repeated 1000 times and the
variation in the resampled data was used to find the confidence
intervals.
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