Seeing black, white and gray surfaces, called lightness perception, might seem simple because white surfaces reflect 90% of the light they receive while black surfaces reflect only 3%, and the human retina is composed of light sensitive cells. The problem is that, because illumination varies from time to time and from place to place, any amount of light can be reflected from any shade of gray. Thus the amount of light reflected by an object, called luminance, says nothing about its lightness. Experts agree that the lightness of a surface can be computed only by using the surrounding context, but they disagree about how the context is used. We have tested an image in which two major classes of theory, contrast theories and frame-of-reference theories, make very different predictions regarding what gray shades will be seen by human observers. We show that when frame-of-reference is varied while contrast is held constant, lightness varies strongly. But when contrast is varied but frame-of-reference is held constant, little or no variation is seen. These results suggest that efforts to discover the exact algorithm by which the human visual system segments the image received by the retina into frames of reference should be given high priority

Alan Gilchrist

Ana Radonjic

English

Nature Precedings

1 
Visual computation of surface lightness: Local contrast 
vs. frames of reference 
Alan L. Gilchrist
1
 & Ana Radonjic
2
 
1
Rutgers University, Newark, USA 
2
University of Pennsylvania, Philadelphia, USA 
 
Seeing black, white and gray surfaces, called lightness perception, might seem 
simple because white surfaces reflect 90% of the light they receive while black 
surfaces reflect only 3%, and the human retina is composed of light sensitive cells. 
The problem is that, because illumination varies from time to time and from place 
to place, any amount of light can be reflected from any shade of gray. Thus the 
amount of light reflected by an object, called luminance, says nothing about its 
lightness. Experts agree that the lightness of a surface can be computed only by 
using the surrounding context, but they disagree about how the context is used. We 
have tested an image in which two major classes of theory, contrast theories and 
frame-of-reference theories, make very different predictions regarding what gray 
shades will be seen by human observers. We show that when frame-of-reference is 
varied while contrast is held constant, lightness varies strongly. But when contrast 
is varied but frame-of-reference is held constant, little or no variation is seen. 
These results suggest that efforts to discover the exact algorithm by which the 
human visual system segments the image received by the retina into frames of 
reference should be given high priority. 
The challenge confronting the human visual system in assigning black, white, and 
gray shades to visible surfaces is illustrated in Figure 1. Three identical disks have been 
pasted into this photograph. One appears black, one appears gray and one appears white 
even though all three send exactly the same amount of light to the eye. Clearly the 
2 
luminance value of the light reflected by an object says nothing about its perceived 
lightness value. 
 
Or consider Adelson’s Checker shadow illusion in Figure 2. Although the two 
squares A and B are identical in luminance, they appear very different in lightness. 
These examples make it obvious that 
the human visual system uses the 
surrounding context to compute the 
lightness of a given surface. Here we 
report a test between two general 
ways of looking at context: local 
contrast theories and frame-of-
reference theories. 
3 
Local contrast theories. In perhaps the clearest formulation of this point of view, 
Wallach proposed in 1948 that object lightness is determined, not by the luminance of a 
surface, but by the luminance ratio between the surface and its immediate surround
1
. 
Contrast theories
2, 3 
and brightness induction theories
4
, which derive from Hering
5
, are 
couched in physiological terms, invoking the mechanism of lateral inhibition, but they 
share with Wallach the view that lightness is directly tied to local relative retinal 
stimulation.  
Frame-of-reference theories. This approach takes into account a larger context and 
exploits more of the structure of the retinal image. The gestalt theorist Koffka proposed 
that lightness depends on higher order luminance relationships and that the field of 
illumination in which a surface is embedded serves as a frame of reference against 
which the luminance of the surface is evaluated
6
. Gilchrist has demonstrated that, within 
such a framework, the highest luminance serves as an anchor and is assigned the value 
of white. The lightness of other surfaces within the framework depends on the 
luminance ratio between the surface and the highest luminance
7, 8
. 
These two classes of theory are both consistent with the appearance of the disks in 
Figure 1. Notice that the three disks have very different disk/surround luminance ratios, 
but they also lie in very different frameworks of illumination. We sought an image in 
which the two approaches would predict different lightness values. To this end we 
pasted four identical disks into the Checker shadow image, as shown in Figure 3, and 
asked human observers to match each disk to a Munsell chart of gray shades ranging 
from white to black. If lightness depends primarily on local contrast, the upper and 
lower rightmost disks should appear as the same shade of gray, because they have the 
same local contrast (remember that the squares on which they lie are equal in luminance 
and all the disks are equal in luminance). And the two upper disks that have different 
local contrast should appear very different from each other, as should the two lower 
4 
disks. But if lightness is determined primarily by frame of reference, then the two upper 
disks in the light should appear approximately equal, and much darker than the two 
lower disks in the shadow, which should also appear approximately equal to each other.  
The results shown in the graph, confirming what is obvious from mere inspection, are 
consistent with the frame of reference hypothesis. 
In short, any effect of local contrast is small relative to the effect of illumination 
framework.  
Although the data were analyzed in terms of log reflectance, the results are more 
intuitively described in Munsell values, ranging from a typical black at Munsell 2.0 to a 
typical white at Munsell 9.5. The mean lightness matches for each disk are shown in 
Figure 4a.  
5 
 
The average lightness of the disks in the shadow was 2.3 Munsell units (0.49 
units of log reflectance) higher than that of the disks in the light. We compared the 
lightness of each disk with every other disk on the checkerboard using pairwise 
comparisons, with Boniferroni adjustment for multiple comparisons. We found that 
each disk in the shadow was perceived as lighter than each disk in the light (p < 0.001), 
but that the two disks in the shadow did not significantly differ in matched lightness, 
despite their different local contrasts. Outside the shadow, the disk on the light square 
6 
appeared darker than the disk on the dark square (p = 0.015) but the difference was very 
small, 0.6 Munsell units (0.15 units of log reflectance). 
To confirm that these results are not the product of a particular value of disk 
luminance, we repeated the experiment using a lighter set of disks, as shown in Figure 
4b. We obtained the same pattern of results. The average lightness of the disks in the 
shadow was 2.8 Munsell units (0.42 units of log reflectance) higher than that of the 
disks in the light. Pairwise comparisons showed that each disk in the shadow was 
perceived as lighter than each disk in the light (p < 0.001). And in this case, the two 
disks in the shadow showed no significant difference in matched lightness, despite their 
different local contrasts. Nor did the two disks in the light.  
These results suggest that the dramatically different appearance of the three disks 
in Figure 1 is due, not to their different local contrasts, but to the different frames of 
reference within which they lie. This in turn reveals the compelling need for a better 
grasp of the nature of the software by which the visual system segments a complex 
scene into frameworks of illumination. 
Local contrast theories have the distinct advantage of being clearly 
operationalized, but this does not excuse their clear failure against more sophisticated 
models. Frame-of-reference theories are criticized as ambiguous but advances have 
been made. The rules of lightness computation within a framework of illumination are 
by now quite well worked out
9, 10
. Perhaps the biggest remaining challenge concerns 
how such frameworks are extracted from the complex image on the retina. To a first 
approximation, there are two main features of the image that functionally segment the 
image: penumbrae (blurred edges) and depth boundaries (corners and occlusion 
boundaries)
8, 9
. 
7 
More recently the basic contrast theory of Hering has morphed into more than a 
dozen models called spatial filtering models. The ODOG model of Blakeslee and 
McCourt is a prominent example
11
. Because these models invoke center/surround 
receptive fields of different spatial scales, they are not tied to local contrast. Typically 
one cannot predict how a given model will compute lightness values for a given image 
without actually feeding the image into a computer program that instantiates the model. 
But in general, spatial filtering models fail to predict lightness values in images 
containing pronounced spatial variations in illumination level, as do most real world 
scenes.  
Methods  
The Adelson Checker shadow image was downloaded (source: 
http://web.mit.edu/persci/people/adelson/checkershadow_downloads.html) and 
displayed on a 20” Apple Multiple Scan CRT monitor (resolution of 1280 x 960 pixels 
at 75Hz refresh rate) in a dark room, using Microsoft PowerPoint® 2004 software 
(Microsoft Corporation WA, USA). Four circular gray disks were compressed to 
ellipsoidal shape, to match the perspective projection of the checkerboard (but only 
roughly, being done manually in PowerPoint, using the cylinder top as a template). A 
dark gray set, with triple values of 80 in RGB notation, was shown to one group of 15 
observers while a light gray set with values of 127 was shown to another group of 15.  
At the viewing distance of 80 cm, each disk subtended 2.1° of visual angle 
horizontally and 1.1° of visual angle vertically, while the entire image subtended 26° 
horizontally and 20° vertically. Measurements with a Konica Minolta LS-100 spotmeter 
showed an average luminance of the disks in the dark disk condition of 13.65 cd/m2 
(+/- 2%, equivalent to the measuring error) and in the light disk condition 31.3 (+/- 2%). 
Thus, within a condition, all disks were practically equiluminant. The luminance of the 
light and the dark check, respectively, was 50.8 cd/m2 and 22.3 cd/m2 in the light and 
8 
22.3 cd/ m2 and 9.5 cd/m2 in the shadow. The highest luminance on the screen was 71.0 
cd/m2.  
A gray scale housed in a metal chamber and separately illuminated by a 15W 
fluorescent tube was located just to the right of the observer, who was seated and 
instructed “to pick a chip from the scale for each disk that is the same color (shade of 
gray) as that disk, like they were cut from the same piece of paper”. The scale consisted 
of 16 Munsell chips (each 1x3 cm) mounted on a white background and arranged in 
ascending reflectance order from black (Munsell 2.0) to white (Munsell 9.5). The 
luminance of the white chip was 395 cd/m2.  
Three observers (one from the dark disks and two from the light disks condition) 
were excluded because their matches fell 3 standard deviations or more from the mean 
of the group. Each was replaced by a new observer.  
References:  
1. Wallach, H. (1948). Brightness constancy and the nature of achromatic colors. 
Journal of Experimental Psychology, 38, 310-324.  
2. Jameson, D., and Hurvich, L.M. (1961). Complexities of perceived brightness. 
Science, 133, 174-179. 
3. Cornsweet, T. N. (1970). Visual Perception. New York: Academic Press.  
4. Heinemann, E. G. (1955). Simultaneous brightness induction as a function of 
inducing- and test- inducing luminances. Journal of Experimental Psychology, 50, 89-
96.  
5. Hering, E. (1974/1964). Outlines of a Theory of the Light Sense. Cambridge, MA: 
Harvard University Press.  
9 
6. Koffka, K. (1935). Principles of Gestalt Psychology. New York: Harcourt, Brace & 
World, Inc.  
7. Li, X., and Gilchrist, A.L. (1999). Relative area and relative luminance combine to 
anchor surface lightness values. Perception & Psychophysics, 61(5), 771-785.  
8. Gilchrist, A. L., Kossyfidis C., Bonato F., Agostini T., Cataliotti, J., Li X., Spehar, 
B., Annan V. & Economou, E. (1999). An Anchoring Theory of Lightness Perception. 
Psychological Review, 106(4), 795-834.  
9. Gilchrist, A. L. (2006). Seeing black and white. New York: Oxford University Press, 
Inc. 
10. Bressan, P. (2006). The place of white in a world of grays: a double-anchoring 
theory of lightness perception. Psychological Review, 113, 526-553.  
11. Blakeslee, B. & McCourt, M.E. (2004). A unified theory of brightness contrast and 
assimilation incorporating oriented multiscale spatial filtering and contrast 
normalization. Vision Research, 44, 2483-2503. 
 
Author Contributions: A.G. and A.R. designed the experiments and created the stimulus display. A.R. 
tested the subjects and analyzed the data. A.G. and A.R. wrote the paper. 
Competing financial interest statement: There are no competing financial interests. 
Correspondence and requests for materials should be addressed to alan@psychology.rutgers.edu. 
Figure legends  
Figure 1: The three disks that have been pasted into this photograph appear 
black, gray and white, although they are identical. 
Figure 2: Adelson’s Checker shadow illusion: Squares A and B are identical in 
luminance, but they appear different in lightness.  
10 
Figure 3: Adelson’s checker shadow illusion with equluminant probe disks 
(dark-disk condition). The upper and lower rightmost disks have the same local 
contrast, but they appear different in lightness. The two lower disks have 
different local contrast but they appear almost the same shade of gray; the 
same is true for the two upper disks. 
Figure 4. Perceived disk lightness in the dark-disk (top: Figure 4a) and the light-
disk condition (bottom: Figure 4b). Each data point represents the mean 
matched lightness of a separate group of 15 observers (total N=60) expressed 
in log reflectance with error bars indicating ± 1 between-subject SEM. For 
clarity, we added a gray-scale on the Y-axis that (approximately) corresponds to 
each value of log-reflectance. The relative position of the target disk is plotted 
on the X-axis. Black lines connect the data points corresponding to disks that lie 
in the same framework (Shadow vs. Light). Horizontal gray arrows indicate pairs 
of disks that have different contrast, but belong to the same framework. Vertical 
gray arrow indicate a pair of disks that have the same local contrast, but belong 
to different frameworks of illumination. 


A unified theory of brightness contrast and assimilation incorporating oriented multiscale spatial filtering and contrast normalization.

An Anchoring Theory of Lightness Perception.

Brightness constancy and the nature of achromatic colors.

Complexities of perceived brightness.

Outlines of a Theory of the Light Sense.

Principles of Gestalt Psychology.

Relative area and relative luminance combine to anchor surface lightness values.

Seeing black and white.

Simultaneous brightness induction as a function of inducing- and test- inducing luminances.

The place of white in a world of grays: a double-anchoring theory of lightness perception.

Visual Perception.

Visual computation of surface lightness: Local contrast vs. frames of reference

http://precedings.nature.com/documents/4244/version/1

Visual computation of surface lightness: Local contrast vs. frames of reference

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