Color Constancy as Counterfactual
Color constancy is a fascinating phenomenon in its own right, and also
has implications regarding the ontology of color.
In this paper I'll argue that the usual understanding of color
constancy in the philosophical and empirical literature are
unsatisfactory, and the propose a novel account of the phenomenon
that (i) offers gains in descriptive adequacy, and (ii) undercuts
ontological conclusions often drawn from color constancy.
In recent years, vision scientists and philosophers of perception have
devoted considerable attention to questions about color constancy.
Among the most important issues surrounding color constancy are
those about how we should understand the phenomenon and those about
what the phenomenon shows about the nature of color.
I believe that the phenomenon of color constancy has been
misunderstood, and that correcting this misunderstanding will have the
effect of undercutting the apparent support the phenomenon provides to
accounts of color as illumination-independent properties.
1 Constancy as Invariance
Since color constancy is easier to recognize than to define, I'll
begin with an example - a coffee cup on a table, partially in direct
sunlight and partially in shadow.2
Figure 1: Partially sunlit coffee cup.
Consider the region of the coffee cup (and the region of the table) in
direct sunlight, and compare it against a similar-sized, adjacent
region of the coffee cup (and a region of the table) that are in
If you are like most (normally sighted) subjects, you will find that
these two regions are, in some sense to be explained, alike in their
On the other hand, again assuming you are like most (normally sighted)
subjects, you will also find that the regions are easily, obviously,
and quickly visually discriminable.
Moreover, you are likely to explain this easy, obvious, and quick
visual discriminability in terms of the readily apparent difference in
illumination between the two regions.
These two reactions to a pair of visual stimuli (in this case, the
pair consists of the two simultaneously presented regions of the
coffee cup) are the hallmarks of color constancy.
These two reactions lead naturally to what has become a standard
understanding of color constancy as a kind of invariance.
In particular, on this view (henceforth, invariantism), color
constancy is an invariance of apparent color across changes in
The main problem that I wish to press against invariantism comes from
something already noted.
Namely, in paradigm cases of color constancy, subjects canonically
have two different reactions: they judge not only that the members of
the pair of surfaces are alike in apparent color, but also that they
are easily and obviously visually discriminable.
Of course, it does not seem (in general) that this discriminability
can be accounted for in terms of a difference in the size, form, or
texture (etc.) between the surfaces.
Rather, we seem forced to admit, subjects are able to discriminate the
members of the pair because they take the members to differ in respect
of their apparent color.5
But to say this is to say that, while there is a sense in which
subjects judge that the members of the pair are alike in apparent
color, there is another sense in which they judge that the members of
the pair are unalike in apparent color.
This fact is, I want to suggest, a serious problem for invariantist
accounts of color constancy.
For, if the foregoing is correct, then it is at best seriously
misleading to say, with the invariantist, that color constancy
involves an invariance of apparent color across variations in
This claim respects only only one of the two reactions (normally
sighted) subjects have to these cases.
While it respects one of their reactions (their reaction that the two
members of the pair of stimuli are alike in apparent color), it
ignores their reaction to the effect that the members of the pair
differ in apparent color - that there is not an
invariance of apparent color across changes in the
Now, the argument above turns crucially on the claim that subjects
find there to be some sort of difference in apparent color between the
surfaces in question (for example, between the two adjacent regions of
the coffee cup depicted in figure 1)?
What support is there for this claim?
Let us begin with a fairly crude, qualitative test: let us ask whether
the adjacent surfaces are different in apparent color by asking
whether subjects can visually discriminate between them.
The answer that I've received from 100% of the subjects I've asked to
consider figure 1 is that they can visually
discriminate between the two adjacent surfaces.
This presumably means that there is some perceptually salient
difference between the two surfaces; and, for reasons rehearsed, this
difference most plausibly understood as a difference in apparent
On the other hand, it may be reasonably objected that the test of
qualitative discriminability relied upon in the foregoing is a
blunt (and outdated) instrument for investigating color constancy.
Let us consider, therefore, how the line of argument I am running
fares in the face of the sharper, quantitative measurements used in
contemporary psychophysical investigations of color constancy.
The main quantitative measure by which contemporary psychophysicists
assess color constancy, known as asymmetric color matching
[Wyszecki and Stiles, 1967], involves asking subjects to change the
chromaticity (or lightness, in lightness constancy experiments) of a
test patch under one illuminant until it perceptually matches a
standard patch under a different illuminant.
Since the subject eventually arrives at a perceptual match,
investigators regard the chromaticity (/lightness) difference between
the test and the standard patches as a quantitative measure of the
perceptual effect of the illumination difference.
Unsurprisingly, asymmetric color matching brings out the points
considered above even more clearly than the qualitative measure
Roughly, it seems that (most) subjects can respond in two different
modes - one mode that assimilates surface pairs like that in
figure 1, and one that distinguishes such pairs.
Moreover, it seems that (most) subjects can be made to switch between
these two modes of response as a result of experimental instructions:
instructions to "adjust the test patch to match its hue and saturation
to those of the standard patch" lead subjects to distinguish members
of such pairs, while instructions to "adjust the test patch to look
as if it were `cut from the same piece of paper' as the standard,
i.e., to match its surface color" ([Arend and Reeves, 1986], 1744) lead
subjects to assimilate members of such pairs.7
(I'll follow [Bäuml, 1999] in talking about the first sort of
matches - those that distinguish the two surfaces - as
appearance matches, and the second sort of matches - those that
assimilate the two surfaces - as surface matches.
Obviously, no substantive conclusions should be inferred from the
choice of these labels.)
To repeat, then: invariantism characterizes cases of color constancy
as cases where there is an invariance of apparent color despite
changes in the illuminant.
But in fact, in what would pre-theoretically count as cases of color
constancy, subjects can be made to judge either that there is a single
color (hence that there is an invariance of apparent color) or that
there are two colors (hence that there is not an invariance of
This means that, in order to sustain her account in the face of the
experimental results, the invariantist owes us some reason for
ignoring fully half of the data, as well as an account of the relation
between appearance and surface matches.
2 Color Constancy and Color Ontology
At this point I want to consider the role color constancy has figured
in philosophical arguments about the nature of color.
I want to suggest that these arguments have problems quite independent
of the points made above - that they fail on their own terms.
As noted, philosophical appeals to color constancy have generally been
in the course of arguments to the conclusion that colors are
objective, illumination-independent properties of some sort (e.g.,
surface spectral reflectance distributions).
For example, here is Michael Tye: "The fact that objects appear to
retain the same color through a wide variety of changes in
illumination conditions (though certainly not all) strongly suggests
that colors are illumination-independent properties of those objects"
([Tye, 2000], 147-148).
Similarly, Hilbert begins with the claim that "The existence of color
constancy should lead us to suspect the existence of some
illumination-independent property of objects that is correlated with
color," goes on to note that "The obvious candidate for such a
property is ... surface spectral reflectance" ([Hilbert, 1987],
65), and ends up concluding that colors are indeed identical to
(classes of) surface spectral reflectance distributions (see also
[Byrne and Hilbert, 2002], §3.1 for a compact and explicit formulation
of the same thought).
It seems that these philosophers are urging upon us something like the
following chain of (non-deductive) reasoning (henceforth, the
On an invariantist account, premise (1) of the objectivist's inference
amounts to the following, understood as an empirical claim:
- There is color constancy.
- Reflectance distributions are illumination-independent.
- Therefore, colors are identical to reflectance
Of course, (1¢) will not, by itself, give us any reason to believe
the intended conclusion (3) unless we take (1¢) to tell us something
about color, as opposed to apparent color.
The thought, then, must be that (1¢) is a (defeasible) reason for
- The apparent color of a surface is invariant across
changes in illumination.
The objectivist's inference, on this reading, comes out as a pair of
inferences - namely, a pair of inferences to the best explanation.
It moves first from the empirical premise (1¢) to the effect that
apparent colors are illumination-independent to the allegedly best
explanatory conclusion (1*) to the effect that colors are
illumination-independent; and from (1*) and the definitionally true
premise (2) to the effect that reflectance distributions are
illumination-independent, to the allegedly best explanatory conclusion
(3), that colors are identical to reflectance distributions.
Understood in this way, the objectivist's inference invites a number
First, there is a concern that, in the context of a debate about what
the empirical results about apparent color tell us about color, the
inference from (1¢) to (1*) will strike many as too hasty
(cf. note 3).
Although I am sympathetic to this criticism, I'll put it aside,
insofar as I believe there is a more fundamental problem with the
This problem arises from the observation that there are many
uncontroversial cases - cases that even Hilbert and Tye would accept
- where the alleged invariance cited in (1) fails.
I take it that this much would conceded by all
Indeed, I take it that the parenthetical qualification in the
quotation above from ([Tye, 2000], 147-148) is intended to concede
that the claimed invariance fails in at least some
But if the invariance fails in many cases, then we are justified in
wondering why it is properly thought of as an invariance at all
(rather than a variance).
And given that Tye, Hilbert, and others are prepared to take the
invariance of apparent color across changes in illumination as
evidence that (apparent colors, and therefore) colors are
illumination-independent, why should we not take the failures of
invariance as showing that (apparent colors, and therefore) colors are
illumination-dependent properties of objects?
Tye and Hilbert are, of course, aware of this worry, and their
attempts to answer it are instructive.
They propose to regarding the violations of invariance as exceptional
cases to the general rule (viz., the rule of invariance) on the
grounds that these cases are cases of color misperception
(cf. [Hilbert, 1987], 71-72, [Tye, 2000], 153ff).
Unfortunately, it is not clear to me that there are theory-independent
reasons for endorsing this view.
Of course, if colors are assumed to be illumination-independent
properties, then cases in which apparent color is shown not to be
illumination-independent are plausibly described as cases where the
apparent color fails to reveal the true color of objects - as cases
of color misperception.
But this result, of course, turns on assuming that colors are
illumination-independent, and presumably this is not a supposition
that we should make in our characterization of color constancy if we
hope to appeal to color constancy to motivate the view that colors
Thus, short of begging the ontological question that color constancy
is being enlisted to answer (via the objectivist's inference), it is
not clear why the acknowledged failures of invariance should not be
regarded (pace Hilbert and Tye) as evidence for the
illumination-dependence of (apparent color, and therefore)
Without answers to these questions, it seems that the inavariantist
account of color constancy cannot be used to show that colors are
- The color of a surface is invariant across changes in
3 Color Constancy as Counterfactual
I want to propose an alternative understanding of color constancy, and
then argue that it is superior to invariantism.
Finally, in §4, I'll consider the implications this
revised account of color constancy holds for color ontology.
Our problem is to characterize the phenomenon involving our perception
of the adjacent regions of the coffee cup in figure 1.
The discussion so far suggests two desiderata that an acceptable
account of color constancy should meet.
First, we want to say that there is some sense in which the colors of
these two regions appear relevantly alike to subjects; this
desideratum surely captures one intuition that we have about cases of
color constancy, and it comes out clearly in subject judgments about
Second, we need a way of articulating this last idea while (unlike the
invariantist) avoiding the straight-out insistence that the two
regions are identical in apparent color, since, as shown by the
appearance matching data, they are not.
As a way of meeting these desiderata, I propose to understand color
constancy as an ability to make counterfactual verdicts - verdicts
about the color appearance that objects would have if they were viewed
in non-actual perceptual circumstances.
In particular, I suggest, surface match responses answer this
question: would region R1 (presented under illumination I1)
share a color appearance with region R2 (presented under
illumination I2) if, contrary to fact, both regions were presented
under the same illumination?
This account (henceforth, counterfactualism) respects the desiderata
First, it offers a direct account of the sense in which the colors
of the two regions appear relevantly alike.
Namely, the two regions appear alike in that they would share
a color appearance if both regions were presented under the same
Second, and unlike invariantism, counterfactualism explains this
likeness in appearance while simultaneously respecting the facts about
Namely, the counterfactualist allows that the two regions of interest
in a case of color constancy can (i) appear relevantly similar in
respect of color, even though (ii) they differ in color appearance.
In addition, counterfactualism has the advantage that, unlike
invariantism, it provides a plausible understanding of the
relationship between surface matches and appearance matches.
For, if counterfactualism is correct, then surfaces match judgments
are naturally understood as results computed by the visual system from
the evidence of non-matching color appearances.
Of course, appearance matches are, on this story, made by comparing
the same color appearances that serve as evidence for surface match
But if this is right, then surface match judgments are the results of
computations that begin where appearance match judgments end.
Consequently, counterfactualism predicts that appearance matches
should be less difficult and faster than surface matches.
I take the confirmation of these predictions ([Arend and Reeves, 1986],
1747-1748) as a further piece of support for the view.
4 Ontological Implications
The counterfactualist account of color constancy is explicated in
terms of apparent colors, rather than colors.
However, the question that has made color constancy worth caring about
for most philosophers is whether colors are
But what we have learned about apparent color surely bears on the
question of interest about color.
For, if the apparent color of surface region R varies with the
illumination, then to say that the color of R is stable across
changes in illumination is to say that at most one of the distinct
apparent colors that R has across a range of illuminations
veridically represents the color that R has.
Therefore, given that apparent colors are illumination-dependent, we
can ask whether colors are illumination-independent by asking which
among the various color appearances that R has (when presented under
various illuminations) veridically represents the color of R.
In particular, in view of the illumination-dependence of color
appearance, the defender of the thesis that colors are
illumination-independent owes us a principled reason for singling out
(at most) one of the various color appearances that R has as its
veridical color appearance - as the unique appearance that
veridically represents R's color.
I shall not reiterate the arguments I have made elsewhere that such a
principled reason is not forthcoming.9
Instead, I want to draw two morals of more immediate importance.
First, I want to note that, if counterfactualism is the right
understanding of color constancy, then appeals to that phenomenon do
not suffice to answer the question just bruited (assertions to the
contrary in the literature notwithstanding).
For, if counterfactualism is correct, then color constancy tells us
nothing that would single out any one of the (phenomenally distinct)
color appearances of R as veridical.
On the contrary, it tells us only that subjects make counterfactual
judgments about a range of color appearances that R would have under
a range of illuminations.
This is a significant lesson to draw, since, it seems to me,
philosophers who appeal to color constancy often do so precisely in
order to motivate a choice of a single color appearance among many
(e.g., [Tye, 2000], 147-148, [Hilbert, 1987], chapter
My first moral, then, is that if counterfactualism is the correct
understanding of color constancy, then the phenomenon cannot serve to
show that colors are illumination-independent.
My second moral is that, on the contrary, a descriptively adequate
understanding of color constancy is fully compatible with the view
that colors are illumination-dependent.
For if (as I believe) there is no principled reason for singling out
any one of the range of color appearances of R as veridical, and
if, therefore we conclude that the color of R is an
illumination-dependent property of R, we can and should acknowledge
the phenomenon of color constancy.
- [Arend and Reeves, 1986]
Arend, L. and Reeves, A. (1986).
Simultaneous color constancy.
Journal of the Optical Society of America A, 3(10):1743-1751.
- [Arend et al., 1991]
Arend, L., Reeves, A., Schirillo, J., and Goldstein, R. (1991).
Simultaneous color constancy: patterns with diverse Munsell values.
Journal of the Optical Society of America A, 8:661-672.
- [Bäuml, 1999]
Bäuml, K.-H. (1999).
Simultaneous colour constancy: how surface color perception varies
with the illuminant.
Vision Research, 39(8):1531-1550.
- [Beck, 1972]
Beck, J., editor (1972).
Surface Color Perception.
Cornell University Press, Ithaca.
- [Brainard et al., 2002]
Brainard, D. H., Kraft, J. M., and Longere, P. (2002).
Color constancy: Developing empirical tests of computational models.
In Mausfeld, R. and Heyer, D., editors, Colour Perception: From
Light to Object. Oxford University Press, New York.
- [Byrne and Hilbert, 1997]
Byrne, A. and Hilbert, D. R. (1997).
Readings on Color, Volume 2: The Science of Color.
MIT Press, Cambridge, Massachusetts.
- [Byrne and Hilbert, 2002]
Byrne, A. and Hilbert, D. R. (2002).
Color realism and color science.
Behavioral and Brain Sciences.
- [Cohen, 2000]
Cohen, J. (2000).
Color Properties and Color Perception: A Functionalist Account.
PhD thesis, Rutgers University, New Brunswick, New Jersey.
- [Cohen, 2002]
Cohen, J. (2002).
Color properties and color ascriptions: A relationalist manifesto.
- [Cohen and Meskin, 2003]
Cohen, J. and Meskin, A. (2003).
Photographs are not transparent.
- [Cornelissen and Brenner, 1995]
Cornelissen, F. W. and Brenner, E. (1995).
Simultaneous colour constancy revisited: an analysis of viewing
Vision Research, 35:2431-2448.
- [Evans, 1948]
Evans, R. M. (1948).
An Introduction to Color.
Wiley, New York.
- [Goldstein, 1999]
Goldstein, E. B. (1999).
Sensation & Perception (5th Edition).
Brooks/Cole Publishing, Pacific Grove, California.
- [Hilbert, 1987]
Hilbert, D. R. (1987).
Color and Color Perception: A Study in Anthropocentric Realism.
- [Lennie, 1999]
Lennie, P. (1999).
Color coding in the cortex.
In Gegenfurtner, K. R. and Sharpe, L. T., editors, Color Vision:
From Genes to Perception, pages 235-247. Cambridge University Press,
- [Stoerig, 1998]
Stoerig, P. (1998).
Wavelength information processing versus color perception:evidence
from blindsight and color-blind sight.
In Backhaus, W. G. K., Gliegl, R., and Werner, J. S., editors,
Color Vision: Perspectives From Different Disciplines, pages 131-147.
Walter de Gruyter, Berlin.
- [Troost and deWeert, 1991]
Troost, J. M. and deWeert, C. M. M. (1991).
Naming versus matching in color constancy.
Perception & Psychophysics, 50:591-602.
- [Tye, 2000]
Tye, M. (2000).
Consciousness, Color, and Content.
MIT Press, Cambridge, Massachusetts.
- [Walton, 1984]
Walton, K. (1984).
Transparent pictures: On the nature of photographic realism.
Critical Inquiry, 11:246-276.
- [Wyszecki and Stiles, 1967]
Wyszecki, G. and Stiles, W. S. (1967).
Wiley, New York.
- [Zaidi, 1999]
Zaidi, Q. (1999).
Color and brightness induction: from Mach bands to
In Gegenfurtner, K. R. and Sharpe, L. T., editors, Color Vision:
From Genes to Perception, pages 317-343. Cambridge University Press,
1Department of Philosophy, University of
California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0119,
joncohenREMOVETHIS@aardvark.ucsd.edu (omit text in caps, which reduces automated spam)
The case I have in mind is one in which the subject is visually
perceiving a coffee cup, not a photograph of the coffee cup
(notwithstanding the arguments of [Walton, 1984], I take it that
when a subject sees a photograph of x, she does not ordinarily see
x as well; see [Cohen and Meskin, 2003]).
Hence, I am using figure 1 to depict the
stimulus - I am not using it as the stimulus.
This will matter, since it is plausible that there is a variation in
the illumination under which the coffee cup is perceived, whereas it
is doubtful that there is a significant variation in the illumination
under which figure 1 is perceived.
For ease of expression, I'll be pretending that the reader can
perceive the depicted coffee cup in what follows.
3As noted, invariantism has become the de
facto standard understanding of color constancy in both
philosophical and scientific work on color.
For example, versions of this characterization can be found in many
recent textbooks and anthologies on color and vision including
([Byrne and Hilbert, 1997], 445), ([Zaidi, 1999], 339),
([Goldstein, 1999], 567), ([Stoerig, 1998], 141), and
([Brainard et al., 2002], 2).
In several cases these paginations point to glossary entries for
Why an invariance of apparent color rather than an invariance
As I shall discuss below, many invariantists want to appeal to color
constancy in the course of arguing for a particular way of
individuating colors; as such, it will not suit their purposes to
describe the phenomenon in a way that depends on a particular (and
controversial) way of individuating colors.
In contrast, characterizing color constancy as an invariance in
apparent color has the dialectical advantage that it does not beg the
ontological questions that the phenomenon is enlisted to answer.
5Of course, there is one salient
dimension along which the adjacent regions are unlike: they are unlike
in respect of the illumination that falls on them.
Does this mean that we should set aside subjects' visual
discrimination of the regions as a way of determining whether the
regions share an apparent color?
Surely that policy would be unwise in the present setting; for if
we are debarred from considering discriminations between regions that
differ in illumination, then we can never decide whether regions are
invariant in apparent color across variations in illumination.
But variations in illumination are precisely the variations that we
must consider in assessing whether or not there is color constancy, as
that phenomenon is understood by an invariantist; therefore, the
proposed strategy of setting aside subjects' visual discriminations in
such cases would mean that these cases - paradigmatic cases, and
therefore precisely the cases that an adequate understanding of color
constancy ought to capture - could never be regarded as instances of
color constancy (on an invariantist account).
It seems, therefore, the present response on behalf of the
invariantist is unsatisfactory.
6Of course, the invariantist could avoid the
difficulty we are now discussing by insisting that, when subjects have
such conflicting reactions to a pair of surfaces, the case is not an
instance of color constancy.
But this alternative strategy seems inadvisable.
After all, insofar as the pair of conflicting responses is taken as a
hallmark of paradigm cases of color constancy, the strategy in
question amounts to emptying the phenomenon of instances merely to
save a favored theory.
Presumably this is unacceptable.
have been confirmed by a number of studies.
See [Evans, 1948], 163-164 and [Beck, 1972], 66-67 for an
overview of some of the earlier work; more recent findings to the same
effect are reported in [Arend and Reeves, 1986],
[Arend et al., 1991], [Troost and deWeert, 1991],
[Cornelissen and Brenner, 1995], and [Bäuml, 1999].
8Certainly it is uncontroversial for color scientists,
who frequently take such cases to show the limitations on human color
constancy (thus, in an entirely typical passage, Peter Lennie writes
that "Formal accounts of color constancy characterize mechanisms that
perform better than human observers: Human color constancy is
imperfect" ([Lennie, 1999], 245-246)).
9See [Cohen, 2000]
and [Cohen, 2002].
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