Reflectance realism and colour constancy: What would count as scientific evidence for hilbert's ontology of colour?

Abstract

Reflectance realism is an important position in the philosophy of colour. This paper is an examination of David R. Hilbert's case for there being scientific support for the theory. The specific point in question is whether colour science has shown that reflectance is recovered by the human visual system. Following a discussion of possible counter-evidence in the recent scientific literature, I make the argument that conflicting interpretations of the data on reflectance recovery are informed by different theoretical assumptions about the nature of colour, and of perception. If this is so, there cannot be neutral empirical evidence on this point, and this does seem to undermine Hilbert's claim for empirical support. In the end, I suggest alternative ways of thinking about the relationship between colour ontology and empirical work on colour.

Acknowledgments

I would like to thank Laurence Maloney and Qasim Zaidi for discussions about their work and comments on the manuscript, and for permission to use the figures. I also thank Ian Gold for reading various drafts, and the AJP referees for their comments. This research was supported by the Australian Research Council.

Notes

¹Scientific terms will be discussed more fully in section II. But briefly, reflectance is a property which indicates how much of light incident on a surface is reflected rather than absorbed. Surface spectral reflectance (SSR) measures how the proportion of light reflected varies with wavelength of the incident light. Reflectance recovery is the putative process of inferring reflectance properties of surfaces from ambiguous photoreceptor signals which confound information about incident light and reflectances.

²As far as I am aware, Hilbert does not ever discuss the possibility that scientists studying reflectance recovery share his theoretical views. When Hilbert does mention the philosophical commitments of scientists it is to point out the prevalence of subjectivism [Byrne and Hilbert 2003: 3–4], but he does not suggest how the view might influence their empirical work. However, I in no way mean to suggest that Hilbert is a naïve reader of the science, oblivious of any theoretical commitments. The point I am making is that Hilbert's case for scientific support, as put forward in the sections quoted above, does rest on the assumption of neutrality, i.e. the philosophical innocence of Maloney and Wandell's finding that reflectance recovery algorithms can explain features of human colour perception. If I am accusing Hilbert of anything it is of being a selective reader of the scientific literature. There is no charge of naïvety because it is not obvious that theoretical commitments are playing a decisive role in the work on reflectance recovery, but this becomes more obvious when one reads the work of other scientists, whose approach is fundamentally different from Maloney and Wandell's. This is what I aim to show in sections III–IV below.

³E.g. Brown 2003: 257], ‘Many [computational models of colour constancy] are even designed to reconstruct the full spectral reflectance functions of surfaces; this seems akin to suggesting that the goal of olfaction is to reconstruct three-dimensional molecular models of oderants.’

⁴No vision scientist has argued that reflectance might be more than approximately resolvable by our visual system, nor does Hilbert's theory require this (see Hilbert 1987: chap 6]). Maloney (personal communication) notes that the goal of his work, strictly speaking, has not been to devise algorithms to reconstruct reflectance, but rather to assign invariant colour descriptors to surfaces, and these descriptors are correlated with SSR.

⁵Note Maloney's explicit mention of colour and albedo (or lightness i.e. achromatic reflectance) constancy phenomena as ‘inverse problems’. This is central to his approach to vision, and in section II.A we will see how these theoretical assumptions play out in his work on lightness constancy.

⁶Maloney and colleagues use the term ‘albedo’, and Zaidi and colleagues, ‘lightness’, though the two are equivalent.

⁷Some readers may also be reminded of the issue between Descartes's and Berkeley's theories of vision. See, e.g., Atherton 1990. I would agree that the conceptual difference between Maloney and Zaidi shares something with this longstanding philosophical debate, but I do not trace out the links in what follows.

⁸However, Maloney (personal communication) has emphasized that an important difference between his own understanding of inverse problems and Hilbert's reflectance realism is that Maloney sees no requirement for explicit representation of recovered properties (reflectances), or of any of the estimates of illuminant chromaticities used to recover them. Though this may not be a requirement of Hilbert's either – see note 10.

⁹Foster 2003 distinguishes this from colour constancy in a more absolute sense, which would entail some sort of reflectance recovery.

¹⁰One objection that might be raised here by a proponent of reflectance recovery is, ‘What would be matched across illuminants if not reflectance? Reflectance realism might not, in the end, require any explicit representation of reflectance, only correlation between perceived colour and SSR.’ But what is different about Zaidi's approach might be brought out with the analogy with light adaptation: when, because of retinal light adaptation, one sees a white sheet as near equally bright inside as outside in the sunshine, one might say that the visual system has matched a property of the object (namely, lightness or albedo). That seems an artificial way of putting it, though. Light adaptation stops photoreceptor responses carrying on increasing linearly to saturation as overall illumination levels increase. This is useful because it means that retinal responses do not saturate out, and that the magnitude of responses to specific objects can stay approximately the same as the illumination intensity goes up. A more natural way of describing the mechanism is that adaptation aims to keep the retinal response to one environmental feature (overall illumination) steady so that differences in another environmental feature (object lightness) will always be detectable, being within the dynamic range of the cells' responses. One might say that lightness is being recovered, but that is an unnecessary step. My point is that the heuristics approach to colour constancy is like this, explaining visual function as a trade-off between sensitivity to environmental changes that are more interesting or less interesting to the animal.

¹¹The difference between the heuristics and the Marrian approaches is subtle because the two views are not mutually exclusive in principle: it could turn out that the heuristic that best captures human colour performance is an inverse optics algorithm. But the heuristics school is not committed to inverse optics in the way that Marrians are. What is crucially different is that the two stances recommend diverging lines of experiment—they constitute different ‘research programmes’.

¹²E.g. Jackson 1998 calls his microphysical realism ‘The Primary Quality View of Colour’.

¹³In this section my intention is to remain neutral as to whether the distinction between sensation and perception is justifiable and useful. It might be objected that brightness appearance is not a ‘sensation’ because the psychophysical evidence shows that it is the result of much visual processing. But my point is just that Zaidi and colleagues treat brightness as a sensation (a proximal stimulus), comparing it to lightness which would be a perceived distal property. Nor am I suggesting that, in ignoring the distinction, the Maloney group is denying sequential processing in the visual system.

¹⁴Talk of ‘changing the subject’ is reminiscent of the old debate about incommensurability. I do not wish to argue here that the different scientific opinions over reflectance recovery are incommensurable in any loaded sense, though the bearing of these cases on some of the wider issues in the philosophy of science will be touched on in the conclusions below.