SURFACE COLOR PERCEPTION AND ENVIRONMENTAL CONSTRAINTS

SURFACE COLOR PERCEPTION AND ENVIRONMENTAL CONSTRAINTS LAURENCE T MALONEY Department of Psychology Center for Neural Science New York University New York, NY 10003 ltm@cns.nyu.edu Draft: May 22, 2000 In Colour Vision: From Light to Object Mausfeld, R & Heyer, D [Eds.] Oxford: Oxford University Press, in press Surface Color Perception in Constrained Environments … I shall now remind you, that I did not deny, but that colour might in some sense be considered a quality residing in the body that is said to be coloured Robert Boyle (1663) If you and I were to disagree concerning the lengths of two rods, we might send out for a measuring tape or arrange to put the two rods next to each other so that they could be directly compared In contrast, if we were to disagree about the relative redness of two surfaces, it is not at all clear what we might to resolve the dispute A physicist, called in for consultation, could readily provide a summary of how a small, designated patch of a surface interacts with light, its bi- ( )  directional reflectance density function, S λ ; v , l This bi-directional reflectance density function (BRDF) is, roughly speaking, the probability1 that a photon of wavelength λ , arriving at the   surface from direction l , will be re-emitted in the direction of the viewer v (See Fig 1) It is plausible to assume that, if there is an objective correlate of the perceived color of a surface, the intrinsic color of the surface (Shepard, 1992), then some computation applied to the BRDF of the surface should serve to measure it But which computation, exactly? INSERT FIG ABOUT HERE The values of the BRDF are probability densities, not probabilities It is the probability that photons arriving along a   narrow cone centered on the vector l will be re-emitted along a narrow cone centered on the vector v See Cohen & Wallace (1993) Surface Color Perception in Constrained Environments In the quotation that heads this chapter, the celebrated chemist Robert Boyle allows for the possibility that colors correspond to objective properties of surfaces, but is evidently uncertain as to how that could be Indeed, the argument to the contrary has considerable force There is considerable psychophysical evidence indicating that there can be no intrinsic colors Color judgments depend not only on the BRDF of the surfaces involved, but also on the illumination of the scene (Helson and Judd, 1936), atmospheric haze (Brown & MacLeod, 1997), and the presence or absence of other surfaces not directly involved in the judgment, among other factors These effects are not small: ‘If changes in illumination are sufficiently great, surface colors may become radically altered [W]eakly or moderately selective illuminants with respect to wavelength leave surface colors relatively unchanged but a highly selective illuminant may make two surfaces which appear different in daylight indistinguishable, and surfaces of the same daylight color widely different’ (Helson & Judd, 1936, pp 740-741) Over the range of experimental conditions considered by Helson and Judd, this lack of constancy of surface color suggests that the relation between the BRDF of a surface patch and its perceived color is slight: there are no intrinsic colors Evans (1948, Color plate 13) illustrates how saturated, bright objects can change color dramatically with a change in illuminant: yellow becomes red, green becomes neutral Nassau (1983, Color plate) includes a color photograph of the gemstone alexandrite which can appear emerald green under daylight and ruby red under ordinary, indoor, incandescent illumination Yet we need not visit a laboratory to observe large failures of color and lightness2 constancy When you attend a movie, for example, you view a flat, white surface onto which is projected a complicated, dynamic pattern of light, the illuminant Your estimates of the surfaces in Lightness, roughly speaking, refers to the light-dark dimension of surface color perception (Gilchrist, 1994) Throughout this chapter I will use the term ‘surface color’ to refer to black, white, and grey stimuli as well as surfaces that are colored in the everyday use of the term Surface Color Perception in Constrained Environments front of you likely corresponds to the filmmaker’s conception of the film You see people, cars, explosions, and so on, just as the script of the film predicted None of these objects or their surfaces are present, and yet you ‘see’ them, occasionally forgetting about the only surface truly present, the uniform white screen A small patch of the screen, during the course of the movie, might appear to be any and all colors in rapid succession The failure of constancy in your perception of surface color could not be larger Mathematical analyses (Ives, 1912; Sällström, 1973; Maloney, 1984) confirm this conclusion: it is simply not possible to go from the kind of information available to biological visual systems to estimates of properties of the BRDFs of surfaces without some restriction on possible illuminants and possible surfaces in scenes There cannot be objective correlates of perceived surface color (intrinsic surface colors) that a biological visual system can estimate under all possible choices of BRDFs, illuminants, and spatial layout of lights and surfaces in scenes The Concept of Environment Yet, recent research indicates that, under certain circumstances, human observers seem to estimate intrinsic surface colors accurately (Brainard, Brunt & Speigle, 1997; Brainard, 1998) Other species are known to exhibit some degree of color constancy (Neumeyer, 1981; Werner, 1990) We can reconcile the apparent impossibility of surface color perception in ‘arbitrary’ environments with the evident competence exhibited by human observers and other animals in psychophysical experiments and much of everyday life by recognizing that we not live in ‘arbitrary environments’ It is specific constraints present in our immediate surroundings that permit us to succeed in perceiving stable surface colors These constraints can be thought of as a list of precise assertions concerning a visual scene If all of the assertions on the list are true of the Surface Color Perception in Constrained Environments scene, then human color vision will assign colors to surfaces in that scene that are the same as those it assigns to these surfaces in another scene that also satisfies these assertions Judd (1940), for example, notes that with “moderate departures from daylight in the spectral distribution of energy in the illuminant, external objects are seen … nearly in their natural, daylight colors.” In making this statement, Judd dichotomizes scenes into those satisfying the stated condition on the scene illumination and those that not In any near-daylight scene, he asserts, the human color visual system assigns nearly the same color to any surface patch as in any other Judd’s specification is not correct (the spectral distribution of the light used in projecting a movie is not from daylight) but it seems plausible that it can be extended to a description of the scenes where our color visual system assigns intrinsic colors to surfaces If we succeed, then we have established an operating range for the human color visual system, which I will refer to as its environment, over which it is capable of assigning stable colors to surfaces With no further specification of what that environment might be, this environmental hypothesis is neither falsifiable nor useful Indeed, we run the risk of developing a deus ex machina that we trot out at the end of every experiment We explain observed failures of color constancy by asserting that the ‘environment was bad’, and we explain success by asserting that the ‘environment was good.’ The environmental hypothesis has scientific content only to the extent that we can precisely state, in advance, what it is about an environment that permits or precludes accurate surface color perception For human vision, this environment does not include movie theaters or the conditions of many psychophysical experiments It does include the conditions of much of our everyday color experience, but, as we shall see, not all of it Surface Color Perception in Constrained Environments In the past twenty years, a number of researchers have studied the link between environmental constraints, the mathematical possibility of accurate surface color perception, and human performance in color tasks in real and simulated environments Four new areas of research have emerged The first comprises development of algorithms that make use of explicit constraints in estimating properties of the BRDF (See Hurlbert, 1998; Maloney, 1999 for reviews) If the constraints corresponding to an algorithm are satisfied, then the algorithm can estimate intrinsic colors of surfaces Once beyond its operating range, an algorithm will typically fail; the link between its color estimates and the properties of surfaces is severed In raising the environment hypothesis for human color vision, we emphasize the analogy between human color visual processing and these sorts of algorithms, each of which has its own specified operating range or environment The second area of research involves study of the constraints present in actual physical environments (See Bonnardel & Maloney, 2000, for a review) If we thought that we knew the operating range over which human surface color perception could function, then we would certainly be interested in learning whether and to what extent that operating range resembled our everyday world If we were uncertain what this operating range might be, it seems reasonable to look for clues in the structure of the environments we live in The third concentrates on measured human performance in real or simulated environments, attempting to determine which environmental constraints affect human color perception and over what ranges color perception is stable (Brainard, Brunt & Speigel, 1997; Brainard, 1998; Yang & Maloney, under review) Surface Color Perception in Constrained Environments As implied above, I will use the term environment to refer to a collection of mathematical descriptions of constraints (Maloney, 1999) This usage is unusual, but has much to recommend it The surface color perception algorithms just mentioned each come with a paired environment in which the algorithm will function correctly We are considering the hypothesis that human color vision, confined to a specified environment, will assign colors to surfaces that are in correspondence with certain properties of surfaces that also remain to be specified When necessary, I will contrast ideal environments (mathematical descriptions) with the real environments that they are intended to describe By means of computer graphics it is now possible to embed human observers in simulated environments that correspond to ideal environments That is, we can simulate a world that satisfies a specified collection of constraints and record an observer’s color judgments in that world and thereby explore how specific constraints affect human color vision Maloney & Yang (THIS VOLUME) describe experiments using such stimuli Fig illustrates the inter-relations among environments and algorithms in modeling human color perception INSERT FIG ABOUT HERE In the remainder of this chapter I will summarize what we know about environmental constraints, their relevance to surface color perception, and the accuracy with which they describe the world around us Surface Color Perception in Constrained Environments FLAT WORLD ENVIRONMENTS The first class of environments that we will consider are missing any information concerning the three-dimensional layout of surfaces in normal scenes The observer, in effect, views a scene painted on a large, distant planar surface, or perhaps the inside of a large sphere centered on him or her The scene is illuminated uniformly by a single light source (the illuminant) There is no interreflection (‘mutual illumination') among surfaces nor any specularity or shadows I'll refer to environments that omit the three-dimensional structure of scenes as Flat World Environments (Maloney, 1999) Such environments are idealizations of typical experimental arrangements that have been used to measure human surface color perception, e.g., in Mondrian displays (Land & McCann, 1971) If human color visual processing did not in fact make use of any information concerning the three-dimensional layout of the scene, then such environments could serve as accurate models of the world as ‘seen’ through human visual processing of color Very recent work (Bloj, Kersten & Hurlbert, 1999) indicates that information concerning the three-dimensional layout of scenes does affect color appearance, calling into question the adequacy of Flat World Environments and algorithms as models of human surface color perception A second piece of evidence hinting that Flat World Environments are not appropriate for human color processing is that we not yet have any Flat World algorithms that mimic human color vision in such scenes (Hurlbert, 1998; Maloney, 1999) Of course, this might be due to a lack of imagination on our part Yet it suggests that surface color perception in Flat World is difficult The Flat World Environments are worth consideration not only because of their historical importance but also because they serve as an introduction to more sophisticated models of light and surface in the world around us Surface Color Perception in Constrained Environments Lights and Surfaces Let’s begin by precisely specifying the elements common to every Flat World Environment: light from a single, distant, punctate light source (the ‘illuminant’) is absorbed by surfaces within a scene and re-emitted E(λ) will be used to denote the spectral power distribution of the incident illuminant at each wavelength λ in the electromagnetic spectrum It is not important to specify the location of the light source or its size and shape Light from this single source is absorbed by surfaces and re-emitted The re-emitted light that reaches the observer will be referred to as the color signal Its spectral power distribution is denoted L(λ): we assume that L(λ) = E(λ) S(λ), (1) where S(λ) denotes the surface spectral reflectance of the surface There may be many surfaces in a scene, each with a distinct surface spectral reflectance function, but we will assume that the light incident at one point in the scene is exactly the same as the light at any other point The color signal contains the information available to the observer about illuminant and surface at each point in the scene The Flat World constraints are diagrammed in Fig INSERT FIG ABOUT HERE The color signals reaching the observer (Fig 1) are imaged onto the retina3 We assign coordinates xy to each point in the retina, and it is convenient to label the color signal arriving at xy by Lxy(λ) We also denote the spectral reflectance function S(λ) of the surface patch imaged at point xy in the retina by Sxy(λ) We not need to superscript the light arriving at the surface patch since we have assumed it is uniform across the scene To repeat Eq with retinal coordinates inserted: Lxy(λ) = E(λ) Sxy(λ) We will only be concerned with monocular viewing conditions in Flat World (2) Surface Color Perception in Constrained Environments 10 In environments more complex than Flat World, the function S(λ) for a surface patch depends on the viewing geometry: the location in three dimensions of the surface patch, the locations of other surfaces, the location of the observer, and that of the illuminant We will return to this point below when we consider Shape World Environments Photoreceptor classes The retina is assumed to contain three distinct classes of photoreceptor classes differing in their spectral sensitivities, denoted Rk(λ) , k = 1, 2, These three spectral sensitivity functions are often denoted L, M, and S to reflect their differential sensitivity to Long, Medium, and Short wavelength light The initial visual information available to the color system at a single retinal location is just the excitation of each of the three classes of receptor in response to incident light, ρ1xy = ρ 2xy = ρ 3xy = ∫ L ( λ ) R ( λ ) dλ ∫ L ( λ ) R ( λ ) dλ ∫ L ( λ ) R ( λ ) dλ = = = xy xy xy ∫ E ( λ ) S ( λ ) R ( λ ) dλ ∫ E ( λ ) S ( λ ) R ( λ ) dλ ∫ E ( λ ) S ( λ ) R ( λ ) dλ xy xy (3) xy ( ) xy xy xy xy The three numbers at each location xy form a vector ρ = ρ1 , ρ , ρ Evidently the entries of the vector ρ xy depend on both the spectral power distribution, E(λ) , of the illuminant and on the surface spectral reflectance function, Sxy(λ) Intrinsic Colors In Flat World, we define the intrinsic colors of a surface with surface spectral reflectance as a vector ( C1 ( S ( λ ) ) , C ( S ( λ ) ) , C ( S ( λ ) ) ) , where the functions4 C i ( ) represent computations applied to the surface spectral reflectance function that return a single number We are simply providing notation (Maloney, 1984) for what was said before: intrinsic colors depend Precisely, functionals whose arguments are themselves functions Surface Color Perception in Constrained Environments 29 ACKNOWLEDGMENTS The initial quote is taken from Nicolas Wade’s wonderful book (Wade, 1998, p 123) Grant EY08266 from the National Institute of Health, National Eye Institute provided partial support for much of the work described here The author thanks Lars Chittka for access to the surface reflectance data of Chittka et al (1994) Several people were kind enough to read this chapter in earlier drafts and comment on it I especially want to thank Michael Landy for detailed comments and criticisms Last of all, the author is grateful to the Computer Science Institute at Hebrew University, Jerusalem for support as Forchheimer Professor while writing this chapter Surface Color Perception in Constrained Environments 30 REFERENCES Apostol, T M (1969), Calculus, 2nd Ed., Volume II Waltham, Massachusetts: Xerox Bloj, M G., Kersten, D & Hurlbert, A C (1999), Perception of three dimensional shape influences colour perception through mutual illumination Nature, 402, 877-879 Bonnardel, V & Maloney, L T (2000), Daylight, biochrome surfaces, and human chromatic response in the Fourier domain Journal of the Optical Society of America A, 17, 677-687 Brill, M H (1978), A device performing illuminant-invariant assessment of chromatic relations, Journal of Theoretical Biology, 71, 473 Brill, M H (1979), Further 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Illuminant cues and surface color perception: Tests of three candidate cues Vision Research, under review Surface Color Perception in Constrained Environments 41 Yilmaz, H (1962), Color vision and a new... of empirical illuminants and surfaces (Marimont & Wandell, 1992) The results of this section suggest that surface reflectance functions and illuminants in Surface Color Perception in Constrained... physical surface exhibit physical constraints and what these constraints might be If we understood Surface Color Perception in Constrained Environments 21 the theoretical bases for these constraints,