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Scalar Invariance in Opponent Colour Theory and the ‘Discounting the Background’ Principle
Abstract
The present paper discusses some theoretical questions pertaining to the ‘discounting the background’ hypothesis and its relation to opponent colour theory. Different such hypotheses are distinguished and their relation is outlined. Emphasis is placed on juxtaposing qualitative laws and quantitative representations thereof, as common in measurement-theory.
Centre-surround stimuli evoke colour appearances (resembling surface colours) which cannot be produced by a single homogeneous spot of light alone (eg brown or grey). Although this seems of great impact to a general theory of colour (including 'colour constancy'), the psychophysics of these 'minimal relational stimuli' is still less well understood than often assumed. On the basis of empirical as well as theoretical observations concerning centre-surround-type stimuli we introduce a relational model of colour coding. At the core of this model is the concept of a three-dimensional linear incremental colour code which behaves differently for increments and decrements. This model takes into account results on 'discounting the background' mechanisms and it is closely related to ratio-based relational concepts and to certain opponent-colour theories. In addition, it provides an analogue to the classical distinction between light and object colours, and covers colour appearances related to object colours as well. Within the conceptual framework offered, problems of complex colour perception (eg 'colour constancy') and judgmental modes are discussed. Conclusions regarding general limitations of three-dimensional modelling in colour perception are derived and corresponding refinements of the relational perspective are briefly outlined.
The paper gives a short account of a new model for asymmetric colour matching. It generalizes affine models previously proposed in the literature, starting from Walraven’s (1976) “discounting the background” principle. The characteristic feature of the model proposed is that it allows different v.Kries-type multiplicative transformations for increments and decrements. Due to the qualitative laws implied, the model is particularly attractive from a measurement-theoretic ‘Grassmannian’ perspective. Some empirical and theoretical aspects of the model are briefly discussed.
This chapter deals with the problems of chromatic adaptation and its mechanisms. In our analysis of chromatic adaptation and its use to reveal specific properties of the mechanism of color vision, we shall discuss sensitivity changes, contrast effects and after-images. Despite the intrinsic interest of each of these topics, we are not here concerned with a detailed and comprehensive description of the multiplicity of visual effects conventionally grouped under the separate rubrics, contrast, after-images, etc.
A red/green equilibrium light is one which appears neither reddish nor greenish (i.e. either uniquely yellow, uniquely blue, or achromatic). A subset of spectral and nonspectral red/green equilibria was determined for several luminance levels, in order to test whether the set of all such equilibria is closed under linear color-mixture operations. The spectral loci of equilibrium yellow and blue showed either no variation or visually insignificant variation over a range of 1-2 log10 unit. There were no trends that were repeatable across observers. We concluded that spectral red/green equilibria are closed under scalar multiplication; consequently they are invariant hues relative to the Bezold-Brücke shift. The additive mixture of yellow and blue equilibrium wavelengths, in any luminance ratio, is also an equilibrium light. Small changes of the yellowish component of a mixture toward redness or greeness must be compensated by predictable changes of the bluish component of the mixture toward greenness or redness. We concluded that yellow and blue equilibria are complementary relative to an equilibrium white; that desaturation of a yellow or blue equilibrium light with such a white produces no Abney hue shift; and that the set of red/green equilibria is closed under general linear operations. One consequence is that the red/green chromatic-response function, measured by the Jameson-Hurvich technique of cancellation to equilibrium, is a linear function of the individual's color-matching coordinates. A second consequence of linear closure of equilibria is a strong constraint on the class of combination rules by which receptor outputs are recoded into the red/green opponent process.
For trichromatic color measurement, the empirically based structure consists of the set of colored lights, with its operations of additive mixture and scalar multiplication, and the binary relation of metameric matching. The representing numerical structure is a vector space. The important axioms are Grassmann's laws. The vector representation is constructed in a canonical or coordinate-free manner, mainly using Grassmann's additivity law. Trichromacy is used only to fix the dimensionality.Color theories attempt to get a more unique homomorphism by enriching the basic empirical structure with new empirical relations, subject to new axioms. Examples of such enriching relations include: discriminability or dissimilarity ordering of color pairs; dichromatic matching relations; and unidimensional matching relations, or codes. Representation theorems for the latter two examples are based on Grassmann-type laws also. The relationship between a Grassmann structure and its unidimensional Grassmann codes is modeled by the relationship between a vector space and its dual space of linear functionals. Dual spaces are used to clarify theorems relating to the three-pigment hypothesis and to reduction dichromacy.
Quantitative opponent-colors theory is based on cancellation of redness by admixture of a standard green, of greenness by admixture of a standard red, of yellowness by blue, and of blueness by yellow. The fundamental data are therefore the equilibrium colors: the set A1 of lights that are in red/green equilibrium and the set A2 of lights that are in yellow/blue equilibrium. The result that a cancellation function is linearly related to the color-matching functions can be proved from more basic axioms, particularly, the closure of the set of equilibrium colors under linear operations. Measurement analysis treats this as a representation theorem, in which the closure properties are axioms and in which the colorimetric homomorphism has the cancellation functions as two of its coordinates.Consideration of equivalence relations based on opponent cancellation leads to a further step: analysis of equivalence relations based on direct matching of hue attributes. For additive whiteness matching, this yields a simple extension of the representation theorem, in which the third coordinate is luminance. For other attributes, precise representation theorems must await a better qualitative characterization of various nonlinear phenomena, especially the veiling of one hue attribute by another and the various hue shifts.
This investigation explores the color appearance changes resulting from a continuously presented adapting field. In every experiment, an incremental mixture of red and green monochromatic lights was superimposed on top of a steady red background field. On each experimental trial the intensities of the red background and the red increment were fixed: the subject adjusted the intensity of the green light so that the incremental mixture appeared a “pure” (neither slightly reddish nor greenish) yellow. In one experiment, the increment was a steadily viewed thin annulus seen on a larger background: in another experiment the increment was identical to the background in size and retinal location but was presented as a brief ( 150 msec) flash: in the final experiment the increment was a briefly flashed thin annulus seen on a larger background.For any fixed, relatively dim background level the intensities of the red and green increments were approximately in constant ratio over a nearly 2 log unit range of test intensities. However, with more intense adapting fields the green light to red light incremental intensity ratio decreased as the test intensity was increased, with the ratio asymptoting at high test levels to an adaptation-intensity dependent value.The empirical observations reject both von Kries' Coefficient Law and the notion that only spatial (and or temporal) transients contribute to color signals. The results are consistent with a “two-process” theory where the adapting field is assumed both to contribute directly to the chromatic signal and simultaneously to alter the amplitudes (but not shapes) of the spectral sensitivity functions associated with the three receptor-types of color vision.
A yellow/blue equilibrium light is one which appears neither yellowish nor bluish (i.e. uniquely red, uniquely green, or achromatic). The spectral locus of the monochromatic greenish equilibrium (around 500 nm) shows little, if any, variation over a luminance range of 2 log10 units. Reddish equilibria are extraspectral, involving mixtures of short- and long-wave light. Their wavelength composition is noninvariant with luminance: a reddish equilibrium light turns bluish-red if luminance is increased with wavelength composition constant.The additive mixture of the reddish and greenish equilibria is again a yellow/blue equilibrium light.We conclude that yellow/blue equilibrium can be described as the zeroing of a nonlinear functional, which is, however, approximately linear in the short-wavelength (“blue”) and middle-wavelength (“green”) cone responses and nonlinear only in the long-wavelength (“red”) cone response. The “red” cones contribute to yellowness, but via a compressive function of luminance. This effect works against the direction of the Bezold-Brücke hue shift.The Jameson-Hurvich yellow/blue chromatic-response function is only approximately correct: the relative values of yellow/blue chromatic response for an equal energy spectrum must vary somewhat with the energy level.
Using a cancellation technique (maintaining a pure yellow hue) chromatic induction was measured in the configuration of a 30′–90′ annular test field fully surrounded by a 7° red inducing field. Analysis of these data revealed the hitherto unrecognized fact that the part of the light that the test stimulus has in common with the surround does not contribute to its perceived hue. In addition to this, in essence, subtractive effect of the inducing field it was found that the latter also causes a (colour-selective) change of gain, consistent with the much disputed von Kries coefficient law. The often reported invalidity of the latter should be attributed to the fact that in the past no allowance has been made for the aforementioned differencing mechanism.
It is a cultural commonplace deriving from Newton that the colour of an object we see in the world around us depends on the relative amounts of red light, green light, and blue light coming from that object to our eyes. For a very long time it has been known that the colour of the object when it is part of a general scene will not change markedly with those considerable changes in the relative amounts of red, green, and blue light in the illumination which characterize sunlight versus blue skylight versus grey day versus tungsten light versus fluorescent light. This contradiction was named “colour constancy.” Rather than dwelling on the explanations of colour constancy by Helmholtz and those who have followed him during the last century let us go on to show that the paradox does not really exist because it is not true that the colour of a point on an object is determined by the composition of the light coming from the object.
Achromatic colors are usually considered to be specifiable by a single perceptive variable, although a few bidimensional systems for specification of such colors have previously been presented. Some of the most important concepts of achromatic color are reviewed, and evaluated against the color variations observable in a disc-ring configuration of fields. Four different types of achromatic color variations are distinguished. It is shown that the unidimensional concept is untenable, and several limitations of the previous bidimensional systems are pointed out. A new bidimensional system is introduced which, contrary to the former, incorporates both the aperture and the surface colors within an orthogonal structure, and accounts for both the intensive and qualitative variations encountered in both modes.
Interocular brightness matches were made between flashes of light, one to each eye. added to large steady uniform backgrounds of different luminances. The backgrounds were binocularly superimposed. Under these conditions, constant-brightness curves (Log ΔI vs. Log I) were of approximately the same shape as the increment threshold curve. The brightness of a flash in one eye was unaffected by a background in the other. It is argued that these experiments measure only the contribution of retinal mechanisms. Further experiments provide some evidence of central influences. The relation between retinal and central mechanisms in the perception of brightness is discussed.
* Some of my research reported here was supported by National Institutes of Health grant MH-8786-02 and by National Science Foundation grant GB-2000. This paper was written while I was an NIH special postdoctoral fellow at the Kyoto (Japan) Prefectural University of Medicine. I would like to express my appreciation for the cordial hospitality of Professor Hisato Yoshimura, head of the First Department of Physiology. I am grateful to my colleague, Dr. David Krantz, for his careful reading of and provocative commentary on a manuscript of this paper.
The opponent yellow/blue mechanism is studied by means of an iso-cancellation technique. A qualitative and quantitative analysis of different photopigment models for the yellow/blue code is presented. On the basis of this analysis we provide a new model which ascribes the nonlinear character of the code to a power transformation of the short wave cone activity. This new model leads to predictions concerning the wavelength shift of the short wave component of a unique red. Tests of these predictions support the new model.
Observers viewed a thin (0.8-1.3) annulus composed of a mixture of 540 and 660 nm monochromatic lights (denoted delta G and delta R, respectively). The annular mixture was superimposed upon a larger (2.7) 660 nm circular background field. The observer adjusted the radiance of either delta G or delta R so that the annulus appeared a perfect (i.e. neither reddish nor greenish) yellow. In the first experiment, the background and annulus both were presented steadily. The results showed that the background, varied over a range from 10 to 1000 td. always contributed less to the color appearance of the annular test area than would be expected from the simple admixture of lights. The second experiment examined the effect of briefly removing the background-field quanta during the period when the annulus was judged. After several minutes of adapting to the background, the background was momentarily extinguished for 1 sec once every 6 sec; the observer adjusted the radiance of delta R so that during the 1 sec period the continuously presented annular mixture appeared equilibrium yellow. With steady backgrounds, the delta G to delta R luminance ratio decreased with test annulus luminance; for judgments made while the background momentarily was extinguished, the luminance ratio generally increased with annulus luminance. All of the empirical observations can be accounted for quantitatively by a two-process theory of chromatic adaptation; in two processes are (1) gain changes and (2) a restoring signal that tends to drive back toward equilibrium the opponent response resulting from the adapting light. Results from a third experiment, in which the background-off interval was reduced from 1 sec to 500, 200 or 150 msec. also are consistent with this model.
Two superposed annular test lights of complementary spectral composition were presented as 60-90' incremental test flashes on 480' steady backgrounds. Two observers adjusted the ratio of the two test lights to maintain an achromatic appearance under conditions of adaptation that varied with respect to background luminance, chromaticity and stimulus contrast. The shift in chromaticity of the achromatic point was in the direction of the chromaticity of the background, while the magnitude of the shift increased as an increasing function of background luminance and as a decreasing function of contrast. These data confirm and extend a model of chromatic adaptation that has the following properties: (1) non-additivity of transient test and steady background fields, in the sense that the background, although physically adding to the test flash, only affects its hue by way of altering the gain of cone pathways; (2) Vos-Walraven cone spectral sensitivities; and (3) adaptation sites in the cone pathways having the same action spectra as Stiles' pi 5, pi 4 and (modified) pi 1 mechanisms, and which generate receptor-specific attenuation factors (von Kries Coefficients) according to Stiles' generalized threshold vs intensity function, zeta (x).
The luminance invariance and additivity of red/green opponent equilibria were tested under conditions of chromatic adaptation. Four empirical relationships were found. (1) At high test intensities on all adapting fields luminance invariance holds. (2) Luminance invariance holds for all test intensities measured when the adapting field is in red/green equilibrium. (3) At high test intensities on all adapting fields additivity of red/green equilibria holds. (4) At low test intensities on non-equilibrium adapting fields luminance invariance fails. These empirical findings can be explained in terms of a two process model of chromatic adaptation.
Chromatic adaptation was studied with the method of maintaining a constant hue (unique yellow) of the test flash. The test field was presented super-imposed on backgrounds varying in wave-length (540–660 nm) and retinal illuminance (0.5–5 log td). The results can be described by assuming non-addivity of test and adapting light, cone spectral sensitivities as estimated by Vos and Walraven (1970), and receptor-specific gain controls that have the same action spectra and gain characteristics as Stiles' π mechanisms.
Die Gesichtsempfindungen und ihre Analyse
- J V Kries
- J Kries v
Chromatic induction. Psychophysical studies on signal processing in human colour vision
- J Walraven
Grundlinien einer Theorie der Farbenmetrik im Tagessehen
- E Schrödinger