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Are unique and invariant hues coupled?
Vision Res. Printed
Vol. 26.
in Great
No. 2. pp. 337-342.
Bnlam.
ARE
All
rights
1986
0042~69X9 Copyright
reserved
UNIQUE
AND INVARIANT
HUES
(
X6 $3.00 + 0.00
1986 Pergamon
Prew
Ltd
COUPLED?
J. J. Vos Institute for Perception TNO, Kampweg 5, 3769 DE Soesterberg, The Netherlands (Received
19 June 1984; in revised form
IS August 1985)
Abstract-Unique hues do not nicely coincide with hues that are invariant with intensity. This is at variance with theories that relate both to the zero crossings of opponent mechanisms. It is shown that. in the Walraven theory of the Bezold-Briicke effect which is based, both on diminishing return receptor characteristics and on zero crossings, the latter assumption is superlluous. That means that the Bezold-Briicke effect can be explained completely . . in terms of receptor behaviour and that unique and invariant hues have no direct theoretical coupling.
INTRODUCTION
The unique spectral hues, pure yellow, pure green and pure blue, seem to coincide, roughly, with the invariant hues, i.e. those colors that do not change in hue with intensity. This observation has led many authors to assume an identity between the two. To quote Hurvich (1980): “These invariant hues as they are called correspond to the unique spectral hues blue, green and yellow”; or Linksz (1964): “There are three pivotal areas in the spectrum-the spectral loci of pure yellow, pure green and pure bluein which increasing stimulus intensity causes no change in hue”. One may wonder how strongly these casual statements are supported by facts. Neither Hurvich nor Linksz apparently felt a need to produce evidence, as if the coincidence were selfevident. Their concept of a mechanism of color vision may presuppose such an identity, but that may never be an argument, of course. If one scans the literature for data, the evidence appears to be rather weak. Boynton and Gordon (1965) for instance, found that their unique yellow (c. 579 nm) was distinctly different from their invariant yellow (c. 570 nm). Purdy (1931) had earlier found some discrepancy in the same direction (576 vs 571 nm) but hestitated to call it significant. However, he expressed himself quite clearly on the discrepancy between unique red (Urror) and invariant red, although he unfortunately provided no quantitative data. A survey by Judd (1940) indicates that most authors locate unique red very near to the extreme of the visual spectrum or even just around the corner in the color diagram, i.e. on the purple line. More recent determinations by Larimer et
al. (1975) and by Burns et al. (1984) confirmed this location. The only experimental determination of the non-spectral invariant hue was reported by Walraven (1961) who located it rather close to the violet corner on the purple line. We may summarize by saying that there is a statistical correspondence over subjects between the spectral regions of unique and invariant hues, but that an examination of individual subject data disturbs the simplicity of their coincidence. My interest in the problem was raised when my investigations on color vision mechanisms increasingly led me to believe that the two phenomena should be located at different processing levels: invariant hues at the receptor level, unique hues at the level of opponent processing. So, if there is a relation, it should be sought in terms of understanding the zero transits of the spectral opponency curves from the receptor action spectra. It is the aim of this paper to clarify this viewpoint.
THE BEZOLD-BRUCKE
EFFECT
The discovery that colors change in hue with intensity was made in the middle of the 19th century and the effect is generally known as the Bezold-Brucke effect after their discoverers. Purdy (1931) was the first to make a careful quantitative study and to determine accurately the hue-invariant wavelengths. His findings were reconfirmed in great outline by later investigations (e.g. Van der Wildt and Bouman, 1968) though differences, possibly due to
338
J J. Vos
differences in stimulus conditions (e.g. Cohen. 1975: Savoie. 1973) cannot be denied. For our purpose it is not necessary to take sides and for reasons of historical fairness and simplicity we may stick here to Purdy’s data (Fig. 1). Purdy tried to explain the effect on the basis of Peirce’s (1877) idea that the receptors gradually saturate so that all hues would converge towards a few equilibrium hues at the cross-over points of the action spectra of the three systems. Unfortunately, the generally accepted short wavelength cross-over points between, on the one hand the short (S), and on the other hand the middle (M) and long (L) wavelength sensitive systems, both lie near 440 nm, whereas the invariant blue is located near 476 nm. This discrepancy led Purdy to drop this explanation. This line of thinking was picked up again, though, by Walraven (1961), and further elaborated by Vos and Walraven (1971) with the following reasoning. The 440 nm location of the S/M and S/L cross-overs only holds for coneFig. 2. Two different locations of the saturation effect. indicated by the arrows. (a) In the opponent channels. according to Walraven (1961). (b) Directly behind the receptors. as proposed here. L. M and S denote the long. middle and short wavelength receptor systems. Y = L + M and LUM = L + M + S neural signals associated with yellowness and luminance. respectively.
system
150
650 -
500 (a)
QoQoo --
[
+20t , 100
PUROY 1931 lxpmmental
--theorelwd
, f*
so0
600
wavelength. &,,, of the to00
td field
i 700 (nm)
(b) Fig. 1. (a) Wavelengths of constant hue determined by Purdy (1931, thin lines). compared with calculated lines according to Walraven (1961, thick lines). (b) Hue shift between IO0 and IO00 td expressed in terms of a compensatory wavelength shift. The theoretical relation holds both for the Walraven (1961) model and the model proposed here.
spectral sensitivities. If we take into account that the three cone systems may be represented by different numbers of receptors we have to adjust the various spectral sensitivities in mutual height to find the cross-over points on a single receptor-basis-and that is what should count if receptor saturation would be the cause of the Bezold-Brticke effect. It is not our purpose here to repeat the detailed reasoning of the 1971 paper, but we the final quanti~tive may just mention result. that the location of the invariant hues could be predicted on the assumption that the relative receptor population densities are N.Y:N,w:N, = I : 16:32 (Walraven, 1974). This explanation brought one new difficulty. though: when we assume a saturating input/output relation at the receptor level, how can we deal with Abney’s additivity law for luminance? Walraven solved this problem by assuming that the saturation effect did not
actually occur at the receptor level, but in the supply lines of the opponent processing, after the luminance channel has branched ofI (Fig. 2a)
339
Are unique and invariant hues coupled?
Although this solution saved the explanation, it was not quite as elegant as locating saturation at the receptor level, which would have been in better agreement with electrophysiological evidence on receptor input/output relations (Boynton and Whitten, 1970; Valeton and Van Norren, 1983). We solved this dilemma a few years ago (Vos, 1978a) by showing that locating saturation at the receptor level did not violate the additivity law within its limits of validity: On the contrary, Walraven’s precaution not only was unnecesary, it was even undesirable since the small deviations predicted turned out to be in agreement, roughly, with known small deviations from the additivity rule. So rather than being at variance with strict additiuity, the distal location of the saturation phenomenon became a corroboration of the near-validity of Abney’s law. The changed location of the saturation phenomenon in the model (Fig. 2b) led us to speculate whether the explanation of the Bezold-Briicke effect would still require a specific assumption on the mechanism of opponent processing. We investigated this possible and attractive consequence in the following, straight forward way. Take a color, characterized by x, y and a luminance value and convert these values to receptor inputs L, M, S on the basis of receptor action spectra (Vos, 1978b). Then apply the saturation rule to determine receptor outputs L*, M*, S*. Finally reconvert these values to x*, y* as if L*, M* and S* had been receptor inputs, rather than outputs. The shift from x, y to x*, y* then should characterize the shift in hue at the assumed luminance. Details of the calculation can be found in the Appendix. Here it may suffice to indicate this general outline and to draw attention to the fact that no assumption whatsoever is made on antagonistic signal processing. The results of this conversion calculation is shown in Fig. 3a in which subsequent points along hue shift lines indicate increasing values of the retinal illuminance in trolands. The picture is different from the normal data presentation (Fig. 1) in that it shows color shifts that include sizable desaturation effects. The picture clearly shows how reds and greens move toward yellow before they turn inward towards white and desaturate. Similar trends can be noticed in the 475 and 550nm regions. To reconvert these calculated hue shift data into dominant wavelength shifts we have re-
plotted the color points in a uniform chromaticity plot and projected them on the nearest part of the spectral or non-spectral enclosure (Fig. 3b). The first try, on the basis of the 1:16:32 receptor population density assumption yielded a rather satisfactory first order fit between calculated and experimentally measured invariant hues. Small discrepancies, in particular in the blue and purple region, led us to make some readjustments in this ratio, to obtain an even better second-order fit. The final diagrams of Fig. 3 were actually calculated on the basis of N,:N,:N,
= 1: 10:20.
Since the data fit was not discernable from that obtained by Walraven, it may suffice to refer to Figs la and 1b again. We conclude that the Bezold-Briicke effect may indeed be described as a purely receptoral phenomenon. This proves that Walraven’s assumption of opponent mechanisms was, in fact, unnecessary to explain the effect. CONSEQUENCES
A direct consequence of our theoretical formulation was the adjustment of the receptor population density ratio, from N,:N,:N,
= I : 16:32 to 1:10:20.
This adjustment is not dramatic and may even be insignificant in view of the mentioned experimental differences in the exact location of the invariant hues. It is worthwhile, however, to recall why we could arrive at different ratios on the basis of the same data set: we were no longer bound to strive for an exact cross-over at the wavelengths of invariant hue. This freedom has solved at the same time a former dilemma: were we to take, as the relevant cross-over, that of Sj, and L;,, or of S;, and M,, or may be, that of Sj, and L;, + M,? In the new scheme, the cross-over problem has just vanished, as a non-problem. Therefore the new formulation can certainly be considered as a gain in simplicity. A second consequence is that the location of the invariant hues is completely uncoupled, now, from the location of the unique hues, since these are related in general to the zero crossings of the opponent response curves. We are no longer forced to assume a coincidence between invariant and unique hues as they are now postulated to originate from different processing layers: the first in the receptor layer, the second
340
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06
05
04
03
02
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02
05
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03
06
06
07
09
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(a) I-
06"
12
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S' r
I
LOO%
33-
’ 55
31
1
02
I
I
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03
04
05
I
"
IJ
06
(b)
Fig. 3. (a) Calculated hue shift with increasing light level. Squares indicate spectral calorimetric lock. circles the calculated apparent location at 100 td. (b) Same data. for three light levels (IO. 100 and 1000 td). replotted in the CIE uniform chromaticity diagram. A few examples indicate how the dominant wavelength shift was constructed. Arrows indicate experimentally determined invariant hues. according to Purdy (1931) and Walraven (1961). The resulting calculated hue shifts coincide with those calculated by Walraven (1961) and plotted in Fig. I.
in the subsequent opponent processing layer. This also holds for unique white which most authors locate near the center of the chromaticity diagram (Werner and Walraven, 1982)
whereas the invariant counterpart is expected to be much bluer (Vos, 1972). That means that we need not stick to the wiring scheme of Fig. 2 anymore. Other schemes. such as L/M and L/S.
341
Are unique and invariant hues coupled?
or L,lN and M/S might do better in describing the unique hues. We will not offer a specific model here, but refer to the choice offered in the chapter on color vision models in Hurvich’s book Color Vision (1980). We may only conclude that a source of standing controversy is thus eliminated. Of course this uncoupling leaves us with a new challenge: since the original observation that unique hues coincide with invariant hues, though not exactly true, is not completely untrue either. So instead of just postulating their coincidence in the way Hurvich and Linksz did, we should ask the question why the opponent sensitivity functions have their zero crossings so near to the spectral invariant hues. It is obvious that the answer should be sought in terms of optimal color processing. Being no expert in that field, I may only refer to the type of theory recently published by Buchsbaum and Gottschatk (1983). They showed that the requirement of optimality leads to the prediction of opponent processing with specific cross overs. An interesting prediction from their optimum data transmission theory is that the shape of the opponent sensitivity functions should change with chromatic adaptation. Since dete~ining unique hues encompasses chromatic adaptation we may expect that unique hues are a function of luminance-a suggestion already made by Boynton and Gordon. If so, this would be another reason to disconnect invariant and unique hues, as invariant hues are luminance independent by their very definition. CONCLUSION
In the sixties, the old Helmholtz-Hering controversy on the interpretation of color vision phenomena was solved by the general acceptance of zone models. But that acceptance to some extent diffused and confused the issue, since it was not always clear which phenomena to Iocate in which zone. Color mixture laws, no doubt, had a receptor site; and unique hues are always associated with the zero crossings of the opponent systems. However, the Bezold-Briicke effect and invariant hue phenomena had a less clear status. The present paper makes a distinct choice and interprets the Bezold-Briicke effect completely in terms of receptor physics and physiology. That means that unique hues are essentially different from invariant hues. If, nevertheless, they show a spectral correspondence, this
should be taken as a phenomenon to be interpreted (e.g. in terms of an optimal recoding theory), rather than taken as a token of their identity. Acknow~ledgemen+--The author thanks Mr Jan Varkevisser and Ing. Yvonne Hartmann for their help in making the calculations and preparing the chromaticity diagrams. REFERENCES Boynton R. M. and Gordon J. (1965) Bezold-Briicke hue shift measured by color naming technique. 1. opr. Sot. Am. 55, 78-86. Boynton R. M. and Whitten D. N. (1970) Visual adaptation in monkey cones: recording of late receptor potential. Science 170, 1423-1426. Buchsbaum G. and Gottschalk A. (1983) Trichromacy, opponent colors coding and optimum information transmission in the retina. Proc. R. Sac. Lot&. B 220, 89-l 13. Burns S. A., Elsner A. E., Pokorny J. and Smith V. C. (1984) The Abney effect: chromaticity coordinates of unique and other constant hues. Vision Res. 24, 479-489. Cohen 3. D. (1975) Temporal independence of the Bezold-Briicke hue shift. Vision Res. 15, 341-351. Hurvich L. M. (1980) Color Vision, p. 73. Sinauer, Sunderland. Massachusetts. Judd D. 8. (1940) Hue saturation and surface colors. J. opt. Sot. Am. 30, 2-32. Larimer J., Krantz D. H. and Cicerone C. M. (197.5) Opponent process additivity II. Yellow equilibria and non-linear models. Vision Rex IS, 723-731. Linksz A. (1964) An Essay on Color Vision, p. 34. Grune & Stratton, New York. Peirce C. S. (1887) Note on the sensation of color. Am. J. Sci. Ser. 3 13, 247-259. Purdy D. MCI. (1931) Spectral hue as a function of intensity. Am. J. PsychoI. 43, 541-559.
Savoie R. E. (1973) Bezold-Briicke effect and visual nonlinearity. J. opt. Sot. Am. 63, 1253-1261. Valeton J. M. and Van Norren D. (1983) Light adaptation of primate cones: an analysis based on extracellular data. Vision Rex 23, 1539-1547. Van der Wildt G. J. and Bouman M. A. (1968) The dependence of Bezold-Brilcke hue shift on spatial intensity distribution. Vision Res. 8, 303-313. Vos J. J. and Walraven P. L. (1971) On the derivation of fovea1 receptor primaries. Vision Res. II, 799-818. Vos J. J. (1972) Discussion on the location of the white point. In Color Merrics. Proc. AK Symposium Driebergen, The Netherlands, p. 97. Institute for Perception TNO. Vos J. J. (t978a) Is linearity at the receptor level a prerequisite for the zone-fluctuation model of color vision? Proc. ICO Congress. p. 89-92. Madrid. Vos J. J. (1978b) Calorimetric and photometric properties of a 2’ fundamental observer. Color Res. Appl. 3, 125-128. Walraven P. L. (1961) On the Bezold-Briicke phenomenon. J. opt. Sot. Am. 51, 1113-1116. Walraven P. L. (1974) A closer look at the tritanopic confusion point. Vision Res. 14, 1339-1343. Werner J. S. and Walraven J. (1982) Effect of chromatic adaptation on the achromatic locus: the role of contrast, luminance and background color. Vision Res. 22, 924-943.
J. J. Vtn
342 APPENDlX
The procedure described in the text is a slightly simplified version. for the sake of clarity. of what actually happened. Therefore this full account. (1) The conversion from chromaticity coordinates to values of S. M, L was done on the basis of the slightly modified (x. r) values given in Vos (1978b) and the there given transformation matrix T. (2) The saturation relation applied was that. given by Vos (I 978), reading:
with 1 and I* (in td) for S, respectively, and S,, M,,, L, (:) experimental domain of interest relation shows the same trend
A4, L and S’. M*. L* Ns, N,, N,. Within the this theoretically derived as the Boynton-Whitten
equation ( 19701:
that can be constdered to be the best descriptron 01.receptor adaptation behavior (Valeton and Van Norren. 1983) Note that. for small values of 1. equatmn (I ) reduces to
which is important for the reconversron to (s*, ; *j (3) Because of the above mentroned initial square root power law. we could not directly reconvert (S*. M*. I *) to is*, r*). but had tirst to square I* (smce It2 is identical to I at low intensities). (4) Only then S*‘. A#*‘. L*’ could be reconverted with T-‘, to I* and .r*. Of course the equations (I) and (2) only apply within a certain experimental range. We have used them. though, to far higher values in order to calculate the convergence center of the hue-shift lines. The tsoland values indicated have no physiological significance in that range. of course.
Vol. 26.
in Great
No. 2. pp. 337-342.
Bnlam.
ARE
All
rights
1986
0042~69X9 Copyright
reserved
UNIQUE
AND INVARIANT
HUES
(
X6 $3.00 + 0.00
1986 Pergamon
Prew
Ltd
COUPLED?
J. J. Vos Institute for Perception TNO, Kampweg 5, 3769 DE Soesterberg, The Netherlands (Received
19 June 1984; in revised form
IS August 1985)
Abstract-Unique hues do not nicely coincide with hues that are invariant with intensity. This is at variance with theories that relate both to the zero crossings of opponent mechanisms. It is shown that. in the Walraven theory of the Bezold-Briicke effect which is based, both on diminishing return receptor characteristics and on zero crossings, the latter assumption is superlluous. That means that the Bezold-Briicke effect can be explained completely . . in terms of receptor behaviour and that unique and invariant hues have no direct theoretical coupling.
INTRODUCTION
The unique spectral hues, pure yellow, pure green and pure blue, seem to coincide, roughly, with the invariant hues, i.e. those colors that do not change in hue with intensity. This observation has led many authors to assume an identity between the two. To quote Hurvich (1980): “These invariant hues as they are called correspond to the unique spectral hues blue, green and yellow”; or Linksz (1964): “There are three pivotal areas in the spectrum-the spectral loci of pure yellow, pure green and pure bluein which increasing stimulus intensity causes no change in hue”. One may wonder how strongly these casual statements are supported by facts. Neither Hurvich nor Linksz apparently felt a need to produce evidence, as if the coincidence were selfevident. Their concept of a mechanism of color vision may presuppose such an identity, but that may never be an argument, of course. If one scans the literature for data, the evidence appears to be rather weak. Boynton and Gordon (1965) for instance, found that their unique yellow (c. 579 nm) was distinctly different from their invariant yellow (c. 570 nm). Purdy (1931) had earlier found some discrepancy in the same direction (576 vs 571 nm) but hestitated to call it significant. However, he expressed himself quite clearly on the discrepancy between unique red (Urror) and invariant red, although he unfortunately provided no quantitative data. A survey by Judd (1940) indicates that most authors locate unique red very near to the extreme of the visual spectrum or even just around the corner in the color diagram, i.e. on the purple line. More recent determinations by Larimer et
al. (1975) and by Burns et al. (1984) confirmed this location. The only experimental determination of the non-spectral invariant hue was reported by Walraven (1961) who located it rather close to the violet corner on the purple line. We may summarize by saying that there is a statistical correspondence over subjects between the spectral regions of unique and invariant hues, but that an examination of individual subject data disturbs the simplicity of their coincidence. My interest in the problem was raised when my investigations on color vision mechanisms increasingly led me to believe that the two phenomena should be located at different processing levels: invariant hues at the receptor level, unique hues at the level of opponent processing. So, if there is a relation, it should be sought in terms of understanding the zero transits of the spectral opponency curves from the receptor action spectra. It is the aim of this paper to clarify this viewpoint.
THE BEZOLD-BRUCKE
EFFECT
The discovery that colors change in hue with intensity was made in the middle of the 19th century and the effect is generally known as the Bezold-Brucke effect after their discoverers. Purdy (1931) was the first to make a careful quantitative study and to determine accurately the hue-invariant wavelengths. His findings were reconfirmed in great outline by later investigations (e.g. Van der Wildt and Bouman, 1968) though differences, possibly due to
338
J J. Vos
differences in stimulus conditions (e.g. Cohen. 1975: Savoie. 1973) cannot be denied. For our purpose it is not necessary to take sides and for reasons of historical fairness and simplicity we may stick here to Purdy’s data (Fig. 1). Purdy tried to explain the effect on the basis of Peirce’s (1877) idea that the receptors gradually saturate so that all hues would converge towards a few equilibrium hues at the cross-over points of the action spectra of the three systems. Unfortunately, the generally accepted short wavelength cross-over points between, on the one hand the short (S), and on the other hand the middle (M) and long (L) wavelength sensitive systems, both lie near 440 nm, whereas the invariant blue is located near 476 nm. This discrepancy led Purdy to drop this explanation. This line of thinking was picked up again, though, by Walraven (1961), and further elaborated by Vos and Walraven (1971) with the following reasoning. The 440 nm location of the S/M and S/L cross-overs only holds for coneFig. 2. Two different locations of the saturation effect. indicated by the arrows. (a) In the opponent channels. according to Walraven (1961). (b) Directly behind the receptors. as proposed here. L. M and S denote the long. middle and short wavelength receptor systems. Y = L + M and LUM = L + M + S neural signals associated with yellowness and luminance. respectively.
system
150
650 -
500 (a)
QoQoo --
[
+20t , 100
PUROY 1931 lxpmmental
--theorelwd
, f*
so0
600
wavelength. &,,, of the to00
td field
i 700 (nm)
(b) Fig. 1. (a) Wavelengths of constant hue determined by Purdy (1931, thin lines). compared with calculated lines according to Walraven (1961, thick lines). (b) Hue shift between IO0 and IO00 td expressed in terms of a compensatory wavelength shift. The theoretical relation holds both for the Walraven (1961) model and the model proposed here.
spectral sensitivities. If we take into account that the three cone systems may be represented by different numbers of receptors we have to adjust the various spectral sensitivities in mutual height to find the cross-over points on a single receptor-basis-and that is what should count if receptor saturation would be the cause of the Bezold-Brticke effect. It is not our purpose here to repeat the detailed reasoning of the 1971 paper, but we the final quanti~tive may just mention result. that the location of the invariant hues could be predicted on the assumption that the relative receptor population densities are N.Y:N,w:N, = I : 16:32 (Walraven, 1974). This explanation brought one new difficulty. though: when we assume a saturating input/output relation at the receptor level, how can we deal with Abney’s additivity law for luminance? Walraven solved this problem by assuming that the saturation effect did not
actually occur at the receptor level, but in the supply lines of the opponent processing, after the luminance channel has branched ofI (Fig. 2a)
339
Are unique and invariant hues coupled?
Although this solution saved the explanation, it was not quite as elegant as locating saturation at the receptor level, which would have been in better agreement with electrophysiological evidence on receptor input/output relations (Boynton and Whitten, 1970; Valeton and Van Norren, 1983). We solved this dilemma a few years ago (Vos, 1978a) by showing that locating saturation at the receptor level did not violate the additivity law within its limits of validity: On the contrary, Walraven’s precaution not only was unnecesary, it was even undesirable since the small deviations predicted turned out to be in agreement, roughly, with known small deviations from the additivity rule. So rather than being at variance with strict additiuity, the distal location of the saturation phenomenon became a corroboration of the near-validity of Abney’s law. The changed location of the saturation phenomenon in the model (Fig. 2b) led us to speculate whether the explanation of the Bezold-Briicke effect would still require a specific assumption on the mechanism of opponent processing. We investigated this possible and attractive consequence in the following, straight forward way. Take a color, characterized by x, y and a luminance value and convert these values to receptor inputs L, M, S on the basis of receptor action spectra (Vos, 1978b). Then apply the saturation rule to determine receptor outputs L*, M*, S*. Finally reconvert these values to x*, y* as if L*, M* and S* had been receptor inputs, rather than outputs. The shift from x, y to x*, y* then should characterize the shift in hue at the assumed luminance. Details of the calculation can be found in the Appendix. Here it may suffice to indicate this general outline and to draw attention to the fact that no assumption whatsoever is made on antagonistic signal processing. The results of this conversion calculation is shown in Fig. 3a in which subsequent points along hue shift lines indicate increasing values of the retinal illuminance in trolands. The picture is different from the normal data presentation (Fig. 1) in that it shows color shifts that include sizable desaturation effects. The picture clearly shows how reds and greens move toward yellow before they turn inward towards white and desaturate. Similar trends can be noticed in the 475 and 550nm regions. To reconvert these calculated hue shift data into dominant wavelength shifts we have re-
plotted the color points in a uniform chromaticity plot and projected them on the nearest part of the spectral or non-spectral enclosure (Fig. 3b). The first try, on the basis of the 1:16:32 receptor population density assumption yielded a rather satisfactory first order fit between calculated and experimentally measured invariant hues. Small discrepancies, in particular in the blue and purple region, led us to make some readjustments in this ratio, to obtain an even better second-order fit. The final diagrams of Fig. 3 were actually calculated on the basis of N,:N,:N,
= 1: 10:20.
Since the data fit was not discernable from that obtained by Walraven, it may suffice to refer to Figs la and 1b again. We conclude that the Bezold-Briicke effect may indeed be described as a purely receptoral phenomenon. This proves that Walraven’s assumption of opponent mechanisms was, in fact, unnecessary to explain the effect. CONSEQUENCES
A direct consequence of our theoretical formulation was the adjustment of the receptor population density ratio, from N,:N,:N,
= I : 16:32 to 1:10:20.
This adjustment is not dramatic and may even be insignificant in view of the mentioned experimental differences in the exact location of the invariant hues. It is worthwhile, however, to recall why we could arrive at different ratios on the basis of the same data set: we were no longer bound to strive for an exact cross-over at the wavelengths of invariant hue. This freedom has solved at the same time a former dilemma: were we to take, as the relevant cross-over, that of Sj, and L;,, or of S;, and M,, or may be, that of Sj, and L;, + M,? In the new scheme, the cross-over problem has just vanished, as a non-problem. Therefore the new formulation can certainly be considered as a gain in simplicity. A second consequence is that the location of the invariant hues is completely uncoupled, now, from the location of the unique hues, since these are related in general to the zero crossings of the opponent response curves. We are no longer forced to assume a coincidence between invariant and unique hues as they are now postulated to originate from different processing layers: the first in the receptor layer, the second
340
07
06
05
04
03
02
01
00
so
01
02
05
OL
03
06
06
07
09
x
(a) I-
06"
12
i
S' r
I
LOO%
33-
’ 55
31
1
02
I
I
I
03
04
05
I
"
IJ
06
(b)
Fig. 3. (a) Calculated hue shift with increasing light level. Squares indicate spectral calorimetric lock. circles the calculated apparent location at 100 td. (b) Same data. for three light levels (IO. 100 and 1000 td). replotted in the CIE uniform chromaticity diagram. A few examples indicate how the dominant wavelength shift was constructed. Arrows indicate experimentally determined invariant hues. according to Purdy (1931) and Walraven (1961). The resulting calculated hue shifts coincide with those calculated by Walraven (1961) and plotted in Fig. I.
in the subsequent opponent processing layer. This also holds for unique white which most authors locate near the center of the chromaticity diagram (Werner and Walraven, 1982)
whereas the invariant counterpart is expected to be much bluer (Vos, 1972). That means that we need not stick to the wiring scheme of Fig. 2 anymore. Other schemes. such as L/M and L/S.
341
Are unique and invariant hues coupled?
or L,lN and M/S might do better in describing the unique hues. We will not offer a specific model here, but refer to the choice offered in the chapter on color vision models in Hurvich’s book Color Vision (1980). We may only conclude that a source of standing controversy is thus eliminated. Of course this uncoupling leaves us with a new challenge: since the original observation that unique hues coincide with invariant hues, though not exactly true, is not completely untrue either. So instead of just postulating their coincidence in the way Hurvich and Linksz did, we should ask the question why the opponent sensitivity functions have their zero crossings so near to the spectral invariant hues. It is obvious that the answer should be sought in terms of optimal color processing. Being no expert in that field, I may only refer to the type of theory recently published by Buchsbaum and Gottschatk (1983). They showed that the requirement of optimality leads to the prediction of opponent processing with specific cross overs. An interesting prediction from their optimum data transmission theory is that the shape of the opponent sensitivity functions should change with chromatic adaptation. Since dete~ining unique hues encompasses chromatic adaptation we may expect that unique hues are a function of luminance-a suggestion already made by Boynton and Gordon. If so, this would be another reason to disconnect invariant and unique hues, as invariant hues are luminance independent by their very definition. CONCLUSION
In the sixties, the old Helmholtz-Hering controversy on the interpretation of color vision phenomena was solved by the general acceptance of zone models. But that acceptance to some extent diffused and confused the issue, since it was not always clear which phenomena to Iocate in which zone. Color mixture laws, no doubt, had a receptor site; and unique hues are always associated with the zero crossings of the opponent systems. However, the Bezold-Briicke effect and invariant hue phenomena had a less clear status. The present paper makes a distinct choice and interprets the Bezold-Briicke effect completely in terms of receptor physics and physiology. That means that unique hues are essentially different from invariant hues. If, nevertheless, they show a spectral correspondence, this
should be taken as a phenomenon to be interpreted (e.g. in terms of an optimal recoding theory), rather than taken as a token of their identity. Acknow~ledgemen+--The author thanks Mr Jan Varkevisser and Ing. Yvonne Hartmann for their help in making the calculations and preparing the chromaticity diagrams. REFERENCES Boynton R. M. and Gordon J. (1965) Bezold-Briicke hue shift measured by color naming technique. 1. opr. Sot. Am. 55, 78-86. Boynton R. M. and Whitten D. N. (1970) Visual adaptation in monkey cones: recording of late receptor potential. Science 170, 1423-1426. Buchsbaum G. and Gottschalk A. (1983) Trichromacy, opponent colors coding and optimum information transmission in the retina. Proc. R. Sac. Lot&. B 220, 89-l 13. Burns S. A., Elsner A. E., Pokorny J. and Smith V. C. (1984) The Abney effect: chromaticity coordinates of unique and other constant hues. Vision Res. 24, 479-489. Cohen 3. D. (1975) Temporal independence of the Bezold-Briicke hue shift. Vision Res. 15, 341-351. Hurvich L. M. (1980) Color Vision, p. 73. Sinauer, Sunderland. Massachusetts. Judd D. 8. (1940) Hue saturation and surface colors. J. opt. Sot. Am. 30, 2-32. Larimer J., Krantz D. H. and Cicerone C. M. (197.5) Opponent process additivity II. Yellow equilibria and non-linear models. Vision Rex IS, 723-731. Linksz A. (1964) An Essay on Color Vision, p. 34. Grune & Stratton, New York. Peirce C. S. (1887) Note on the sensation of color. Am. J. Sci. Ser. 3 13, 247-259. Purdy D. MCI. (1931) Spectral hue as a function of intensity. Am. J. PsychoI. 43, 541-559.
Savoie R. E. (1973) Bezold-Briicke effect and visual nonlinearity. J. opt. Sot. Am. 63, 1253-1261. Valeton J. M. and Van Norren D. (1983) Light adaptation of primate cones: an analysis based on extracellular data. Vision Rex 23, 1539-1547. Van der Wildt G. J. and Bouman M. A. (1968) The dependence of Bezold-Brilcke hue shift on spatial intensity distribution. Vision Res. 8, 303-313. Vos J. J. and Walraven P. L. (1971) On the derivation of fovea1 receptor primaries. Vision Res. II, 799-818. Vos J. J. (1972) Discussion on the location of the white point. In Color Merrics. Proc. AK Symposium Driebergen, The Netherlands, p. 97. Institute for Perception TNO. Vos J. J. (t978a) Is linearity at the receptor level a prerequisite for the zone-fluctuation model of color vision? Proc. ICO Congress. p. 89-92. Madrid. Vos J. J. (1978b) Calorimetric and photometric properties of a 2’ fundamental observer. Color Res. Appl. 3, 125-128. Walraven P. L. (1961) On the Bezold-Briicke phenomenon. J. opt. Sot. Am. 51, 1113-1116. Walraven P. L. (1974) A closer look at the tritanopic confusion point. Vision Res. 14, 1339-1343. Werner J. S. and Walraven J. (1982) Effect of chromatic adaptation on the achromatic locus: the role of contrast, luminance and background color. Vision Res. 22, 924-943.
J. J. Vtn
342 APPENDlX
The procedure described in the text is a slightly simplified version. for the sake of clarity. of what actually happened. Therefore this full account. (1) The conversion from chromaticity coordinates to values of S. M, L was done on the basis of the slightly modified (x. r) values given in Vos (1978b) and the there given transformation matrix T. (2) The saturation relation applied was that. given by Vos (I 978), reading:
with 1 and I* (in td) for S, respectively, and S,, M,,, L, (:) experimental domain of interest relation shows the same trend
A4, L and S’. M*. L* Ns, N,, N,. Within the this theoretically derived as the Boynton-Whitten
equation ( 19701:
that can be constdered to be the best descriptron 01.receptor adaptation behavior (Valeton and Van Norren. 1983) Note that. for small values of 1. equatmn (I ) reduces to
which is important for the reconversron to (s*, ; *j (3) Because of the above mentroned initial square root power law. we could not directly reconvert (S*. M*. I *) to is*, r*). but had tirst to square I* (smce It2 is identical to I at low intensities). (4) Only then S*‘. A#*‘. L*’ could be reconverted with T-‘, to I* and .r*. Of course the equations (I) and (2) only apply within a certain experimental range. We have used them. though, to far higher values in order to calculate the convergence center of the hue-shift lines. The tsoland values indicated have no physiological significance in that range. of course.