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Additivity of yellow chromatic valence
Vi.non Res. Vol. 26, So. 5. pp. 763-769. 1986 Printed tn Great Bnram. All a-t&s rcscrved
ADDITIVITY
00514989 86 53.00 + 0.00 Copyright 2 1986 Pergamon Press Lrd
OF YELLOW
CHROMATIC
MIYOSHZ AYAMA and Mnwo
Department of
VALENCE
IKEDA
informationProcessing, Tokyo Institute of Technology, Nagatsuta, Midori-ku. Yokohama 227, Japan (Rewired
8 September 1983: in recised form 28 Nocember 1985)
Abstract-The additivity of yellow chromatic valence was investigated by the hue cancellation method for two normal observers. Additivity held in 530-550 nm and 600430 nm pairs, while additivity failure of reduction type occurred in 530-570 nm pair for both observers. Additivity failure of enhancement type occurred in 53G600 and 530-630 nm pairs in which one observer showed reduction type failure when mixture ratio of 530 nm is greater than 600 or 630 nm. The results suggest a nonlinear property of the yellow-blue process and are discussed in an interaction between the two opponent processes. Color
Opponent process
Chromatic valence
INTR.ODUCTION
The yellow-blue opponent process for normat trichromats has been reported to possess a nonlinearity. Larimer et al. (1975), Nagy (1979), Elizinga and de Weert (1984) and Ejima and Takahashi (1984) showed violation of the yellow-blue equilib~a invariance with intensity, i.e. a scalar multiplication does not hold in the process. Werner and Wooten (1979), Takahashi and Ejima (1984) showed the yellow-blue chromatic valence function can not be fitted by a linear combination of the cone spectral sensitivities while Romeskie’s (1978) results for normals can. Ikeda and Ayama (1980) showed additivity failure of yellow chromatic valence. Burns et al. (1984) concluded a nonlinearity of the process from their results of the yellow-blue equilibrium, i.e. unique red and green loci in the chromaticity diagram. In the previous paper (Ikeda and Ayama, 1980), a marked additivity failure of the enhancement type was found for yellow chromatic valence in some wavelength combinations for two observers among three. Additivity failure implies that outputs of at least two different underlying mechanisms should be summed in a non-linear manner to input to the higher process. The most likely underlying mechanisms for yellow are R- and G-cones. Although the additivity failure results were conspicuous, the range of mixture ratios was 20% (40-60%) and thus they did not provide a full characterization of additivity between the two stimuli. Within
Hue cancellation
Additivity
that smail range, the results did not show a clear asymmetry against mixture ratio. If a mixture ratio is unbalanced from the equal point, it may reveal some asymmetrical property due to unequal contributions of different underlying mechanisms. In this study, we extended the range of the mixture ratio to 50% (25-75%). Based on the measurements, a possible relation between cones and the yellow-blue process is discussed.
METHOD To measure the additivity of chromatic valence between two wavelengths %, and E.,, the cancellation technique (Jameson and Hurvich, 1955) was used. The reference blue was presented with a fixed luminance. The test stimuli L, and j-2were chosen from the yeflowish region in the spectrum. First, A, alone was superimposed on the reference blue and its radiance was adjusted by an observer until the field appears neither reddish nor greenish (the yellow-blue equilibrium). Let the radiance of Ai be N;.,. Second, the same procedure was repeated for another stimulus E,,and its radiance N,, at the equilibrium was obtained. Third, both %, and ,& were added together to the same reference blue in a fixed mixture ratio. The total radiances of I, and _.$were adjusted so that the equilibrium of the field was reached again ;vhile the radiance ratio of i., and AZ was kept constant. Let the radiances of i., and E., in 763
ths mixture be .V,,_ and .Y,. , respectively. The summation index (Ikeda. I-463; Bob ton er ~1.. 1964; Stiles, 1967) was used as an index of additivity. It is defined as follows Summation
Index = 0.3 - log ( pI + p:)
where p, = N,,,iN,,, and p2 = N,.2m,N,,. If additivity holds, p, + p2 must be equal to one, i.e. the summation index is 0.3 for the whole range of mixture ratio. If p, + p? > 1. then the index becomes less than 0.3 which means more radiance is necessary in the mixture than in the single presentation of i., alone and i.? alone. This is called additivity failure of the reduction type because the efficiency is reduced in the mixture stimuli. If p, + pz < 1, i.e. the summation index becomes greater than 0.3, it is called additivity failure of the enhancement type. APPARATUS
A four channel Maxwellian-view optical system was used. The light source, which was common to all channels, was a 500 W Xenon arc lamp. Two channels produced monochromatic lights of two test stimuli I., and i.Z by means of monochromators (Nikon G-250). The entrance and exit slits of each were set to yield a theoretical half-bandwidth of 3 nm. The third channel produced a monochromatic light of the reference stimulus by use of an interference filter which had half-amplitude bandpass of 11 nm. The forth channel produced the white surround and its chromaticity coordinates were x = 0.32, ~3= 0.35. Each chromatic channel had a neutral density wedge to control the radiance of the light in the channel. Each neutral density wedge was coupled to a potentiometer to read the position. Solenoid shutters were placed near the exit slits of the monochromators. When the test stimulus was composed of a single wavelength, e.g. L, alone, then the channel for E,, was closed by the shutter, and vice versa. In the case of the mixture test stimuli, both shutters were open. Light beams from three chromatic channels, J.,, i.?, and the reference were combined by means of the beamsplitters. The stimulus presentation was controlled by the third solenoid shutter placed behind the beamsplitter which was combining the two test stimuli and the reference. The white surround light and three chromatic lights were combined by means of the final beamsplitter. The chromatic field was a foveally-viewed circular field with 2” in diameter and it was presented I set duration followed by
1 set dark incrrval. The irhite surround had LrI outer diameter of 7 and inner diameter ~)t’2 It leas presented steadily during a session. The center and surround fields were formed b> the two apertures placed in proper positions. Retinal illuminance of the white surround was maintained at 100 td to keep the observer’s eye in a photopic condition throughout a session. The wavelength of the reference blue was fixed at 470 nm. which is close to the unique blue for the two observers. Its retinal illuminance was kept at 20 td. We chose six wavelength combinations of i, and &: 530-550 nm, 530-570 nm, 530-600nm, 53@-630nm. 60&630nm. and 570-630 nm. One of the authors, M.A.. female, age 28, and S.S., male, age 24, both with normal color vision served as observers. PROCEDURE
Each session began with 1Omin dark adaptation followed by 5 min white adaptation. A method of adjustment was used to determine the equilibrium point. At the beginning, Ni, and N;., were roughly determined. In a standard session; six different pairs of the neutral density wedge positions for 1, and If.?were determined from the rough setting of Nj,, and N,z. Each pair gives a certain mixture ratio of i., and &, usually three of them were set to be p2/p, < I and the others were p2/p, > I, however, these values were not the final ratios. In a main part of a session, mixture stimuli of six different ratios and monochromatic stimuli of E., alone and Lz alone were presented in a random order and five trials were repeated in each of them. The radiances of N,,, and N,,, measured in each mixtures and N,, and N;_, were measured. Therefore, the final values of p,,-pz, and the ratio p2/p, for each mixture were determined at the end of each session. RESULTS
Figure 1 is the result of 530-550nm pair for the two observers. Summation index was plotted against the mixture ratio log pJp,. Horizontal lines at 0.3 represent additivity. Vertical bars denote the three maximum range of five repetitions. Most of the points are close to 0.3 of additivity except MA’s result in the region of log pJp, < -0.2. The results of the pair 530-570 nm given in Fig. 2 show a distinctive deviation from additivity. The values of summation indices are
765
Additivity of yellow chromatic valence I
A,=530om
1
Xe=550nm
02 t
I
I -0.8
t
-0.4
-0.6
1
I
-0.2
0.0
m
P*/P
I
04
0.2
0.6
08
,
Fig. 1. Summation indices against log &pi for observers M.A. (top) and S.S. (bottom). Horizontal line at 0.3 represents the theoreticat line of additivity. Vertical bars denote maximum three ranges of five repetitions. i., = 530 nm, 1, = 550 nm.
indicating the additivity failure of enhancement type. In this observer’s results, the summation index value becomes maximum around at the ratio of log pJp, = 0.22 and 0.05 for 530600 nm, respectively. M.A.‘s results show more complicated nature of additivity failure: the summation indices are smaller than 0.3 when
smaller than 0.3 for both observers, indicating the additivity failure of reduction type, Different types of additivity failure are observed in the results of the pairs 530-600 nm and 530-630 nm shown in Fig. 3 and Fig. 4, respectively. For S.S., the data points are above the additivity line in a wide range of log pJp,
a,
=JX)nm
a2 = 570nm
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Fig. 2. Similar ptots as in Fig. I but i., = 530 nm, i., = 570 nm.
08
0.1
-0.8
-06
-0.4
-0.2
0.0 w
02
04
0.6
06
Pz /PI
Fig. 3. Similar plots as in Fig. 1 but i., = 530 nm, & = 600 nm.
log pz/p, c - 0. I2 and become greater than 0.3 when log p2/p, > -0.12. The additivity failure varies from a reduction type to an enhancement type as the amount of %, in the mixture increases. Summation index curves show cIear asymmetry here. Within a narrow range near Iog PtIP1 = 0, an average value of the summation index would be cIose to 0.3 apparently indicating additivity. In the previous study
(Ikeda and Ayama, I980), this observer showed an additive result with a large standard deviation in the pair of 533-607 nm while the other two observers showed an enhancement type additivity failure. The results here suggest that her previous result is due to the measurement within a small range of the mixture ratio around the point (log pJp, = 0) where her summation index curve is crossing the additivity line at 0.3.
:: 0.3 a 5 02 s z 2 E 3 *
0.5 04 0.3
-08
-0.6
-04
-02
0.0
0 2
0.4
06
f-09 Pz IFt
Fig. 4. Similar plots as in Fig. I but i, = 530 nm, i.2= 630 nm.
0.5
767
Additivity of yeIlow chromatic valence
-0.1
0. I
I -06
-06
I - 0.4
I 0.2
I -0.2
0.0 tog
P2 fP
I 0.4
I 0.6
I 0.6
,
Fig. 5. Similar plots as in Fig. 1 but ,I, = 570 nm, ,I2= 630 nm.
pair. M.A.‘s data show small reduction type failure especially in log p2jp, > 0. Wide repetition ranges for S.S. might be due to a small amount of yellowness in the test stimuh especially in &. By increasing the relative amount of 630 nm, the yellowness in the test stimuli decreases, and therefore, detecting the change of yellowness in the field would become difficult with a large amount of redness. How-
The measurement in a wide range of mixture ratios revealed a nonadditive nature of the yehow chromatic valence for this observer. Figure 5 shows the results of 570-630 nm pair. For M.A., the summation indices are along the 0.3 line indicating additivity except log p2/p1 < -0.2. For S.S., a small amount of reduction type is found. Figure 6 shows the results of 600-630 nm
0.5
- 0.2
0.4
-01
03
0.0
0.2
0.1
-
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0.5
-0.2
0.4
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0.2
0.3
-0.6
-0.6
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00 w
pt fP
0.2
0.4
0.6
1
Fig. 6. Similar plots as in Fig. 1 but 1, = 600 nm, 2, = 630 nm.
08
3
eser, for both observers, most of the data points do not deviate from the additivity line to a large extent. DISCL’SSION
Additivity failure of the yellow chromatic valence agree with previous studies which showed nonlinear properties of the yellow-blue process. One advantage of the method used in this study is to demonstrate nonlinear property directly without any assumption. The conclusion from a large deviation from a linear equation (Werner and Wooten, 1979; Ejima and Takahashi, 1984) or the colinearity between the unique red and green loci in the chromaticity diagram (Burns et al., 1984) was based on some assumption of observer’s cone spectral sensitivities. In 530-600 nm and 530-630 nm pairs in this study, color appearance of the field changes from desaturated green to red with the amount of 600 or 630 nm increases in the mixture. In these pairs, maximum additivity failure of enhancement type occurred at the mixture ratio where both observers reported that the field looked nearly white. Burns er al.‘s (1984) results are qualitatively consistent with our data. If the yellow-blue were a linear process, the unique red and green loci should be one straight line in the chromaticity diagram. Their unique red and the unique green loci are not colinear and bend near the white point. The results of two different experiments suggest that there exist some discontinuity or change in the yellow-blue process between the greenish and the reddish equilibria. The relation between additivity and the color appearances of the two stimuli is noteworthy. Nearly additive results were found for both observers in the pairs of 530-550 nm and 600-630nm with the whole range of log pJp, measured. For the former pair, both i., and L, are greenish yellow, while the latter pair both stimuli are reddish yellow. For 530-570 nm pair which showed the reduction type additivity failure, L, is greenish yellow while i.? is near unique yellow and has Iittte red-green component. The pairs 530-600 nm and 530-630 nm, which are combination of greenish and reddish yellows, showed the enhancement type additivity failure for S.S. and a complex behavior that varied from a reduction to an enhancement type failure for M.A. When two stimuli with the same kind of red-green component are added, additivity holds, while two stimuli with different red-green
component are mixed. additiiit! failure ~xcur.~ except the result of 570-63) nm pd~r for ‘~1 -1 One possibility suggested b\ the above reiultj 15 that the red-green process affects the hdllo~+ chromatic valence. The results for dichromatic observers partly support this assumption. The additivity of the yellow chromatic valence holds for any wavelength combinations for a protanope (Ikeda and Ayama. 1983). Knoblauch et al. (1985) showed that the yellow-blue process satisfies linearity properties for protanopes and deuteranopes. Generally, protanopes and deuteranopes are considered to missing R-cones and G-cones, respectively. and consequently display no red-green process in their color vision. Without the red-green process, the yellow-blue process sho\vs linearity. Thus the red-green process is a possible cause of the yellow-blue nonlinearity for normal observers. Physiological evidence about interactions between opponent processes has not yet been provided. However, Zrenner and Gouras’s (1981) interpretation about their results are suggestive. They investigated characteristics of blue sensitive ganglion celis of rhesus monkeys. All of 22 blue sensitive cells but one show excitatory and inhibitory signals from B-cones and R- and/or G-cones, respectively, with coextensive receptive field structure. They suggested that, in these cells. only the excitatory signal carries the relevant information because its dynamic range is much larger than that of the inhibitory ones. Since the yellow excitatory cell is very rare, they suggested that there exists no “yellow” process at ganglion cell level and the yellow-blue opponent process is formed at later stages with yellow signal carried by the redgreen opponent ganglion cells. A preliminary model of blue cone mechanisms (Zrenner, 1983) shows inhibitory interactions from the red-green cells to the yellow-blue process at visual cortex. However, the yellow excitatory and blue inhibitory ganglion cells have been reported by other investigators (de Monasterio and Gouras, 1975; de Monasterio et af., 1975a, 1975b). In these studies, although the number of the cell is always less than other color opponent cells, the percentage is larger than that of Zrenner and Gouras’s study. Our results are consistent with a nonlinear conclusion in previous studies. However, quantitative relations between the results here and results in other studies, e.g. nonsmooth curve shape of the yellow-blue chromatic valence function, or non colinearity between unique
Additivity of yellow chromatic valence
green and unique red loci in the chromaticity diagram, have not been elucidated. Although nonlinear yellow-blue models have been proposed by some investigators (Larimer er al., 1975; Werner and Wooten, 1979; Elzinga and de Weert, 1984), none of them does not seem to succeed in explaining a variety of results mentioned above. An interaction between the two opponent processes is one approach to interpreting complex properties of the yellow-blue process (Ejima and Takahashi, 1983; Burns et al., 1984). Further efforts to investigate the opponent process both experimentally and theoretically in a wide range of stimulus space is awaited.
769
codes of the yellowjblue mechanism. Visian Res. 2d, 91 I-922. Ejima Y. and Takahashi S. (1983) Chromatic valence and hue sensation. J. opt. Sot. Am. 73, 1048-1054. Ejima Y. and Takahashi S. (1984) Bezold-Briicke hue shift and nonlinearity in opponent process. Vision Res. 24, 1897-1904.
Ikeda M. (1963) Study of interrelations between mechanisms at threshold. J. opt. Sot. Am. 53, t305-1313. Ikeda M. and Ayama M. (1980) Additivjty of opponent chromatic valence. Vision Rex 20, 995-999. Ikeda M. and Ayama M. (1983) Non-linear nature of the yellow chromatic valence. In Colour Vision (Edited by Mellon J. D. and Sharpe L. T.). Academic Press, New York. Jameson D. and Hurvich L. M. (1955) Some quantitative aspects of an opponent-colours theory. 1. Chromatic responses and spectral saturation. J. opr. Sot. Am. 45, 546552.
Acknowledgements-The
authors wish to thank Dr P. K. Kaiser, Dr K. Knoblauch, and Dr K. Uchikawa for their helpful comments.
REFERENCES Boynton R. M., Ikeda M. and Stiles W. S. (1964) Interactions among chromatic mechanisms as inferred from positive and negative increment thresholds. Vision Res. 4, 87-l 17. 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. de Monasterio F. M. and Gouras P. (1975) Functional properties of gangiion cells of the rhesus monkey retina. J. Physiut. 251, 167-195.
de Monasterio F. M., Gouras P. and Tolhurst D. J. (1975a) Trichromatic coiour opponency in ganglion cells of the rhesus monkey retina. J. Physiui. 251, 197-216. de Monasterio F. M., Gouras P. and Tolhurst D. J. (197Sb) Concealed colour opponency in ganglion cells of the rhesus monkey retina. J. Physiol. 251, 211-229. Elzinga C. H. and de Weert C. M. M. (1984) Nonlinear
Knoblauch K., Sirovich L. and Wooten B. R. (1985) Linearity of hue cancellation in sex-linked dichromacy. J. apt. sot. Am. A 2, 136-146. Larimer J., Krantz D. H. and Cicerone C. M. (1975) Opponent process additivity II. Yeilow/blue equilibria and nonlinear models. Vision Res. 15, 723-73 I. Nagy A. L. (1979) Unique hues are not invariant with brief stimulus durations. Vision Res. I9, 1427-1432. Romeskie M. (1978) Chromatic opponent-response function of anomalous trichromats. Vision Res. 18, 15211532.
Stiles W. S. (1967) Mechanism concepts in colour theory. J. Colour Group 11, 106-123.
Takahashi S. and Ejima Y. (1984) Spatial properties of red-green and yellow-blue perceptual opponent-color response. Vision Res. 24, 987-994. Werner J. S. and Wooten B. R. (1979) Opponent chromatic mechanisms: Relation to photopi~ents and hue naming. J. opt. Sot. Am. 69, 422-434. Zrenner E. (1983) ~europh.~siolagirai Aspects of Color Vision in Primates, Vol. 9, Studies of Brain Function (Edited by Braitenberg V.). Springer, Berlin. Zrenner E. and Gouras P. (198 I) Characteristics of the blue sensitive cone mechanism in primate retinal ganglion cells. Vision Res. 21, 1605-1609.
ADDITIVITY
00514989 86 53.00 + 0.00 Copyright 2 1986 Pergamon Press Lrd
OF YELLOW
CHROMATIC
MIYOSHZ AYAMA and Mnwo
Department of
VALENCE
IKEDA
informationProcessing, Tokyo Institute of Technology, Nagatsuta, Midori-ku. Yokohama 227, Japan (Rewired
8 September 1983: in recised form 28 Nocember 1985)
Abstract-The additivity of yellow chromatic valence was investigated by the hue cancellation method for two normal observers. Additivity held in 530-550 nm and 600430 nm pairs, while additivity failure of reduction type occurred in 530-570 nm pair for both observers. Additivity failure of enhancement type occurred in 53G600 and 530-630 nm pairs in which one observer showed reduction type failure when mixture ratio of 530 nm is greater than 600 or 630 nm. The results suggest a nonlinear property of the yellow-blue process and are discussed in an interaction between the two opponent processes. Color
Opponent process
Chromatic valence
INTR.ODUCTION
The yellow-blue opponent process for normat trichromats has been reported to possess a nonlinearity. Larimer et al. (1975), Nagy (1979), Elizinga and de Weert (1984) and Ejima and Takahashi (1984) showed violation of the yellow-blue equilib~a invariance with intensity, i.e. a scalar multiplication does not hold in the process. Werner and Wooten (1979), Takahashi and Ejima (1984) showed the yellow-blue chromatic valence function can not be fitted by a linear combination of the cone spectral sensitivities while Romeskie’s (1978) results for normals can. Ikeda and Ayama (1980) showed additivity failure of yellow chromatic valence. Burns et al. (1984) concluded a nonlinearity of the process from their results of the yellow-blue equilibrium, i.e. unique red and green loci in the chromaticity diagram. In the previous paper (Ikeda and Ayama, 1980), a marked additivity failure of the enhancement type was found for yellow chromatic valence in some wavelength combinations for two observers among three. Additivity failure implies that outputs of at least two different underlying mechanisms should be summed in a non-linear manner to input to the higher process. The most likely underlying mechanisms for yellow are R- and G-cones. Although the additivity failure results were conspicuous, the range of mixture ratios was 20% (40-60%) and thus they did not provide a full characterization of additivity between the two stimuli. Within
Hue cancellation
Additivity
that smail range, the results did not show a clear asymmetry against mixture ratio. If a mixture ratio is unbalanced from the equal point, it may reveal some asymmetrical property due to unequal contributions of different underlying mechanisms. In this study, we extended the range of the mixture ratio to 50% (25-75%). Based on the measurements, a possible relation between cones and the yellow-blue process is discussed.
METHOD To measure the additivity of chromatic valence between two wavelengths %, and E.,, the cancellation technique (Jameson and Hurvich, 1955) was used. The reference blue was presented with a fixed luminance. The test stimuli L, and j-2were chosen from the yeflowish region in the spectrum. First, A, alone was superimposed on the reference blue and its radiance was adjusted by an observer until the field appears neither reddish nor greenish (the yellow-blue equilibrium). Let the radiance of Ai be N;.,. Second, the same procedure was repeated for another stimulus E,,and its radiance N,, at the equilibrium was obtained. Third, both %, and ,& were added together to the same reference blue in a fixed mixture ratio. The total radiances of I, and _.$were adjusted so that the equilibrium of the field was reached again ;vhile the radiance ratio of i., and AZ was kept constant. Let the radiances of i., and E., in 763
ths mixture be .V,,_ and .Y,. , respectively. The summation index (Ikeda. I-463; Bob ton er ~1.. 1964; Stiles, 1967) was used as an index of additivity. It is defined as follows Summation
Index = 0.3 - log ( pI + p:)
where p, = N,,,iN,,, and p2 = N,.2m,N,,. If additivity holds, p, + p2 must be equal to one, i.e. the summation index is 0.3 for the whole range of mixture ratio. If p, + p? > 1. then the index becomes less than 0.3 which means more radiance is necessary in the mixture than in the single presentation of i., alone and i.? alone. This is called additivity failure of the reduction type because the efficiency is reduced in the mixture stimuli. If p, + pz < 1, i.e. the summation index becomes greater than 0.3, it is called additivity failure of the enhancement type. APPARATUS
A four channel Maxwellian-view optical system was used. The light source, which was common to all channels, was a 500 W Xenon arc lamp. Two channels produced monochromatic lights of two test stimuli I., and i.Z by means of monochromators (Nikon G-250). The entrance and exit slits of each were set to yield a theoretical half-bandwidth of 3 nm. The third channel produced a monochromatic light of the reference stimulus by use of an interference filter which had half-amplitude bandpass of 11 nm. The forth channel produced the white surround and its chromaticity coordinates were x = 0.32, ~3= 0.35. Each chromatic channel had a neutral density wedge to control the radiance of the light in the channel. Each neutral density wedge was coupled to a potentiometer to read the position. Solenoid shutters were placed near the exit slits of the monochromators. When the test stimulus was composed of a single wavelength, e.g. L, alone, then the channel for E,, was closed by the shutter, and vice versa. In the case of the mixture test stimuli, both shutters were open. Light beams from three chromatic channels, J.,, i.?, and the reference were combined by means of the beamsplitters. The stimulus presentation was controlled by the third solenoid shutter placed behind the beamsplitter which was combining the two test stimuli and the reference. The white surround light and three chromatic lights were combined by means of the final beamsplitter. The chromatic field was a foveally-viewed circular field with 2” in diameter and it was presented I set duration followed by
1 set dark incrrval. The irhite surround had LrI outer diameter of 7 and inner diameter ~)t’2 It leas presented steadily during a session. The center and surround fields were formed b> the two apertures placed in proper positions. Retinal illuminance of the white surround was maintained at 100 td to keep the observer’s eye in a photopic condition throughout a session. The wavelength of the reference blue was fixed at 470 nm. which is close to the unique blue for the two observers. Its retinal illuminance was kept at 20 td. We chose six wavelength combinations of i, and &: 530-550 nm, 530-570 nm, 530-600nm, 53@-630nm. 60&630nm. and 570-630 nm. One of the authors, M.A.. female, age 28, and S.S., male, age 24, both with normal color vision served as observers. PROCEDURE
Each session began with 1Omin dark adaptation followed by 5 min white adaptation. A method of adjustment was used to determine the equilibrium point. At the beginning, Ni, and N;., were roughly determined. In a standard session; six different pairs of the neutral density wedge positions for 1, and If.?were determined from the rough setting of Nj,, and N,z. Each pair gives a certain mixture ratio of i., and &, usually three of them were set to be p2/p, < I and the others were p2/p, > I, however, these values were not the final ratios. In a main part of a session, mixture stimuli of six different ratios and monochromatic stimuli of E., alone and Lz alone were presented in a random order and five trials were repeated in each of them. The radiances of N,,, and N,,, measured in each mixtures and N,, and N;_, were measured. Therefore, the final values of p,,-pz, and the ratio p2/p, for each mixture were determined at the end of each session. RESULTS
Figure 1 is the result of 530-550nm pair for the two observers. Summation index was plotted against the mixture ratio log pJp,. Horizontal lines at 0.3 represent additivity. Vertical bars denote the three maximum range of five repetitions. Most of the points are close to 0.3 of additivity except MA’s result in the region of log pJp, < -0.2. The results of the pair 530-570 nm given in Fig. 2 show a distinctive deviation from additivity. The values of summation indices are
765
Additivity of yellow chromatic valence I
A,=530om
1
Xe=550nm
02 t
I
I -0.8
t
-0.4
-0.6
1
I
-0.2
0.0
m
P*/P
I
04
0.2
0.6
08
,
Fig. 1. Summation indices against log &pi for observers M.A. (top) and S.S. (bottom). Horizontal line at 0.3 represents the theoreticat line of additivity. Vertical bars denote maximum three ranges of five repetitions. i., = 530 nm, 1, = 550 nm.
indicating the additivity failure of enhancement type. In this observer’s results, the summation index value becomes maximum around at the ratio of log pJp, = 0.22 and 0.05 for 530600 nm, respectively. M.A.‘s results show more complicated nature of additivity failure: the summation indices are smaller than 0.3 when
smaller than 0.3 for both observers, indicating the additivity failure of reduction type, Different types of additivity failure are observed in the results of the pairs 530-600 nm and 530-630 nm shown in Fig. 3 and Fig. 4, respectively. For S.S., the data points are above the additivity line in a wide range of log pJp,
a,
=JX)nm
a2 = 570nm
-
0.5-
-02
M.A --01
04-
03-
:*
I*
0.2 -
1
.
0.0
. l*y*j
:,,
l
_:..
0..
.:
-
0.1
a.” + Q-
0.5 -
--02
Gi
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Fig. 2. Similar ptots as in Fig. I but i., = 530 nm, i., = 570 nm.
08
0.1
-0.8
-06
-0.4
-0.2
0.0 w
02
04
0.6
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Pz /PI
Fig. 3. Similar plots as in Fig. 1 but i., = 530 nm, & = 600 nm.
log pz/p, c - 0. I2 and become greater than 0.3 when log p2/p, > -0.12. The additivity failure varies from a reduction type to an enhancement type as the amount of %, in the mixture increases. Summation index curves show cIear asymmetry here. Within a narrow range near Iog PtIP1 = 0, an average value of the summation index would be cIose to 0.3 apparently indicating additivity. In the previous study
(Ikeda and Ayama, I980), this observer showed an additive result with a large standard deviation in the pair of 533-607 nm while the other two observers showed an enhancement type additivity failure. The results here suggest that her previous result is due to the measurement within a small range of the mixture ratio around the point (log pJp, = 0) where her summation index curve is crossing the additivity line at 0.3.
:: 0.3 a 5 02 s z 2 E 3 *
0.5 04 0.3
-08
-0.6
-04
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0 2
0.4
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Fig. 4. Similar plots as in Fig. I but i, = 530 nm, i.2= 630 nm.
0.5
767
Additivity of yeIlow chromatic valence
-0.1
0. I
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-06
I - 0.4
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I -0.2
0.0 tog
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I 0.4
I 0.6
I 0.6
,
Fig. 5. Similar plots as in Fig. 1 but ,I, = 570 nm, ,I2= 630 nm.
pair. M.A.‘s data show small reduction type failure especially in log p2jp, > 0. Wide repetition ranges for S.S. might be due to a small amount of yellowness in the test stimuh especially in &. By increasing the relative amount of 630 nm, the yellowness in the test stimuli decreases, and therefore, detecting the change of yellowness in the field would become difficult with a large amount of redness. How-
The measurement in a wide range of mixture ratios revealed a nonadditive nature of the yehow chromatic valence for this observer. Figure 5 shows the results of 570-630 nm pair. For M.A., the summation indices are along the 0.3 line indicating additivity except log p2/p1 < -0.2. For S.S., a small amount of reduction type is found. Figure 6 shows the results of 600-630 nm
0.5
- 0.2
0.4
-01
03
0.0
0.2
0.1
-
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0.5
-0.2
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0.3
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0.2
0.3
-0.6
-0.6
- 0.4
-0.2
00 w
pt fP
0.2
0.4
0.6
1
Fig. 6. Similar plots as in Fig. 1 but 1, = 600 nm, 2, = 630 nm.
08
3
eser, for both observers, most of the data points do not deviate from the additivity line to a large extent. DISCL’SSION
Additivity failure of the yellow chromatic valence agree with previous studies which showed nonlinear properties of the yellow-blue process. One advantage of the method used in this study is to demonstrate nonlinear property directly without any assumption. The conclusion from a large deviation from a linear equation (Werner and Wooten, 1979; Ejima and Takahashi, 1984) or the colinearity between the unique red and green loci in the chromaticity diagram (Burns et al., 1984) was based on some assumption of observer’s cone spectral sensitivities. In 530-600 nm and 530-630 nm pairs in this study, color appearance of the field changes from desaturated green to red with the amount of 600 or 630 nm increases in the mixture. In these pairs, maximum additivity failure of enhancement type occurred at the mixture ratio where both observers reported that the field looked nearly white. Burns er al.‘s (1984) results are qualitatively consistent with our data. If the yellow-blue were a linear process, the unique red and green loci should be one straight line in the chromaticity diagram. Their unique red and the unique green loci are not colinear and bend near the white point. The results of two different experiments suggest that there exist some discontinuity or change in the yellow-blue process between the greenish and the reddish equilibria. The relation between additivity and the color appearances of the two stimuli is noteworthy. Nearly additive results were found for both observers in the pairs of 530-550 nm and 600-630nm with the whole range of log pJp, measured. For the former pair, both i., and L, are greenish yellow, while the latter pair both stimuli are reddish yellow. For 530-570 nm pair which showed the reduction type additivity failure, L, is greenish yellow while i.? is near unique yellow and has Iittte red-green component. The pairs 530-600 nm and 530-630 nm, which are combination of greenish and reddish yellows, showed the enhancement type additivity failure for S.S. and a complex behavior that varied from a reduction to an enhancement type failure for M.A. When two stimuli with the same kind of red-green component are added, additivity holds, while two stimuli with different red-green
component are mixed. additiiit! failure ~xcur.~ except the result of 570-63) nm pd~r for ‘~1 -1 One possibility suggested b\ the above reiultj 15 that the red-green process affects the hdllo~+ chromatic valence. The results for dichromatic observers partly support this assumption. The additivity of the yellow chromatic valence holds for any wavelength combinations for a protanope (Ikeda and Ayama. 1983). Knoblauch et al. (1985) showed that the yellow-blue process satisfies linearity properties for protanopes and deuteranopes. Generally, protanopes and deuteranopes are considered to missing R-cones and G-cones, respectively. and consequently display no red-green process in their color vision. Without the red-green process, the yellow-blue process sho\vs linearity. Thus the red-green process is a possible cause of the yellow-blue nonlinearity for normal observers. Physiological evidence about interactions between opponent processes has not yet been provided. However, Zrenner and Gouras’s (1981) interpretation about their results are suggestive. They investigated characteristics of blue sensitive ganglion celis of rhesus monkeys. All of 22 blue sensitive cells but one show excitatory and inhibitory signals from B-cones and R- and/or G-cones, respectively, with coextensive receptive field structure. They suggested that, in these cells. only the excitatory signal carries the relevant information because its dynamic range is much larger than that of the inhibitory ones. Since the yellow excitatory cell is very rare, they suggested that there exists no “yellow” process at ganglion cell level and the yellow-blue opponent process is formed at later stages with yellow signal carried by the redgreen opponent ganglion cells. A preliminary model of blue cone mechanisms (Zrenner, 1983) shows inhibitory interactions from the red-green cells to the yellow-blue process at visual cortex. However, the yellow excitatory and blue inhibitory ganglion cells have been reported by other investigators (de Monasterio and Gouras, 1975; de Monasterio et af., 1975a, 1975b). In these studies, although the number of the cell is always less than other color opponent cells, the percentage is larger than that of Zrenner and Gouras’s study. Our results are consistent with a nonlinear conclusion in previous studies. However, quantitative relations between the results here and results in other studies, e.g. nonsmooth curve shape of the yellow-blue chromatic valence function, or non colinearity between unique
Additivity of yellow chromatic valence
green and unique red loci in the chromaticity diagram, have not been elucidated. Although nonlinear yellow-blue models have been proposed by some investigators (Larimer er al., 1975; Werner and Wooten, 1979; Elzinga and de Weert, 1984), none of them does not seem to succeed in explaining a variety of results mentioned above. An interaction between the two opponent processes is one approach to interpreting complex properties of the yellow-blue process (Ejima and Takahashi, 1983; Burns et al., 1984). Further efforts to investigate the opponent process both experimentally and theoretically in a wide range of stimulus space is awaited.
769
codes of the yellowjblue mechanism. Visian Res. 2d, 91 I-922. Ejima Y. and Takahashi S. (1983) Chromatic valence and hue sensation. J. opt. Sot. Am. 73, 1048-1054. Ejima Y. and Takahashi S. (1984) Bezold-Briicke hue shift and nonlinearity in opponent process. Vision Res. 24, 1897-1904.
Ikeda M. (1963) Study of interrelations between mechanisms at threshold. J. opt. Sot. Am. 53, t305-1313. Ikeda M. and Ayama M. (1980) Additivjty of opponent chromatic valence. Vision Rex 20, 995-999. Ikeda M. and Ayama M. (1983) Non-linear nature of the yellow chromatic valence. In Colour Vision (Edited by Mellon J. D. and Sharpe L. T.). Academic Press, New York. Jameson D. and Hurvich L. M. (1955) Some quantitative aspects of an opponent-colours theory. 1. Chromatic responses and spectral saturation. J. opr. Sot. Am. 45, 546552.
Acknowledgements-The
authors wish to thank Dr P. K. Kaiser, Dr K. Knoblauch, and Dr K. Uchikawa for their helpful comments.
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