Opponent-color models and the influence of rod signals on the loci of unique hues

Vision Research 40 (2000) 3333 – 3344 www.elsevier.com/locate/visres

Opponent-color models and the influence of rod signals on the loci of unique hues Steven L. Buck *, Roger F. Knight, John Bechtold Department of Psychology, Uni6ersity of Washington, PO Box 351525, Seattle, WA 98195, USA Received 16 September 1999; received in revised form 9 May 2000

Abstract To investigate how rod signals influence hue perception and how this influence can be incorporated into opponent-color models, we measured the shift of unique-hue loci under dark-adapted conditions compared with cone-plateau conditions. Rod signals produced shifts of all spectral unique hues (blue, green, yellow) but in a pattern that was inconsistent with simple additive combinations of rod and cone inputs in opponent-color models. The shifts are consistent with non-linear models in which rod influence requires non-zero cone signals. Cone-signal strength may modulate or gate rod influence, or rod signals may change the gain of cone pathways. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: Color vision; Rod–cone interaction; Unique hues; Perceptual color opponency

1. Introduction Human color vision has long been modeled in terms of the outputs of the three types of cone photoreceptors. However, there is long-standing psychophysical evidence that signals from rod photoreceptors can also influence human color vision. In order to specify more accurate and generalized models of color vision, the role of rods must be integrated with that of cones. Prior studies have described a variety of rod influences on hue perception. As detailed in Section 4, some studies have concluded that rod excitation creates or increases perceived blueness (Hunt, 1952; Richards & Luria, 1964; Trezona, 1970, 1974; Ambler, 1974; Stabell & Stabell, 1994; Buck, 1995, 1997). Other studies have suggested that rod excitation strengthens the blue/yellow (b/y) opponent-hue dimension relative to the red/ green (r/g) dimension (Stabell & Stabell, 1975, 1976, 1979; Frumkes, Lembessis, Vollaro, & McMullen, 

Different portions of this work were first reported at the 1996 ARVO (Buck, Knight, & Bechtold, 1996), 1996 OSA (Buck & Knight, 1997; Buck, Knight, & Bechtold, 1997), and 1997 ARVO (Fowler, Buck, & Knight, 1997) annual meetings. * Corresponding author. Tel.: +1-206-5436789; fax: + 1-2066853157. E-mail address: [email protected] (S.L. Buck).

1997). And still other studies have suggested that rod excitation strengthens both b/y and r/g hue dimensions asymmetrically (Volbrecht, Nerger, & Ayde, 1993; Nerger, Volbrecht, & Ayde, 1995). At present, it is difficult to see how to reconcile these different results and how to incorporate rod influences into current models of color vision. To address these issues, the present study evaluates the incorporation of rod influences into opponent-color models, which directly link photoreceptor excitations and perceptual hue dimensions. Two current versions of perceptual opponent-color models are those of Hurvich and Jameson (Hurvich, 1981) and of DeValois and DeValois (1993). In both models, signals from all three cone types (L, M, S) are weighted by coefficients and combined linearly in both r/g and b/y opponent hue dimensions that are often referred to as channels. A benefit of these opponent-color models is that they make quantitative predictions for the three spectral unique-hue loci (blue, green, and yellow). For given cone spectral sensitivities and weighting coefficients, each model predicts specific wavelengths at which one or the other hue dimension will be nulled, leaving only the remaining hue dimension to determine a unique hue. Thus, nulls on the r/g dimension yield unique blue and unique yellow, while nulls on the b/y dimension

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S.L. Buck et al. / Vision Research 40 (2000) 3333–3344

yield unique green and unique red (although the latter is extraspectral and cannot be represented by a single wavelength). If rod signals differentially influence one side or the other of an opponent hue dimension, rod signals will shift the resulting spectral locus of the null point. Thus, any specific way of incorporating rod signals into the opponent-color equations produces a specific prediction for the pattern of shifts of loci of the spectral unique hues. The classical opponent-color models have served well as first-order bases for elaboration and testing of models and descriptions of color vision. Both their failures and their successes at accounting for details of color vision can be informative. Determining the ways that rod influences can or cannot be described in the context of these classical models is a first step toward building models of color vision that include the role of rod signals. The specific ways in which these models fail or succeed may reveal important features of the rod influence on hue to guide future models and studies of neural substrate. In the present study, we measure unique-hue shifts produced by rod excitation and use the resulting pattern of rod influence to evaluate the incorporation of rod signals into opponent-color models. We find that the observed rod influence is inconsistent with an additive (i.e. linear) combination of rod and cone signals and is instead consistent with non-linear combinations of rod and cone signals that allow rod influence only when combined with a non-zero cone signal. This implies that at least some rod influence on hue is modulated or gated by cone activity. We describe a possible substrate for these interactions in the retinal neural pathways.

2. Methods

2.1. Subjects Five observers (two males, ages 26 and 40; three females, ages 23, 24, and 45) participated. All had apparently normal color vision as assessed by Nagel Anomaloscope and FM100-Hue Test. An observer’s head was stabilized with a full-mouth dental-impression bar mounted on a three-dimensional (3D) manipulator. Each observer used his or her right eye to view the stimuli. Observers RK and BP wore clinically prescribed corrective lenses. All observers had considerable experience at the task before the data were collected.

2.2. Apparatus All observations were made with a computer-controlled Maxwellian-view apparatus having five optical

channels derived from two 12-V tungsten–halogen sources driven by a regulated d.c. power supply. Electromagnetic shutters regulated stimulus duration and the synchronization among the channels. Spectrally calibrated neutral density filters controlled the illuminance of all stimuli. One channel contained a PTR Optics monochromator having a full bandwidth at half transmission of less than 2 nm. The spectral composition of the light emerging from the other channels was controlled by interference filters that had full bandwidths at half transmission of 10–12 nm and that were spectrally calibrated at 3-nm intervals to 1% of the peak transmission. Polarizers with 180° phase relation were used to exchange two channels. Each polarizer provided up to 4 log units extinction and was calibrated at 15° intervals. All calibrations were performed in situ by means of a calibrated Gamma Scientific spectroradiometer.

2.3. Stimuli The stimulus configuration consisted simply of a test field — with a fixation stimulus added for extrafoveal conditions — that the observer adjusted to appear as a specific unique hue. Testing conditions varied factorially along the following dimensions: unique hue (blue, green, yellow or red), stimulus configuration (size/eccentricity), and prior adaptation state (dark-adapted or cone-plateau). In addition, each condition was presented at several light levels. All four unique hues were measured. Spectral unique hues (blue, green, yellow) were produced by light from the monochromator. Adapting the method of Larimer, Krantz, and Cicerone (1975), we produced unique red by optically combining a fixed 650-nm light with a mixture of 450 and 500-nm lights that were proportionally exchanged at equal photopic illuminance. The illuminances of the 650 and 450/500-nm mixture lights were preset at 4:1 by the experimenter. Observers adjusted the overall hue of the test stimulus by exchanging the 450 and 500-nm channels (during these adjustments, the photopic illuminance of the test stimulus remained constant but the scotopic illuminance varied). There were three stimulus configurations: the large/ extrafoveal condition (a 7.6° test field presented at 7° eccentricity), a small/extrafoveal condition (2° test field also presented at 7° eccentricity) and a foveal condition (a 2° test field foveally centered). The small/extrafoveal condition approximated the configuration used by Buck (1997) in his scotopic contrast study (2° test field, 5° eccentricity). The large/extrafoveal condition was used because we thought it might further increase rod influence at 7° eccentricity. The foveally-centered condition was used because we thought it might reduce rod influence.

S.L. Buck et al. / Vision Research 40 (2000) 3333–3344

The test field cycled continuously throughout a trial, 1 s on and 1 s off, until the observer pushed a response key signaling that the criterion hue had been achieved. For extrafoveal conditions, there was a dim red fixation cross of about 1° height and width. For foveal conditions, there was no fixation stimulus. There were two prior adaptation states: cone plateau and dark adapted. For the cone-plateau conditions, the observers viewed a 10°-diameter xenon flash centered at the retinal eccentricity to be tested and produced by a 150 W/s Quantum Qflash model T (1/300 s flash duration, 5400 K color temperature). During the period from 3 to 8 min after the flash bleach, observers made repeated settings of a single unique hue under a single stimulus condition. This condition was intended to minimize rod influence on hue but could not assure that it was entirely eliminated because test stimuli were suprathreshold. In the dark-adapted conditions, the observer’s test eye was patched for a minimum of 30 min before a session and for 3-min between conditions. Whenever possible, corresponding cone-plateau and dark-adapted conditions were presented in successive sessions. Each unique-hue locus was measured under both adaptation states over a 2 – 3.5 log-unit range of light levels and was generally between 0.5 and 4 log units above absolute photopic detection threshold. Scotopic troland values for each condition and observer are shown in Tables 1 and 2. Light levels were always presented in ascending order within a session. Light levels for corresponding dark-adapted and cone-plateau conditions sometimes differed slightly due to the different final wavelength settings of the test-field monochromator. (Because transmittance of the monochromator varied with wavelength, a rod influence on unique-hue locus could also cause the final light levels to differ slightly between adaptation states. While these light level differences could conceivably either accentuate or reduce the difference in unique-hue locus between adaptation conditions, they could not by themselves cause a difference to exist. That is, rods or something else would have to cause unique-hue loci to differ between adaptation conditions before a light-level difference would exist.)

2.4. Procedures All data were obtained by means of the method of adjustment. For the three spectral unique hues, observers adjusted the monochromator until a stimulus was found that was judged to be the unique hue of interest for that trial. A computer-generated random movement occurred after each trial. For unique red, the observer adjusted the 450–500-nm exchange until the hue of the test field was uniquely red. After each unique red trial, observers moved the polarizers so that the test stimuli

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appeared to have a considerable amount of blue or yellow (alternating the direction after each trial). In all cases, observers were blind to the wavelength of the stimulus and had only their hue perceptions to provide feedback. Trials were replicated five or six times within a condition during a session. Conditions were replicated three times in separate sessions.

3. Results

3.1. Unique-hue measurements Table 1 presents the mean wavelengths of the spectral unique hues for all conditions and observers. Table 2 presents the mean 450/500-nm ratio that, when mixed with 650 nm light, produced unique red for all conditions and observers. Note that RK was tested only in extrafoveal conditions and that BP was tested only in unique red conditions. In all cases, S.E.M. were calculated across individual session means. The empirically-determined rod influence on unique hue loci is depicted in Fig. 1 by the difference between mean unique-hue settings made for corresponding dark-adapted and cone-plateau conditions. Thus, rod influence is seen as a deviation from the zero difference line. For the spectral unique hues, where light level varied slightly for corresponding dark-adapted and cone-plateau conditions, the data are plotted at the average of the actual light levels, which are shown in Tables 1 and 2. Unique red and unique green conditions are grouped together to facilitate comparison of the rod influence on the b/y opponent channel. Similarly, unique blue and unique yellow conditions are grouped in order to facilitate comparison of the rod influence on the r/g opponent channel. The rationale for this analysis is as follows. By definition, both unique red and unique green represent nulls or balances of blue and yellow. If rod signals contribute differentially to blue or yellow, then rod signals will shift the b/y balance point found under dark-adapted conditions compared with that found under cone-plateau conditions (when rods are not effectively stimulated). The direction and magnitude of this difference indicate whether rod signals contribute more strongly to blue or to yellow and by how much, respectively. Analogously, differences between dark-adapted and cone-plateau conditions for the wavelengths of unique yellow and unique blue indicate the direction and magnitude of the rod influence on the balance between red and green. The assignment of labels of direction of rod influence, e.g. a blue-bias or a yellow-bias, warrants an illustration. Suppose that an observer sets unique green (a b/y balance point) at a longer wavelength under the dark-adapted condition than under the cone-plateau

Test level in log scotopic trolands.

1.2 0.7 0.8 0.9 1.0 3.4 0.4 1.4 3.6 0.6 0.8 2.4 1.5 1.2 1.9

Small fo6eal-centered test Blue 1.6 471.4 2.0 468.5 2.6 469.4 3.0 466.7 3.5 467.7 Green 1.6 507.3 1.9 499.6 2.3 494.4 2.8 492.4 3.3 490.7 Yellow 1.6 570.2 2.0 572.3 2.5 573.5 2.9 575.6 3.4 574.1

a

1.9 3.1 2.0 1.0

1.1 2.3 2.4 3.4

569.3 573.2 571.1 568.6

Yellow

0.7 1.4 1.3 1.0 0.8 5.3 4.1 3.5 1.1

Small extrafo6eal test Blue 2.0 465.2 2.4 464.3 3.0 460.3 3.6 459.8 4.1 458.6 Green 2.1 499.3 2.7 497.2 3.1 486.2 3.7 488.6

5.7 3.7 1.3 2.2

0.6 1.2 2.4 0.8

1.4 1.9 2.4 2.9

Yellow

509.9 494.8 491.3 486.4

575.0 575.0 574.0 574.7

1.8 2.0 2.5 2.9

Green

2.5 1.8 0.5 2.5

485.8 481.7 477.3 462.3 509.9 511.5 509.9 508.2 582.1 575.4 574.6 579.9

1.7 2.8 3.5 4.1 1.4 2.5 3.3 3.7 0.0 1.4 2.6 3.2

578.8 573.8 575.1 579.9

512.7 515.6 501.7 503.1

1.5 2.1 2.9 3.7 0.1 1.3 2.6 3.3

475.2 476.6 473.6 469.9

572.5 582.7 581.4 572.2

508.2 518.4 512.4 507.2

480.1 477.0 471.5 463.1

Setting (nm)

1.6 2.5 3.1 4.2

0.6 1.0 1.7 2.8

1.3 2.0 2.7 3.7

1.6 2.5 3.1 3.8

Test level

S.E.

Test levela

Setting (nm)

JB

AN

Large extrafo6eal test Blue 1.5 466.9 2.0 465.0 2.5 462.3 3.0 461.9

Observer

Dark adapted

Table 1 Spectral unique hues for all conditions

0.4 4.1 0.4 3.5

3.1 3.4 0.1 1.9

1.6 1.1 4.6 4.5

2.6 2.5 2.4 1.5

1.0 8.1 1.6 0.5

3.0 1.4 1.6 3.9

1.2 1.3 1.0 0.8

4.4 1.3 1.6 3.3

0.9 1.7 1.0 6.2

S.E.

2.0 2.9 4.0

2.0 2.9 3.9

2.0 2.9 3.9

1.4 2.4 3.2

1.5 2.3 2.8 3.4

2.1 2.6 3.3 4.1

2.3 2.7 3.1

1.7 2.3 2.7 3.1

2.0 2.6 3.1

Test level

MC

565.6 568.9 565.8

507.1 501.6 501.2

462.0 455.5 451.4

567.0 571.4 570.3

504.8 513.5 507.3 502.3

468.6 463.4 463.0 458.0

567.9 572.4 575.7

514.4 514.8 514.2 511.3

471.2 460.5 456.4

Setting (nm)

0.5 0.5 0.7

5.5 4.0 2.9

2.6 4.3 3.6

2.7 2.7 0.7

3.7 5.5 3.4 1.5

0.4 3.9 0.4 3.9

0.8 1.7 1.4

4.9 3.9 3.2 2.5

1.3 1.5 0.5

S.E.

1.7 2.1 2.4 3.0 3.7 1.7 1.9 2.4 3.0 3.5 0.8 1.4 2.1 2.8

1.5 1.8 2.3 2.8 3.2 1.6 2.0 2.4 2.8 3.2 1.7 2.0 2.5 3.0 3.4

Test level

RK

474.8 474.7 462.5 466.6 461.5 511.5 521.8 496.6 492.7 493.3 572.0 574.0 576.3 569.4

479.0 470.0 468.3 465.4 462.8 516.5 504.0 498.2 492.8 488.8 571.4 572.7 572.5 573.7 577.6

Setting (nm)

1.9 1.5 2.5 1.6 2.3 4.9 6.3 3.4 2.2 2.2 2.1 2.8 2.0 3.1

2.1 0.4 1.6 2.4 2.9 3.8 1.2 1.6 2.0 0.9 2.3 1.5 0.3 1.2 1.6

S.E.

1.6 2.2 2.7 3.1 3.6 1.2 1.7 2.2 2.7 3.2 1.6 2.1 2.6 3.1 3.7

1.1 2.4 2.8 3.6

2.1 2.3 3.0 3.6 4.1 2.0 2.5 3.2 3.4

1.5 2.0 2.5 3.0

1.3 1.9 2.3 3.0

1.5 2.0 2.5 3.0

Test level

AN

471.8 473.0 473.2 472.9 472.4 486.8 485.7 487.5 488.7 488.9 562.7 567.7 564.4 566.0 562.9

567.5 571.2 566.2 558.5

470.3 457.1 461.5 462.1 459.4 494.0 490.7 491.7 489.4

565.0 565.7 565.4 566.2

482.9 488.6 483.8 492.0

463.7 462.4 464.3 467.1

Setting (nm)

Cone plateau

2.4 1.8 2.1 1.8 0.3 4.4 1.0 2.1 1.1 2.5 0.7 1.4 2.2 2.8 4.1

1.5 2.2 1.2 0.5

7.0 1.4 0.1 0.1 1.8 2.4 2.8 2.2 1.7

4.2 2.5 3.8 1.6

0.4 3.4 0.5 1.8

1.2 4.0 1.7 2.8

S.E.

0.1 1.4 2.6 3.2

1.4 2.5 3.2 3.8

1.6 2.7 3.3 4.2

0.2 1.5 2.7 3.5

1.4 2.1 2.9 3.8

1.6 2.6 3.3 4.4

0.6 1.1 2.0 2.8

1.0 1.9 2.5 3.6

1.1 2.4 3.1 3.9

Test level

JB

580.9 573.4 572.6 580.1

506.1 508.6 508.5 510.7

478.1 475.1 471.9 465.4

572.2 565.9 570.5 570.7

509.4 515.5 503.9 513.6

478.8 482.5 481.2 476.4

569.8 577.2 571.2 569.4

490.5 501.1 498.6 500.7

465.5 473.0 472.9 471.9

Settings (nm)

2.2 7.1 2.9 2.4

4.5 3.2 4.5 3.5

1.8 1.3 5.5 4.5

3.1 2.1 1.0 0.7

2.5 7.2 3.8 4.1

2.6 2.5 3.1 2.4

1.1 0.5 1.1 1.3

4.3 3.4 4.6 1.4

3.0 2.1 1.6 0.6

S.E.

2.0 2.9 4.0

1.9 2.9 3.9

2.0 2.9 3.9

1.4 2.5 3.2

1.6 2.3 2.8 3.3

2.1 2.5 3.3 4.1

2.3 2.8 3.3

1.6 2.2 2.6 3.1

1.9 2.6 3.1

Test level

MC

565.1 567.8 565.2

505.0 502.0 504.3

460.5 454.1 451.5

563.1 565.5 565.9

515.4 509.4 503.6 500.2

464.2 462.1 460.9 457.3

559.6 563.0 564.7

506.8 503.9 504.2 504.1

466.6 460.9 458.6

Settings (nm)

2.1 0.4 1.2

3.9 1.6 2.2

1.1 2.5 0.9

2.9 2.1 1.3

3.4 2.8 3.6 0.9

2.0 1.4 2.9 1.2

1.7 0.7 1.6

4.5 2.3 1.8 1.8

1.0 0.3 3.2

S.E.

1.8 2.0 3.0 3.6 3.7 1.6 1.8 2.4 3.2 3.6 0.9 1.6 2.3 2.8

1.3 1.8 2.3 2.8 3.3 1.6 1.9 2.5 2.9 3.4 1.7 2.2 2.6 3.1 3.6

Test level

RK

475.7 469.9 469.2 466.5 464.3 507.0 503.3 496.5 499.4 497.9 564.0 563.4 566.0 568.2

473.6 473.7 472.3 469.0 470.2 518.9 504.0 502.7 499.2 497.5 559.3 558.8 564.9 564.5 567.5

Settings (nm)

2.8 2.8 2.2 3.1 1.8 5.8 1.0 6.5 2.9 3.1 5.1 0.6 5.9 1.9

1.1 0.9 1.2 1.3 1.4 3.0 5.0 4.2 3.0 0.6 2.7 2.0 0.8 1.3 0.9

S.E.

3336 S.L. Buck et al. / Vision Research 40 (2000) 3333–3344

a

0.112 0.082 0.092 0.087 0.065

0.043 0.064 0.076 0.081 0.182

0.08 0.076 0.068 0.091 0.111

Setting

JB

Test level in log scotopic trolands

Small fo6eal-centered test 1.7 2.2 2.7 3.2 3.5

0.019 0.008 0.009 0.008 0.007

Small extrafo6eal test 1.7 0.086 2.2 0.092 2.7 0.070 3.2 0.052 3.5 0.049

S.E.

0.023 0.014 0.025 0.012 0.016

Setting

Test levela

Large extrafo6eal test 1.7 0.052 2.2 0.085 2.7 0.101 3.2 0.100 3.5 0.071

AN

Observer

Dark adapted

Table 2 Unique red: proportion of 450 nm in mixture

0.035 0.021 0.021 0.024 0.008

0.010 0.011 0.012 0.008 0.043

0.016 0.006 0.012 0.028 0.012

S.E.

0.032 0.027 0.021 0.013 0.010

0.035 0.028 0.024 0.019 0.010

0.014 0.031 0.029 0.023 0.013

Setting

MC

0.005 0.007 0.006 0.003 0.002

0.004 0.007 0.005 0.004 0.001

0.003 0.003 0.003 0.004 0.002

S.E.

0.311 0.220 0.176 0.184 0.169

0.294 0.201 0.153 0.110 0.093

Setting

RK

0.033 0.019 0.002 0.002 0.005

0.052 0.031 0.037 0.022 0.017

S.E.

0.110 0.086 0.090 0.056 0.048

0.069 0.090 0.080 0.074 0.051

0.056 0.118 0.082 0.076 0.080

Setting

BP

0.010 0.014 0.006 0.004 0.006

0.021 0.013 0.010 0.013 0.007

0.012 0.009 0.003 0.007 0.007

S.E.

0.055 0.044 0.045 0.064 0.040

0.086 0.092 0.070 0.052 0.049

Setting

AN

0.018 0.002 0.005 0.007 0.003

0.019 0.008 0.009 0.008 0.007

S.E.

Cone plateau

0.101 0.054 0.041 0.069 0.079

0.055 0.069 0.077 0.098 0.190

0.076 0.051 0.058 0.128 0.094

Setting

JB

0.030 0.006 0.013 0.003 0.015

0.018 0.010 0.014 0.019 0.079

0.037 0.015 0.013 0.029 0.020

S.E.

0.057 0.035 0.039 0.025 0.016

0.045 0.041 0.046 0.020 0.014

0.014 0.031 0.029 0.023 0.013

Setting

MC

0.023 0.006 0.012 0.012 0.005

0.011 0.012 0.004 0.005 0.004

0.003 0.003 0.003 0.004 0.002

S.E.

0.214 0.197 0.153 0.118 0.088

0.139 0.117 0.058 0.048 0.038

Setting

RK

0.012 0.010 0.026 0.022 0.003

0.016 0.020 0.005 0.007 0.004

S.E.

0.033 0.059 0.056 0.054 0.033

0.054 0.041 0.046 0.039 0.042

0.086 0.060 0.064 0.068 0.046

Setting

BP

0.012 0.009 0.012 0.013 0.014

0.012 0.015 0.005 0.013 0.009

0.022 0.008 0.015 0.011 0.010

S.E.

S.L. Buck et al. / Vision Research 40 (2000) 3333–3344 3337

Fig. 1. Empirically-determined rod influence on loci of all four unique hues (columns) for three different test-stimulus conditions (rows). Rod influence is shown by deviation from the ‘zero’ line in each panel but the metrics differ for unique red (right axis) and the other unique hues (left axis) as explained in the text. The double-headed arrows between panels provide an interpretation of the direction of rod influence on r/g (left columns) and b/y (right columns) opponent hue dimensions. Observers are shown by different symbols, RK by inverted filled triangles; AN by filled circles; JB by open squares; MC by upright open triangles; and BP by open diamonds.

3338 S.L. Buck et al. / Vision Research 40 (2000) 3333–3344

S.L. Buck et al. / Vision Research 40 (2000) 3333–3344

condition. This result would plot above the zero line of our rod influence metric of Fig. 1. We inferred that the shift was due to a net blue-bias of rod signals because, under dark-adapted conditions, the balance point shifted toward wavelengths that produced more photopic yellowness, in order to balance the added scotopic blueness. Note that we cannot distinguish whether rod signals reduce yellow or add blue because both would have identical effects. Thus the designation of a rod hue bias is a description of a net behavioral effect, not of a physiological mechanism. Note also that the panels have been arranged so that a given rod hue effect (e.g. red-bias) is shown by change in the same vertical direction (upward in this case) for the two relevant unique hues (unique blue and unique yellow), even though this involves opposite directions of rod-driven wavelength change (longer for unique blue, shorter for unique yellow). Fig. 1 shows that rod influence on hue is generally most pronounced for the large/extrafoveal condition. In this condition, rod influence (deviations from the zerodifference line) is not generally the same for the two independent tests of r/g balance, unique blue and unique yellow. Nor is rod influence generally the same for the two independent tests of b/y balance, unique red and unique green. More specific aspects of the rod influence on unique hues can also be discerned from Fig. 1, as noted below (the following section focuses on general patterns that recur across observers or conditions rather than on detailed differences among them). 1. The rod influence at both unique red and unique yellow tends to be constant over light level. Under dark-adapted conditions, unique yellow judgments shift toward longer wavelengths, indicating a net green-bias of rod signals, for all observers in both extrafoveal conditions and for one observer for the foveal condition. The overall effect of rods on unique red judgments is less clear. On the one hand, across all conditions, more data points fall below the zero line than above it, perhaps indicating an overall rod yellow-bias. Also, observer RK (inverted filled triangles) shows both a net rod yellow-bias (in both extrafoveal conditions) and a light level dependence (in the large/extrafoveal condition). On the other hand, the number of observers whose data fall entirely below the zero line indicating unequivocal rod yellow-bias, is only 1 of 5, 2 of 5, and 1 of 3 for the large/extrafoveal, small/extrafoveal, and foveal conditions, respectively. Other than for observer RK (inverted filled triangles), there are no overall patterns of net rod influence or light-level dependence for unique red that are sufficiently large and consistent to allow us confident interpretation. Further study will be needed to assess the generality of a possible rod yellow-bias on unique red. In any case, the issue is not crucial here because unique red

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judgments cannot be used to assess the opponentcolor models described in this paper. 2. The rod influence at unique blue and unique green tends to be dependent on the light level of the test field, as indicated by non-zero slopes in Fig. 1. These effects are most pronounced in the large/extrafoveal condition, as expected, but also appear in other conditions for some observers. For unique blue judgments, rod signals tend to provide a greenbias at higher light levels which appears generally similar in magnitude to the rod green-bias observed at unique yellow for both large/extrafoveal and foveal conditions. However, as light level is reduced the rod influence shifts toward that of a red-bias. This suggests that as cone signals become weaker relative to rod signals, there is an increasing rod red-bias that appears at unique blue but not at unique yellow. Some observers also appear to show a rod yellow-bias on unique green at higher light levels. There are two respects in which the direction of light-level dependence can be separated from the absolute direction (i.e. sign) of the rod influence on the respective opponent channel. First, the lightlevel dependence can involve a ‘crossover’ of sign of rod influence on an opponent channel, as already mentioned for unique blue judgments. Second, the light-level dependence is found even for observers whose sign of rod influence is opposite to each other. For example, for unique green in the large/extrafoveal condition, the rod influence is always a blue-bias for observer JB (open squares) and always a yellow-bias for observer RK (inverted filled triangles). Yet both observers show the same direction of light-level dependence: a shift toward a blue-bias with decreased light level. 3. For the extrafoveal conditions, the magnitude of rod influence tended to be as large or larger for the 7.6° stimuli than for the 2° stimuli. This confirmed our prior expectations but stands in contrast to previous findings of the opposite direction of size dependence of rod influence on unique-hue loci for stimuli smaller than 2° by Nerger et al. (1995) and Nerger, Volbrecht, Ayde, and Imhoff (1998). 4. The rod influences tended to be larger and more consistent in the extrafoveal conditions but, for some observers, they survived even with foveally centered 2°-diameter stimuli. Observer AN (filled circles) showed particularly strong rod influences in the foveally centered conditions for all three spectral unique hues, whereas observer MC never did. For unique blue, observers AN (filled circles) and JB (open squares) both showed some light-level dependence but opposite directions of dominant rod bias. Differences among observers in the magnitude of foveal effects could reflect differences of fixation stability or near-foveal rod density but we have no

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information about these characteristics for our observers. In any case, the lack of consistent rod effects for the foveally-centered conditions argues against explanations of either foveal or extrafoveal effects on the basis of systematic artifacts, such as prolonged effects of the bleaching light (also see Section 4). In summary, for large extrafoveal stimuli at lowest light levels (conditions in which rod signals are presumed to be strongest relative to cone signals) the rod influence on the spectral unique hues is generally to drive them to longer wavelengths. This means that rods produce a red-bias at unique blue, a blue-bias at unique green, and a green-bias at unique yellow under these conditions. At higher light levels, the most consistent rod effect is a green-bias at both unique yellow and unique blue. The rod influence on unique red is unclear from the present study.

3.2. E6aluation of models 3.2.1. Original cone-only models Eqs. (1) and (2), respectively, give the original coneonly forms of the Hurvich and Jameson (Hurvich, 1981) and of DeValois and DeValois (1993) opponentcolor models (hereafter referred to as the HJ and DD models) that were used for this analysis. (1)

r/gHJ = 1.66(L+ a1ROD)−2.23(M+ a2ROD) + 0.37(S+ a3ROD), y/bHJ = − 0.34(L+ a4ROD)−0.06(M+ a5ROD) + 0.71(S+a6ROD)

(3)

+ 25(S+ a3ROD), y/bDD = − 130(L+a4ROD)+95(M+ a5ROD)

r/gDD =90L− 115M+25S, y/bDD = − 130L+ 95M + 35S

3.2.2. Additi6e rod influences We can add rod signals into the HJ and DD models in various ways. For example, the rod signal can be added with different weighting to different cone terms, including the possibility of zero weighting (no rod influence) to one or more cone terms. Also, the rod signal can be added to a cone term either before or after multiplying by the cone-weighting coefficient. One general example is shown in Eqs. (3) and (4).

r/gDD = 90(L+ a1ROD)−115(M+ a2ROD)

r/gHJ =1.66L−2.23M+ 0.37S, y/bHJ = − 0.34L−0.06M + 0.71S

cones on the b/y channel. In the HJ model, M-cones contribute to the yellow side of the y/b channel, while in the DD model M-cones contribute to the blue side. Second, the two models assign different values to the cone weighting coefficients. In the DD model, the cone weights within each hue dimension sum to zero, resulting in a prediction of no net rod influence for some model variants. In the HJ model, the cone weights do not sum to zero, so all model variants predict some net effect of rod influence.

(2)

We evaluate both the HJ and DD models because they can make different predictions about the direction of rod influence on hue for at least two reasons. First, the models differ in the direction of influence of M

Fig. 2. Possible additive rod influences on red/green opponent-color functions. When the cone-only r/g function (solid line) is distorted upward by net positive rod influence (dotted line), the wavelengths of the cross-over points (corresponding to unique blue and unique yellow) move toward each other. When net rod influence is negative (dashed line), the cross-overs move away from each other. No additive rod influence can make both cross-overs shift in the same direction.

+ 35(S+ a6ROD)

(4)

For these and subsequent equations, L, M, and S represent the cone fundamentals of DeMarco, Pokorny, and Smith (1992), ROD represents the 1951 CIE scotopic efficiency function (Wyszecki & Stiles, 1982), and ai represents a rod weighting coefficient that can vary from zero to arbitrary positive values. No matter their specific form, every additive rod model can be reduced to r/g and b/y equations that each have a single overall (net) rod contribution term that can vary from zero in only one direction, either negative or positive. Thus, in any specific additive model, rod signals can distort the opponent-response function in only one direction, as determined by the sign of the net rod influence. This is illustrated in Fig. 2, which shows how the original HJ cone-only r/g model (solid line) is distorted upward by positive net rod signal (dotted line) or downward by negative net rod signal (dashed line). The magnitude of the distortion varies with wavelength and is determined by model-specific factors such as scotopic spectral efficiency and the absolute size of the cone and/or rod weighting coefficients. Thus, different specific additive rod models will produce different distortions of shape

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of the opponent-response function but, for any given model, distortion of all points will be in the same direction. A key implication of this property of additive rod models is that rods can either shift unique blue and unique yellow toward each other (dotted line in Fig. 2) or apart from each other (dashed line in Fig. 2) but can never shift them both in the same direction. This means that while additive models that provide net rod influence in the same direction as S-cone signals can describe the observed shifts of unique blue and unique green to longer wavelengths, such models must also predict a shift of unique yellow to shorter wavelengths, which is opposite to our empirical result. Thus, as a class, purely additive rod influence on color-opponent models can be rejected for the r/g hue dimension on the basis of our data.

for all three spectral unique hues. At short wavelengths, strong weighting of rod influence on the S-cone term drives the r/g functions toward a red-bias. At long wavelengths, the S-cone signal approaches zero, the rod influence associated with it therefore also approaches zero, and the stronger weighting of rod signals on the M-cone term compared with the L-cone term drives the r/g function toward a green-bias. The arithmetic arrangement of this model was also selected to allow each cone term to revert to its original cone-only form when either ai or ROD are zero, and not by considerations of best fit or substrate plausibility. Cone control of rod signal strength is shown for each cone term for consistency, even though the present data only require it on the S-cone term of the r/g function.

3.2.3. Non-linear rod influences To model rod-induced shifts of both unique blue and unique yellow to longer wavelengths, we need a statedependent, non-linear model that allows rod influence to operate in opposite hue directions in different spectral regions (i.e. a rod red-bias at unique blue and a rod green-bias at unique yellow). This constraint can be satisfied if rod influence on the S-cone term of the r/g function varies with the magnitude of S-cone signal. This would allow rod signals to exert a red-bias via S-cone pathways in the spectral region of unique blue, where S-cone efficiency and relative signal strength is high, and to exert a green-bias via M-cone pathways in the spectral region of unique yellow, where S-cone efficiency and relative signal strength is low. The present empirical data are not sufficient to determine a unique best-fit non-linear model that accomplishes these goals. However, an example of one model by which cone signals could continuously modulate rod influence is shown in Eqs. (5) and (6).

4. Discussion

r/gHJ =1.66L(1+a1ROD) − 2.23M(1 +a2ROD) + 0.37S(1+ a3ROD), y/bHJ = − 0.3L(1+a4ROD) − 0.06M(1 + a5ROD) +0.71S(1+a6ROD)

(5)

r/gDD = 90L(1+a1ROD) −115M(1 +a2ROD) +25S(1+a3ROD), y/bDD = − 130L(1+ a4ROD) + 95M(1 +a5ROD) +35S(1+ a6ROD)

(6)

When a given cone signal approaches zero, the rod influence through that cone term also approaches zero. With appropriate choices of values for ai (most importantly, a3, greater than a1 and a2), Eqs. (5) and (6) can describe the shifts to longer wavelengths we observed

4.1. Obser6ed rod hue influences Our empirical study of rod influence on unique-hue loci provides evidence of multiple rod influences on hue — a red-bias, a blue-bias and a green-bias. These influences are most pronounced for large, extrafoveal stimuli but are sometimes seen in other situations. In addition to occurring over different spectral regions, these rod hue influences appear to fall into two categories with respect to light-level dependence: the redbias and the blue-bias become stronger as light level drops while the green-bias does not change systematically with light level. These patterns of rod influence on hue are consistent, both in direction and in light-level dependence, with those found in other studies from our laboratory on rod influences on the hue-scaling of spectral lights (Buck, Knight, Fowler, & Hunt, 1998) and on the loci of spectral binary hues, which are perceptually equal combinations of two unique hues (Buck et al., 1997). In the latter study, rod influence changed most with light level for blue–green, which is composed of the two unique hues that changed most with light level in the present study. Rod influence changed least with light level for orange, which is composed of the two unique hues that changed least with light level in the present study. The agreement among all three studies highlights the robustness and generality of the present patterns of rod influence. We have also reported an analogous division of rod hue influences on the basis of temporal dynamics (Knight & Buck, 2000a,b). A modified probe-flash paradigm reveals that the rod green-bias is present at full strength as quickly as we can measure it, while the rod red- and blue-biases are slower to rise to peak magnitude. These studies, which involve measurement of full hue-scaling functions, show that the initial rod

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green-bias affects both shorter and longer wavelengths but that the slower rod red-bias counteracts it only at shorter wavelengths. The longer duration stimuli used for the present study apparently reveal a net combination of both slower and faster rod hue influences. The convergence of these lines of evidence leads us to distinguish the rod green-bias from the rod red-bias and rod blue-bias of the basis of temporal and light-level properties, as well as possible retinal substrate, as discussed below. The multiple rod hue biases we find (red, blue, and green) differ from those previously suggested by other investigators. At least three general patterns of rod influences on perceptual color opponency have been suggested, each coming from different sets of studies. 1. Rod excitation creates or increases perceived blueness. Richards and Luria (1964) and Trezona (1970) and Trezona (1974) concluded that rod signals increased perceived blueness in their color-matching studies. Hunt (1952) and Ambler (1974) concluded that rod signals created blueness in scotopic or dimly mesopic stimuli, independent of spectral composition. Stabell and Stabell (1994) and Buck (1995, 1997) concluded that rod signals exert a blue-bias in successive scotopic color contrast. The present results confirm that a rod blue-bias exists but shows that it is not the only rod hue bias. A possible but unconfirmed reconciliation is that the previously reported rod blue-bias represents a net influence in stimulus situations in which multiple hue biases can operate simultaneously (as with broad-band lights). It could be that in these situations the rod blue-bias is the strongest influence and/or that simultaneous green- and red-biases (such as we found for different spectral lights) tend to cancel each other leaving only the blue-bias apparent. 2. Rod excitation strengthens the b/y dimension relative to the r/g dimension. Stabell and Stabell (1975, 1976, 1979) and Frumkes et al. (1997) concluded from color-matching and hue-threshold studies, respectively, that rod activity either strengthens the b/y hue dimension, weakens the r/g hue dimension, or both. The present study does not disprove this hypothesis but shows that it is insufficient to explain the full range of rod hue biases. 3. Rod excitation strengthens both b/y and r/g hue dimensions asymmetrically. Volbrecht et al. (1993)Nerger et al. (1995) concluded from studies of the loci of unique hues that rod signals can exert both yellow- and green-biases. However, a more recent study by Nerger et al. (1998) of only the r/g dimension found results more like ours (i.e. a tendency toward rod red-bias at unique blue and rod green-bias at unique yellow) but only for stimuli much smaller than we used. This provides additional evidence for multiple rod influences on the r/g

hue dimension and suggests that the size-dependence of rod influences on hue may be more complex than revealed by the present study.

4.2. Implications of modeling The present analysis makes clear that simple additive models cannot account for the different directions of rod influence on the r/g hue dimension. The specific failure we observed implies that the rod influence that operates on the r/g hue dimension via S-cone pathways must be somehow eliminated when S-cone-signal strength approaches zero. Mathematically, this can be accomplished by opponent-color models in which rod and cone signals interact non-linearly in the manner shown in Eqs. (5) and (6). Functionally, these equations can be interpreted in different ways. One possibility is that rod signals do not combine directly with cone signals but instead serve to adjust the gain of cone pathways. Alternatively, rod and cone signals could combine in common neural pathways in a manner that cone-signal strength continuously modulates rod influence. Another possibility, not captured in Eqs. (5) and (6), is that cone signals could provide a binary gating function that would either block or pass rod signals but not otherwise alter their magnitude. Thus, rod signals on each cone term could combine (linearly or not) with cone signals after passing through a non-linear gating operator. The present data only require non-linear modeling of rod influence on the r/g hue dimension of opponentcolor models. Because the b/y hue dimension has only a single cross-over (unique green) the present tests could not reveal the type of non-linearity found for the r/g function. More stringent tests, such as comparison of model predictions with full-spectrum hue-scaling functions, will be needed to evaluate the linearity of rod influence on the b/y dimension.

4.3. Possible retinal substrates As we have previously suggested (e.g. Buck et al., 1998), a parsimonious way to account for the different rod hue influences is to suggest that they are mediated by two different retinal pathways, specifically the midget and small-bistratified ganglion-cell pathways, which are the most likely retinal substrate for color vision (Dacey & Lee, 1994). By this scheme, the rod green-bias we observe at unique yellow could be mediated by unbalanced weighting of rod signals in the two midget pathways (stronger for M-center than for L-center). The rod blue-bias we observe at unique green and the rod red-bias we observe at unique blue could both be mediated by rod signals combining with same sign as S-cone signals in small-bistratified pathways. This scheme assumes that small-bistratified ganglion cells

S.L. Buck et al. / Vision Research 40 (2000) 3333–3344

provide the S-cone (and rod) signals that ultimately enhance the blue side of the b/y hue dimension and the red side of the r/g hue dimension. Also, it assumes that midget ganglion cells provide the M- and L-cone (and rod) signals that enhance the green and red sides, respectively, of the r/g hue dimension. This is consistent with the receptor-percept linkages of both HJ and DD opponent-color models. Left unspecified by this scheme is the substrate for interaction of rod and cone signals in each of the two retinal ganglion-cell pathways. It is also unclear what causes the differences between the two pathways in light-level dependence of rod influence. An unanswered puzzle may lay at the core of both issues: Why does S-cone-pathway rod influence become stronger as absolute S-cone signals decrease with decreased light level for shorter wavelengths but become weaker as absolute S-cone signals decrease with increased wavelength at any light level? A possible clue is that, in the former situation, S-cone signals are strongest relative to M- and L-cone signals, while in the latter situation, S-cone signals are weak relative to Mand L-cone signals. Thus, cone-cone interactions may play a key role in regulation of rod influence. Small-bistratified ganglion cells would be a suitable substrate for such interaction because they receive S-cone input that is opposed by M- and L-cone input and because any light-level dependent rod influence they create would ultimately affect both r/g and b/y hue dimensions, which is consistent with what we observe.

4.4. Methodology and interpretation issues The comparison of measurements made under darkadapted and cone-plateau conditions has been long and widely used to study rod influences on color vision (e.g. Stabell & Stabell, 1975, 1976, 1979Nerger et al., 1995Nerger et al., 1998Frumkes et al., 1997). This methodology has been the only one available to study a wide range of stimulation conditions of rods and cones, especially with spectral stimuli. An inherent potential threat to the methodology is long-lasting distortions of cone influence on color vision during the cone-plateau measurements caused by the flash bleach. Such distortions could cause differences between cone-plateau and dark-adapted conditions to be misinterpreted as rod effects. Our lab has sought to minimize the likely extent of this confound by making cone-plateau measurements during periods of stable performance (typically 3 – 8 min post-flash), by seeking to find conditions in each study that show no difference between dark-adapted and cone-plateau conditions, and by using different judgment tasks across studies, when possible, to seek evidence of task-dependent distortions. In the present study, the most obvious bleaching distortions would appear as consistent hue biases across

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observers and across different stimuli testing the same hue bias. These biases might also be expected to be apparent in the foveal-centered conditions, where rod stimulation is minimized. There are no such ubiquitous hue biases in the present data. None of the foveallycentered conditions show hue biases that are consistent across observers. While, all observers show a green bias in the two extrafoveal conditions unique yellow conditions, none shows a consistent green bias in the corresponding unique blue conditions, and two of three show no bias for the corresponding foveal condition. Evaluation of the possibility of more subtle bleaching distortions will have to await application of different methodologies. An intriguing interpretation issue arises from the parallels between our reported rod hue biases and the Abney effect, hue biases that occur in photopic vision with decrease in saturation (Abney, 1910). Although there are variations in directions and magnitudes of hue change due to the Abney effect among observers and studies (e.g. Burns, Elsner, Pokorny, & Smith, 1984; Kurtenback, Sternheim, & Spillmann, 1984; Ayama, Nakatsue, & Kaiser, 1987), the parallel is strong enough to ask whether some or all rod hue effects are actually secondary to rod desaturation effects. Further study of the relationship between rod hue and saturation effects will be needed to resolve this issue.

Acknowledgements Supported by NIH grant EY03221 awarded to SLB.

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