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University Microfilms International 300 North Zeeb Road Ann Arbor, Michigan 48106 USA St John's Road, Tyler s Green High Wycombe. Bucks. England HP10 8HR 7902212
REA, MARK STANLEY INTENSITY DEPENDENT CHANGES IN HUE AND SATURATION AS DETERMINED BY A NEW METHOD.
THE OHIO STATE UNIVERSITY, PH.D., 1978
University Microfilms InternationalAnn , Arbor, Michigan 48106 INTENSITY DEPENDENT CHANGES IN HUE AND SATURATION
AS DETERMINED BY A NEW METHOD
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Mark Stanley Rea, B.A., M.A. , M.S.
* * *
The Ohio State University
1973
Reading Committee:
Dr. Carl R. Ingling, Jr. Dr. William Biersdorf Dr. Stanley W. Smith Dr. Karl Kornacker ______Advis Department of Bi( ACKNOWLEDGMENTS
I would like to thank my thesis advisor Professor Carl R.
Ingling, Jr. for the many insightful comments since the inception of these experiments as well as participating as a subject. I would also like to thank my other subject Mr. Phillip W. Russell and Dr. Brian H.-P. Tsou for their substantial assistance through out the period of work on this document.
I would also like to take this opportunity to express by sincerest thanks to Professor Stanley W. Smith for his invaluable assistance and friendship throughout my stay at the Institute for
Research in Vision.
My wife Mary deserves special thanks for her patience, wit, and charm without which this thesis could not have been completed.
ii VITA
October 5, 1950 ...... Born - Jacksonville, Florida
1972 ...... B.A., The Ohio State University, Columbus, Ohio
1972-1978 ...... Research Associate, The Institute for Research in Vision, The Ohio State University, Columbus, Ohio
1 9 7 4 ...... M.A., The Ohio State University, Columbus, Ohio
1977-1978 ...... Research Assistant, The Institute for Research in Vision, The Ohio State University, Columbus, Ohio
1978 ...... M.S,, The Ohio State University, Columbus, Ohio
iii TABLE OF CONTENTS
ACKNOWLEDGMENTS ...... ii
VITA ...... ill
LIST OF TABLES ...... v
LIST OF FIGURES ...... Vi
INTRODUCTION ...... 1
METHODS ...... 9
Apparatus and Calibration ...... 9
Conditions and Procedures ...... 13
Subjects ...... 21
RESULTS ...... 23
DISCUSSION ...... 72
APPENDIXES ...... 83
BIBLIOGRAPHY ...... 87
iv LIST OF TABLES
Table Page
1. Monochromatic Wavelengths and 16 Blocking Filters
2. Test Wavelength and Matching Primaries 22 for the Saturation Study
3. Data from Wavelength and Polarizer 24 Adjustment Methods
4. Primary Weightings for the Color Channels 48
5. Color Corrected Hue Coefficients 49
6. Data for the Saturation Study 63
v LIST OF FIGURES
Figure Page
1. Schematic diagram of the three channel, 11 haploscopic Maxwellian-view apparatus used in the experiment
2. Stimulus display 15
3. Constant wavelength contours (Subject Cl) 28
4. Constant wavelength contours (Subject PR) 29
5. Yellow and blue spectral hue coefficients 35 (Subject Cl)
6. Yellow and blue spectral hue coefficients 36 (Subject PR)
7. Unique green under saturated conditions as a 38 function of intensity (Subject Cl)
8. Unique green under saturated conditions as a 38 function of intensity (Subject PR)
9. Predicted constant wavelength contours 43 (Subject Cl)
10. Predicted constant wavelength contours 44 (Subject PR)
11. The saturated r-g and y-b spectral sensitivity 46 functions at 100 trolands
12. The spectral sensitivity of y-b relative to 54 r-g at seven intensities
13. The growth of color corrected hue coefficients 58 with intensity
vi Figure Page
14. The growth of the color corrected hue 60 coefficients with Intensity
15. Desaturation of unique hues with intensity 65 (Subject Cl)
16. Desaturation of unique hues with intensity 66 (Subject PR)
17. Corrected saturation data plotted with 71 comparable color corrected hue coefficients
vii INTRODUCTION
Lights of fixed spectral composition change in appearance when their intensity is changed. The most obvious change is, of course, brightness, but changes in both saturation and hue are also perceived.
The present experiments are concerned with the hue change called the
Bezold-Brucke effect but some data are presented regarding saturation changes as well. The Bezold-Brucke effect has been studied over the last 100 years (Peirce, 1877; Helmholtz, 1924; Purdy, 1931, 1937;
Judd, 1951; Boynton & Gordon, 1965; Jacobs & Wascher, 1967; Smith,
Porkorny, Cohen, & Perera, 1968; Coren & Keith, 1970; Cohen, 1975;
Nagy & Zacks, 1977). All studies show that red or green predominates at low intensities while yellow or blue predominates at high inten sities (Hurvich & Jameson, 1957). However, a completely satisfactory theory of the Bezold-Brucke effect has not been developed. The present experiment attempts to quantitatively relate the perceived hue and saturation of fixed monochromatic stimuli to intensity changes and to incorporate the finding into a comprehensive theory of color vis i o n .
Early thinking on the Bezold-Brucke effect centered around the
Young-Helmholtz theory of color vision (Boring, 1942). In regard to the Bezold-Brucke effect it was believed that there existed three univariant color channels, and differential adaptation of one
1 mechanism with intensity produced the perceived shift in hue. This hypothesis qualitatively accounts for hue shifts at long wavelengths.
For example, stimulation with a light of 610 nm at moderate intensi ties produces activation primarily in the red mechanism. Due to a compressive transfer function (e.g., Peirce, 1877) there is a gain of the green mechanism relative to the red mechanism as intensity is
Increased, thus, producing a shift toward more equal stimulation, or yellow. Besides the well-known awkwardness of trichromatic theory in accounting for hue sensations (Boring, 1942) this hypothesis is unsatisfactory in accounting for hue shifts of fixed wavelengths
In the violet region of the spectrum, as pointed out by Purdy (1931, p. 545). For violet wavelengths the adaptation hypothesis predicts a shift toward redness, but empirically there is a decrease in the amount of perceived red with increases in intensity. This notion has been more recently revived by Walraven (1961). Like Peirce he proposes a compressive function for the receptor mechanisms. In addition, he postulates a linear amplification of the chromatic signal from the blue mechanism to place the cross point of the red and blue fundamentals at 475 nm. This theoretical cross point then corresponds to the empirically found invariable hue. Because all
the receptor mechanisms hypothetically have the same compressive
function, the red and blue fundamentals are always equally stimu
lated at all intensities at 475 nm and, therefore, there would be no predictable shift in hue. Despite the apparent graphical agreement of Walraven’s theory and the empirical hue shifts for
spectral and nonspectral colors (p. 1113, Fig. 1) his interpretations are still subject to the criticisms outlined above and, in addition, to the following criticisms. First, there is an implicit assumption throughout the paper that the fundamental curves correlate in some way with hue. He states, for example, "In the purple region of the color diagram color perception is governed by the interaction of the red and the blue system, because there the green system has a
/ negligible sensitivity." If it is true then that purple hues are based upon the red and blue fundamentals without green, it predicts that the wavelengths below the hypothetical cross point at 475 nra
(i.e., in the violet region of the spectrum) also look blue-red and not look blue-green (at least to 440 nm where the red and green fundamentals again cross). Further, like all trichromatic schemes it is difficult to account for the four unique hues. Most important ly, however, to account for the empirical data presented by Purdy on hue shift Walraven arbitrarily shifted part of his theoretical curve along the wavelength axis to "fit" the data. The displaced short wavelength segment of his theoretical curve is exactly opposite the general predictions based upon the trichromatic
scheme he discussed in the text. He lays out carefully (p. 1114) why differential adaptation of the fundamental curves produces the hue shift in the orange region of the spectrum to shorter wave
lengths (as described above). But if this general scheme is true
then very short wavelength lights should produce more relative
growth in the red mechanism than in the blue mechanism, and conse
quently, there should be a perceived shift toward red with intensity.
As was noted above, this is opposite of the empirical findings (e.g., Purdy) and is even opposite the "fitted" theoretical curves he presented.
A more likely hypothesis accounting for hue shift (Purdy, 1931;
Judd (1951); Hurvich & Jameson, 1955, 1957) is based upon the color opponent thoery of Hering. Specifically two color channels, yellow versus blue (y-b) and red versus green (r-g), produce different relative outputs at different intensities with r-g dominating at low intensities and y-b at high intensities. This general theory is a more parsimonious hypothesis than that proposed by Peirce and
Walraven in that perceived hue shifts are based upon simple changes in the dominance of the two color channels. This opponent channel hypothesis is consistent with the data without special additional assumptions and is also consistent with perceptual reports.
Judd (1951) and Hurvich & Jameson (1955) showed some 25 years ago that a relative shift in the preponderance of the y-b color channel with respect to the r-g could predict the hue shift data presented by Purdy, Later Boynton and Gordon (1965), Luria (1967), and
Jacobs and Wascher (1967) showed that color naming procedures, some of which rely on the fundamental assumptions of Hering*s theory, were also consistent with hue shift data; that is at higher intensi ties observers typically give more yellow and blue responses to spectral lights. Finally, the electrophysiological data first reported by De Valois and his coworkers (1966a, 1966b, 1968, 1971) have demonstrated that there is a physiological correlate in the lateral geniculate nucleus to the opponent stage proposed by Hering over 100 years ago. They also report (1968, p. 539) that there is no known univariant color channel with narrow band spectral sensi tivity that would be consistent with the trichromatic hue theory proposed by the Young-Helmholtz theory. All these experiments point strongly to an opponent theory of color vision as a starting point for an explanation of the Bezold-Brucke effect.
To account for the dominance of y-b over r-g at high intensities
Judd proposed a nutritive imbalance between the two channels. He supported his notion by pointing out that prolonged viewing of a light also induced a hue change away from red or green. His explana tion of Purdy’s data was based upon the free viewing conditions in the experiment. He postulated that a negative afterimage from the bright field interacted with the perception of the dimmer field with changes in fixation. Hypothetically, the higher relative adaptation of the r-g system produced a dominance of the y-b in perception of the hues. One problem with this theory which is immediately obvious is why red and green hues ever dominate at threshold and low intensities (Bouman & Walraven, 1957; Ingling,
Schreibner & Boynton, 1970). Certainly if there was a simple nutritive preponderance of the y-b channel then it should manifest itself at all intensities.
Hurvich and Jameson, on the other hand, proposed a mechanism of differential amplification with intensity of the two color channels to account for the perceived hue change. Thus, the y-b channel grows at a faster rate than the r-g channel. As pointed out by
Coren and Keith (1970, p. 559) support for the amplification hypothesis rather than the nutritive imbalance hypothesis comes from color naming (Boynton & Gordon, 1965; Jacobs & Wascher, 1967;
Luria, 1967). Only one patch of light is presented in color naming
procedures. Because the observed Bezold-Brucke effect is not con
founded by changes in fixation and, thus, negative afterimages,
Judd's hypothesis seems untenable.
Recent evidence by Cohen (1975) also lends indirect support for
the amplification hypothesis. Cohen demonstrated that the intensity dependent changes in hue, i.e., the Bezold-Brucke effect, were dif
ferent than time dependent changes in hue that Judd used to support his nutritive hypothesis. This, of course, does not entirely
eliminate the possibility that there are two adaptational processes,
(e.g., Cohen), one for prolonged viewing and one for intensity, but
the nutritive hypothesis certainly becomes more cumbersome. Indirect
support for a neural amplification has also been recently given by
Coren and Keith (1970). They showed that the Bezold-Brucke effect
was not a pigment phenomenon but rather linked with neural processes
in the visual system. They showed that surround conditions rather
than the physical intensity of the light per se determined the
perceived hue changes. While this again does not directly eliminate
the nutritive hypothesis as proposed by Judd it does seem to indicate
that neural interaction and amplification processes, rather than
nutritive processes at the site, are directly involved in the
Bezold-Brucke effect. Finally, De Valois (1966) has documented that
the y-b color channel grows at a faster rate than the r-g with
intensity, thus the amplification hypothesis of Hurvich and Jameson
seems much more likely. Very recent work In our laboratory has suggested that the
Bezold-Brucke effect may not be based upon simple differences be tween the two channels as proposed by Judd (1951) and by Hurvich and Jameson (1955). Rather, Ingling, Tsou, Burns, and Gast (in preparation) have argued that each receptor mechanism feeding the channel may have different transfer functions. Thus, rather than simple channel amplification as proposed by Hurvich and Jameson there may be individual receptor amplifications which give a composite or average amplification of the channel. Hypothetically then the yellow, the blue, the red, and the green responses may all grow at different rates with intensity.
The present experiments were designed to psychophysically explore this last hypothesis for the Bezold-Brucke effect and to relate the data to a comprehensive theory of color vision. Two methods, one traditional and one recently developed in our laboratory, were em ployed to study the effects of intensity on perceived hue. One major modification of these two methods was employed; namely, haploscopic presentations were used to avoid known chromatic induc
tion effects produced at the retina (Cornsweet, 1970; Coren & Keith,
1970). While cortical induction effects definitely exist, these effects are smaller than retinal induction effects (Wright, 1946, p. 216).
Three assumptions are made in this experiment: first, that observers can estimate hue independent of saturation and bright ness; second, haploscopic hue matches may be used to quantify the
Bezold-Brucke effect; third, hue is based upon some cortical combination of the outputs of two color channels. The first and third assumptions have precedence; (e.g., Judd, 1951; Hurvich and
Jameson, 1955; Boynton and Gordon, 1965). The second assumption has also been made by Cohen (1975). METHODS
Apparatus and Calibration
A three channel Maxwellian-view optical apparatus was employed for all conditions and experiments; see Figure 1.
The light source was a single tungsten-halogen projector lamp
(Sylvania, FCS 150W-24V). Fixed density, Wratten 96 neutral density filters in the collimated portion of the beams and/or Inconel neutral density wedges at planes conjugate to the source controlled intensity in the experiment. Channels 1 and 3 contained linear polarizers, perpendicularly oriented. After the polarized channels were combined at a beam splitter, a linear analyzer in the common beam could be rotated by the subject to proportion the amount of light coining from
the two channels without affecting the total intensity. For some
conditions the polarizer in channel 1 was removed.
All intensity calibrations were done at the exit pupils. This
technique avoids tedious wedge and filter calibrations and more
importantly eliminates the possibility of not detecting changes in
the apparatus. An EMI 6094 photomultiplier tube^ was used to measure
the set light intensities; the photocurrent was measured with a
Keithley picoammeter (Model 440). The photomultiplier tube is
^ The tube is periodically calibrated by professor Ingling.
9 Figure 1. Schematic diagram of the three channel, haploscopic
Maxwellian-view apparatus used in the experiment.
Symbols: description
DI: dental impression AP: artificial pupil AL: achromatizing lens L: lens A: aperture M: mirror AN: analyzer (variable polarizer) BS: beam splitter BF: blocking filter P: polarizer IW: interference (wavelength) wedge W: circular, continuous, neutral density (Inconel) wedge SH: ryclonotne shutter NDF: Wratten 96 neutral density filters WC: water cell containing solution of HjO + CuSO^ CM: cold mirror S: tungsten-halogen projector lamp 11
W C T l !
I i
11^ NDF NDF NDF EE1
IW I, 1W
Ch 2
I I 4 - 4 BF
n n AI I' * 1 * I '
P BF BS A ! i, A ■I i •i •l AN ti II if II il
i S > « AL * J AL A P v 'I r AP
M
Figure 1 12 linear for photocurrents less than two microamperes (Ingling, Tsou,
Gast, Burns, Emerlck and Riesenberg, 1978). Absolute calibrations were determined by comparing the candle power produced at the exit pupil to that of a standard traceable to the National Bureau of
Standards. The candle power measurements give the retinal illuminance directly in trolands, because one microcandle in the plane of the pupil will produce a retinal illuminance of 1 troland. The area of 2 the exit pupils in the present experiment were tr nm .
All intensities for the experiment were determined by setting the exit pupil candlepower with the photomultiplier tube except the equal luminance, 100 troland spectrum employed for the Purdy method
(see below) which was determined by flicker photometry (Graham,
1965, p. 268-270). For the flicker matches channels 1 and 3 were successively substituted to the subject's right eye by counter phased cyclonome shutters. The shutters were driven by an Inconix
6210 preset control. Variable flicker speeds were obtained by subjects with a variable external time base apparatus in conjunction with an Iconix 6255 fixed time base (Gast, 1977).
Three Schott Veril S-200 continuous running interference filters
(half bandwidth 10-15 mm) and appropriate blocking filters were employed in the experiment to present monochromatic stimuli. The wedges were calibrated prior to the collection of data using a mercury-cadmium line source. These calibrations agreed well with those supplied by the manufacturer. 13
Conditions and Procedures
Two procedures were employed in the present experiment to measure the Bezold-Brucke effect.
One method was very similar to that first employed by Purdy (1931) and subsequently others (e.g. Boynton and Gordon, 1965). With this method a bisected circular field is usually presented monocularly.
The test half of the field contains a fixed wavelength at some fixed intensity. The wavelength in the other half may be varied by the subject while the luminance is kept constant. The subject's task is to match the hue (i.e. ignore saturation and brightness differences
that might exist in the two fields) of the fixed side by adjusting
the wavelength of the other side. On subsequent trials the intensity of one field is changed while the other is kept constant, and new hue matches are obtained.
The "wavelength adjustment method" used in the present experiment was identical to that employed earlier except the two half fields were presented separately to each eye of the subject (Figure 2).
Thus* on a particular trial the subject was instructed to match the hue of the fixed stimulus in the left eye (top half of the display) 2 by varying the wavelength presented to the right eye while a con
stant luminance was maintained. The experimenter adjusted an
Inconel wedge in channel 1 to keep the luminance constant while the
subject changed wavelengths (see Appendix A for details). The
^ See Table 1 14
Figure 2. Stimulus display. With both methods the top half of the display contained the test wavelengths; these were always presented to the subject’s left eye through channel 2. With the wavelength adjustment method the bottom half contained a 100 troland variable spectrum; these were always presented to the subject's right eye through channel 1. With the polarizer adjustment method the bottom half contained a 100 troland mixture of two appropriate unique hue primaries; these were always presented to the subject's right eye by a combination of channels 1 and 3. 15
Test
Variable Spectrum or Primary Mixture
Figure 2 16
Table 1
Monochromatic Wavelengths and Blocking Filters
Test wavelengths Blocking in channel 2 filters
420 nm B&L 90-1-540 t« 450 480 It II 490 tl 500 It 520 540 Wratten 12 560 II 580 CS-4-102 610 it it 630 •i 650
Wavelength adjustment method
Spectral range Blocking in channel 1 filters
570-700 nm Wratten 15 530-590 Wratten 12 415-540 B&L 90-1-540
Polarizer adjustment method
Channel 1 primary Blocking filters
680 nm Wratten 25 515 (subject Cl) Wratten 55 510 (subject PR)
Channel 3 primary Blocking filters
580 nm Wratten 15 683 B&L 90-1-540 480 it 17
wavelengths set by the subject were recorded by the experimenter.
Subjects made three wavelength settings (trials) at each test wave
length during three separate sessions.
The other method employed was recently originated in our labora
tory and was first used in a series of experiments designed to obtain
the spectral sensitivity of the opponent channels (Ingling, Russell,
Rea and Tsou, 1978, in press). With this method two monochromatic, 3 unique hue primaries are combined into half of a bipartite field, and
this combination is hue matched to a test monochromatic wavelength in
the other half. The combination of primaries are mixed with two
orthogonal polarizers behind a variable analyzer. The proportion of
the two primaries, that is the perceived hue of the mixture, may be changed without significantly changing the overall luminance.
The "polarizer adjustment method" used in the present experiment was identical to that described above except the half fields were presented haploscopically. The subject was presented test wavelengths of different intensities in the left eye and appropriate unique hue 4 primaries in the right eye (Figure 2). The unique hue primaries were identical to those used earlier by Ingling, et al. (in press)
3 In order to have sensible data it is important to have two unique hues as primaries. Since all hues are combinations of the outputs from the two color channels and since the unique hue primaries in dependently produce output from each color channel, then combinations of two appropriate unique hue primaries should duplicate all hues. Thus, when a hue match is made between the test wavelength and the mixture, the proportion of the two primaries in the mix is a direct Index of the relative activation of the two color channels produced by the test.
4 See Table 1. with two exceptions. 510 nm was slightly too short for subject Cl as unique green, and, therefore, he used a 515 run unique green as a primary throughout the experiment. Also the 480 nm primary was slightly too violet for both observers. This error was small and not noticeable when combined with the red primary but was quite apparent when combined with a green primary. As pointed out by Ingling, et al.
(in press) when the primaries were mixed the small amount of red in the 480 nm required a large amount of green to cancel it. For this reason the blue primary was moved to 483 nm in order to avoid a large error in the estimation of the amount of green necessary to match a blue green test. The subject's task was to adjust the analyzer until a hue match was obtained between the test wavelength in. the left eye and the mixture in the right eye. The angle of the analyzer set by the subject was recorded by the experimenter. Sub jects made three analyzer settings (trials) at each test wavelength intensity during three separate sessions. After completing a series of trials the retinal illuminance of the median matching primaries in the mix channel were separately measured and recorded.
With both methods subjects were instructed to make equal hue judgments when the two hemifields were approximately posiitoned as in Figure 2. Subjects viewed the two hemifields without the aid of fixation or fusion points. While this seemed to be somewhat dif ficult at the start of the experiment, subjects quickly "learned" to keep the two fields positioned for several trials without dif ficulty. 19
Free viewing was allowed for both methods. Subjects were, however, instructed to avoid staring at the two fields for very long periods of time before making a hue match. This was done to minimize extensive adaptation. This method seemed acceptable since Cohen (1975) found no effect of exposure duration up to two seconds for Bezold-Brucke shifts.
With both methods the same test stimuli of fixed wavelengths and intensity were presented as independent variables in the top half of 5 the display (i.e. to the subject's left eye). Each test wavelength was presented at intensities of approximately 3, 10, 30, 100, 300, and 3000 trolands. Intensity levels were changed by inserting or removing fixed Wratten 96 filters into the channel 2 beam. (Intensi ties differed slightly between wavelengths; these are listed in
Table 3.) Intensities were presented in increasing order from 3 to
3000 trolands for a test wavelength in order for readaptation to occur quickly. (Since both methods are matching procedures and show little variability, counterbalancing or randomization was unnecessary).
The red and the green primaries and the yellow and the blue primaries were normalized in terms of the effects on their respective color channels by a hue cancellation procedure (Hurvich and Jameson,
1955). In the mixture (Channel 1 + Channel 3) presented to the right eye the 100 troland red or yellow primary used in the experiment was set in channel 3 and combined with the opponent wavelength in
^ See Table 1. 20 channel 1 (after the polarizer in channel 1 was removed). By adjusting the intensity of channel 1 the observer canceled the opponent hue in channel 3. The observer also made flicker matches between the opponent pairs. The median setting from the two pro cedures was obtained and their ratio used to scale the paired opponent primaries.
The polarizer adjustment method was also employed in a small study to measure the desaturation of a unique hue test wavelength as a function of intensity. The rationale and methodology were similar to that employed to measure the Bezold-Brucke effect described above.
Opponent unique hues were combined in the mixture channel (right eye) and one of the unique hues in the mixture channel was presented in the test channel (left eye). The subject made a saturation match between the two fields by rotating the analyzer in the mixture channel. A small amount of one unique hue added to its opponent unique hue serves to desaturate the latter without seriously affecting its dominant wavelength.^
Two test fields of identical wavelengths but different intensities have different degrees of saturation; the brighter field is always equally or less saturated. In order to obtain an estimate of the intensity dependent desaturation produced in the unique hue test
This is not strictly true when unique red and unique green are com bined in various proportions due to the Abney effect (see Larimer, Krantz and Cicerone, 1975). However, over the intensity range used here to produce desaturation the Abney effect was noticeable but not large enough to make the estimate impossible* 21 wavelength the mixture field had to be of equal or lower intensity.
Naturally when both the test and the mixture channels are at the
same intensity, no desaturant has to be added. Lowering the intensity
of the mixture or increasing the intensity of the test requires in
creasing the amount of the desaturant necessary to make a saturation match to the test.
All measurements were made in this study with respect to the 100
troland match between the test and the mixture fields. Three sets of
saturation matches were made when the mixture field was lower than the
test at 100 trolands and three saturation matches were made when the
test field was higher than the mixture at 100 trolands. One was made when both were at 100 trolands. Three to five settings were made at each intensity. After completing a series of trials the
retinal illuminance of the median matching primaries in the mix
channel were separately measured and recorded. Table 2 lists the
test wavelengths and the primaries used to make the matches.
Subjects
The data were obtained from two subjects experienced as psycho
physical observers. Subject Cl and PR have been documented in an
earlier study as Class II color normals (Ingling, ejt al_., in prepara
tion) . Both observers were nearly emmetropic- Subject Cl was 42
years old and Subject PR was 25 years old. 22
Table 2
Test Wavelength and Matching Primaries for the Saturation Study
Test Wavelength Mixture Wavelength (nm) (Ch 1 + Ch 3) (nm) 480 480 + 580* 580 480* + 580 515 (Subj ect Cl) 515 + 680* 510 (Sub j ect PR) 510 + 680* 680 515* + 680 (Subject Cl) 680 510* + 680 (Subject PR)
Note: Blocking filters for the test and the primary wavelengths may be seen in Table 1.
* The desaturating wavelength RESULTS
The basic data are presented in Table 3 for both subjects. Each cell represents the median of three session medians. Each session median was typically based upon three trials except when subjects' first two settings were identical. Thr retinal illuminances of each test wavelength are given in log trolands.
Figures 3 and 4 are plotted results from the wavelength adjust ment method for subjects Cl and PR, respectively, In this figure the independent variable, log retinal illuminance, is plotted on the ordinates. This was done to present data in a familiar manner similar to that given by Purdy (1937).
The data for both subjects are similar. For example, at the spectral extremes there is a tendency for both subjects to shift the matching wavelengths toward the center of the spectrum with increased intensities. Since less red is seen by observers with normal color vision toward the center of the spectrum, one may infer from these contours that the subjects perceive a shift away from red as the in tensity increased at both spectral extremes. In the center of the spectrum there is a similar trend away from green with increased intensity. This is demonstrated by the "fanning out" of the contours from around 500-520 nm at the lowest intensities with Intensity increments. These results confirm the classic findings, namely there
23 24
Table 3
Data from Wavelength and Polarizer Adjustment Methods
Subject: Cl Subject: PR Test Log Median Median Median Median Wavelength Trolands Wavelength Blue or Yellow Wavelength Blue or Yellow (nm) of Test Match (nm) Hue Coefficient Match (nm) Hue Coefficient * * --- 420 .21 .617 * .683 .82 408 .632 .670 1.4 412 .677 414 .670 2.0 420 .722 420 .670 2.5 431 .889 425 .670 3.2 488 .999 434 .736
450 .31 416 .675 425 .779 .89 424 .757 428 .795 1.5 431 .795 438 .808 2.0 442 .893 449 .848 2.6 480 .979 463 .894 3.1 489 .999 472 .931 * * 3.6 491 .999 476 .946
480 .46 489 .765 490 .701 .95 488 .755 490 . 664 1.5 485 .939 485 .664 2.0 484 .979 484 .861 2.6 485 .986 483 .984 3.1 485 .986 483 .991 3.7 485 .986 483 .991
490 .48 492 .281 499 .262 .95 494 .261 496 .288 1.5 494 ,306 495 .412 2.0 492 .328 494 .395 2.5 491 .359 491 .581 3.1 492 .421 491 .713 3.6 490 .489 489 .738
500 .48 500 .065 506 .168 .95 501 .084 505 .133 1.5 501 .106 505 .004 2.0 501 .115 512 .004 2.5 501 .135 511 .064 3.1 500 .142 506 .214 3.6 500 .171 499 .262 25 Tabic 3 (continued)
Subject: Cl Subject: PR Test Log Median Median Median Median Wavelength Trolands Wavelength Blue or Yellow Wavelength Blue or Yellow (nm) of Test Match (nm) Hue Coefficient Match (nm) Hue Coefficient
520 .49 509 .015 520 .007 .96 510 .020 513 .007 1.5 511 .014 521 .007 2.0 520 .014 530 .071 2.5 530 .213 535 .183 3. 1 532 .287 538 .227 3.6 530 .314 539 .267
540 .52 510 .009 539 .369 .98 511 .009 539 .369 1.5 519 . 046 539 .325 2,0 534 .220 542 .417 2.5 547 .397 546 .453 3.1 553 .500 548 .487 3.6 560 .569 548 .520
560 .53 553 .397 555 .540 .98 550 .483 558 .540 1.5 551 .519 559 .576 2.0 560 .551 560 .573 > 2.5 566 .634 560 .609 3.0 570 .690 560 .624 3.6 570 .721 560 .624
580 .52 582 .994 579 .998 .99 585 .989 580 .998 1.5 589 .976 580 .996 2.0 586 .962 578 .998 2.5 588 .968 578 .999 3.1 588 .975 577 .999 3.6 589 .967 577 .998
610 .57 642 .154 639 .179 1.0 630 .258 622 .223 1.5 619 .349 620 .283 2.0 615 .449 614 .433 2.5 610 .536 604 .616 3.0 610 .579 596 .729 3.6 609 .613 586 .908 26 Table 3 (continued)
Subject: Cl Subject: PR Test Log Median Median Median Median Wavelength Trolands Wavelength Blue or Yellow Wavelength Blue or Yellow (nm) of Test Match (nm) Hue Coefficient Match (nm) Hue Coefficient * * 630 .52 .006 660 1.0 692 .024 661 .001 1.5 649 .079 650 .091 2.0 634 .157 639 .210 2.6 625 .271 620 .487 3.1 622 .366 605 .684 3.6 619 .421 590 .876 * * * 650 .48 * .006 * .96 .006 1.5 689 .012 691 .019 2.0 649 . 120 650 .125 2.6 632 .168 619 .346 3.1 630 .198 604 .637 3.6 621 .271 591 .851
* Sufficient retinal illuminance was not available to make a hue match. 27
Figure 3 (subject Cl) and Figure 4 (subject PR). Constant wave length contours. The figure shows empirically determined hue contours for 12 test wavelengths. The abscissas correspond to the 100 troland spectrum in the right eye match field. The ordinates correspond to the test wavelength intensity in the left eye. The contours indicate the shift in hue with intensity; at high intensities there is a shift toward yellow or blue and at lower intensities there is a shift toward red and green. Los Trolands - 1 2 - 3 4 T 4 - i i i 5 50 5 60 650 600 550 500 450 t i i ( i i i i > » l i iii i« i|i i i i i -sr CO o © o Figure 3 (subject CX) (subject 3 Figure aeegh (nm) Wavelength CM U1 o 420 5 50 5 60 650 600 550 500 450 o o u"l o o 00 © ov o r ■ tr> <■ sr • • I • * I I I 1 4 t • • Figure 4 (subject PR) (subject 4 Figure (nm) Wavelength * • > to m V> o There are, however, several differences between the behavior of the two subjects worth noting. In the violet region of the spectrum there is a stronger shift toward blue (approximately 480 nm) with intensity increments for subject Cl than for subject PR. Conversely, subject PR shows a marked shift toward yellow (approximately 580 nm) with intensity in the orange region of the spectrum which is not nearly so pronounced for subject Cl. This would indicate a difference between the y-b color channels for the two subjects. Specifically, subject Cl appears to have a blue mechanism which dominates the red mechanism more quickly with intensity than it does for subject PR, Subject PR seems to have a similar relationship between the yellow mechanism and the red mechanism not shown by subject Cl. Further, subject Cl appears to have a blue mechanism that grows more quickly than his yellow mechanism with intensity; with subject PR the converse is true. This conclusion seems warranted despite the potential scal ing differences between the short and long wavelength regions of the 7 spectrum , since the two subjects showed complementary large growths Figures 3 and 4 show that the relative shift in wavelength in the center of the spectrum is less than at the extremes. This does not necessarily mean that there is a smaller shift in the perceived hue in these regions. As has been pointed out by many investigators, the wavelength discrimination at the spectral extremes is poorer than at the center (see, for example, Judd, 1932). Therefore, a small shift in perceived hue at the spectral extremes would be expected to produce a relatively larger shift in a matching wavelength than it would produce in the center of the spectrum. Since the wavelength abscissa is not scaled in terms of equal jnds, it is difficult to ascertain the absolute magnitude in perceived hue shifts for different test wavelengths in this type of plot. 31 In different parts of the sepctrum. Informal inquiries while the experiment was progressing also supported these conclusions. Another difference between subjects occurred for the test wavelength 500 nm. Subject Cl shows what might be considered an invariant point; whereas subject PR shows a shift toward longer wavelengths and then back to shorter ones. The nonmonotonic behavior of subject PR was quite con sistent with his responses and his informal reports while the experi ment was progressing. This was the only test wavelength where a clear nonmonotonic behavior was evidenced for either subject. One slightly annoying feature of the data revealed in these plots is the discrepancy between test wavelengths and matched wave lengths at 100 trolands. (Cohen (1975) also mentioned that there were discrepancies at equal luminance levels but not how large.) The matched wavelengths should be identical to the test wavelengths at this intensity. At several wavelengths there was, in fact, little or no discrepancy between test and match wavelengths for both sub jects. However, there were also some relatively large differences. The largest disagreement was 12 nm for subject PR for the 500 nm test wavelength. Importantly, however, subject Cl showed only a 1 nm difference at this wavelength. Thus, many of the discrepancies between match and test wavelengths were not repeated by both subjects. Each subject's matches were fairly consistent and the large dis crepancies could not be accounted for by imprecision in their settings. Differences between calibrated and actual intensities and wavelengths would, of course, be expected to contribute to these mismatches and, perhaps, these existed in several regions of the 32 spectrum. But by visual inspection of certain wavelengths prior to the experiment these differences were small or nonexistent. Further, if calibration of the wedges was a problem, one would expect subjects to be more consistent in their mismatches. A casual test comparing the subjectst two eyes was done at test wavelengths where the dis- crepancies were large. Specifically, the subject inspected the two fields successively with one eye after he had made a haploscopic match. In some instances there was a definite difference in the perception of the two fields. This would indicate, then, that the subjects' eyes differed slightly in their color information processing. Since we are primarily interested in the relative shift in hue with intensity, this effect was not pursued further in this experiment, although this is a very interesting effect and merits closer examina tion. As pointed out by Hurvich and Jameson (1955, 1957) the chromatic response (i.e. hue) at any wavelength may be quantified as the ratio of one color channel response to the total chromatic response. This ratio may be conceived simply as the percent of the color signal determined by'a given color channel. Since, according to color opponent theory, every hue is a combination of two biphasic chro matic responses and since the polarizer adjustment method combines two approximate unique hues (i.e. ones producing output from only one channel), then the relative amounts of the primaries used to match the test wavelength should give the hue coefficients directly. 33 g Table 1 lists hue coefficients for the y-b system. (The r-g hue coefficients are, of course, redundant since they are simply 1.0 minus the values entered in the table.) Figures 5 and 6 are hue coefficient functions for the y-b system for subjects Cl and PR, respectively. Each function represents different intensities. Due to slight differences in the spectral transmission of the fixed Wratten filters in the test channel, the connected points actually differ slightly in intensity so that a given function is only approximately true for the retinal illuminance presented in the figure. Dashed lines are inferred; these will be described below. Since the hue coefficient functions presented are for the y-b system, they reach maximum values at the unique blue and unique yellow points. Minima are, of course, at the unique green and unique red points. One can see from inspection of these two figures that at most wavelengths the amount of yellow and blue increases with intensity. This qualitatively confirms the classic findings (see Hurvich and Jameson, 1955) as well as those presented for the wavelength adjust ment method described above; at the higher intensities the spectrum is dominated by yellow and blue and at low intensities it is dominated by red and green. One very interesting discovery with this method was the confirma tion of Richards (1967), Jacobs and Wascher (1967), and Ingling, et al. (in preparation) that unique green shifts with intensity. Class II See Appendix B. 34 Figure 5 (subject Cl) and Figure 6 (subject PR). Yellow and blue spectral hue coefficients. The figures show empirically determined hue coefficients for two subjecLs at s e v e r , different intensities. The abscissas correspond to the wavelength of the test stimulus in the left eye. The ordinates correspond to the yellow or blue hue coeffi cient determined by the unique hue primary mixtures in the right eye. The functions indicate the amount of yellow and blue in the spectrum at different intensities. Comparison of the functions indicates a change in the amount of yellow or blue with intensity; for a given wavelength more yellow or blue is seen at high intensities and corre spondingly more red or green is seen at low intensities. r Legend: ■ « .5 log trolands X- 1.0 log trolands As 1.5 log trolands 2.0 log trolands A- 2.5 log trolands • ■ 3.1 log trolands O ■ 3.6 log trolands Hue Coefficient 1.0 1 Legend: log trolands log trolands log log trolands trolands log trolands log trolands log trolands log trolands log 7 / aeegh (nm) Wavelength iue (subj PR) 6 ect Figure O' u> observers like subjects Cl and PR have characteristically long unique green points at low intensities. On the low intensity plots (Figures 5 and 6) this is indicated by minima near 540 nm. As the intensity increases Class II observers* unique green shift to shorter wave lengths. This can be seen clearly by comparing the 100 troland function with the 10 troland function for observer Cl in Figure 5. Some of the other shifts are not so obvious due to the coarse sampling of test wavelengths in the critical region (i.e. only at 500 nm, 520 nm and 540 nm). Fortunately, however, both observers have been measured for their unique greens under comparable condi- « tions. Although these original plots (Ingling, et aT., in prepara tion) were determined by a different technique, the unique green functions under saturated conditions have been reproduced in Figures 7 and 8 and were used to roughly determine the unique hue points on the abscissa for different intensities. The dashed lines in this region connect the empirical points measured in this experiment with the estimated unique green points. Combining the data from these two experiments provides estimates of the hue coefficient functions at different intensities. It should be noted that Ingling, et al. discovered that many measurements had to be taken to determine the unique green at low intensities. Conversely, at high intensities this determination was very easy. This finding is supported by the data presented here. At low intensities there is very little perceived yellow or blue from 500 nm to 540 nm. This, of course, would lead to a great deal of variability since at low intensities in this region of the spectrum Figure 7 (Subject Cl) and Figure 8 (Subject PR). Unique green under saturated conditions as a function of Intensity. The figur shows the change in unique green, under saturated conditions, as function of log retinal illuminance as determined by Ingling, et. (in preparation). The figure was replotted with permission from the author. Wavelength (nm) Wavelength (nm) 510 520 540 530 550 570 550 570 560 520 560 510 530 1 1 iue (ujc Cl) (subject 7 Figure iue (ujc PR) (subject 8 Figure o Trolands Log Log Trolands Log 2 2 3 4 3 40 green dominates strongly. Likewise, at high intensities the wave length range where no yellow or blue is perceived is appreciably narrower. For example, both observers reliably saw blue at 500 nm and yellow at 520 nm at high intensities. The empirically determined hue coefficient functions are very useful in making several predictions. They may be used to predict the wavelength adjustment results presented in Figures 3 and 4. Be cause the hue shifts plotted in these figures were determined relative to a 100 troland spectrum, the 100 troland hue coefficient function was used as the reference to predict hue shifts. Each empirical point plotted in Figures 5 and 6 corresponds to a particular hue coefficient determined at some particular test wavelength intensity match. The comparable hue coefficient at 100 trolands for each match may be obtained by simply projecting a line parallel to the abscissa from the point until it intersects the 100 troland hue coefficient function. (The 100 troland function was extrapolated (dashed lines) to make predictions in certain regions of the spectrum.) At the intersection projections to the abscissa give the predicted wavelength an observer would see at 100 trolands having the same hue coefficient. Plotting this predicted wavelength against the intensity of the test wavelength where the polarizer match was made determines the plotted points and the contours in Figures 9 and 10 for subjects Cl and PR, respectively. One can see by comparing these plots with those in Figures 3 and 4 that there is a remarkable similarity between the predicted and empirical contours for each observer. It should be emphasized that 41 Figure 9 (subject Cl) and Figure 10 (subject PR). Predicted constant wavelength contours. The figure shows predicted hue contours for 12 test wavelengths. The abscissas correspond to the predicted wavelength seen at 100 trolands as determined by the hue coefficients in Figures 5 and 6. The ordinates correspond to the intensity of the test wavelength in the left eye. The contours should be compared to those in Figures 3 and 4, Log Trolanda ls» o> iy» O 480 490 *n H- 500 *c 520 vD u» M L n C O' l—u <® 540 o rr 560 580 610 630 650 ZV ■ r "i- " i-i '-n i t t ■r"i- "i-i '-ni 420 5 50 550 500 450 * * T o ST o o o o o o n o o o o> in oo • • * • • • I • * I • II * —i —i i —r i— “i— i— p— i— i— — / / Figure 10 (subject PR) (subject 10 Figure aeegh (nm) Wavelength • • I I I * in (VI o r © vr m m O © m 00 o 1 I 1 1 I I I 1“ ” “ T ~ T - 0 650 600 « • -- 1 650610 \630 -- " I I 1" OJ xs 44 these predictions and the empirical functions were determined by com pletely independent methods for the two observers. The hue coefficients presented in Figures 5 and 6 were used to directly predict the change in hue as measured with the wavelength adjustment method. The same data used to calculate these coefficients may also be used to determine the spectral sensitivity of the y-b channel given two sets of information. First one needs to know the r-g spectral sensitivity. Ingling, et al. (1978, in press) have measured the saturated r-g spectral sen sitivity for subject Cl using the polarizer adjustment method mono- cularly. Their fitted r-g spectral sensitivity function is plotted 9 in Figure 11. Second, one needs to have color corrected hue coefficients. Each segment of the hue coefficient functions for subject Cl presented in Figure 5 are in different color units because they had been equated in terms of V^, not in terms of the effect on their respective color channels. To put the unique red and unique green primaries in equal color units they were presented in combina tion to the observer's right eye and his task was to make the mixture neither red nor green. The red and green are set chromatically equal by a null method. An identical procedure was empolyed for the yellow and blue primaries. These data are presented in Table 4 for subjects Cl and PR. To obtain the color corrected hue coefficients q The equation for the plotted red-green function is: (r-g)= -(1.48M 9 0.428S - L) where M, S, and L are the cone fundamentals as determined by Smith and Porkorny (see Ingling, et al., in press, 1978) and 9 is defined as minus when kM > kS and kM 9 kS = 0 when kM < kS. Figure 11 (Subject Cl). The saturated r-g and y-b spectral sensitivity functions at 100 trolands. The r-g function was determined monocularly using the polarizer adjustment method by Ingling, et.al. (1978, in press). The y-b function was derived using the computed equal energy hue coefficient data presented in Table 5 and the r-g curve described above. The abscissa is the wavelength (nm) of the test and the ordinate is the output of the channels in arbitrary units. Relative Amount -3.0 -2.5 - -1.5 2.0 1.5 .5 .0 .5 .0 0 - 450 iue 1 Sbet Cl) (Subject 11 Figure \ (nm)7\ 550 600 650 O' 47 the green and blue primaries were arbitrarily normalized to the red and yellow primaries, respectively; R = K^G and Y ** K^B. Therefore, the color corrected hue coefficients for the different segments of the spectrum are: Yellow-red = Y/(Y+R) Yellow-green = Y/CY+K^G) Blue-green - K 2B/ (l^B+I^G) Blue-red = K2B/(K2B+R)' The color corrected hue coefficients are presented in Table 5. Naturally the color corrected hue coefficients for the orange region are identical to those in Table 3. Knowing the r-g function and the color corrected hue coefficients for Subject Cl at each test wavelength it is easy to solve for the spectral sensitivity of his y-b color channel: ( y - b ) , - ’ * 1 - H C where HC^ *= the color corrected hue coefficient at X When the color corrected hue coefficient at X = 1 or r-g = 0, it is impossible to obtain correct estimates of y-b- Therefore, these points were omitted from the calculations. The derived saturated y-b spectral sensitivity at 100 trolands for Subject Cl is plotted with his r-g curve in Figure 11- The computed y-b are corrected by straight lines only. Table 4 Primary Weightings for the Color Channels Primaries for Primaries for (y-b) Channel (r-g) Channel Subject Y 580 B480 B483 R680 C 510 C515 Cl 100 11.3 100 14.8 100 126.1 PR 100 21.9 100 28.5 100 172.6 49 Table 5 Color Corrected Hue Coefficients Test Log Median Wavelength Trolands Blue or Yellow (nm) of Test Color Corrected Hue Coefficient Subject Cl Subject PR 420 .21 .934 .908 .82 .938 .903 1.4 .949 .903 2.0 .958 .903 2.5 .986 .903 3.2 .999 .927 450 .31 .948 .941 .89 .965 .947 1.5 .972 .951 2.0 .987 .962 2.6 .998 .975 3.1 .999 .984 3.6 .999 .988 480 .46 .965 .934 .95 .963 .923 1.5 .992 .923 2.0 .998 .974 2.6 .998 .997 3.1 .998 .998 3.7 .998 .998 490 .48 .769 .683 .95 .751 .711 1.5 .790 .810 2.0 .802 .798 2.5 .827 .894 3.1 .861 .938 3.6 .891 .947 50 Table 5 (continued) Test Log Medlan Wavelength Trolands Blue or Yellow (nm) of Test Color Corrected Hue Coefficient Subject Cl Subject PR 500 .48 .371 .550 .95 .439 .483 1,5 .503 .023 2.0 .526 .023 2.5 .571 .294 3, 1 .586 .623 3.6 .638 .683 520 .49 .117 .012 .96 .147 .012 1.5 .107 .012 2.0 . 106 .117 2.5 .254 .278 3.1 .337 .336 3.6 .365 .386 540 .52 .011 .503 .98 .011 .503 1.5 .058 .454 2.0 .262 .552 2.5 .454 .589 3. 1 .558 .621 3.6 .625 .652 560 .53 .454 .670 .98 .541 .670 1.5 .558 .701 2.0 .608 .698 2.5 .686 .729 3.0 .737 .741 3.6 .765 .741 580 .52 .994 .998 .99 .989 .998 1.5 .976 .996 2.0 .962 .998 2.5 .968 .999 3.1 .975 .999 3.6 .967 .998 51 Table 5 (continued) Test Log Median Wavelength Trolands Blue or Yellow (nm) of Test Color Corrected Hue Coefficient Subject Cl Subject PR 610 .57 .154 .179 1.0 .258 .223 1.5 .349 .283 2.0 . 449 .433 2.5 .536 .616 3.0 .579 .729 3.6 .613 .908 * 630 .52 .006 --- 1.0 .024 .001 1.5 .079 .091 2.0 .157 .210 2.6 .271 .487 3.1 .366 .684 3.6 .421 .876 * 650 .48 .006 *" * .96 .006 1.5 .012 .019 2.0 .120 .125 2.6 . 168 .346 3.1 . 198 .637 3.6 .271 .851 * Sufficient retinal illuminance was not available to make a hue match. 52 Larimer, Krantz and Cicerone (1974) have shown that the set of r-g equilibrium lights, that is unique yellow and unique blue, are closed under both Grassraan's laws of scalar multiplication (i.e. they are invariant with intensity) and addition (i.e. they remain equi librium lights when combined in any proportion). They maintain that this evidence is sufficient to demonstrate that the r-g color channel grows linearly over the moderate intensity range considered (1 log unit). Given their suppositions about the r-g channel are correct and may extended to a wider intensity range, one may adjust the amplitude of the r-g spectral sensitivity by a simple scalar multi plier and examine the relative change in the amount of the y-b channel at the other six intensity levels. Derived relative y-b spectral sensitivity curves for subject Cl are plotted in Figure 12 for all seven intensity levels used in the present experiment. All curves were fit with simple straight lines. A special note should be made here concerning Figure 12. The relative size of the yellow and blue components in Figure 12 are probably correct only for the 100 troland level. This is the level at which a direct estimate was made to relate the color power of yellow and blue. The other intensities1 spectral sensitivities in clude the assumption that this scale factor remains constant at all intensities, since they are based upon a single adjustment of the hue coefficients. As Larimer, et al. (1975) have pointed out the y-b channel grows nonlinearly with intensity. Therefore, the height of yellow with respect to blue for a given intensity function is probably in error. This may account for the very large estimates 53 Figure 12 (Subject Cl). The spectral sensitivity of y-b relative to r-g at seven intensities. The abscissa is the spectral wave lengths (nm) and the ordinate is the amplitude of response in arbitrary units. Assuming the output of r-g may be adjusted to a constant amplitude by a simple scalar, the relative increase in the output of y-b at seven intensities is plotted as seven functions. The seven curves represent nominal half log unit increments in retinal illuminance; the lowest is .5 log trolands and the highest is 3.6 log trolands. See the legend of Figure 3 for nominal inten sities. The figure shows that as intensity increases there is a relative increase in the output of y-b relative to r-g. R ela tiv e Amount - -1-5 -1-5 J -2.OH -2.5 -2.5 l.oH 1.0 4 J 450 Figure 12 (Subject Cl) (Subject 12 Figure 550 7\ (nm) 600 650 55 of blue which will be discussed later. If all of the color channels grow linearly, then fixed correction coefficients may be introduced into the hue coefficient formulation for each opponent hue pair (i.e. those in Table 4) and apply at all intensity levels. With such a correction it should be possible to put all color corrected hue coefficients for all test wavelengths on a single transfer function. However, Ingling (personal communication) has pointed out that at least one color channel must grow nonlinearly, because the ratio (hue coefficient)^ of any two linear transfer functions would be a constant. If the hue coefficients were constant, then one could not have the Bezold-Brucke effect. Larimer, at al. (1974, 1957) have maintained that the r-g channel grows linearly over a restricted range, but y-b does not grow linearly over any tested range. If it is true that only the r-g channel grows linearly then the yellow-reds and yellow-greens would have a common transfer function different than a common one for the blue—reds and blue—greens. Therefore, as a check and extension of their findings an attempt was made to plot the yellow and blue color corrected hue coefficients for Subject Cl as a function of relative intensity of the test. Each test wavelength produces matching hue coefficients that show the relative growth of yellow and blue with intensity over three log units. Because different test wavelengths produce different A ratio model for hue seems to be the most reasonable. Cornsweet (1970) gives a good account of this assumption. amounts of stimulation in the two color channels when equated in terms of luminance, they naturally would be expected to produce different matching hue coefficient functions for the same luminances even if they were operating on the same underlying mechanisms. Since they are assumed to be operating on the same underlying mechanism, it should be possible to "piece" together each relevant test wave length function in terms of "effective trolands" for the y-b channel relative to the r-g channel. Graphically this may be accomplished by shifting each test wavelength set horizontally along the relative log intensity axis and visually placing each set on a common transfer function. The data from Table 5 were plotted in this fashion in 11 12 Figures 13 and 14 for Subjects Cl and PR, respectively. * Figure 13 (Subject CX) supports the notion that r-g grows linearly with intensity while the yellow and blue do not. In particu lar, the yellow-reds and yellow-greens may be grouped together as may the blue-reds and blue-greens. Thus, it appears that the red and green mechanisms grow similarly because they may be grouped together when paired with either blue or yellow hues. Further it appears that yellow grows more rapidly than blue with intensity because the slope for the former is steeper over the range tested. The r-g spectral sensitivity for Subject PR has. never been ob tained, so his y-b spectral sensitivities could not be calculated. ^ See Appendix C. 12 The 580 nm data were not presented because they were always at maxima for all intensities, and therefore, difficult to fit in a common place. 57 Figure 13 (Subject Cl). The growth of color corrected hue coeffi cients with intensity. The abscissa represents the relative intensity of the test in log trolands. The ordinate is the color corrected hue coefficients value in linear units. The sets of color corrected hue coefficients for each test wavelength were shifted horizontally on the abscissa to align on a visually deter mined common function. The figure shows that the blue red and blue green hues fit on a common function as did the yellow red and yellow green hues. Color Corrected Hue Coefficients . 01 f I * o If * ft g 1.00-1 . .70 . .30- o .50-1 W . .90- .40- 8 - 0 ° 0 .80-1 20 10 - - 1 2 0 1 12 11 10 9 8 7 6 5 4 3 2 1 ------0 1 ------o . 1 ------o 1 ------iue 3 (Subject Cl) 13 Figure Log Relative Intensity Relative Log O 1 ------° o 1 ------Blue hues Blue 1 ------<* o X X o — i — i x* o X * hues Green * ^ ^ * * hues Red « ^ x I ------Yellow hues Yellow < X * 0 t»K ft * o X 8 i < x ° o o Ln OD 59 Even if his r-g curve were known, another factor would lead to serious objections about the evaluation of the y-b curves. The color corrected hue coefficients in Table 5 were plotted together for Subject PR in Figure 14. This figure is comparable to Figure 13 for Subject Cl. The agreement between the color corrected hue coefficients for yellow-reds and the yellow-greens and for the blue-reds and the blue-greens is not nearly so good as for Subject Cl. Two factors could contribute to this disagreement between reds and greens. First, red and green mechanisms are not the same and have different, nonlinear growths with intensity, or second, the weighting factors listed in Table 4 are in error for Subject PR. In regard to the first possibility other evidence is consistent with the notion that Subject PR's red and green grow linearly. It will be recalled that the linearity conditions for the r-g channel as out lined by Larimer, et: al. require unique blue and yellow to be invariant with intensity and that there be no Abney effect when these two hues are combined in various proportions. As reported in the wavelength adjustment method results Subject PR had only a slight change in 480 nm and 580 nm, his unique blue or yellow, with intensity. In a study to be reported below there was no evidence for an Abney effect when 480 nm and 580 nra were combined in various proportions. Al though these effects were not rigorously investigated for their own sake, there was no clear indication that either of these linearity assumptions were violated for this subject. In regard to the second possibility if one assumes a color ratio of red to green closer to 100:100 rather than the 100:172.6 as measured, the reds and the greens 60 Figure 14 (Subject PR). The growth of the color corrected hue coefficients with intensity. The plots and their rationale are the same as for Subject Cl. Although an attempt was made to align the blue red and blue green hues as well as the yellow red and yellow green hues, there is less evidence for two common functions. Color Corrected Hue Coefficients 00- o o o o -* 0 .0 1 . .40- 6- elwhe * hues Yellow .60- . .30- H 0 7 * 5- • „ • • .50-1 .80- 9- x x x X x x x x0 * .90- 20 0 1 - - 1 2 4 6 8 1 1 1 1 14 13 12 11 10 9 8 7 6 5 4 3 2 1 ------o o 0 0 1 ------Blue hues Blue 1 ------° • 1 ------1 ------iue 4 Sbet PR) (Subject 14 Figure Log Relative Intensity Relative Log 1 ------• • 8 . . — ---- Sx o " * i 1 i 1 X * x * x ° I t v Green hues Green v It o ------X x x o X -r x o x ------ o x x o X r ~ x ■ Redhues ■ x X °o 0 X o r - ------t - 0 O 62 are in closer agreement for the yellow and blues. Therefore, assuming a different relation between red and green than that listed in Table h would be consistent with a linear r-g channel hypothesis. However, even with a "better" estimate of the red and green color power the data are still noisy, so no attempt was made to present these adjusted data here. A closer examination of Subject PR’s data is warranted and will be attempted in a separate study. The results of the desaturation study are presented in Table 6 and in Figures 15 and 16. It will be recalled that identical unique hues were presented in the test and in the mixture channels. In the latter channel the opponent unique hue was added as a desaturant. The percent of desaturant required to make a saturation match between the two fields, relative to 100 trolands, is presented graphically in Figures 15 and 16 for Subjects Cl and PR, respectively. Calcula tion of the data followed the formula: saturation coefficient trolands P^/(trolands P^ + trolands P^), where P^ and P^ were opponent hues. These data reveal that red, green, and blue desaturate with increasing intensity differences between test and mixture fields, but yellow remains constant for all intensity differences. From these plots one may infer that, consistent with pehnomenal reports by the observers, all hues except pure yellow desaturate with increas ing intensities, but yellow remains desaturated (or saturated) a constant amount at all intensities. This finding has not been re- 13 ported elsewhere (see Hunt, 1965). Scaling procedures have been 13 Judd (1951) states that all hues desaturate with intensity, how ever, no experimental evidence is cited. 63 Table 6 Data for the Saturation Study - Subject: Cl Subject: PR Test Log Log Percent Log Percent Wavelength Trolands Trolands Desaturation Trolands Desaturation (nm) of Test of Mix Relative to of Mix Relative to 100 Trolands 100 Trolands 480 2.0 .44 -40.79 .43 -28.09 2.0 .94 -44.99 .95 ' -26.01 2.0 1.5 -31.60 1.5 -10.14 2.0 2.0 -.28 2.0 -1.23 2.6 2.0 25.28 2.0 10.77 3.1 2.0 45.24 2.0 16.98 3.7 2.0 52.73 2.0 22.40 515(Cl) 2.0 .45 -14.34 .42 -15.79 510(PR) 2.0 .96 -15.02 .98 -14.51 2.0 1.5 -11.36 1.5 -1.33 2.0 2.0 -5.49 2.0 0 2.5 2.0 9.28 2.0 .33 3.1 2.0 17.30 2.0 8.31 3.6 ______* ______* 2.0 17.09 580 2.0 ,49 0 .49 0 2.0 .96 0 .96 0 2.0 1.5 0 1.5 0 2.0 2.0 0 2.0 0 2.5 2.0 0 2.0 0 3.1 2.0 0 2.0 0 3.6 2.0 0 2.0 0 680 2.0 .42 -39.02 .45 -11.79 2.0 .95 -40.14 .97 -24.12 2.0 1.5 -29.27 1.5 -12.88 2.0 2.0 -14.69 2.0 0 2.5 2.0 28.68 2.0 11.72 3.0 2.0 40.72 2.0 23.97 3.6 2.0 45.55 2.0 38.36 * No data obtained at this intensity. Figure 15 (Subject Cl) and Figure 16 (Subject PR). Desaturation of unique hues with intensity. The figures show empirically deter mined desaturation functions for the four unique hues for two subjects at seven different intensities. The abscissas correspond to the intensity of the comparison field. At 100 trolands and below the comparison field was the mixture field presented to the subject's right eye. Above 100 trolands the comparison field was the test field presented to the subject's left eye. The ordinates correspond to the percent of desaturant relative to 100 trolands needed to match the desaturation (whiteness) of its opponent unique hue. The figure shows the relative effects of intensity on desaturation of pure hues. % % Desaturant Relative to 100 Trolands -50 -40- -30- - 20 30- 10 0 1 - - - 1.0 Log Intensity of Comparison Field Comparison of Intensity Log iue 5 Sbet Cl) (Subject 15 Figure 2.0 3.0 Green Red Yellov Blue i O % Desaturant Relative to 100 Trolands 40- 30-1 20 30- 10 10 - - - Log Intensity of Comparison Field Comparison of Intensity Log Figure 16 (Subject PR) (Subject 16 Figure 2.5 3.0 3.5 Yellov Green Red •Blue O' 67 employed to study intensity dependent changes in saturation (e.g. Onlye, Klingberg, Dainoff, and Rollman, 1963). Onley, et al. pointed out that these techniques are subject to many problems in volving individual and procedural differences. A comparison be tween these scaling techniques and the method presented would seem interesting, but would require more extensive data than presented here. The desaturation plots are similar to the uncorrected hue coeffi cients in Figures 5 and 6. They both represent the proportion of one component (channel output) in a bimixture at a standard 100 trolands necessary to match a wavelength at another intensity. The proportion of the y-b channel relative to the r-g channel in a test stimulus is given for the hue coefficients while the proportion of the achromatic channel relative to one color channel is given for the data presented in this section. It should be possible to relate the data from the two experiments by putting the data in the same physiological units. That is, as the hue coefficients were put in terms of color units (Table 5 and Figure 13) it should be possible to put the data from the saturation study in color units. Because yellow did not change saturation with intensity, yellow and seems to have the same intensity dependent growth function. It should be legitimate, therefore, to relate these two studies by assuming * y. In particular the growth of yellow with respect to red and green should be identical to the growth of desaturation with respect to red and green. However, because different desaturating stimuli were employed for each 68 primary rather than a standard white, the primaries must be normalized Into the same units. The slopes of the hue coefficient data have, of course, already been adjusted and presented in Figure 13. To adjust the slopes of the saturation data for these data two corrections must be employed. First, the red and green primaries must be corrected in terms of their color strength and second, they must be corrected in terms of yellow, here assumed to be identical to V^. The red and green pri maries from the previous study were identical to those employed in the saturation study and these were related in color strength by the measurements presented in Table 4. From Wyszecki and Stiles (1967, Table 5.8, p. 436) the relative weighting of the green primary relative to the yellow in terms of the achromatic channel may be obtained. Because we are concerned with comparing the slopes of the yellow and the achromatic channels' growths with intensity rather than their absolute magnitude, both the saturation data and the hue data were plotted together. (As mentioned above the data for Subject PR are questionable in terms of the color correction pro cedure, therefore, only the computations for Subject Cl are presented.) In order to present the saturation data in terms of the color corrected hue coefficient data the trolands of the green primary measured were adjusted in terms of yellow, again assumed to be equal to V^. So G* was determined where: 69 G' *■ (color correction from Table 4) (yellow- achromatic correction)(trolands of G) G* = (100/126.1)(.6065/.87)(trolands of G) G* “ C(trolands of G) Therefore: red saturation data = G*/(G* 4- R) green saturation data = R/(R + Gr) The red and green saturation data are presented with the yellow hue data from Figure 13 in Figure 17. Although not perfect the data are in quite close agreement considering the various measurements and assumptions. It should be noted that the red and green saturation data both appear to have the same transfer functions as did the yellow-red and the yellow-green data. Therefore* these data also support the notion that red and green grow similarly with intensity. 70 Figure 17 (Subject Cl). Corrected saturation data plotted with comparable color corrected hue coefficients. The abscissa repre sents the relative intensity of the test in log trolands. The ordinates represent the adjusted percentage of yellow or white added to a mixture field to match the test. The figure shows that the corrected saturation data agree well with the color corrected data replotted from Figure 13. % Yellow 80 - 80 70 - 70 60 60 - 50 50 - 40 - 20 30 - 10 0 - - - , , > , , , 1 > I o>r 9 2 4 6 7 6 5 4 3 2 1 *■ K ° D &Dstrtd es f* 20 — reds A & Desaturated XeYlo rd hues red X e Yellow * o eaie Intensity Relative Log [5 iue 7 Sbet Cl) (Subject 17 Figure elw re us j hues green o Yellow “ j P X x ° x A eauae greens “ Desaturated □ X o* ° ° 0 4 ^ o o --- r h -10 40 30 20 0 10 % Desaturant 71 DISCUSSION As mentioned above, the present set of data confirms many of the aspects of the previous literature (e.g. that of Purdy, 1931, 1937; Boynton and Gordon, 1965; Jacobs and Wascher, 1967). However, the procedures employed in this experiment are improvements over those used previously. First, because the experiment was done haploscopic- ally it avoided the problem of retinal chromatic induction between the test and the match fields. This effect has been demonstrated to be powerful in determining perceived hue, most notably in regard to the Bezold-Brucke effect by Coren and Keith (1970). The only haploscopic experiment designed to study the Bezold-Brucke effect was performed by Cohen (1975) and his experiment was designed to answer questions not of direct interest in this experiment. Second, measurements were taken over a wide range of both intensity and wavelength. This has not always been the case; many studies have employed only two intensity levels and/or a limited spectral region when studying the Bezold-Brucke effect. Third, extensive measure ments were made on particular individuals, and for reasons pointed out above the individual differences seem quite reliable and important. Because of the clear differences between subjects, it is, perhaps, inappropriate to average their drta (e.g. Boynton and 72 73 Gordon, 1965; Jacobs & Wascher, 1967) in evaluating theoretical problems in color vision. For example, Subjects Cl and PR differed in their blue and yellow mechanisms and when averaged these differences would disappear. Therefore, this study is the first to give extensive data over a wide range of stimulus conditions and to avoid several potentially important artifacts, in particular retinal chromatic induction and dilution of important individual differences by averaging procedures. Perhaps as a minor improvement, the wavelength adjustment method employed here seems to be better than that employed earlier. The plots in Figure 3 are different than the classic curves presented by Purdy (1937). His curves are constant hue contours; they represent the wavelength at different intensities needed to match the hue of a fixed 100 troland wavelength. The present curves are constant wavelength contours; they represent the wavelength at 100 trolands needed to match the hue of a fixed wavelength at different intensi ties. These latter plots are clearer than Purdy*s, because the shifts in hue may be seen directly. Purdy was apparently aware of the possible confusion of the hue contours as he states, "...the reader must remember that the contours, in order to maintain hue constant, deviate in the direction opposite to the direction in which the hue tends to change (1937, p. 313)." The hue coefficient functions presented in Figures 4 and 5 are conceptually identical to the hue coefficients determined by color naming first presented by Boynton and Gordon (1965). Both types of hue coefficient functions give the percent of chromatic signal attributive to the y-b channel at different intensities. Both sets of hue coefficients have been used to predict perceived hue changes with the wavelength adjustment method. Importantly, however, there are fundamental differences between the hue coefficient functions presen ted by Boynton and Gordon and those presented here. The major dif ferences between the two types of hue coefficients lies first in how they were measured and second, how the basic data were manipulated. Boynton and Gordon attempted to measure the hue coefficients directly through color naming. They assumed that each perceived hue was an amalgamate of output from the two color channels. For each test wavelength subjects gave two (or one) responses which theoretical ly correlated with the ordinal amounts of the output from the y-b and r-g channels. The first response was assigned the arbitrary number two and the second number, one. If only one response was given (i.e. for a unique hue), the value of three was assigned. This convention was used to scale response magnitudes of the channels for two intensi ties at several wavelengths. The problem with this procedure is the arbitrary assignment of magnitudes to the subject's responses. This technique is subject to the same criticism of all indirect scaling methods. Boynton and Gordon simply used particular weighted fre quencies to scale the output of the color channels; however, there is no ji priori justification for these weights. A change in the convention will change the hue coefficients. Thus, despite their assertion that hue coefficients obtained by color naming are direct, it is, in fact, an indirect method since it relies upon arbitrary scaling procedures. 75 The hue coefficients presented in this experiment (shown in Figures 5 and 6) were derived directly. It was assumed, as for color naming, that each perceived hue was an amalgamate of output from the two color channels. Because the method employed the mixing of two unique hues, the relative magnitude of the channel responses could be measured directly without relying upon ordinal data and arbitrary weightings. Boynton and Gordon relied upon a simple ratio of the y-b and r-g channels for their hue coefficients rather than the hue coefficients as outlined by Hurvich and Jameson and used in the present experiment. The author attempted such a measurement for some of the wavelengths to predict the data from the wavelength adjustment method and found the agreement unsatisfactory. Even a log transformation of the ratio produced poorer predicted wavelength contours than those which relied on the percentage calculation. Boynton and Gordon's color naming predictions for wavelength shift are somewhat discrepant with those measured by a wavelength adjustment procedure (Figure 4, p. 84). Whether these discrepancies resulted from the method used or the ratio procedure or both cannot be easily ascertained, but certainly the color naming procedure as employed by Boynton and Gordon is inferior to the procedure presented here in predicting the shift in matching wavelength with intensity. A great deal may be said about the hue coefficients and determina tion of the y-b spectral sensitivity. The hue coefficients as first described by Hurvich and Jameson (1955) are based upon.the proportion of the computed channel outputs, that is their spectral sensitivities. 76 Spectral sensitivities are based upon equal energy spectra. Assuming linearity a constant criterion method may also be employed to deter mine these spectral sensitivities. The hue coefficients presented by Hurvich and Jameson (1955) were derived from a linear transformation of the CIE standard observer's fundamentals. The transformation chosen was similar to the empirically determined cancellation data they obtained on themselves. The cancellation method is a null, criterion method and the curves which serve as a basis for all the computations made in their subsequent papers relied upon the correct ness of the linearity assumption for determining the spectral sensi tivity of the channels. As mentioned several times above, Larimer, et. al. (1975) have demonstrated that the y-b channel is not a linear transformation of the fundamentals. The data presented here are consistent with this notion entirely. Therefore, one must conclude that the y-b curves used by Hurvich and Jameson to compute the hue coefficients at different intensities are in error and so must be the hue coefficients themselves. Even if the r-g channel is a linear transformation of the funda mentals as we suppose, Ingling, et al. (1978, in press) have demonsta- ted that cancellation estimates of it are in error for saturated conditions in the violet region of the spectrum. The cancellation procedure overestimates the amount of red in violets by nearly thirty times relative to a saturated matching procedure (i.e. the polarizer adjustment method) * Ingling, e_t al. argue that this effect is due to the desaturating influence of the green cancellation 77 stimulus used to estimate the red contribution. In essence the green added to the violet field is physiologically nulled by a blue silent surround mechanism until a point where its excitatory effect exceeds the surround's inhibitory effect. It is only then that the added green may cancel the perceived red. Therefore, the r~g spectral sensitivity used by Hurvich and Jameson overestimates the contribu tion of red in the short wavelength end of the spectrum and, thus, the hue coefficients must also be in error in this region. The present experiment attempted to eliminate any assumptions about the hue coefficients to predict the wavelength adjustment method and relied strictly upon a direct method as outlined above. This technique was apparently very successful in making these predictions. However, in regard to "working backward" from the hue coefficients to determine the spectral sensitivity of the y-b channel certain assump tions necessarily had to be made. First, it was assumed that the r-g spectral sensitivity was correct for Subject Cl. It will be recalled that his measurement was done with the polarizer adjustment method but had been measured monocularly. This was believed satisfactory, since both the test and mixture fields were done at the same intensity and matching fields would be expected to interact minimally. Second, it was assumed that the color power of the opponent hues could be deter mined at 100 trolands and be used to rescale the hue coefficient data. This technique like that used by Hurvich and Jameson assumes linearity in the color channel. In particular it is assumed that a single cor rection may be applied at every intensity and at every wavelength. It was pointed out that for Subject Cl this assumption seemed correct 78 for the r-g channel but not for the y-b channel. It was argued that the relative heights of the y-b channel (i.e. the yellow and the blue components) were probably Improperly scaled, because the single relation between Subject Cl's unique yellow and blue probably could not apply at every intensity level. Tha data for Subject PR were sufficiently in doubt as to the linearity assumption even for r-g to merit further examination, although it did appear that subsequent measurement might rectivy his data to be consistent with the linearity assumption for the r-g channel. One problem with these data used to determine the y-b spectral sensitivity is the crude estimates of the hue coefficients. In cer tain regions the estimates are satisfactory, however, in other regions estimates are as much as 30 nm apart and are, therefore, too widely spaced to obtain a reasonable spectral sensitivity. Thus, one needs to obtain more data in various spectral regions in order to get a better estimate of the true y-b curve. One point should be made concerning the determination of the y-b channel with this technique. The hue coefficient formulation may be used to determine any value of y-b except where r-g » 0 or the hue coefficient ** 1.0. Whether the determination is correct, of course, relies upon the error variability associated with the data used to compute it. Unfortunately error may inflate certain regions of the spectrum more than others. In particular when r-g approaches zero or the hue coefficient approaches one, the errors may become arti ficially enlarged or reduced and produce distortions in the y-b determination. Because the hue coefficients were very nearly 1.0 79 tn the violet region for Subject Cl, one should be cautious in assum ing that the amplitude of the blue region of the y-b is correct. The curves in Figure 12 show the blue component of the y-b channel as very large and as growing very rapidly with intensity. However, the plots in Figure 13 show yellow, in fact, growing faster than blue. This leads one to question the preciseness of the y-b estimate in this violet region. Nonetheless, the technique seems sound and it appears to require only some "tuning" in order to make it more exact. The saturation study presented here seems the first real attempt since Hurvich and Jameson to describe the intensity dependent factors concerning desaturation. Many studies have been conducted on satura tion discrimination at particular intensities, but little is know about the desaturation of stimuli with intensity (However, see Hunt, 1965). Theoretically each of the three visual channels grow with intensity and the relative faster growth of the achromatic channel produces the desaturation effect. Hurvich and Jameson attempted to predict the changes in saturation with intensity based upon Purdy*j empirical data and their derived spectral sensitivity functions described above. Purdy found and they predicted desaturation with intensity for nearly all spectral wavelengths. No data were obtained by Purdy in the pure yellow region (i.e. around 580 nm), so Hurvich and Jameson could not check their predictions in this region, but they predicted a desaturation of 580 nm with intensity. It will be recalled that no desaturation effect was found for yellow in the present experiment. It was shown that the rate of change in yellow with red and green was directly related to the rate of change of \ 80 saturation for red and green. This leads one to wonder if perhaps +y and have a common origin. Many of the other characteristics are the same; for example, receptive field sizes, longer latencies, and their spectral sensitivities are nearly the same (Ingling and Tsou, 1977). Work is currently being conducted in our laboratory to ascertain the relation between +y and V^. The present experiments are consistent with and extend the know ledge of color opponent theory. The color opponent theory proposes that all preceived hues are mixtures in relative proportions of the y-b and r-g channels. The present experiments directly tested this assumption by combining unique hues in various proportions to match the hue of test stimuli of various intensities. It was shown that by experimentally employing these assumptions one could predict the results from the wavelength adjustment method. Perfect matches (i.e. of the Brindley (1970) type A) were not obtained due to intensity dependent saturation differences between the two fields. It was shown, however, that intensity dependent changes in the saturation of stimuli were also consistent with the intensity dependent changes in hue. Thus, the present experiments are entirely consistent with the color opponent scheme of three visual channels, two opponent chromatic and one achromatic. This experiment also gives a clearer picture of the hue computa tion performed by the cortex. It was shown that the hue coefficient formulation first employed by Hurvich and Jameson could be used to predict changes in matching wavelengths at standard Intensity. Several other formulations were employed which did not predict the data nearly 81 so well. It is argued that the early predictions by Hurvich and Jameson regarding the cortical hue computation were correct; however, this Is the first real demonstration of the aptness of this model. The saturation computations are also similar to the hue coefficient computations in that the desaturation of reds and greens may be plotted on the same intensity transformation functions as yellow-reds and yellow-greens. Thus, both saturation.and hue computations in the brain are approximately based upon a percentage calculation. The present experiments also extend the knowledge about the characteristics of the two color channels in terms of their growth functions. It has been argued throughout this paper that the r-g channel grows linearly over the range tested while the y-b channel grows at a faster, nonlinear rate. As was argued by Ingling this nonlinear, faster growth accounts for the Bezold-Brucke effect. It also appears that the yellow mechanism grows at a faster rate than the blue mechansim within the y-b channel. This implies that it is the differential growths of the input mechanisms rather than a channel amplification per se that determines the Bezold-Brucke effect. The faster growth of yellow with respect to blue is consistent with the shift In unique green to shorter wavelengths with intensity. That is, if yellow grows faster than blue with intensity, the differencing procedure in the channel necessarily produces a shift to shorter wavelengths with intensity. Too, the faster rate of growth of yellow with respect to blue is consistent with the findings in this experiment that blue desaturates with intensity but yellow does not. If this were true and desaturation results from the faster growth rate of V^, then we would, in fact, expect blue to desaturate but not yellow. Thus, the achromatic channel and +y appear to share yet another characteristic; in addition to latency, receptive field size, and spectral sensitivity, they also have similar Bezold-Brucke gain factors. APPENDIX A Prior to data collection with the wavelength adjustment method a 100 troland spectrum was determined for each subject by flicker photo metry (Graham, 1965). In the right eye a 100 troland, 580 nm light in channel 3 was alternated with spectral lights in channel 1 (Channel 2 was not presented during flicker matches). To minimize the flicker subject adjusted one of the Inconel wedges in channel 1. Near the experimenter's station a wheel, with a removable paper strip around its circumference, was mechanically linked to this circular Inconel wedge. Flicker settings were recorded by the experimenter on this strip of paper at 10 nm intervals. Several strips were necessary for each observer to cover the range of wavelengths from 400 nm to 700 nm. During experimental trials the experimenter monitored the subject's wavelength changes and "tracked" these adjustments by compensatory changes of the wheel, and, thus, the Inconel wedge to maintain a constant luminance spectrum. To compress the range of flicker settings with the Inconel wedge it was necessary at the two spectral extremes to attach a compensating wedge, black and white 35 mm film, directly to the Schott interference wedge. The film gradually Increased in density from one end to the other. The film was attached to the wedge so that at the red end the density increased with shorter wavelengths and at the blue end it in creased with longer wavelengths. 83 APPENDIX B The hue coefficients (HC) calculations are based upon the trolands of the median unique hue primaries used to match the hue of a test wavelength. The values entered in Table 1 were com puted from the formula: Each point in Figures 5 and 6 corresponds to the hue coefficient (ordinate) used to match the test wavelength (abscissa) for one of seven intensities. As will become clear later, the saturation calculations also followed the same general formula. 84 APPENDIX C The data in Figures 13 and 14 were plotted in semilog plots in order to show the operational range of the hue coefficients more clearly* Log-log plots were also attempted to see if the hue coefficients followed a power law. That is, the data were plotted on log-log plots to see if the log of the hue coefficients were pro portional to log trolands. They were not. Further, a plot of the log of the ratio of the two components was also attempted with no evidence for proportionality, It would appear, therefore, that the hue calculation is not computed from channel exponential transfer functions. The author also informally tried various hyperbolic tangent transformations of the form: Input*1/(Iiiputn + K) (Boynton and Whitten, 1970). No simple combination of two hyperbolic tangent transformations seemed to work satisfactorily. 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