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Color Discrimination at Threshold Using Asymmetric Color Matching and Method of

Adjustment Discrimination to Test a Six Mechanism Theory of Color Vision

Safiya I. Lahlaf

Undergraduate Honors Thesis

for

Honors in Behavioral Neuroscience

Departmental Committee:

Rhea T. Eskew, Jr. (Advisor)

Peter Bex

Department of Psychology

Northeastern University

May 2016

COLOR DISCRIMINATION AT THRESHOLD 2

Abstract

Human color vision is a vital aspect of our perception of the world. We rely on color perception

on a day-to-day basis, ranging from object discrimination and face recognition to the detection and

determination of whether food is spoiled. Color vision is caused by the differential activation of

three cone photoreceptors, each of which is sensitive to a distinct range of wavelengths. However,

we have the ability to detect and discriminate between a variety of colors much finer than the broad

and overlapping wavelengths that activate the cones. One theory posits that numerous neural

mechanisms are required. Another theory holds that as few as six such mechanisms are sufficient,

and a later recombination of the signals from these mechanisms gives rise to the variety of

discriminable colors. In the present study, using barely-detectable chromatic stimuli, we conducted

color matching and method of adjustment discrimination experiments on human subjects to help

us understand the number and the characteristics of these post-receptoral mechanisms. Cluster

analysis of the color matching data and examination of the discrimination boundaries revealed six

unique color categories, which provides further support for a simple six mechanism model. The

six mechanism model does an excellent job of accounting for the psychophysical data and helps

resolve a current dispute in color vision research on post-receptoral processing.


Color Discrimination at Threshold Using Asymmetric Color Matching and Method of

Adjustment Discrimination to Test a Six Mechanism Theory of Color Vision

Introduction

Human vision is usually considered to be the most important sense and our primary

connection to the outside world. One major component of human vision, the perception of color,

greatly enhances our experience of viewing the world around us. It is so fundamental to us that we

often errantly believe that the color we perceive is inherently part of every object that we view.

However, this is not the case. Color perception is simply an interpretation that the mind gives to

the physical stimuli that it receives. How this interpretation is constructed is still actively being

studied.

The physiological explanation for vision is based upon the action of two types of cells

located in the retina of both eyes. The following description of the physiology is based upon Wolfe,

Kluender, & Levi (2011). These cells, rods and cones, respond to inputs of light. However, rods

and cones are active under different conditions. The rod cells are only active in dim light, or

scototopic, conditions. Because there is only one kind of rod photoreceptor, there is no

discrimination of the signal based upon color. This explains why the world appears black-and-

white at night. On the other hand, cone photoreceptors are active under brighter light, or

phototopic, conditions. Because there are several types of cone photoreceptors, we can

discriminate different colors under usual daylight conditions.

The basis of color discrimination has to do with the cone cells’ responses to different

wavelengths of light. There are three types of cone cells: long (L), medium (M), and short (S).

Each type responds maximally to different wavelengths of light: L cones to 565 nm, M to 535 nm,

and S to 440 nm (Figure 1). Because these wavelengths are associated with different colors, the


cones are commonly referred to as the red, green, and blue cones, respectively. However, this

categorization is not correct, as the cones respond to wavelengths, not to color. Color perception

occurs at higher-order levels of the visual processing system.

Cone response is based upon the number and wavelengths of the photons it receives.

Therefore, although each cone responds differently to various wavelengths of light, the response

is also dependent upon the intensity of the light. The higher the intensity, the more photons. At the

level of a single cone receptor, because the response is based upon both the wavelength and the

intensity, the level of activation cannot accurately predict the wavelength of light. This is called

univariance, and it explains the necessity of having multiple cones in order to interpret different

wavelengths of light as different colors.

The trichromatic theory of color vision was developed to explain our perception of color.

Because we now know about the three different types of cones, it is easy to conjecture that color

vision is based upon relationships between the three. However, before the existence of cones was

even discovered, the trichromatic theory had been developed. Early experiments carried out by

Hermann von Helmholtz built the foundation of this theory. In his experiments, Helmholtz

presented subjects with a color composed of one wavelength of light. Simultaneously, he presented

a color that was composed of three different wavelengths (Figure 2). A mixture of multiple

wavelengths of light that combine to produce a single color is called a metamer. He allowed the

subjects to manipulate the intensities of the three wavelengths until the metamer matched the

original, single-wavelength light. He found that the task could not be done with a two-wavelength

metamer. Further, he discovered that four wavelengths were more than needed. This led to the

trichromatic theory of color vision.

The second stage of visual processing has to do with how the signals from the three cone


cells interact. Ewald Hering’s opponent color theory helps to explain this. He found that we cannot

see any reddish-green nor any bluish-yellow colors, suggesting a pattern of interaction between

the three cone, or Stage 1, signals. The signals from the L and M cones interact such that

subtracting the M cone response from the L cone response (L-M) is perceived as red, while

subtracting the L from the M cone response (M-L) is perceived as green. Similarly, blue can be

perceived from the difference between the S cones signal and the sum of the L and M cones signals

(S-(M+L)), while yellow is perceived from the sum of the M and L cone signals minus the S cone

signal ((M+L)-S) (Figure 3). The sum of the M and L cones signals is also known as luminance.

Stage 2 is defined as these interactions between Stage 1 signals (Figure 4). These represent the

neural pathways that eventually lead to the brain.

The cone signal interactions are supported with physiological findings. In the lateral

geniculate nucleus (LGN), there are cells that respond preferentially to the colors described above.

In the magnocellular layer, cells respond to luminance; in the parvocellular layer, cells respond to

red-green; and in the koniocellular layer, cells respond to blue-yellow information (Figure 5). The

cellular responses in the LGN support the color opponent theory, as the cells in each layer have

excitatory responses to one end of the spectrum and inhibitory responses to the other end.

We need to understand color vision mechanisms in order to understand higher-level visual

processing. “A color mechanism may be defined as a fixed (relative) combination of cone signals

that is correlated with the observer’s behavior in psychophysical experiments,” (Eskew, 2009).

One explanation is known as the cardinal axis theory (Figure 6). This theory is based upon the

channels described above, which are viewed to be symmetric and bipolar: the achromatic

luminance, the red/green, and the blue/yellow channels (Boynton, 1979). This is a broadly-tuned

explanation for color vision.


Support for the cardinal axis thory can be seen in psychophysical data. Subjects’ intensity

thresholds (the intensities where the stimulus is just barely visible) for various wavelengths of light

were initially measured. Then, the subjects were adapted either along the red/green channel or the

blue/yellow channel. This caused increased thresholds in the adapted channel but had little or no

effect on the other channel (Krauskopf, Williams, & Heeley, 1982). These results indicate that the

two channels are formed from distinct mechanisms. Further support for the cardinal axis theory

with its three cone-opponent signals seemed to solidify the validity of this theory (Buchsbaum &

Gottschalk, 1983; Hurvich & Jameson, 1957; Lennie & D'Zmura, 1988; Rubin & Richards, 1988).

However, it is now clear that mechanisms are unipolar. This classical model describes six

mechanisms, the four chromatic—red (R), green (G), blue (B), and yellow (Y)—and the two

achromatic—increments (I) and decrements (D) (Eskew R. T., 2008). Thus, every mechanism is

independent of each of the others and formed by the opponent combination of signals from the

cone photoreceptors.

The broadly-tuned explanation for color vision described in the classical mechanism theory

is contested. Some believe that there are many more mechanisms than those designated by the

classical model. This higher-order theory is based on the recombination of the classical signals,

creating distinct channels for very specific colors in addition to the cardinal (D'Kmura, Lennie, &

Krauskopf, 1987; D'Zmura, 1991; Gegenfurtner & Kiper, 1992; Gegenfurtner, Kiper, & Levitt,

1997; Kiper, Fenstemaker, & Gegenfurtner, 1997; Krauskopf, Williams, Mandler, & Brown, 1986;

Lennie, Krauskopf, & Sclar, 1990; Webster & Mollon, 1994). Conflicting results have come from

studies designed to elucidate the number and form of mechanisms. In one study, noise masks used

during detection tasks had a significant effect on threshold for a wide range of colors but had little

effect on other colors, supporting the broadly-tuned model with only a few mechanisms (Giulianini


& Eskew, 1998). A different study found that noise masking had an effect only at very specific

colors, supporting a broadly-tuned model but with many color mechanisms (Hansen &

Gegenfurtner, 2010). This contention is the basis for the research addressed in this study.

This study was designed to help determine the nature of the different color mechanisms.

Like in the studies of Guilianini and Eskew (1998) and Hansen and Gegenfurtner (2010), stimuli

were restricted to the LM plane of color space, in which only the L and M cones are modulated

while the S cone response is kept constant (Figure 7). The experiments were designed to test a six

mechanism model (Shepard, Eskew, McCarthy, & Ochandarena, 2015). The mechanism model

depends upon the labeled line assumption, which says that stimuli detected by different

mechanisms must be discriminable at all intensities because each mechanism is associated with a

distinct hue. As will be shown below, this study used three procedures: detection, color matching,

and color discrimination. The mechanism model was based off of the results of the detection task.

In the color matching test, stimuli detected by different mechanisms were each matched separately

to one of the six different color clusters, allowing for a label to be given to each of the six

mechanisms. In the discrimination test, color cues were presented in pairs: a “standard” and a

“test” cue. The cues were unipolar (i.e., a single color). Using the method of adjustment, the

subjects changed the color angle of the presented test cue, moving in one direction per trial, until

it was distinguished from the standard. Because colors are indeed detected with only six broadly-

tuned mechanisms, the standard and test colors were indistinguishable until the test color crossed

over into detection by a different mechanism. On the other hand, if there were many color

mechanisms, the standard and test cues would have been easily distinguishable over very short

ranges. The results of these experiments support the six mechanism model of post-receptoral color

processing. Therefore, this study adds to the research explaining color vision mechanisms.


Methods

Observers

Participants in the study had normal color vision, as evaluated by the Farnsworth-Munsell

100 Hue Test (Farnsworth, 1943). Visual acuity was corrected, if necessary, with a trial lens placed

in front of their dominant eye while the other eye was patched. All experiments were conducted in

a dark room.

Stimuli

The stimuli were unipolar Gaussian blobs, σ =1°, presented against a gray background field

with a rapid-start profile “sawtooth” of 333 ms total duration—with energy equivalent to a 200 ms

rectangular flash of the same peak (Figure 8a, b). Detection was tested on at least twenty different

chromatic angles per noise condition in the LM plane (3-4 blocks of 100 trials at each angle), with

0° referring to an L cone increment, 90° to an M cone increment, 180° to an L cone decrement,

and 270° to an M cone decrement. In the no noise condition, 0°, 15°, 35°, 42°, 45°, 48°, 52°, 64°,

90°, 135°, 180°, 195°, 215°, 222°, 225°, 228°, 232°, 244°, 270°, and 315° were run. In 42° noise,

0°, 15°, 35°, 41°, 42°, 43°, 45°, 48°, 52°, 90°, 135°, 180°, 195°, 215°, 221°, 222°, 223°, 225°,

228°, 232°, 270°, and 315° were run. In 64° noise, 0°, 15°, 35°, 45°, 48°, 52°, 64°, 70°, 90°, 135°,

180°, 195°, 215°, 225°, 228°, 232°, 244°, 250°, 270°, and 315° were run.

In some conditions, chromatic masking noise was added to the stimulus field. To

accomplish this, all of the stimuli were “half-toned” along a vertical line on the screen; alternating

regions were assigned to the test or to the noise lines—in this case, the mean gray field (see

Giulianini & Eskew, 1998). Each region was two pixels in height and extended vertically across

the entire stimulus (Figure 8c). The test stimulus was created in the gaps between the noise lines.

Since it was assumed that chromatic mechanisms have low spatial resolution, the high spatial


frequency components created by this half-toning procedure were not visible in the “chromatic

only” detected tests but were occasionally visible for the tests near the corner of the contour

(i.e., ~42-48°, 222-228°).

Stimuli are represented in two color spaces: cone contrast space and MBDKL space

(Derrington, Krauskopf, & Lennie, 1984; MacLeod & Boynton, 1979). Cone contrast space is

achieved by dividing local cone excitation coordinates by the associated cone space coordinate of

the adapting field, giving ΔL/L or ΔM/M (Eskew, McLellan, & Giulianini, 1999). The local cone

excitation coordinates are found by subtracting the baseline excitation levels from the test

excitation levels (ΔL = Ltest – Ladapt). In cone contrast space, the axes delineate 0°/180° and

90°/270°. In MBDKL space, the axes are shifted by 45°, so they delineate 315°/135° and 45°/225°.

This shift is because the axes represent L+M and L–M and are rescaled to threshold units (Eskew

R. T., 2009; Krauskopf, 1999). MBDKL space was used to spread out the corners of the contour,

making it easier to view the points in those regions.

Apparatus and Software

Stimuli were created on a PowerMacintosh and displayed on a SONY GDM-F520 CRT

monitor by a standard video card with a 10-bit digital to analog converter (DACs).

Spectroradiometric calibration was performed at 8 nm intervals across the entire spectrum and the

monitors were then linearized with the Gamma correction lookup tables. Head position was

stabilized with a chin and forehead rest, a corrective lens was placed directly in front of the

observer’s dominant eye if necessary, and an eye-patch was placed over the other eye prior to the

adaptation period.

Model

A model with six detection mechanisms was fit to the data. The colored lines in Figure 9


show an example; each line represents a constant, threshold response of a different color

mechanism. The fitting program finds the best combination of weights applied to the L and M cone

signals to describe a section of the thresholds as a line. The solid closed contour is the probability

sum of the mechanisms, and shows the predicted thresholds based upon all of the mechanisms.

Probability summation refers to the concept that if two stimuli are detected by different

mechanisms, each mechanism’s contributions to the detection process is independent of the

other’s, but these signals are later combined (Kingdom & Prins, 2016).

Detection Procedure

A two-alternative forced-choice, adaptive staircase procedure was used to measure

detection thresholds. Observers adapted to the gray background field for 60 seconds before each

block of 100 trials. In each run, a single test color direction was used. Each trial consisted of two

333 ms intervals signaled by tones and separated by 400 ms. The observer was asked to determine

which interval the test stimulus appeared in and received feedback after each response. The

stimulus contrast was decreased by 0.1 log units after three consecutive correct responses and

increased by the same amount after one incorrect response. Weibull functions were fit to the

frequency-of-seeing data for each run using a maximum likelihood method to estimate two

parameters of the psychometric function—a threshold estimate corresponding to a detection rate

of 82% and an estimate of the psychometric slope. After fitting the Weibull functions, thresholds

from multiple runs were averaged (~3-5 runs at each color angle); standard errors were calculated

using between-run (mostly between-session) variances. Additional runs were added in cases where

the coefficient of variation were unusually high.

Color Matching Procedure

This color matching task was run using two different screens. The stimuli were presented


on the monitor. The color-match selections were made on a MacBook Pro using the Microsoft

PowerPoint program. There was a separate PowerPoint file for each noise condition, as trials were

conducted with and without noise. Within one noise condition file, there were five slides for each

test angle; these slides corresponded with the five blocks per test angle. Each slide was labeled in

the notes section with the test angle for each corresponding block. Every test angle for each noise

condition was tested a total of five times. The slides were arranged in random order. Each slide

consisted of a gray background with a gray circle, outlined in black, of the same hue as the

background. The experimenter used the arrow keys on the keyboard to pseudo-randomly select a

slide, keeping the test angle hidden from the subjects. If the chosen slide had already been

completed, a new slide was selected. The experimenter opened the color selection window for the

circle. The color wheel was positioned in the center of the screen (Figure 10). A black cloth with

a hole the size of the color wheel was used to block extraneous cues; only the color wheel was

visible. After 60 seconds of adaptation, the subjects completed a two-alternative forced-choice

detection test, with the contrast fixed at the previously-determined threshold value (the purpose

was to check that the stimulus was at threshold, and to give the observers some practice with the

particular stimulus). The program was set to display 50 trials, but it could be stopped whenever

the subjects were certain of their color choice. Usually only around 30 trials were required, but

sometimes more than 50 were needed. In this case, the subjects again adapted for 60 seconds before

completing another 50 trials, or however many were necessary. There were no restrictions on the

number of trials.

The subjects made color selections on the PowerPoint file on the laptop. The subjects could

open the laptop screen, which was closed during runs to prevent them from viewing the light, and

make selections on the color wheel. The hue and saturation were adjusted, but the scale designating


color value was kept hidden and remained at 100 for all trials. The subjects could resume the

forced-choice detection task and return to the color matching window to refine their selection.

After they were satisfied, the experimenter used the subjects’ color selection to fill in the circle on

the slide. The subjects then confirmed the choice a final time by looking at the color selection

circle. The stimulus size on the presentation monitor and the color selection circle size were the

same. Also, the gray background on the presentation monitor was measured using a colorimeter to

be the same as the background on the PowerPoint slides. After each block was completed, the HSV

values were measured. The HSV values of the five blocks for each color angle were averaged

together. These average colors were measured using an X-Rite spectrophotometer and converted

to CIE (u,v) color space (Pauli, 1976).

Discrimination Procedure

In each trial of the method of adjustment discrimination experiment, the observers were

presented with two stimuli (a “standard” color angle along with a “test” color angle), both of which

were fixed at their individual thresholds (as determined by the model). Observers were asked to

adjust the color angle of the second stimulus (the test) until it appeared to be different from the

standard; the software kept the second stimulus at threshold (according to the model). The subject

could adjust the test angle in increments of one degree to find the angle that was different in

appearance from the standard (Figure 9). The adjustments were made in both the clockwise and

counterclockwise directions, separately, with five blocks in each direction per run and five runs

per color angle done in total. Since the stimuli were equal in strength, they were only discriminated

on the basis of hue of the stimulus.

In the discrimination task, subjects were adapted for 60 seconds before every run. Each run

consisted of five blocks. Each stimulus was presented at the predicted threshold values, determined


from the model fit. Standards were set at 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°. For each

standard angle, subjects moved clockwise around the contour for one run and counterclockwise

for the other. Therefore, a total of 16 runs were conducted per condition. Each run was repeated a

total of five times, with repetitions conducted on separate days to account for daily differences in

discrimination.

A key pad was used to allow the subjects to adjust the test stimulus. After hitting “enter”

on the key pad, two stimuli flashed on the screen for 200 ms each, with 400 ms between each

presentation. A tone sounded simultaneously with each stimulus presentation. The first stimulus

was the standard color angle, and the second was the test. Subjects had to determine whether or

not the two stimuli were discriminable. At the first presentation, the test was the same angle as the

standard. Subjects then used the keypad to change the color angle of the test stimulus. Pressing

“1” moved the test one degree clockwise, while pressing “3” moved it one degree

counterclockwise; pressing “2” presented the two stimuli again, with the test at the same angle it

was at the previous presentation. Hitting “4” and “6” moved the test angle clockwise and

counterclockwise, respectively, by increments of 5 degrees, while “7” and “9” moved the test angle

clockwise and counterclockwise, respectively, by increments of 10 degrees. There were no time

limits or other restrictions, although subjects generally took about five minutes per run. Hitting the

period button caused the block to end and indicated that the standard and test stimuli were

discriminable. After each block, the angles of the standard and of the discriminable test were

recorded. The average of all twenty-five blocks per boundary (five runs at five blocks per run) was

calculated, as well as the standard deviation. Results were plotted on the subject’s detection

contour. Subjects conducted the method of adjustment discrimination task in several different

conditions, including no noise and at least two other noise conditions.


Results

Threshold averages calculated from the detection data were analyzed and fit with

mechanisms. The model used probability summation and fit the threshold detection data across all

noise conditions simultaneously. It used the Test Energy vs. Noise Power Relationship and fit the

data to k linear mechanisms (Shepard, Eskew, McCarthy, & Ochandarena, 2015). Six, eight, and

sixteen mechanisms were tested, with the fit not improving after more than six mechanisms. For

six mechanisms, the R2 value was 98%.

The detection threshold averages are shown in Figure 11, which has three columns: the

detection data plotted in cone contrast space, the threshold versus color angle plot, and a regression

line with the y-axis denoting the predicted values and the x-axis denoting the observed thresholds.

The first row shows the data for the no noise condition, the second for the 42° noise condition, and

the third for the 64° noise condition (Figure 11a-c). The threshold versus color angle plot includes

error bars.

In the no noise condition, the data fits closely to the contour (Figure 11a, left) and to the

threshold versus color angle plot (Figure 11a, middle). The fit with the regression line is very good

(Figure 11a, right).

In the 42° noise condition (Figure 11b, left), the data also fits closely with the contour.

Additionally, the contour is stretched in the direction of the noise, indicating that the thresholds of

points near the noise chromaticity are increased much more than points along the flanks of the

contour. This is demonstrated in the sensitivity plot, which has much higher values overall than

the no noise plot, but especially along the noise angles (compare Figure 11a and b, middle). The

sensitivity plot also reveals several points that do not lie on the contour, within error: the 41° and

43° degree points lie below the contour peak, while the 222° point extends above it. The data fits


well with the line in the regression plot (Figure 11b, right).

For the 64° noise, the data fits well with the contour (Figure 11c, left). The contour is not

as stretched as the 42° plot in cone contrast space (compare Figure 11b and c, left panels).

However, as the threshold plot indicates, the thresholds are much higher overall in the 64° noise

condition than in the no noise condition, but lower than in the 42° condition (Figure 11, middle

panels). The 15°, 52°, 64°, and 135° points lie slightly above the contour line, while the 15° and

250° points lie slightly below. However, the contour fits the rest of the data well. The data fits well

with the line in the regression plot (Figure 11c, right).

Each noise condition was analyzed independently and the contours with the linear

mechanism lines plotted onto two different planes: cone contrast space and MBDKL space (see

Stimuli). These two plots of the same data and model are shown in the left and right panels of

Figure 12, respectively. For the no noise condition, six mechanisms were fit to the data (Figure

12a). The threshold points fit the mechanisms very well. None of the mechanisms are parallel to

another. The same six mechanisms were fit to the 42° noise data, but the sensitivities were changed

(Figure 12b). However, two of the mechanisms, indicated by the blue and dotted lines in the figure,

were pushed out. Therefore, only four of the mechanisms were necessary to fit these thresholds.

The mechanisms fit the data well. In the 64° condition, the same six mechanisms, with altered

sensitivities, were fit to the data (Figure 12c). In this case, the mechanism indicated by the green

line was pushed out, leaving the remaining five mechanisms to contribute to the contour. The data

fit well with the model mechanisms

The color matching data was also analyzed. As an example, the average color match for

each color angle in the no noise condition was placed over the corresponding data point in the

mechanism plot in cone contrast space (Figure 13). These circular symbols indicate the color


appearance of each test and correspond to the coloring of the mechanism lines that were fit to the

thresholds in the detection experiment. These average color matches were also plotted onto CIE

(u,v) color space (Figure 14a-c). A K-means Euclidean cluster analysis was conducted, in which

individual points were grouped into clusters formed from the points closer to themselves than to

other points on the plane. Therefore, the plane was divided into regions, where every point within

a particular cell was closer to that cell’s centroid than to any other centroid. Within a cluster, the

points are not significantly different than each other, so the variability between angles is the same

as the variability between tests of a single angle in that cluster. However, between clusters, the

points are significantly different from each other. The points in each cluster were colored with a

representative hue for the label given to that specific cluster. The white point on each plot

represents the color coordinates of the gray background that the stimuli were presented over.

The number of clusters of the color matches generally corresponds to the number of

mechanisms that describe the detection data in a particular condition. In the no noise condition,

there were six clusters; in the 42° noise condition, there were four; and in the 64° noise condition,

there were six (Figure 14a-c). The labels given to the clusters were “reddish,” “orangish,”

“yellowish,” “greenish,” “bluish,” and “purplish.” In other words, the color appearance of the test

stimuli maps very well onto the predictions of the model fit to the forced-choice detection

thresholds.

For the method of adjustment test, the regions of indiscriminability, both above and below

each standard, were indicated with arcs that followed the subjects’ contours (Figure 15a, b). Each

arc was colored according to the color label given to that specific mechanism. If two standards fell

within the boundaries of the same mechanism, they were colored the same but differentiated based

upon the style of the line. Both the no noise and the 64° noise condition were tested.


Discussion

The purpose of this study was to help resolve the current contention in color vision research

regarding the nature of higher-order mechanisms that lead to color perception. One theory claims

that there are numerous broadly-tuned mechanisms, even at an early post-receptoral stage in visual

processing (Hansen & Gegenfurtner, 2010). Our theory, based on previous research, supports not

more than six broadly-tuned mechanisms that mediate the L and M cone signals (Giulianini &

Eskew, 1998). The results of this research support the six mechanism theory explaining post-

receptoral color processing.

The detection task was designed to allow us to create a threshold contour, which was then

used to create a computer model for the visual mechanisms. As the results indicate, six mechanisms

were sufficient to fit the data across all noise conditions and observers (Figure 11a-c). Within-

subject, the slopes of each mechanism line were constrained to be the same across noise conditions,

maintaining consistency in terms of the described mechanisms (Figure 12a-c). We tested six, eight,

and sixteen mechanisms, but the fit did not improve significantly after six mechanisms, supporting

the theory that only six mechanisms are sufficient to account for the detection data in the LM-

modulated color space used for these experiments. In some noise conditions, one or two

mechanisms were not necessary to fit the data and were pushed out of the contour. This can be

explained by the effects of the noise masking, which increases threshold levels in general and alters

absolute mechanism sensitivity (leaving relative sensitivity to different LM angles unchanged, so

the slopes of the mechanism threshold lines is always the same). Certain mechanisms require more

stimulation than others in order to be activated—these are the ones that get pushed out, while the

other mechanisms compensate. Nevertheless, all six mechanisms were required to fit the data over

all the noise conditions in aggregate. The distinct stretch of the 42° noise contour demonstrates the


presence of selective masking, which is accounted for by the six mechanism model. The high

goodness of fit, with an R2 of 98%, and the ability of the model to account for selective masking,

supplies the initial evidence for the validity of the model.

The color matching test was designed to further test the model and to allow us to associate

a color with each of the six defined mechanisms. Subjective examination of the color matches

when plotted with the mechanism lines over the contour suggests that each mechanism is

associated with a corresponding color (Figure 13). A K-means Euclidean cluster analysis of the

color matches, displayed in CIE (u,v) color space, revealed distinct groups (Figure 14a-c). Within

each cluster, the individual angles should not be discriminable; the differences in color coordinates

only represent variance, no different than the variance in coordinates of each individual angle’s

five test blocks. However, any two points that lie in different clusters should be discriminable.

Interestingly, the red, orange, and yellow clusters were very close to the white point, indicating

that they were much less saturated than the green, blue, and purple clusters.

The number of clusters can be used to test the validity of the six mechanism model, because

the number of clusters should correspond to the number of mechanisms that contribute to each

noise condition. The no noise condition had six clusters, which corresponds to the number of

mechanisms defined by the model (Figure 14a). The 42° noise condition had four clusters, which

also corresponds to the number of contributing mechanisms in the model of that noise condition

(Figure 14b). The 64° noise condition was more complicated; it had six clusters, but the associated

model only allowed for five to contribute (Figure 14c). Interestingly, the sixth “cluster” is made

up of only one test angle, the 64° stimulus. This matches the angle of the noise. Perhaps the

stimulus presented as a more highly saturated region of the noise, prompting the subject to assume

that the color of the test matched the color of the noise, allowing for a relatively accurate color


match despite the presence of adapting noise. This would explain the additional cluster, which

actually only comprised of a single point.

Each cluster is clearly associated with a specific color designation. Interestingly, there are

points that shift in apparent hue when viewed under different noise conditions. For example, a 45°

stimulus appears to be yellow, green, or orange when viewed under the no noise, 42° noise, and

64° noise conditions, respectively. This indicates that color is not an inherent property of the

physical world, nor is it even directly associated with specific wavelengths of light. Rather, color

is associated with the mechanism that is activated. In other words, each mechanism has an

associated color. Activation of a mechanism leads to a perception of the corresponding color. If a

specific mechanism is pushed out due to the presence of noise, then the other mechanisms

compensate. Whichever mechanism detects a specific stimulus dictates the perceived color of that

stimulus. This supports the labeled-line model of color vision, with each mechanism associated

with a specific color.

The third experiment was the method of adjustment discrimination task. This test was

designed to allow us to quickly determine the boundaries of discrimination between colors (Figure

15a, b). Because the stimuli were presented at the threshold levels predicted by the detection

model, they were difficult to see. At such a low level, discrimination would rely on differential

activation of the mechanisms. If one stimulus activated the same mechanism as another stimulus,

they would not be discriminable. The results of the test appear to agree with this assumption,

providing further evidence in support of the six mechanism model.

The no noise condition discrimination data supports the six mechanism theory. Conversely,

at first look, there would appear to be only four boundaries (Figure 15a). However, the 0° standard

appears to lie directly on the boundary between the red and orange mechanisms. Therefore, the


upper region actually encompasses the orange mechanism, while the lower region, like the regions

of the 270° and 315° standards, encompasses the red mechanism. The 45° standard range denotes

the boundaries of the yellow mechanism. The yellow and green boundaries almost directly meet,

indicating the point of separation between the two mechanisms. The apparent boundary between

the green and blue mechanism appears to be very noisy, as the 90°, 135°, and 180° upper

boundaries do not quite end in the same location. There is also a sizeable gap between these green

mechanisms and the purple mechanism, denoted by the region measured with the 225° standard.

The model indicates that the blue mechanism is located in this region. Because it encompasses a

short range of the contour, there was no standard tested within its boundaries, so its presence can

be inferred from the gaps between the green and purple mechanisms. Overall, this data seems to

corroborate with the six mechanism theory, but more data is needed.

The method of adjustment discrimination data for the 64° noise condition also appears to

support the six mechanism theory. The rough boundaries delineate five mechanisms (Figure 15b).

The 315° and 0° standards lie in the orange mechanism. However, because 270° appears to be

located in the corner of two mechanisms, the upper limit of the 270° standard also appears to be

within the boundaries of the orange mechanism. The 45° standard is in the yellow mechanism.

There is a slight gap between the yellow and blue mechanism boundaries. The 90°, 135°, and 180°

standards are in the blue mechanism. The 225° standard appears to be in the corner of the blue and

purple mechanisms, so the lower region is within the boundaries of the blue mechanism as well.

The upper range appears to be within the purple mechanism. There is another gap, this one between

the purple and red mechanisms. The lower range of the 270° standard appears to fall within the

red mechanism. Overall, five rough mechanisms are outlined here, although this data is quite noisy.

More follow-up is necessary. However, the 64° noise condition discrimination data appears to the


match the model prediction, lending further support to the six mechanism model.

There are several potential reservations to this study. First, the model is based off of a high-

threshold model of detection, which has been generally discarded in favor of signal detection

theory (Wickens, 2002). Contrary to signal detection theory, the high-threshold model holds that

errors are due to guessing, not due to the effect of noise (Burmester & Wallis, 2012). However, in

the case of these experiments, the high-threshold model is a reasonable approximation. This is

because we use the two-alternative forced-choice method for the collection of detection data.

Another possible issue is that data from only one subject are demonstrated here. However,

detection models and color matching data from two other subjects show similar results to the data

presented here. Also, preliminary method of adjustment data from another subject also follow the

same patterns exhibited here. Therefore, the data in this paper is representative.

The compatibility between the discrimination data and the mechanism model lends further

support to the six mechanism theory, which is based upon a labeled-line assumption. The labeled-

line theory derives from Müller’s Law of Specific Nerve Energies, which is based upon the

assumption that the strength of two stimuli that lie on the same mechanism can be adjusted such

that the two stimuli are indiscriminable, and that any two stimuli that lie on difference mechanisms

are as discriminable as they are detectable (Boring, 1942; Eskew, Newton, & Giulianini, 2001;

Graham, 1989; Watson & Robson, 1981). In these experiments, discrimination only occurred when

the stimuli were detected by different mechanisms, lending evidence to the labeled-line theory of

color vision. Each mechanism is distinct from the others, and activation of one mechanism

corresponds to the perception of a specific color. However, activation of the same mechanism with

threshold-level stimuli, even if the stimuli are at different angles, leads to a perception that the two

stimuli are the same color, making them indiscriminable. Thus, these two experiments both support


a labeled-line theory of color vision.

The results of this study establish the validity of the six mechanism model calculated from

detection data. The color matching experiment demonstrated that there are six different perceived

colors when stimuli are presented at threshold. This confirmed the number of mechanisms and

provided a label designation for each. The method of adjustment discrimination experiment

demonstrated that stimuli that lie on different mechanisms are discriminable, but stimuli that lie

on the same mechanism are indiscriminable. Also the boundaries delineated by the experiment

correspond to the model predictions, giving further evidence for the existence of six mechanisms.

Therefore, both the color matching and the method of adjustment discrimination experiments

support the detection-derived six mechanism model explaining post-receptoral processing that

contributes to human color vision.

Moving forward, we will conduct more experiments to test the validity of the six

mechanism model. For example, we will perform another discrimination test where subjects are

presented with two different stimuli—a “standard” and a “test”—and will have to indicate the

interval during which the standard was presented. This will be a two-alternative forced-choice test.

This test will be performed within and across mechanism boundaries. Two stimuli that lie on the

same mechanism should not be discriminable when presented at threshold levels, so the

discrimination rate should be at chance level, or 50%. However, two stimuli that are detected by

different mechanisms should be discriminated at the same rate as they are detected—at threshold

level, or 82%. Stimuli that lie near a boundary and are potentially detected by two mechanisms are

discriminated at intermediate levels. Using this additional experiment, we will further demonstrate

the validity of our six mechanism model.

The results of this study support the six mechanism theory explaining intermediate


processing in human color vision. The model fit the detection data well and accurately accounted

for selective masking. Furthermore, the model accurately predicted the results of two different

experiments, a color matching task and a method of adjustment discrimination test. The color

matching task confirmed the number of mechanisms and provided a color label for each. The

method of adjustment test corroborated the number and boundaries of the proposed mechanisms.

Overall, these results, in line with labeled-line theory, support a six mechanism model of color

vision at the post-receptoral stage.


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Appendix A

Figures

Figure 1. Absorption spectra of the three cone photoreceptors (Dartnall, Bowmaker, & Mollon, 1983; Goldstein, 2010).

Figure 2. Helmholtz’s presentation of two different colors. The top portion is composed of a single wavelength, while the bottom portion is a metamer, or mixture of wavelengths (Young, 1802).


Figure 3. The interactions between the cone signals in color opponent theory. Three channels are created: a blue-yellow channel created from the interaction between S, L, and M cone signals; a red-green channel formed from the difference between the L and M cone signals, and a luminance channel based on the sum of the L and M cone signals (Stockman & Brainard, 2010).

Figure 4. Spectral sensitivities. Stage 1 represents the three cone receptors, while Stage 2 demonstrates the interactions between the Stage 1 signals (Stockman & Brainard, 2010).


Figure 5. Left: the lateral geniculate nucleus. Right: color-sensitive cells in the LGN respond preferentially to stimuli in the red-green and blue-yellow color directions (Derrington, Krauskopf, & Lennie, 1984).

Figure 6. Cardinal axis theory of color vision. Modified from Eskew (2009).


Figure 7. LM color plane.

Figure 8. (A) Stimulus presentation. (B) Top: Sample stimuli at suprathreshold levels. Bottom: Sample stimuli at pseudo-threshold levels. (C) Sample noise masking pattern.

A B

C


Figure 9. Color discrimination task. Black circle: standard. Black crosses: indiscriminable test cues. Gray crosses: discriminable test cues. Red circles: measured detection thresholds. Colored lines: modelled linear mechanisms. Top: test angles adjusted in the counterclockwise direction. Bottom: test angles adjusted in the clockwise direction.

M

L

M

L

Figure 10. HSV color wheel.


Figure 11. Left column: Detection data with contour in cone contrast space. Middle column: Threshold versus color angle plot for detection data. Right column: Regression line (y-axis: predicted threshold, x-axis: observed threshold). (A) No noise condition. (B) 42° noise condition. (C) 64° noise condition.

A

B

C

SIL

SIL

SIL


A

B

C

Figure 12. Left column: Detection data with contour and mechanisms in cone contrast space. Right column: MBDKL space. (A) No noise condition. (B) 42° noise condition. (C) 64° noise condition.

A

B

C

SIL

SIL

SIL


Figure 13. Color matches on the no noise contour. Mechanism lines are colored according to the label given by the observer Circles: color matches superimposed onto detection threshold points. Left: cone contrast space. Right: MBDKL space.

SIL


A

B

C

Figure 14. Color matching points in CIE (u,v) color space. Each colored point represents a stimulus angle. The white point represents the white point of the monitor. (A) No noise condition. (B) 42° noise condition. (C) 64° noise condition.

SIL

SIL

SIL

WP

WP

WP

u

u

u

v

v

v


-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.2 -0.1 0 0.1 0.2

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-0.03 -0.02 -0.01 0 0.01 0.02

Figure 15. Method of adjustment data plotted over the detection contour (gray). (A) No noise condition. (B) 64° noise condition.

A

B

SIL

SIL

ΔM/M

ΔL/L

ΔM/M

ΔL/L

0° 45° 90° 135° 180° 225° (lower) 225° (upper) 270° (lower) 270° (upper) 315°

0° (lower) 0° (upper) 45° 90° 135° 180° 225° 270° 315°

Standard Key

Standard Key


Appendix B

Acknowledgments

I would like to extend my full gratitude to Professor Eskew for his support and guidance in class,

in the lab, and throughout the course of this honors project. I would also like to thank Tim Shepard

for his help and instruction over these past two years, always taking the time to answer my

numerous questions. I would like to acknowledge Professor Bex for his insights and for serving

on my departmental honors project committee, and Professor Isaacowitz for his direction

throughout this process. Finally, I would like to thank my family and friends for their constant

support. I could not have completed this project without them.

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