Color Discrimination at Threshold Using Asymmetric Color Matching and Method of

Transcription

1 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

2 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.

3 COLOR DISCRIMINATION AT THRESHOLD 3 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-andwhite 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

4 COLOR DISCRIMINATION AT THRESHOLD 4 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

5 COLOR DISCRIMINATION AT THRESHOLD 5 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.

6 COLOR DISCRIMINATION AT THRESHOLD 6 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

7 COLOR DISCRIMINATION AT THRESHOLD 7 & 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 broadlytuned 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.

8 COLOR DISCRIMINATION AT THRESHOLD 8 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

9 COLOR DISCRIMINATION AT THRESHOLD 9 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, ). 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

10 COLOR DISCRIMINATION AT THRESHOLD 10 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

11 COLOR DISCRIMINATION AT THRESHOLD 11 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

12 COLOR DISCRIMINATION AT THRESHOLD 12 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

13 COLOR DISCRIMINATION AT THRESHOLD 13 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.

14 COLOR DISCRIMINATION AT THRESHOLD 14 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 R 2 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

15 COLOR DISCRIMINATION AT THRESHOLD 15 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

16 COLOR DISCRIMINATION AT THRESHOLD 16 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.

17 COLOR DISCRIMINATION AT THRESHOLD 17 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 postreceptoral 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). Withinsubject, 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 LMmodulated 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

18 COLOR DISCRIMINATION AT THRESHOLD 18 presence of selective masking, which is accounted for by the six mechanism model. The high goodness of fit, with an R 2 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

19 COLOR DISCRIMINATION AT THRESHOLD 19 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

20 COLOR DISCRIMINATION AT THRESHOLD 20 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

21 COLOR DISCRIMINATION AT THRESHOLD 21 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 highthreshold 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 labeledline 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

22 COLOR DISCRIMINATION AT THRESHOLD 22 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

23 COLOR DISCRIMINATION AT THRESHOLD 23 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.

24 COLOR DISCRIMINATION AT THRESHOLD 24 References Boring, E. G. (1942). Sensation and Perception in The History of Experimental Psychology. New York: Irvington. Boynton, R. K. (1979). Human Color Vision (2nd ed.). New York: Holt, Rinehart, and Winston. Buchsbaum, G., & Gottschalk, A. (1983). Trichromacy, opponent colours coding and optimum colour information transmission in the retina. Proceedings of the Royal Society of London B, 220(1218), Burmester, A., & Wallis, G. (2012). Contrasting predictions of low- and high-threshold models for the detection of changing visual features. Perception, 41(5), doi: /p7176 Dartnall, H. J., Bowmaker, J. K., & Mollon, J. D. (1983). Human Visual Pigments: Microspectrophotometric Results from the Eyes of Seven Persons. Proceedings of the Royal Society B, 220(1218), doi: /rspb Derrington, A. M., Krauskopf, J., & Lennie, P. (1984). Chromatic Mechanisms in Lateral Geniculate Nucleus of Macaque. The Journal of Physiology, 357, doi: /jphysiol.1984.sp D'Kmura, M., Lennie, P., & Krauskopf, J. (1987). Hue selectivity revealed by heterochromatic noise masking. Investigative Ophthalmology & Visual Science, 28, 92. D'Zmura, M. (1991). Color in visual research. Vision Research, 31(6), doi: / (91)90203-h Eskew, R. T. (2008). Chromatic Detection and Discrimination. In A. I. Basbaum, A. Kaneko, G. M. Shepherd, G. Westheimer, T. D. Albright, & R. Masland (Eds.), The Senses: A Comprehensive Reference (Vols. II, Vision II, pp ). San Diego: Academic Press.

25 COLOR DISCRIMINATION AT THRESHOLD 25 Eskew, R. T. (2009). Higher order color mechanisms: A critical review. Vision Research, 49, doi: /j.visres Eskew, R. T., McLellan, J. S., & Giulianini, F. (1999). Chromatic detection and discrimination. In K. Gegenfurtner, & L. T. Sharpe (Eds.), Color vision: from genes to perception (pp ). Cambridge: Cambridge University Press. Eskew, R. T., Newton, J. R., & Giulianini, F. (2001). Chromatic detection and discrimination analyzed by a Bayesian classifier. Vision Research, 41(7), doi: /s (00) Farnsworth, D. (1943). The Farnsworth-Munsell 100-Hue and Dichotomous Tests for Color Vision. Journal of the Optical Society of America, 33(10), doi: /josa Gegenfurtner, K. R., & Kiper, D. C. (1992). Contrast detection in luminance and chromatic noise. Journal of the Optical Society of America A, 9(11), doi: /josaa Gegenfurtner, K. R., Kiper, D. C., & Levitt, J. B. (1997). Functional properties of neurons in macaque area V3. Journal of Neurophysiology, 77, Giulianini, F., & Eskew, R. T. (1998). Chromatic masking in the (ΔL/L, ΔM/M) plane of conecontrast space reveals only two detection mechanisms. Vision Research, 38(24), doi: /s (98) Goldstein, E. B. (2010). Sensation and Perception (8th ed.). Belmont, CA: Wadsworth Cengage Learning. Graham, N. V. (1989). Visual pattern analyzers. New York: Oxford University Press. Hansen, T., & Gegenfurtner, K. (2010). Uncovering multiple higher order chromatic mechanisms

26 COLOR DISCRIMINATION AT THRESHOLD 26 in cone contrast space. Journal of Vision, 10(7), 388. doi: / Hurvich, L. M., & Jameson, D. (1957). An opponent-process theory of color vision. Psychological Review, 64(6), Kingdom, F. A., & Prins, N. (2016). Psychophysics: A Practical Introduction (2nd ed.). Waltham, MA: Academic Press. Kiper, D. C., Fenstemaker, S. B., & Gegenfurtner, K. R. (1997). Chromatic properties of neurons in macaque area V2. Visual Neuroscience, 14, Krauskopf, J. (1999). Higher order color mechanisms. In K. R. Gegenfurtner, & I. T. Sharpe (Eds.), Color vision: From genes to perception (pp ). Cambridge: Cambridge University Press. Krauskopf, J., Williams, D. R., & Heeley, D. W. (1982). Cardinal Directions of Color Space. Vision Research, 22, doi: /82/ Krauskopf, J., Williams, D. R., Mandler, M. B., & Brown, A. M. (1986). Higher Order Color Mechanisms. Vision Research, 26(1), doi: Lennie, P., & D'Zmura, M. (1988). Mechanisms of color vision. Critical Reviews in Neurobiology, 3(4), Lennie, P., Krauskopf, J., & Sclar, G. (1990). Chromatic Mechanisms on Striate Cortex of Macaque. The Journal of Neuroscience, 10(2), MacLeod, D. I., & Boynton, R. M. (1979). Chromaticity diagram showing cone excitation by stimuli of equal luminance. Journal of the Optical Society of America, 69, Pauli, H. (1976). Proposed extension of the CIE recommendation on Uniform color spaces, color difference equations, and metric color terms. Journal of the Optical Society of America, 66(8), doi: /josa

27 COLOR DISCRIMINATION AT THRESHOLD 27 Rubin, J. M., & Richards, W. A. (1988). Color Vision: Representing Material Categories. In W. A. Richards (Ed.), Natural Computation (pp ). Cambridge, MA: MIT Press. Shepard, T., Eskew, R. T., McCarthy, C., & Ochandarena, N. (2015). Selective noise masking of L and M cone stimuli: unipolar tests reveal theoretically significant asymmetries. Journal of Vision, 15(12), 260. doi: / Stockman, A., & Brainard, D. H. (2010). Color Vision Mechanisms. In M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald,... E. van Stryland (Eds.), The Optical Society of America Handbook of Optics (3rd ed., Vol. III: Vision and Optics, pp ). New York: McGraw Hill. Watson, A. B., & Robson, J. G. (1981). Discrimination at threshold: labelled detectors in human vision. Vision Research, 21, Webster, M. A., & Mollon, J. D. (1994). The influence of contrast adaptation on color appearance. Vision Research, 34(15), doi: / (94) Wickens, T. D. (2002). Elementary Signal Detection Theory. New York: Oxford University Press. Wolfe, J. M., Kluender, K. R., & Levi, D. M. (2011). Sensation and Perception (3rd ed.). Sunderland, MA: Sinauer Associates, Inc. Young, T. (1802). The Bakerian Lecture: On the Theory of Light and Colours. Philosophical Transactions: The Royal Society London, 92, doi: /rstl

28 COLOR DISCRIMINATION AT THRESHOLD 28 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).

29 COLOR DISCRIMINATION AT THRESHOLD 29 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).

30 COLOR DISCRIMINATION AT THRESHOLD 30 Figure 5. Left: the lateral geniculate nucleus. Right: color-sensitive cells in the LGN respond preferentially to stimuli in the red-green and blueyellow color directions (Derrington, Krauskopf, & Lennie, 1984). Figure 6. Cardinal axis theory of color vision. Modified from Eskew (2009).

31 COLOR DISCRIMINATION AT THRESHOLD 31 Figure 7. LM color plane. A B C Figure 8. (A) Stimulus presentation. (B) Top: Sample stimuli at suprathreshold levels. Bottom: Sample stimuli at pseudo-threshold levels. (C) Sample noise masking pattern.

32 COLOR DISCRIMINATION AT THRESHOLD 32 M L M L 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. Figure 10. HSV color wheel.

33 COLOR DISCRIMINATION AT THRESHOLD 33 A B SIL C SIL 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. SIL

34 COLOR DISCRIMINATION AT THRESHOLD 34 A A B SIL B C SIL 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. SIL

35 COLOR DISCRIMINATION AT THRESHOLD 35 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

36 COLOR DISCRIMINATION AT THRESHOLD 36 A v WP SIL u B v WP SIL u C v WP SIL 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. u