One of the most challenging topics in the study of human color vision is the investigation of the number of hue-selective channels that are necessary for the representation of color appearance at the post-opponent level and the bandwidth of their sensitivity. The present study aims to elucidate this issue by using a chromatic version of the notch-filtered noise (herein, notched-noise) stimulus for contrast adaptation. After adaptation to this stimulus, some color-sensitive mechanisms that selectively respond to missing hues in the notched-noise stimulus may remain sensitive, while the other mechanisms may be desensitized. The shifts in the color appearance of a gray test field after the adaptation to such a notched noise were measured using the method of adjustment. The results showed systematic shifts in the hue and saturation. They showed neither point nor line symmetric profiles with respect to the achromatic point in an isoluminant plane. The fittings of the results, obtained by using a tiny numerical model for assessing the hue-selective mechanisms, suggested that there are at least two narrowly tuned and at least three broadly tuned mechanisms. The narrowly tuned mechanisms are the most sensitive along the blue and yellow directions. The present study confirmed the variation of multiple channels at the post-opponent level and suggested that this variation may be responsible for the processing of color appearance.
© 2007 Optical Society of America
The representation of color signals in the human visual system varies as the level of color-information processing advances. During the initial stage, a color signal is coded by differential activities among three cone classes. Physiological studies have revealed that color representation is transferred to one luminance channel and two opponent-color channels at the second stage; this stage is referred to as the opponent level []. The two opponent-color channels roughly correspond to two major color components—red–green and blue–yellow [, , ]. Although several physiological studies have been conducted on the color selectivity of the cortical neurons in the visual cortices of monkeys [, , , , , , ], a general overview of color representation at the post-opponent level in human color vision remains to be clarified.
One of the distinct differences between opponent- and post-opponent-level mechanisms is the preference of neurons to certain hues: while the opponent-level mechanisms have two main axes that can be defined by the sums and differences of the cone responses [, ], the post-opponent-level mechanisms exhibit a preference to the directions away from the opponent-level axes [, ]. These mechanisms are referred to as multiple mechanisms or off-axis mechanisms.
Several psychophysical studies on post-opponent-level color mechanisms have been conducted using techniques such as contrast adaptation [, , , , ], noise masking [, , , , ], and color naming [, , ]. Studies on the contrast-adaptation technique have shown the possible existence of hue-selective mechanisms that are sensitive to directions away from the cardinal axes [, ], that is, the off-axis directions.
The results of these psychophysical studies mainly revealed the selectivity of the off-axis mechanism in a point-symmetric manner with respect to the origin of the isoluminant color plane (i.e., an achromatic point). However, electrophysiological studies have revealed that the hue selectivity of the neurons in macaque visual cortices showed unidirectional distributions, i.e., the sensitivity distributed along only one side of the color space with respect to the achromatic point in the chromaticity plane [, , ]. One of the simplest methods for investigating hue selectivity is to use unidirectional masking or adaptation stimuli to modify the sensitivity of a particular set of hue-selective mechanisms in the noise range.
An attempt to use the unidirectional chromatic noise-masking technique demonstrated the existence of the unidirectional hue-selective mechanism in the form of detection threshold elevation []. The study also demonstrated the existence of mechanisms responsible for chromatic detection along an oblique direction between the cardinal axes of the opponent-level neurons. In a recent study, an image-classification technique was used to investigate the selectivity bandwidth of the hue-selective mechanisms that could be used to detect each target hue []. In addition, several studies have been conducted on the chromatic property of the mechanisms of form perception [, , , ]; these studies suggested the existence of hue-selective systems along the off-axis directions. However, the number of mechanisms tested in all the abovementioned studies was limited by the number of target hues defined by the researchers, and the basic number of multiple hue-selective channels is still undetermined. In other words, the total number of existing basic channels remains unclear.
The application of the contrast-adaptation technique by using unidirectional hue variations in color space proved the difficulty in using this approach to investigate the color appearance mechanisms at the post-opponent level. In a study by Webster and Wilson [], the subjects were required to match the colors between the adapted and nonadapted visual fields to assess the effect of contrast adaptation, and the results obtained revealed bidirectional desensitization. In other words, a reduction in the color appearance was observed along both the hue direction of adaptation and its opposite direction with respect to the achromatic point. They discussed that this bidirectional desensitization could probably be due to the adaptation of some lower-level mechanism to the mean chromaticity (dc component) of the contrast-adaptation stimulus. The color vision stream beyond the lower-level adaptation site would have mainly received color signals in the form of bidirectional deviations from the mean chromaticity (ac component) of the adapting stimulus. If this is true, the deviation from the white to the mean color of the adapting stimulus should be minimized when investigating the characteristics of the off-axis channels by using the chromatic contrast-adaptation technique. Hence, we developed a novel contrast-adaptation technique to introduce a unidirectional change in the sensitivity of the hue-selective mechanisms.
To investigate the characteristics of unidirectional hue-selective mechanisms, we developed a contrast-adaptation technique that isolates the hue-selective mechanisms that are sensitive to a certain color range. This technique involves the presenting of noise that contains almost all the hues except for those within a certain range. This would reduce the deviation of the mean color from the achromatic point; this in turn may reduce the artifactual effect of the adaptation of the lower-level mechanisms to the dc component of the contrast-adaptation stimulus. The present study reports the observations of the aftereffect of this contrast-adaptation stimulus on the color appearance.
2A. Basic Idea of the Notched-Noise Stimulus
The notched-noise technique is a stimulus-presentation method that can be used to introduce a differential sensitivity distribution among multiple channels. In the field of perceptual study, this type of stimulus was used for studying the frequency-tuning characteristics in the human auditory system []. A similar technique has also been applied in a study on the spatial tuning property in the peripheral visual field [].
In the case of application to a color-appearance study, an advantage of using a notched-noise color stimulus is that the mean chromaticity shift is smaller than that obtained using conventional contrast-adaptation stimulus whose color was selected from a narrow bandwidth. The smaller mean color shift is effective in minimizing the adaptation to the dc component that possibly occurs at a relatively lower level in the human visual system. As stated above, the use of the narrowband adapting stimulus was not successful in establishing a differential adaptation among the hue-selective channels [], probably due to the lower-level adaptation toward the mean chromaticity. In a previous study, the areas of adapting stimulus components were manipulated to realize the polarity-specific adaptation along the luminance direction []. In the present study, we realized a similar polarity-specific adaptation along the hue direction by selecting a color set in the adapting stimulus and presenting these colors in a regularly sectioned mosaic pattern.
The colored version of the notched-noise stimulus has a nonzero shift in the mean chromaticity; however, this shift is relatively small, and the effect of adaptation to the mean chromaticity (dc component) becomes considerable as the notch width becomes larger. To confirm the effect of the notch itself, we compared the change in the color appearance after adaptation with a notched-noise stimulus and an isotropic chromatic noise and also with a uniform stimulus having the same mean chromaticity.
2B. Definition of Color Space
The color space used in the present study was an isoluminant plane (the sum of the L- and M- cone responses are always the same), and the two axes represent the Weber contrast of L- and S-cone responses with respect to the response of each cone to the equal-energy white at . The definition of each axis is as follows:] were used in this study without applying any scaling factor. According to the isoluminant constraint, the changes in the M-cone response were always equal to the changes in the L-cone response . The resulting color space shows some degree of analogy to the one defined by Derrington et al. [] or by MacLeod and Boynton [].
In the results of the present study, the chromatic axes are expressed by the multiples of the color-discrimination threshold for each subject measured in a different experiment. The summary of the method for measuring the thresholds is as follows. A checkered pattern was presented at the center of the screen to present color modulation. The check size was —the same as that used in the main experiments. The stimulus was a checkered pattern modulated in either the L–M or S direction at . The stimulus was presented at the center of the screen with a thin black gap in a gray background (equal-energy white). The color contrast was modulated in time with a raised cosine envelope with duration of . The subject was then instructed to report the direction of the chromatic modulation: either L–M or S. The minimum chromatic modulations necessary to discriminate these two color modulations at 75% were measured in the L–M and S directions. The relative magnitudes of the thresholds in the two directions for color discrimination were slightly different among the subjects, but the threshold for the S-cone direction was approximately ten times as much as that in the L-cone contrast when compared with that of the threshold for the L–M direction.
2C. Selection of Color for Notched-Noise Stimulus
The hue angle was defined in a counterclockwise direction starting from the positive direction of the L–M axis ; the positive direction of the S axis corresponds to in the hue angle. The colors for the following experiments were selected at the intervals of starting from . The distance from the origin (equal-energy white) was 100 times that of the discrimination threshold (Fig. 1 ).
In the notched-noise stimulus, 9 or 10 (depending on the experimental condition) out of 60 colors were excluded to form the “notch.” The center direction of the notch was determined by steps—starting from —and five colors on both sides of the notch-center direction were excluded. For example, in the case of the center direction of the notch at , colors corresponding to , , , , 0, 6, 12, 18, and were excluded. According to the definition, the hues within the range of less than and were excluded, which constituted of the notch. For the condition in which the center direction of the notch is at , the colors at 18, 24, 30, 36, 42, 48, 54, 60, 66, and were excluded.
The saturation of colors was defined by the Euclidean distances in the color space; this was defined by the multiples of the color-discrimination thresholds on both the L–M and the S axes. The maximum saturation was 0.08 in the L-cone contrast , and the maximum saturation in the S-cone direction was approximately 0.8 in the S-cone contrast . Both the saturations roughly correspond to approximately 100 times of the saturation at the threshold. The colors for adapting stimulus were defined as follows:
In most studies, the use of the isoluminant stimulus was aimed at avoiding the stimulation of the magnocellular pathway. However, interactions between the color and motion signals are reported not only from the color to motion signal [, ] but also from motion to color signal []. Moreover, it was not possible to realize an isoluminant surface with complete uniformity for each subject considering the nonuniformity of both the display and visual system. However, the use of the notched-noise stimulus may help to reduce the influence of a motion-sensitive mechanism in the magnocellular stream by desensitizing it using a dynamic stimulus presentation.
2D. Apparatus and Stimulus Size
Stimuli were generated by a Visual Stimulus Generator VSG 2/5 (Cambridge Research Systems, UK), controlled by a personal computer Opti-plex 350 (Dell, USA), and presented on a CRT display GDM F-520 (Sony, Japan). The screen chromaticity and luminance were calibrated with a spectroradiometer SR-3 (Topcon, Japan).
The CRT screen was placed at a distance of away from the subject, and the subject used a chinrest to maintain his/her head position. The screen size subtended in visual angle. The size of the adapting and matching fields was ; the element size of the noise stimulus was , which created a element tiled-mosaic pattern. The center of each field was offset by to the left and right of the fixation point (Fig. 2 ).
Three subjects (AM, II, and IK) participated in experiments 1, 2, and 3. Two subjects (IK and KK) participated in experiment 4. All subjects had normal color vision (AM, II, IK, and KK), and their visual acuity was normal (AM, II, and IK) or corrected to normal (KK). All the subjects except the author (IK) were naïve to the purpose of the experiment.
The subjects were instructed to adapt to the notched-noise stimulus presented on either side of the screen while fixating at a point at the center of screen. The initial adaptation took , and the time for the test stimulus presentation and adjustment took . The top-up adaptation followed this period for , and the test stimulus was presented again to allow the subject to continue adjusting. The reference stimulus to be matched was presented in the noise-adapted field, and the stimulus in the field where no adapting noise had been presented was adjusted to match it. This cycle ( of readaptation and of adjustment) was repeated until the subject reached a satisfactory match (Fig. 3 ). The same stimulus sequence was used in the following experiments. Five trials were repeated for each stimulus condition. The average of five trials was shown in the results. Throughout most of the experiment, the standard deviation of the subjects’ matches was just as large as the size of the symbol or twice its size, unless mentioned otherwise.
The background was a uniform gray with the chromaticity of equal-energy white at ( in CIE 1931 tristimulus value). When the adapting stimulus was absent, the area of the adapting stimulus was replaced by a gray background so that the entire screen was maintained isoluminant except at the edges of the adapting areas and the fixation point.
2G. Confirmation of Color-Space Anisotropy
For confirmation and correction of the anisotropy of the color space induced by the adaptation to the notched-noise stimulus, the aftereffect of adaptation to a noise stimulus without the notch (isotropic-noise stimulus) was measured by the method of adjustment. In this experiment, the stimulus included all hues at intervals of in hue angle to present a dynamic-random mosaic pattern. In the isotropic-noise condition, the subjects were asked to match the 12 hues ( step from ) between the adapted and nonadapted field.
The test stimulus chromaticity, which was presented after the adaptation, was aligned on a circle in the isoluminant plane, but the matched colors are distorted roughly in the shape of an ellipse (Fig. 4 ). The distortion is basically symmetric, and no axis in particular showed a strong asymmetry. However, the distortion is slightly different among the subjects.
There was no particular shift in hue, but there was a reduction in saturation in all the hue directions. The amount of reduction was slightly different among the hues, and this was well fitted by an ellipsoid. The parameters (the center, longer diameter, shorter diameter, and tilt angle) were used for the calibration of the results in the main experiments with adaptation to dynamic random noise. For the correction of the anisotropy of the dynamic stimulation, the results with notched-noise adaptation were scaled in saturation so that the matched point with isotropic noise coincided in chromaticity with the test stimulus being matched.
3. EXPERIMENT 1: ASYMMETRY OF COLOR SENSITIVITY AFTER NOTCHED-NOISE ADAPTATION
The evidence of the asymmetric sensitivity in the hues introduced by the adaptation to the chromatic notched noise will be shown in this experiment. If there were asymmetry in the sensitivity to colors in the direction of the notch and in the direction opposite to it, the apparent colorfulness could be different for these two directions. In the present study, the word “asymmetry” mainly refers to the situation in which the performance in one direction is better compared with the opposite direction with respect to the origin of isoluminant color space (achromatic point).
The adapting angle was set at 45, 135, 225, and in hue angle. The width of the notch was . If the aftereffect of adaptation to notched-noise stimuli in the oblique directions of this color space is asymmetric, it could serve as a strong evidence for the success of the polarity-selective stimulation of the hue-selective channels. On the other hand, if the effect of adaptation were limited to the direction parallel to either of the axes or if there were no directional difference in the effect, it would be possible to infer changes in the individual cone class or in the opponent-color mechanisms to account for the result.
Figure 5 shows the result of color matching for the 12 hues at two levels of saturation. The dotted oblique lines in each panel represent the center directions of the notch in each adaptation condition. The result shows an elongation in addition to a shift of the matched color distribution toward the direction of the notch. If an asymmetry in the color sensitivity exists after adaptation to the notched noise, colorfulness should increase for the direction of the hue-selective mechanism that is intact after the notched-noise adaptation.
Figure 6 shows the distance from the match point for the gray test stimulus (cross symbols) to the match points for the various reference colors. The horizontal axis represents the angle between the reference color vector and the center direction of the notch in the adapting stimulus. If this distance is greater in one direction than in the opposite direction, it suggests an asymmetry in the sensitivity distribution in the color space after adapting to the notched-noise stimulus. It is clear that the results from subjects AM and IK show asymmetry between the direction of the notch (approximately zero on the horizontal axis) and the direction opposite to the notch (around ), although the extent and direction of the asymmetry are not uniform across subjects or across notch directions.
For both subjects the peaks are slightly offset from the center of the notch direction: zero on the horizontal axis. This may suggest that the peak sensitivity of a dominant hue-selective channel is slightly offset from the direction of the notch. This point will be further investigated in the next experiment.
4. EXPERIMENT 2: HUE SHIFTS AFTER NOTCHED-NOISE ADAPTATION
A study of auditory perception has shown the shift in the perceived pitch (perceived frequency of tone) after notched-noise adaptation []. The shift occurs toward the center frequency of the notch, around which the response of the channels sensitive to this range becomes dominant after the adaptation to a notched-noise stimulus.
In the case of color representation, the response of the hue-selective channels can be assumed to code the component of the representative hue for each channel. The responses of the hue-selective mechanisms are distributed in the angular direction of the hue circle. Therefore, it is expected that the shifts in the perceived hue toward the dominant hue-selective mechanism will occur after the notched-noise adaptation. We will attempt to observe the hue shifts across the overall direction of the isoluminant plane, which can be inferred from the relationships between the notch direction and the peak sensitivity among the hue-selective mechanisms.
The ideal method of study for this phenomenon is to make matches for all the 12 test colors under 12 conditions of notch-center directions like those in experiment 1. Such an experiment may provide the complete data to investigate the characteristics of the off-axis channels, but the number of data points would be extremely large and could be redundant. This will be investigated in the future.
Since the scope of the present paper is to demonstrate the usefulness of the notched-noise adaptation technique as a tool to investigate the multiple-channel characteristics, the result of hue shifts for a gray test field will be presented here. If we may assume that the responses of all the channels are integrated as their vector sum, the achromatic point could be represented as a balancing point among all the hue-response vectors. Therefore, the equal-energy white will be used as a test stimulus to probe the direction of the most sensitive hue channel.
Figure 7 shows the colors matched to the gray test color when the gray was viewed after adaptation to the 12 notch-center-direction conditions. The locus of the symbols shows an irregular rounded shape around the origin, and there is no clear axis of symmetry.
The relationships between the notch-center and the matched-hue angles are shown in Fig. 8 . The vertical axis of Fig. 8 shows the difference between the horizontal and vertical axes values in Fig. 7. The trends of the hue shift in Figure 8 are similar across subjects, but differ slightly in detail. Figure 9 shows the difference between the matched hue and the direction of the notch.
If a color-encoding system receives linear inputs from the cone responses adapted by the notched-noise stimulus, the aftereffect would be expected to be almost identical to the direction of notch. However, the present result (Figs. 7, 8, 9) shows that this is not the case. If a small number of hue-selective mechanisms are responsible for the notched-noise adaptation, the dominant mechanism, which is exclusively retained according to the notch, may be the dominant component among the multiple-channel responses to encode for the appearance of the gray test stimulus. Therefore, the shift in the color appearance close to the peak sensitivity of the dominant channel would be toward the preferred direction of the dominant mechanisms as follows: when the notch hue angle is smaller than the preferred direction of the dominant mechanism, the resulting hue shift would be positive and vice versa. Therefore, the zero-crossing points in Fig. 9 with changes in the sign from positive to negative may correspond to the possible peak positions of hue-selective channels, which are visible under the current experimental condition.
5. EXPERIMENT 3: MOSAIC-ELEMENT SIZE (EFFECT OF DC COMPONENT)
It is possible to argue that the hue shifts observed in this experiment are the result of adaptation to a dc component inherent to hue selection of a notched-noise stimulus and are not caused by the contrast adaptation to a notched-noise stimulus. To show that the hue shift is evoked by the dynamic presentation of the notched noise and not due to adaptation to the DC component, an additional experiment was conducted. A static uniform adapting field with chromaticity identical to the mean chromaticity of the notched-noise stimulus was used to demonstrate the difference between the adaptation to the notched-noise stimulus and to a static uniform adapting field. In addition to the adaptation to the uniform field, we varied the size of the element of dynamic random-mosaic pattern, such as (original condition), and . The smallest size condition uses a square mosaic element with the size of pixels. Each element is still just visible to the subjects but the apparent chromatic modulation is less salient. Thus the effect of adaptation to the stimulus with a smaller mosaic-element size is expected to be closer to that of the uniform adapting-field experiment.
Figure 10 shows the result of condition under adaptation to the static uniform field with the same chromaticity as the mean chromaticity of the notched-noise stimulus. The radial dotted lines indicate the hue directions of uniform-field chromaticity. Although the amplitude of chromatic saturations are different among adapted hues, the afterimage shows little shifts in hue direction from the opposite hue direction of the adapting stimulus.
Figure 10 also shows the effect of the mosaic-element size on the appearance of the gray test surface in the form of two dimensional plots in the isoluminant plane and in the profile of the hue shifts. The general tendency of the result showed that with an increase in the mosaic size the hue shift becomes larger but the saturation of the afterimage becomes smaller. The results under the smallest mosaic-element size condition showed almost no hue shifts, which is close to the results measured after the adaptation to the uniform field. However, the chromatic saturation of the afterimage was different by approximately a factor of 2, compared with the uniform-field adaptation. This may be because contrast adaptation reduced the sensitivity to chromatic saturation in the dynamic adaptation condition. Also note that the results under the notched-noise adaptation condition are scaled in the direction of the chromatic saturation for the correction of anisotropy across hues (see Subsection 2G).
Figure 11 shows the changes in hue shifts with the mosaic-element size. As the mosaic-element size became smaller, the amount of hue shift was closer to the results under uniform-field adaptation. This is reasonable because as the element size became sufficiently small and it was difficult to resolve each element on the retina, the effect of adaptation was probably equivalent to the mean chromaticity (i.e., dc component) of the notched-noise pattern.
6. EXPERIMENT 4: CONFIRMATION OF OFF-AXIS CONTRAST ADAPTATION
The presentation of a randomly arranged color-mosaic pattern in a dynamic manner is different from the conventional stimuli for contrast adaptation [, , ]. In this experiment, the effect of contrast adaptation with was compared with the conventional method. The conditioning stimulus was a dynamic random-color-mosaic pattern whose element color was selected along a diagonal line in the or direction in a plane defined by the L vs M axis and the luminance axis. The origin of the coordinates was an equal-energy white at . For comparison, a sinusoidal modulation of color for each axis in a uniformly colored square was also tested as adapting stimulus [, ]. Eight test colors were selected at intervals on a circle with a radius that was 50 times that of the discrimination thresholds. A fixation point, either to the left or right, was used as an adapting field, and a test color was presented at the same position as the adapting field. An identical field was presented on the other side of the fixation point, and the subject adjusted the luminance and chromaticity of this field to match the appearance of both fields.
Figure 12 shows the result of this experiment for two subjects. The data have been normalized by the control condition in which the subject matched colors without contrast adaptation. The normalization was performed by calculating the scaling factor for the distance from the origin so that each matched point would be aligned to the physical chromaticity of the test stimuli. The solid squares show the results of color matching after adaptation to the dynamic random-noise stimulus, and the open circles show the result after adaptation to the sinusoidal color modulation. The resulting colors appeared to be aligned on oblique ellipses, and the directions of the shorter radii were considerably similar to the direction of the contrast modulation (dotted oblique lines) during the adaptation period. The efficiency of the dynamic random-noise presentation varied slightly among the subjects; KK showed almost equivalent effects of contrast adaptation, but IK showed slightly weaker adaptation in a dynamic random-mosaic adaptation.
In summary, the use of a dynamic random-mosaic pattern evoked contrast adaptation similar to that produced by the sinusoidal modulation of color contrast.
7A. Summary of Results
In the present study, we confirmed that the chromatic notched-noise adapting stimulus realized a nonuniform sensitivity distribution with regard to color such that the unidirectional hue-selective mechanisms reduced in sensitivity; i.e., the response strength to the color for one side of the color space was higher than that for the other side with respect to the achromatic point. Contrast adaptation to the chromatic notched noise resulted in systematic hue shifts and some asymmetric reduction in the chromatic saturation gain.
7B. Model of Notched-Noise Adaptation
The result of the present study may permit us to draw some inference regarding the site of the adaptation by the notched-noise stimulus. Since the adaptation asymmetry was observed in the oblique directions in the isoluminant color plane defined by the L–M and S axes (Figs. 4, 5 in experiment 1), it is possible to state that the cone adaptation and the opponent-color-channel adaptation do not account for the results of the present study. Exclusively under the condition of adapting to the stimulus using notched color distribution (notched-noise adaptation), we found shifts in the hues of the afterimages. This hue shift is related to the range of the notch and to the sensitivity distribution of the multiple-color channels. Therefore, more precise observation and analysis are necessary to determine the tuning property of the hue-selective mechanisms in the post-opponent level of human color vision.
We made an informal attempt to fit the data with a small number of hue-selective mechanisms with the selectivity of a Gaussian profile like those adopted in the study by Goda and Fujii []. Each Gaussian-shaped sensitivity distribution is defined by the following three parameters: a center hue angle, a bandwidth, and a scaling factor. The scaling factor is necessary to adjust the balance among the hue-selective mechanisms so that the output for equal-energy white in the isoluminant plane is nullified. In this study, two new assumptions were introduced in addition to the model of Goda and Fujii []. One is a center-of-gravity code for color: the excitation of each hue-selective mechanism represents the hue component of the peak direction. The output of each mechanism acts as a vector, and the sum of all the vectors will result in the corresponding color. The second is that adaptation was implemented by simply dividing the excitations for each mechanism by the sum of the excitations from the colors in the adapting stimulus.
The model parameters were optimized by minimizing the squared sum of distances between the predictions and the observed results shown in Fig. 7. The result showed good matches when the number of hue-selective mechanisms was set between four and six. The goodness of fit became better when a larger number of mechanisms were employed; however, the redundancy increased in such a way that two mechanisms overlapped. After introducing Akaike’s Information Criterion [] to penalize the introduction of added parameters, the optimal number of mechanisms was determined for each subject, and the peak angle and bandwidth was estimated for each mechanism. The result of fitting to experimental data (Fig. 7) when the number of hue-selective mechanisms is set to five is shown in Table 1 . The bandwidths and the number of mechanisms partly agree in terms of the numbers suggested in a study by Goda and Fujii []. However, the assumption regarding the reduction of sensitivity by adaptation is too simple to be plausible from the physiological point of view. It is necessary to improve the quality of the model to acquire the complete profiles of multiple hue-selective mechanisms by the notched-noise-adaptation technique.
7C. Comparison with Previous Studies
Krauskopf et al. [, ] reported an asymmetric threshold elevation after adaptation to the chromatic stimulus with an asymmetric temporal profile of color change, such as a sawtooth pattern. It comprised a phase with a slow color change in a certain direction through the achromatic color and a phase wherein the presented color changes abruptly to the opposite hue. The Fourier analysis of the threshold elevation showed that one of the phase components changed in proportion to the angular direction of the sawtooth modulation axis in the isoluminant plane (Fig. 4 in Krauskopf et al. []). If the number of off-axis mechanisms is small (for example, between four and seven, as suggested by Goda and Fujii []), the effect of the asymmetric changes in the sensitivity of these mechanisms may be less regular.
One subsequent study by Zaidi and Shapiro [] reported that the threshold elevation based on the contrast adaptation to a certain axis in the color space occurs due to the adaptive weight changes of the interactions between the opponent-color mechanisms. This occurs as an attempt to maximize the efficiency of the color signal and implies that the number of channels is not fixed. This study also predicted shifts in the color appearance from the measured changes in the color-discrimination thresholds. A part of the results of this study showed asymmetry across the achromatic point. However, most of the results measured by detection or discrimination thresholds were summarized in a symmetrical manner with respect to the achromatic point in the isoluminant color space. If two major axes were defined to describe the color distribution of our notched-noise stimulus, one axis would be along the orthogonal direction of the notch and the other would be directed through the center of the notch. The dispersion in color distribution is maximal along the orthogonal direction and minimal along the direction of the notch. In the present study, we used a notched-noise stimulus in which one-sixth of the hue was missing. Assuming that the radius of hue distribution is 1.0, the extent of color distribution along the orthogonal direction would be 2.0. On the other hand, the extent of color distribution along the direction of the notch would be or 1.87. The possible difference between the extents of the color-signal amplitude along the two orthogonal axes is approximately 6.5%. Considering that a higher-order color mechanism involves weight adjustments between the opponent-color mechanisms in order to maximize the efficiency of the chromatic-contrast signal, the larger asymmetries observed occasionally in the present study (Figs. 4, 5) should not arise. Therefore, we would infer that the mechanism investigated in the present study is not identical to that suggested in a study by Zaidi and Shapiro [].
Zaidi and Halevy [] investigated a number of possible mechanisms that are sensitive to abrupt color changes. They averaged the results among 16 background phase conditions because they considered that the detection thresholds generally tended to change depending on the difference between the background hue angles and the color-change directions. They proposed a possible mechanism that is the most sensitive to the concurrently presented hue and the least sensitive to the opposite hue. They did not discuss the number of possible mechanisms, and their proposed mechanism was designed to describe the changes in the color-discrimination threshold as a function of the hue-angle difference between the 16 background conditions and color-change directions. Based on the results of the present study, there appeared to be less than 16 mechanisms responsible for the shifts in the color appearance after the adaptation to the chromatic notched-noise stimulus, and the hue directions of the peak sensitivity for the hue-selective mechanisms were irregularly spaced in terms of the hue angle. As discussed above, the mechanisms investigated in their study could probably differ from those investigated by the asymmetric color-matching task after notched-noise adaptation.
Goda and Fujii [] attributed the results of their study to a few hue-selective systems. The number of hue-selective systems was estimated to be between four and seven, which differed among the subjects, and the bandwidth (FWHM) of each hue-selective mechanism was approximately in the isoluminant plane. Several physiological studies on the hue selectivity of neurons in the primary and secondary visual cortices of primates have been performed. They revealed that these selectivities could not be simply predicted by the linear summations of the hue selectivity of the opponent-color systems [, , , , , , ]. It was indicated that considering only the linear summations of the opponent-color channels would give rise to difficulties when the hue selectivity of human visual cortex neurons is determined during the early stages [].
D’Zmura and Knoblauch [] tested the threshold changes for chromatic detection along four particular directions in the color space (orange, red, green, and violet) while varying the angular width of the possible range of noise color. Their method of presenting and selecting color as a noise stimulus was different from our method, but the mechanisms they attempted to reveal might be closely related to those revealed in the present study. Their results showed that the threshold elevation was independent of the bandwidth; this implies that the broadband sensitivity of the hue-selective mechanisms at the post-opponent level ranges along the hue direction. In this study, according to an estimation performed using a numerical model, it was inferred that the possible bandwidth of the hue-selective mechanism is approximately (the σ value) when the sensitivity distribution in the isoluminant plane was simulated by a Gaussian sensitivity distribution. The result of the present study may agree with this result to a certain degree in that the sensitivity bandwidth of certain hue-selective mechanisms is broader. However, there are some differences between our study and that by D’Zmura and Knoblauch [] in that the use of chromatic notched-noise stimulus may be advantageous as a method of investigating the property of hue-selective mechanisms at the post-opponent level. In the study by D’Zmura and Knoblauch [], the parameters for describing the properties of hue-selective mechanisms (the number, preferred hue direction, and bandwidth) were defined by the experimental conditions; however, in the present study, these parameters were considered as unrestricted parameters. Moreover, the noise stimulus used by D’Zmura and Knoblauch [] contained various temporal frequency components because the color changes in the background were a stochastic process, i.e., abrupt changes interleaved with static periods of randomly determined length. On the other hand, compared with their noise stimulus, our adapting stimulus could manipulate the temporal frequency profile more directly by changing the temporal frequency of color alternation.
Hansen and Gegenfurtner [] used the image-classification technique, which is a variation of the noise-masking technique [, ], to investigate the hue selectivity at the higher processing stages of human color vision. Their strategy was to clarify the range of color selectivity for several hue-selective channels by monitoring the colors that interfere or are erroneously identified during target color detection. Their results have revealed the bandwidth and peak direction of each hue-selective channel; however, the number of channels that can be inferred from this technique is limited by the number of test colors employed.
A study by Devalois et al. on unique hue-component distributions in an isoluminant plane in a cone response space revealed an inconsistency between the cardinal directions of the lateral geniculate nucleus neurons and the peak of the unique hue component []. They reported that the hue directions in the isoluminant plane that maximize the reddish and greenish components are not exactly aligned along a straight line running through the achromatic point. Similar misalignment (referred to as “asymmetry” in their description) was also detected for the blue–yellow pair. These misalignments between the opponent unique hue pairs were also reported in another study by Webster et al. []. They also reported that the misalignments differ among individuals. These misalignments (asymmetries) can be attributed to the preferred direction of the unique hue mechanisms. The present study also suggested that two narrowly tuned mechanisms, which have peaks along the bluish and yellowish directions, were not aligned along a straight line running through the achromatic point. The hue-selective mechanisms that were derived from the shifts in the color appearance after the adaptation to chromatic notched noise could be at the same level as the unique hue representations.
There are several psychophysical studies on the chromatic property of the mechanisms of form perception; these studies suggested the existence of the off-axis hue-selective channels. A series of studies [, , ] have suggested two stages of multiple-color channels. One of these stages comprises mechanisms with a narrow bandwidth in terms of the hue angle, and the other involves a wider bandwidth. Two studies using Glass patterns suggested that the mechanism with a narrow color bandwidth is responsible for classifying the numerous dots in the stimulus into two groups [], and the system with a wider color bandwidth is responsible for integrating a pair of patterns to establish a global form perception []. However, another study on the chromatic property of the mechanisms of Glass-pattern perception suggested that the mechanisms at the level of integration have little or no color selectivity []. Since the numerical model used for an informal assessment in the present study comprised a single-stage mechanism with channels of various color bandwidths, and the subjects performed the task of assessing the color appearance, it is difficult to directly compare hue-selective mechanisms of the current study with those of the previous form perception studies. Further precise assessment of the models would be required to evaluate the numbers and bandwidths observed in the present study. However, even after excluding the assessment with a numerical model, the hue shifts observed in the present study showed that there are dominant channels with narrow hue selectivity around the bluish and yellowish regions where color appearance tends to converge after the adaptation to the chromatic notched noise (Figs. 6, 8). Therefore, at least these two channels have narrow bandwidths when assessed under the color-appearance task.
7D. Spatiotemporal Characteristics of Notched-Noise Adaptation
In the present study, adaptation aftereffects with three variations of spatial property—namely, 0.09 (two pixels), 0.36, and of mosaic-element size—were studied using dynamic noise presented at 20 frames per second (fps) in time. As shown in Fig. 10, the chromatic saturation of the afterimage became larger, and the hue shifts became smaller with the decrease in the element size. We also varied the temporal property of the notched-noise stimulus under the variations of 5, 10, 20, and while retaining the mosaic-element size at . The general trend of the result revealed that as the number of frames per second increases, so does the chromatic saturation of the afterimage; however, the hue shift becomes smaller.
Webster et al. [] reported a series of studies on the effect of the contrast and the context of the scene on color appearance. In one of their experiments they used a method of serial presentations of uniform colors that were picked up from an image of a natural scene. They found systematic hue shifts in color appearance after the adaptation. Their study slowly presented various colors of uniform fields, and the adaptation took several minutes. The method of measurement and the spatiotemporal characteristics of the adapting stimulus are both different from those used in our study. The exact tendency of the hue shifts is not identical to our study; however, the hue shifts clearly suggest a mechanism that is different from the linear transformation of cone responses, such as the von Kries adaptation mechanism.
In the present study, our chromatic adaptation method, i.e., chromatic notched-noise adaptation, created a biased state of chromatic adaptation among multiple hue-selective channels. This introduced systematic hue shifts, which were represented by two peaks and troughs when tested using a uniform gray test field. Fitting of the results by using a simple numerical model revealed that two narrowly tuned channels in the bluish and yellowish directions and more than two broadly tuned channels are required to account for the shifts in the color appearance after the contrast adaptation to the chromatic notched-noise stimulus. The present study confirmed the variation of the multiple channels at the post-opponent level and suggested that this variation may be responsible for the processing of the color appearance.
APPENDIX A: NUMERICAL MODEL OF NOTCHED-NOISE ADAPTATION
This model can be expressed with the following formulas:
I thank Kyohei Koizumi, Yoriko Sasaki, and Isao Ishida for their technical assistance. I am also grateful to Donald I. A. MacLeod, Shin’ya Nisida, Isamu Motoyosi, Shigeki Nakauchi, and Takehiro Nagai for the helpful discussions. I thank Makio Kashino, Takehiro Moriya, Shigeru Katagiri, and Haruhisa Ichikawa for their help. I also thank the reviewers and the editor for their critical and constructive comments for improving the manuscript.
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