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Research Article  |   August 2004
Positional adaptation reveals multiple chromatic mechanisms in human vision
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Journal of Vision August 2004, Vol.4, 8. doi:10.1167/4.7.8
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      Paul V. McGraw, Declan J. McKeefry, David Whitaker, Chara Vakrou; Positional adaptation reveals multiple chromatic mechanisms in human vision. Journal of Vision 2004;4(7):8. doi: 10.1167/4.7.8.

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Abstract

Precortical color vision is mediated by three independent opponent or cardinal mechanisms that linearly combine receptoral outputs to form L/M, S/(L+M), and L+M channels. However, data from a variety of psychophysical and physiological experiments indicate that chromatic processing undergoes a reorganization away from the basic opponent model. Frequently, this post-opponent reorganization is viewed in terms of the generation of multiple “higher order” chromatic mechanisms, tuned to a wide variety of axes in color space. Moreover, adaptation experiments have revealed that the synthesis of these mechanisms occurs at a level in the cortex following the binocular integration of the inputs from each eye. Here we report results from an experiment in which the influence of chromatic adaptation on the perceived visual location of a test stimulus was explored using a Vernier alignment task. The results indicate that not only is positional information processed independently within the L/M, S/(L+M), and L+M channels, but that when adapting and test stimuli are extended to non-cardinal axes, the existence of multiple chromatically tuned mechanisms is revealed. Most importantly, the effects of chromatic adaptation on this task exhibit little interocular transfer and have rapid decay rates, consistent with chromatic as opposed to contrast adaptation. These findings suggest that the reorganization of chromatic processing may take place earlier in the visual pathway than previously thought.

Introduction
The perception of color information involves several distinct sequential stages of processing in the visual pathway, extending from early retinal mechanisms through to cortical modulation of early signals. Precortical color vision is mediated by three independent opponent mechanisms that linearly combine receptoral outputs to form L/M, S/(L+M), and L+M channels (DeValois, Abramov, & Jacobs 1966; Derrington, Krauskopf, & Lennie 1984). The chromatic sensitivity of each of these channels is taken to define the cardinal axes in three-dimensional color space. This idea of segregation and functional independence is consonant with both physiological (Lennie, Krauskopf, & Sclar, 1990) and psychophysical evidence (Krauskopf, Williams, & Heeley, 1982; Krauskopf, Williams, Mandler, & Brown 1986; Flanagan, Cavanagh, & Favreau, 1990; Webster & Mollon, 1991; Gegenfurtner & Kiper, 1992; Webster & Mollon, 1994). However, in the primate visual pathway, the neural coding of color information undergoes a transformation away from this basic opponent model between the LGN and the visual cortex (V1). As a result, chromatic processing in the primary visual cortex has a very different organization from the post-receptoral processing stage. Results from single unit neurophysiological studies show that neurons in V1 are tuned to a much wider range of chromaticities than their counterparts in the LGN (Lennie et al., 1990). Therefore, the pattern of sensitivity specific to the cardinal axes, so prominent at the LGN, is lost at the level of the cortex. Behavioral measures also point to the existence of multiple chromatic mechanisms tuned to a wide variety of axes in color space. For example, the phenomenal appearance of colors, color adaptation, and masking effects all suggest the existence of a large number of differentially tuned mechanisms spanning color space (Krauskopf et al., 1986; Webster & Mollon, 1991; Gegenfurtner & Kiper, 1992; Webster & Mollon, 1994). This transformation away from the basic opponent model toward multiple chromatic mechanisms is not the only difference between earlier and later stages. Whereas cells in the LGN sum cone input in a linear fashion (Derrington et al., 1984), many V1 cells show surprisingly narrow tuning, suggesting the operation of a response nonlinearity at the level of the cortex (Lennie et al., 1990; De Valois, Cottaris, Elfar, Mahon, & Wilson, 2000). 
In the present study, we explore issues relating to the multiplicity and specificity of chromatic mechanisms using a suprathreshold positional adaptation paradigm. The influence of adaptation on perceived spatial position in the luminance domain has previously been investigated in our laboratory. Results from these experiments showed that when the adapting and test stimuli are defined by the same visual information (i.e., they are processed by the same physiological mechanism), they interact to produce large positional offsets in the test stimulus. If, however, they activate different physiological mechanisms, little or no interaction occurs (Whitaker, McGraw, & Levi, 1997). In this study, we employ a similar rationale, but use color-defined stimuli. Observers adapt to a range of luminance contrast and isoluminant chromatic contrast-defined stimuli, the chromatic content of which was modulated along numerous axes in color space. We measure the chromatic specificity, the degree of interocular transfer, and the rate of decay of induced positional offsets resulting from chromatic adaptation, in an attempt to characterize the fundamental nature of selectively adaptable chromatic mechanisms. 
Methods
Procedures and stimuli
A three-element Vernier alignment task was used in which three color normal observers were asked to judge the horizontal position of the central element relative to two identical vertically displaced reference elements located 2° above and below fixation (Figure 1b). The elements consisted of symmetric Gaussian patches, with a standard deviation of 0.4°. Before the presentation of this test stimulus, subjects initially adapted to a stimulus comprised of two anti-symmetric elements (see Figure 1a). Positional judgments were made following an initial period of 50 s of adaptation, followed by 5 s of top-up adaptation between each trial. A top-up adaptation period of 5 s was chosen between trials because longer adaptation phases do not produce significantly greater positional offsets (Whitaker et al., 1997). The anti-symmetric stimuli represent the first derivative in the x direction of the Gaussian test elements, and were spatially co-incident with the reference elements of the test stimulus. Following adaptation, the test stimulus was presented for 180 ms, and, under certain conditions, a misalignment of the central element was perceived. The magnitude of this perceived offset was then established using a method of constant stimuli. The data were fitted by a logistic function of the form 
Figure 1
 
a–f: Examples of the luminance- and chromatic-defined stimuli used in the present experiments. The reader should be able to verify the phenomenon under investigation by fixating the small spot at the center of the two anti-symmetric outer blobs in Figure 1a for a period of 10–15 s. If gaze is quickly shifted to the center of Figure 1b, a perceived offset of the central element should be observed, despite the physical alignment of the stimulus elements. If the adapting process is repeated and gaze transferred quickly to Figure 1c, the observer should observe little or no offset. Similarly, adaptation to the L/M axis (red/green) anti-symmetric stimuli (Figure 1d) influences the perceived position of patches defined by the same chromatic content (Figure 1e), but not those defined by orthogonal S/(L+M) (blue-yellow) chromatic (Figure 1f) or luminance (Figure 1b) information. Figure 1g: The location in MBDKL color space of the chromatic and luminance components used in the generation of the adaptation and test stimuli. These include a luminance axis in addition to 6 chromatic axes that incorporate the L/M (0–180°) and S/(L+M) (90–270°) cardinal axes, as well as intermediate, non-cardinal orientations.  
(1)
where y is the percentage of rightward positional judgments, x is the physical position relative to true alignment (x = 0), μ is the offset corresponding to the 50% level on the psychometric function, and θ is an estimate of alignment threshold.
Figure 1
 
a–f: Examples of the luminance- and chromatic-defined stimuli used in the present experiments. The reader should be able to verify the phenomenon under investigation by fixating the small spot at the center of the two anti-symmetric outer blobs in Figure 1a for a period of 10–15 s. If gaze is quickly shifted to the center of Figure 1b, a perceived offset of the central element should be observed, despite the physical alignment of the stimulus elements. If the adapting process is repeated and gaze transferred quickly to Figure 1c, the observer should observe little or no offset. Similarly, adaptation to the L/M axis (red/green) anti-symmetric stimuli (Figure 1d) influences the perceived position of patches defined by the same chromatic content (Figure 1e), but not those defined by orthogonal S/(L+M) (blue-yellow) chromatic (Figure 1f) or luminance (Figure 1b) information. Figure 1g: The location in MBDKL color space of the chromatic and luminance components used in the generation of the adaptation and test stimuli. These include a luminance axis in addition to 6 chromatic axes that incorporate the L/M (0–180°) and S/(L+M) (90–270°) cardinal axes, as well as intermediate, non-cardinal orientations.  
(1)
where y is the percentage of rightward positional judgments, x is the physical position relative to true alignment (x = 0), μ is the offset corresponding to the 50% level on the psychometric function, and θ is an estimate of alignment threshold.
The adaptation and test stimuli consisted of either luminance or isoluminant chromatic modulation. The chromaticities of the adaptation and test stimuli could be independently controlled to produce modulation along a series of axes in MBDKL color space (MacLeod & Boynton, 1979; Derrington et al., 1984). These axes are illustrated in Figure 1g and include a luminance axis in addition to 6 chromatic axes that incorporate the L/M (0–180°) and S/(L+M) (90–270°) cardinal axes, as well as intermediate, non-cardinal orientations. All adapting and test stimuli were presented at 15.2 times their relative detection thresholds. 
Stimuli were generated using the macro capabilities of NIH Image (v1.61) and presented on an Apple Cinema LCD display screen that subtended 40° × 27° at the viewing distance of 64 cm. The mean luminance of the background and all stimuli was 41 cdm−2. The host computer was a Macintosh G4. All stimuli were calibrated with a Photo Research PR650 spectral photometer. 
Curve fitting
Exponent model
To examine the linearity of the positional offsets as a function of color angle, the data were fitted by sinusoidal functions that were raised to the best fitting exponent, n. These functions were of the form  
(2)
where amp is the amplitude, θ represents the color angle, θoff represents the phase offset from sine phase, and n represents the exponent of the exponentiated sine fit (i.e., if n = 1, this constitutes a sin wave). This approach is adapted from nonlinear models that have been utilized to explain neuronal response characteristics in LGN and primary visual cortex (V1)(De Valois et al., 2000). 
Decay function
Data showing the decay of the positional shift as a function of interstimulus interval (ISI) were fitted by an exponential function of the form  
(3)
where 0zero is the perceived offset when ISI = 0, and Tc is time constant of the exponential decay function. 
Results
When the chromatic content of adapting and test stimuli are limited to cardinal axes (L/M, S/(L+M), and L+M opponent mechanisms) in color space, the largest perceived positional shifts are generated when the adapting and test stimuli lie along the same chromatic axis (see Figure 2). The magnitude of the perceived positional offset resulting from prior adaptation is well described by a centroid shift (the weighted mean of the entire luminance distribution) generated by a linear combination of the negative after-image produced by the adapting stimulus, and the test stimulus (McKeefry, McGraw, Whitaker, & Vakrou, in press). In contrast, we found little or no positional shift when the adapting and test stimuli lie on orthogonal axes in color space (see Figure 2). Having established a lack of crossover between the cardinal color and luminance mechanisms, subsequent experiments were directed toward examination of the color tuning properties of mechanisms in the isoluminant plane. 
Figure 2
 
Figure 2. Bar plots for two observers showing the magnitude of the positional shift under three adaptation conditions: L/M (red-green) adapt, S/(L+M) (blue-yellow) adapt, and luminance (black-white) adapt. Large positional offsets are found when the chromatic content of the adapting and test stimuli is identical. However, when adapt and test stimuli differ, little or no positional shift is found. The third observer showed almost identical results to that of the other two.
Figure 2
 
Figure 2. Bar plots for two observers showing the magnitude of the positional shift under three adaptation conditions: L/M (red-green) adapt, S/(L+M) (blue-yellow) adapt, and luminance (black-white) adapt. Large positional offsets are found when the chromatic content of the adapting and test stimuli is identical. However, when adapt and test stimuli differ, little or no positional shift is found. The third observer showed almost identical results to that of the other two.
Figure 3 demonstrates how the magnitude of the positional offset varies as a function of test chromaticity when adaptation takes place along a series of non-cardinal, as well as cardinal, chromatic axes in color space. Importantly, in each case the pattern of adaptation is highly selective: the largest offsets are always generated when the test and adapting stimuli have the same orientation in color space, and the smallest when the test and adapting axes are orthogonal in color space. This occurs regardless of whether adaptation is along a cardinal or an intermediate axis. Interestingly, when adaptation occurs along the L/M axis, best fits are obtained with sine exponents close to unity (PVM = 0.83; DMcK = 1.22; and CV = 0.7), indicating the operation of linear mechanisms in the generation of this effect (see Figure 3a and 3g). However, as the adapting color orientation approaches the S/(L+M) axis, larger sine exponents are required (PVM = 3.19; DMcK = 4.51; and CV = 3.89), suggesting nonlinear behavior, and the operation of more narrowly tuned mechanisms (see Figure 3b and 3h). 
Figure 3
 
a–f. The variation in the magnitude of the positional shift (solid symbols) generated by adapting stimuli that modulate along the (a) 0–180° (L/M), (b) 90–270° S/(L+M), (c) 30–210°, (d) 60–240°, (e) 120-300°, and (f) 150–330° axes (indicated by the arrows), measured as a function of the chromatic axis of the test stimulus. The variations in the perceived positional shift as a function of color angle have been fitted by exponentiated sinusoidal functions (blue lines) (see “Methods”). For L/M adaptation, best fits are obtained with exponents close to unity, indicating the operation of more broadly tuned, linear mechanisms in the generation of this effect. Larger exponents are required the closer the adapting stimulus is to the S/(L+M) axis, indicating the operation of more narrowly tuned, nonlinear mechanisms. Data are shown for subject PVM in a-f and DMcK in Figure 3g–l. Similar results were obtained for a third subject.
Figure 3
 
a–f. The variation in the magnitude of the positional shift (solid symbols) generated by adapting stimuli that modulate along the (a) 0–180° (L/M), (b) 90–270° S/(L+M), (c) 30–210°, (d) 60–240°, (e) 120-300°, and (f) 150–330° axes (indicated by the arrows), measured as a function of the chromatic axis of the test stimulus. The variations in the perceived positional shift as a function of color angle have been fitted by exponentiated sinusoidal functions (blue lines) (see “Methods”). For L/M adaptation, best fits are obtained with exponents close to unity, indicating the operation of more broadly tuned, linear mechanisms in the generation of this effect. Larger exponents are required the closer the adapting stimulus is to the S/(L+M) axis, indicating the operation of more narrowly tuned, nonlinear mechanisms. Data are shown for subject PVM in a-f and DMcK in Figure 3g–l. Similar results were obtained for a third subject.
Figure 3
 
g–l. Data for subject DMcK.
Figure 3
 
g–l. Data for subject DMcK.
To examine the extent of interocular transfer of the color-specific positional offsets reported here, we repeated our initial experiment using a dichoptic stimulus arrangement (i.e., the adapting stimulus was presented to one eye and the test to the other). The results are shown in Figure 4a. When the adapting and test stimulus are presented to the same eye (AR/TR; AL/TL), large positional offsets are observed. However, in marked contrast to previous studies demonstrating the existence of multiple chromatic mechanisms (Krauskopf et al, 1982; Webster & Mollon, 1994), our results clearly demonstrate low degrees of interocular transfer for both the chromatic- and luminance-defined stimuli (AR/TL; AL/TR). A significantly reduced degree of interocular transfer was found for all three subjects. 
Figure 4
 
(a) The magnitude of interocular transfer of the positional offset brought about by chromatic [(L/M) red; (S/(L+M)) blue] and luminance adaptation (black). The data shown are from a dichoptic experiment where the adapting stimulus is presented to one eye and the test stimulus to the fellow eye (AR/TL and AL/TR). Data are shown for subject DMcK; however, the lack of interocular transfer was similar for all subjects. (b) The recovery of the positional offset effect following chromatic adaptation. Filled blue symbols show the recovery data for all 6 axes of chromatic adaptation, and all exhibit a similar time course. The data have been fitted by a single exponential decay function (see “Methods”) with a time constant, Tc= 1.86 s. Also shown in the figure for comparison are data that plot the recovery of sensitivity Tc= 8.68 s) following a “traditional” chromatic adaptation paradigm (data from Krauskopf et al., 1982), and recovery of neuronal function Tc= 14.9 s) in the cat visual cortex following luminance contrast adaptation (data from Albrecht et al., 1984). Data are shown for subject DMcK; however, the rate of decay was similar for all subjects.
Figure 4
 
(a) The magnitude of interocular transfer of the positional offset brought about by chromatic [(L/M) red; (S/(L+M)) blue] and luminance adaptation (black). The data shown are from a dichoptic experiment where the adapting stimulus is presented to one eye and the test stimulus to the fellow eye (AR/TL and AL/TR). Data are shown for subject DMcK; however, the lack of interocular transfer was similar for all subjects. (b) The recovery of the positional offset effect following chromatic adaptation. Filled blue symbols show the recovery data for all 6 axes of chromatic adaptation, and all exhibit a similar time course. The data have been fitted by a single exponential decay function (see “Methods”) with a time constant, Tc= 1.86 s. Also shown in the figure for comparison are data that plot the recovery of sensitivity Tc= 8.68 s) following a “traditional” chromatic adaptation paradigm (data from Krauskopf et al., 1982), and recovery of neuronal function Tc= 14.9 s) in the cat visual cortex following luminance contrast adaptation (data from Albrecht et al., 1984). Data are shown for subject DMcK; however, the rate of decay was similar for all subjects.
The rapid decay characteristics of the positional offsets resulting from chromatic adaptation (blue line) are illustrated in Figure 4b. The time course of recovery is measured by the introduction of a temporal, or interstimulus interval, between the end of the adapting phase and the start of the test phase. Typically, the time constant of the exponential decay function is 2 s. Also shown for comparison are data showing the recovery of sensitivity following chromatic adaptation in the paradigm used by Krauskopf et al. (1982) (Figure 4b, red line). Clearly, this function exhibits a much slower time course of recovery than our positional after-effects, and, moreover, is strikingly similar to the recovery of neural function following contrast adaptation in the visual cortex of cat (Albrecht, Farrar, & Hamilton, 1984) (Figure 4b, black line). 
Discussion
The results of the present study clearly show that when the chromatic content of the adapting and test stimuli are limited to cardinal axes (L/M, S/(L+M), and L+M opponent mechanisms) in color space, the largest perceived positional shifts are generated when the adapting and test stimuli lie along the same cardinal axis. In contrast, little or no positional offset is found when the adapting and test stimuli lie on orthogonal axes in color space. This finding concurs with numerous neurophysiological and psychophysical investigations, which have shown that the cardinal chromatic axes operate in an ostensibly independent manner. 
When the stimuli are extended to include non-cardinal axes, similar results are obtained: the largest positional offsets are found when the adapting and test stimuli have a common orientation in color space, and are minimal when adapt and test axes are orthogonal in color space. If the adaptation effects shown in Figure 3 were the result of the operation of only two cardinal mechanisms, we might expect the maximal offsets to be generated following adaptation along the L/M and S/(L+M) cardinal axes, and correspondingly smaller offsets to result from adaptation along intermediate axes (Krauskopf et al., 1986). In fact, the data show that the point in color space corresponding to the maximum positional offset follows the change in habituating axis around color space. This pattern of results provides prima facie evidence for the existence of multiple chromatic mechanisms of the kind postulated by previous behavioral and neurophysiological experiments (Krauskopf et al., 1982; Krauskopf et al., 1986; Flanagan et al., 1990; Webster & Mollon, 1991; Gegenfurtner & Kiper, 1992; Webster & Mollon, 1994). Alternative models, based on the combination of effects along cardinal directions (Figure 5a5d), fail to describe two critical features of the data. First, they incorrectly predict that the color angle at which adaptation effects are maximal will always remain along one of the cardinal directions. Second, they underestimate the magnitude of adaptation effects along intermediate color axes (Figure 5c and 5d). Although these considerations provide further support for the existence of multiple chromatic mechanisms, it should be noted that this does not unequivocally rule out their generation via adaptive interactions between the color opponent mechanisms (so-called “adaptive orthogonalization”) (Zaidi & Shapiro, 1993). 
Figure 5
 
Comparison of data from Figures 3c, 3d, 3i, and 3j (solid symbols) against model predictions (red line) based on a linear combination of adaptation effects along cardinal color axes. The model assumes an adaptation strength that is proportional to the cosine of the angle between the intermediate adaptation axis and the cardinal axes. Figures a and b represent data for color axis 30–120 deg, whereas c and d represent axis 60–240 deg. For a and b, the model provides a reasonable description of the data, but fails to capture the shift of the peak effects away from 0- and 180-deg test orientations. In Figures c and d, the model suffers from this same failure as well as demonstrating an underestimation of the amplitude of adaptation effects.
Figure 5
 
Comparison of data from Figures 3c, 3d, 3i, and 3j (solid symbols) against model predictions (red line) based on a linear combination of adaptation effects along cardinal color axes. The model assumes an adaptation strength that is proportional to the cosine of the angle between the intermediate adaptation axis and the cardinal axes. Figures a and b represent data for color axis 30–120 deg, whereas c and d represent axis 60–240 deg. For a and b, the model provides a reasonable description of the data, but fails to capture the shift of the peak effects away from 0- and 180-deg test orientations. In Figures c and d, the model suffers from this same failure as well as demonstrating an underestimation of the amplitude of adaptation effects.
Importantly, previous studies that have posited the existence of multiple chromatic mechanisms have considered the cortical site for their generation to be beyond the point where extensive binocular interactions occur (Krauskopf et al., 1986). In addition, other features suggest a cortical locus for “higher order” color mechanisms. As well as being associated with a high degree of interocular transfer, the effects dissipate relatively slowly, and display orientation selectivity (Krauskopf et al.,1982; Webster & Mollon, 1994; Clifford, Spehar, Solomon, Martin, & Zaidi, 2003), all of which are properties commonly associated with cortical visual processing. 
To examine the extent of binocular interaction in the generation of the color-specific positional offsets, we repeated our initial experiment using a dichoptic stimulus arrangement (i.e., the adapting stimulus was presented to one eye and the test to the other). In marked contrast to previous studies demonstrating the existence of multiple chromatic mechanisms (Krauskopf et al.,1982; Webster & Mollon, 1994), our results clearly demonstrate low degrees of interocular transfer for both the chromatic- and luminance-defined stimuli. High degrees of interocular transfer demand the involvement of binocular neurones, which receive an input from each eye, such as those typically found in extra-striate cortical area V2 (Hubel & Wiesel, 1970; Zeki, 1978; Burkhalter & van Essen, 1986). This makes V2 a good candidate as a cortical site that can sustain the high degrees of interocular transfer reported for other chromatic (Webster & Mollon, 1994) and spatial after-effects (Paradiso, Shimojo, & Nakayama, 1989). If the effects produced by chromatic adaptation reported here were mediated by V2, or by any other extra-striate area for that matter, then a much higher degree of interocular transfer would be expected. For example, interocular transfer in excess of 90% has been reported for after-effects generated by subjective contours and incoherent motion (Paradiso et al., 1989; Raymond, 1993). The diminished level of interocular transfer found in this paradigm, in comparison to other cortical effects, suggests that the site of generation occurs at a point antecedent to the locus at which binocular interactions emerge. 
The perceptual errors resulting from adaptation, whether it be the positional shifts we report or the classical misperceptions of orientation seen in the tilt after-effect, are all relatively transient in nature and decay over a period of time. The time taken for after-effects to dissipate can provide important insights regarding the level in the visual pathway where they were originally generated. In general, retinal or precortical after-effects, such as the after-image produced from looking at a bright light, diminish more rapidly than cortically mediated after-effects. Indeed, some cortical after-effects can persist for surprisingly lengthy periods of time. Therefore, we compared the rate of decay, or in other words the time taken to recover veridical perception, of our induced positional offsets against those reported in chromatic adaptation studies where marked interocular transfer was present (Krauskopf, Williams, & Heeley 1982). The results show unequivocally that the rate of decay of the positional offsets resulting from chromatic adaptation, are relatively transient in nature. Indeed, veridical perception is recovered within a period of approximately 5 s. In comparison, previous investigations of chromatic adaptation, where interocular transfer of the effect is marked, require almost four times as long to recover (Krauskopf et al., 1982). The rapid decay characteristic is a robust feature of our chromatically induced positional offsets; the time constant of decay is independent of adaptation duration beyond the period we used. Furthermore, positional adaptation experiments using texture-defined stimuli, which require cortical processing at the level of V2 to recover their image structure (Zhou, & Baker, 1993; Mareschal & Baker, 1998), also show large degrees of interocular transfer and slow rates of recovery, with time constants similar to those reported for contrast adaptation (Whitaker et al., 1997). This indicates that it is the site of adaptation that is the critical factor, rather than the visual task used to measure it. 
Low degrees of interocular transfer in conjunction with rapid decay rates are properties that are consistent with the positional offsets being generated by mechanisms that are more closely related to luminance (in this case chromatic) adaptation rather than contrast adaptation (Georgeson, 1991). The former is primarily retinal in origin and generates a change in the average color of a region in the position of the image (Webster, & Mollon, 1995; Hood, 1998; Webster, & Wilson, 2000), while the latter is cortical, and shows pronounced selectivity for the spatial properties of the stimulus (Whitaker et al., 1997; Blakemore, & Campbell, 1969; Bjorklund, & Magnussen, 1981; Georgeson, & Harris, 1984; Maffei, Bernardi, & Bisti, 1986). 
However, there are key aspects of the physiological properties of cells in the LGN that make a precortical locus for the generation of multiple chromatic mechanisms seem less likely. First, color-opponent cells in the LGN, unlike those in the cortex, do not alter their response level following prolonged visual exposure (i.e., they do not adapt) (Derrington, Krauskopf, & Lennie, 1984). Second, a prominent feature of LGN cells is the linearity with which they respond. Any linear combination of cone inputs should result in a function that varies sinusoidally across color space, due to sinusoidal variations in cone contrast as a function of color angle. This predicted relationship has previously been demonstrated in primate LGN cells (Derrington et al., 1984; De Valois et al., 2000). While a linear model accurately describes our data close to the L/M axis (see Figure 3a and 3g), chromatic adaptation becomes progressively nonlinear as we approach the S/(L+M) axis (see Figure 3b and 3h). This nonlinearity can be quantified using the exponent of the sine function which best describes the data (De Valois et al., 2000), with exponents greater than 1 indicating increasingly nonlinear behavior. This narrowing of chromatic tuning close to the S/(L+M) axis is absent at the level of the LGN but is shown by a substantial number of cells in the primate striate cortex (De Valois et al., 2000). This compression of color space is consistent with observations from color scaling experiments (De Valois, De Valois, & Mahaon, 2000) and with the predictions of a multi-stage color model (De Valois & De Valois, 1993). Cells with narrow chromatic tuning have also been observed beyond V1, in area V2 and V4, although this narrowing is not associated with any particular color axis (Zeki, 1980; Kiper, Fenstemaker, & Gegenfurtner, 1997). Exactly what influence the chromatic tuning of neurons in the striate, and extra-striate cortex, has on human visual performance, is at present difficult to gauge. Behavioral evidence presents a somewhat conflicting picture. Some studies suggest that nonlinear mechanisms, with narrow chromatic bandwidths, underpin performance (Goda & Fujii, 2001), whereas others point to the detection of color being mediated by more broadband, linear mechanisms (D’Zmura & Knoblauch, 1998; Cadinal & Kiper, 2003). 
At first glance, the known properties of LGN physiology make it difficult to ascribe a precortical locus to the generation of these effects. However, although primate neurophysiological investigations suggest that the narrow tuning around the S/(L+M) axis is a distinctly cortical feature of chromatic processing, this does not rule out the possibility that the adaptation responsible for the positional offsets we observe takes place at an earlier level, and is subsequently subjected to a nonlinear transformation at the level of the visual cortex. 
Alternatively, the low degrees of interocular transfer and rapid decay of the position offsets, although more suggestive of a precortical site for this effect, are not beyond a cortical interpretation. Cells in the early input layers of the striate cortex, such as those in 4Cβ, are known to display high degrees of sensitivity to chromatic modulation (Lennie et al.,1990). In addition, these geniculo-recipient layers of the cortex display marked monocular segregation of input (Livingstone & Hubel, 1984). Both of these features would be necessary to explain the psychophysical findings of the present study. What does seem puzzling, however, is the rapid rate of decay of our chromatic positional offsets compared with previous studies examining chromatic adaptation, and, indeed, studies examining the typical recovery of response rates in striate cortical neurones following prolonged visual exposure. This apparent conflict is reconciled by recent evidence showing that, in contrast to previous reports, the visual cortex does indeed display rapid pattern-specific adaptation mechanisms, which can operate over a surprisingly short timescale (Muller, Metha, Krauskopf, & Lennie, 1999). More recently, Shapiro, Beere, and Zaidi (2003) have identified a fast higher order adaptive response in the S/(L+M) pathway. To disentangle the relative contributions of precortical and cortical visual structures to the present psychophysical observations, it would be necessary to employ stimuli that avoid adaptation at the level of chromatically sensitive retinal units. For example, an isoluminant chromatic stimulus, defined by a modulation in chromatic contrast, will produce little or no retinal adaptation, but should be a potent stimulus for cortical adaptation. If the positional offsets measured with these stimuli display similar levels of interocular transfer, compression around the S/(L+M) axis, and rapid rates of decay, we should be able to establish more precisely where the generation of these effects occurs. This is the focus of work ongoing in our laboratory. 
Conclusions
Examination of the effects of chromatic adaptation on spatial localization reveals several important findings. First, within the L/M, S/(L+M), and L+M mechanisms, suprathreshold positional measurements are ostensibly independent, indicating the existence of separate pathways for these judgments. Second, and more importantly, the results reveal the existence of a multitude of independent chromatically tuned mechanisms spanning color space, rather than only the two L/M and S/(L+M) cardinal color mechanisms predicted by the traditional opponent model. The data are equivocal as to whether the mechanisms constitute physiologically separate chromatic channels (Krauskopf et al.,1986; Webster & Mollon, 1991), or whether they arise due to different degrees of interaction between opponent channels (Zaidi & Shapiro, 1993). What does seem clear is that these selectively adaptable chromatic mechanisms are rapid in operation, and are synthesized early in the visual pathway, without any recourse to the operation of binocularly sensitive “higher order” mechanisms. Given that the human visual system displays remarkably high levels of spatial precision, and that naïve observers require little or no explanation, training, or interpretation to make positional judgments, chromatically induced positional offsets may prove to be a very efficient and sensitive method for establishing the isoluminant balance of individuals. 
Acknowledgments
PVM is supported by a Research Career Development Fellowship from the Wellcome Trust. 
Commercial relationships: none. 
Corresponding author: Paul V. McGraw. 
Email: p.v.mcgraw@bradford.ac.uk. 
Address: Department of Optometry, University of Bradford, Richmond Road, Bradford BD7 1DP, UK. 
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Figure 1
 
a–f: Examples of the luminance- and chromatic-defined stimuli used in the present experiments. The reader should be able to verify the phenomenon under investigation by fixating the small spot at the center of the two anti-symmetric outer blobs in Figure 1a for a period of 10–15 s. If gaze is quickly shifted to the center of Figure 1b, a perceived offset of the central element should be observed, despite the physical alignment of the stimulus elements. If the adapting process is repeated and gaze transferred quickly to Figure 1c, the observer should observe little or no offset. Similarly, adaptation to the L/M axis (red/green) anti-symmetric stimuli (Figure 1d) influences the perceived position of patches defined by the same chromatic content (Figure 1e), but not those defined by orthogonal S/(L+M) (blue-yellow) chromatic (Figure 1f) or luminance (Figure 1b) information. Figure 1g: The location in MBDKL color space of the chromatic and luminance components used in the generation of the adaptation and test stimuli. These include a luminance axis in addition to 6 chromatic axes that incorporate the L/M (0–180°) and S/(L+M) (90–270°) cardinal axes, as well as intermediate, non-cardinal orientations.  
(1)
where y is the percentage of rightward positional judgments, x is the physical position relative to true alignment (x = 0), μ is the offset corresponding to the 50% level on the psychometric function, and θ is an estimate of alignment threshold.
Figure 1
 
a–f: Examples of the luminance- and chromatic-defined stimuli used in the present experiments. The reader should be able to verify the phenomenon under investigation by fixating the small spot at the center of the two anti-symmetric outer blobs in Figure 1a for a period of 10–15 s. If gaze is quickly shifted to the center of Figure 1b, a perceived offset of the central element should be observed, despite the physical alignment of the stimulus elements. If the adapting process is repeated and gaze transferred quickly to Figure 1c, the observer should observe little or no offset. Similarly, adaptation to the L/M axis (red/green) anti-symmetric stimuli (Figure 1d) influences the perceived position of patches defined by the same chromatic content (Figure 1e), but not those defined by orthogonal S/(L+M) (blue-yellow) chromatic (Figure 1f) or luminance (Figure 1b) information. Figure 1g: The location in MBDKL color space of the chromatic and luminance components used in the generation of the adaptation and test stimuli. These include a luminance axis in addition to 6 chromatic axes that incorporate the L/M (0–180°) and S/(L+M) (90–270°) cardinal axes, as well as intermediate, non-cardinal orientations.  
(1)
where y is the percentage of rightward positional judgments, x is the physical position relative to true alignment (x = 0), μ is the offset corresponding to the 50% level on the psychometric function, and θ is an estimate of alignment threshold.
Figure 2
 
Figure 2. Bar plots for two observers showing the magnitude of the positional shift under three adaptation conditions: L/M (red-green) adapt, S/(L+M) (blue-yellow) adapt, and luminance (black-white) adapt. Large positional offsets are found when the chromatic content of the adapting and test stimuli is identical. However, when adapt and test stimuli differ, little or no positional shift is found. The third observer showed almost identical results to that of the other two.
Figure 2
 
Figure 2. Bar plots for two observers showing the magnitude of the positional shift under three adaptation conditions: L/M (red-green) adapt, S/(L+M) (blue-yellow) adapt, and luminance (black-white) adapt. Large positional offsets are found when the chromatic content of the adapting and test stimuli is identical. However, when adapt and test stimuli differ, little or no positional shift is found. The third observer showed almost identical results to that of the other two.
Figure 3
 
a–f. The variation in the magnitude of the positional shift (solid symbols) generated by adapting stimuli that modulate along the (a) 0–180° (L/M), (b) 90–270° S/(L+M), (c) 30–210°, (d) 60–240°, (e) 120-300°, and (f) 150–330° axes (indicated by the arrows), measured as a function of the chromatic axis of the test stimulus. The variations in the perceived positional shift as a function of color angle have been fitted by exponentiated sinusoidal functions (blue lines) (see “Methods”). For L/M adaptation, best fits are obtained with exponents close to unity, indicating the operation of more broadly tuned, linear mechanisms in the generation of this effect. Larger exponents are required the closer the adapting stimulus is to the S/(L+M) axis, indicating the operation of more narrowly tuned, nonlinear mechanisms. Data are shown for subject PVM in a-f and DMcK in Figure 3g–l. Similar results were obtained for a third subject.
Figure 3
 
a–f. The variation in the magnitude of the positional shift (solid symbols) generated by adapting stimuli that modulate along the (a) 0–180° (L/M), (b) 90–270° S/(L+M), (c) 30–210°, (d) 60–240°, (e) 120-300°, and (f) 150–330° axes (indicated by the arrows), measured as a function of the chromatic axis of the test stimulus. The variations in the perceived positional shift as a function of color angle have been fitted by exponentiated sinusoidal functions (blue lines) (see “Methods”). For L/M adaptation, best fits are obtained with exponents close to unity, indicating the operation of more broadly tuned, linear mechanisms in the generation of this effect. Larger exponents are required the closer the adapting stimulus is to the S/(L+M) axis, indicating the operation of more narrowly tuned, nonlinear mechanisms. Data are shown for subject PVM in a-f and DMcK in Figure 3g–l. Similar results were obtained for a third subject.
Figure 3
 
g–l. Data for subject DMcK.
Figure 3
 
g–l. Data for subject DMcK.
Figure 4
 
(a) The magnitude of interocular transfer of the positional offset brought about by chromatic [(L/M) red; (S/(L+M)) blue] and luminance adaptation (black). The data shown are from a dichoptic experiment where the adapting stimulus is presented to one eye and the test stimulus to the fellow eye (AR/TL and AL/TR). Data are shown for subject DMcK; however, the lack of interocular transfer was similar for all subjects. (b) The recovery of the positional offset effect following chromatic adaptation. Filled blue symbols show the recovery data for all 6 axes of chromatic adaptation, and all exhibit a similar time course. The data have been fitted by a single exponential decay function (see “Methods”) with a time constant, Tc= 1.86 s. Also shown in the figure for comparison are data that plot the recovery of sensitivity Tc= 8.68 s) following a “traditional” chromatic adaptation paradigm (data from Krauskopf et al., 1982), and recovery of neuronal function Tc= 14.9 s) in the cat visual cortex following luminance contrast adaptation (data from Albrecht et al., 1984). Data are shown for subject DMcK; however, the rate of decay was similar for all subjects.
Figure 4
 
(a) The magnitude of interocular transfer of the positional offset brought about by chromatic [(L/M) red; (S/(L+M)) blue] and luminance adaptation (black). The data shown are from a dichoptic experiment where the adapting stimulus is presented to one eye and the test stimulus to the fellow eye (AR/TL and AL/TR). Data are shown for subject DMcK; however, the lack of interocular transfer was similar for all subjects. (b) The recovery of the positional offset effect following chromatic adaptation. Filled blue symbols show the recovery data for all 6 axes of chromatic adaptation, and all exhibit a similar time course. The data have been fitted by a single exponential decay function (see “Methods”) with a time constant, Tc= 1.86 s. Also shown in the figure for comparison are data that plot the recovery of sensitivity Tc= 8.68 s) following a “traditional” chromatic adaptation paradigm (data from Krauskopf et al., 1982), and recovery of neuronal function Tc= 14.9 s) in the cat visual cortex following luminance contrast adaptation (data from Albrecht et al., 1984). Data are shown for subject DMcK; however, the rate of decay was similar for all subjects.
Figure 5
 
Comparison of data from Figures 3c, 3d, 3i, and 3j (solid symbols) against model predictions (red line) based on a linear combination of adaptation effects along cardinal color axes. The model assumes an adaptation strength that is proportional to the cosine of the angle between the intermediate adaptation axis and the cardinal axes. Figures a and b represent data for color axis 30–120 deg, whereas c and d represent axis 60–240 deg. For a and b, the model provides a reasonable description of the data, but fails to capture the shift of the peak effects away from 0- and 180-deg test orientations. In Figures c and d, the model suffers from this same failure as well as demonstrating an underestimation of the amplitude of adaptation effects.
Figure 5
 
Comparison of data from Figures 3c, 3d, 3i, and 3j (solid symbols) against model predictions (red line) based on a linear combination of adaptation effects along cardinal color axes. The model assumes an adaptation strength that is proportional to the cosine of the angle between the intermediate adaptation axis and the cardinal axes. Figures a and b represent data for color axis 30–120 deg, whereas c and d represent axis 60–240 deg. For a and b, the model provides a reasonable description of the data, but fails to capture the shift of the peak effects away from 0- and 180-deg test orientations. In Figures c and d, the model suffers from this same failure as well as demonstrating an underestimation of the amplitude of adaptation effects.
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