shows responses of two neurons to illustrate different tuning characteristics. The neuron on the left is tuned broadly in the (L-M,S) plane (top graph), and it responds to all hues, but stronger to some than to others. The neuron on the right shows opponency, being excited by some hues and inhibited by others. It has a narrower tuning in the (L-M,S) plane. As the plots on the bottom show, tuning width along a vertical meridian in three-dimensional color space, i.e., for brighter and darker stimuli, cannot be inferred from the tuning width for isoluminant stimuli. The neuron on the left has a relatively broader tuning in azimuth than in elevation, while the opposite is the case for the neuron on the right.
Chromatic Tuning of Two V1 Neurons
In the following, we consider tuning in the (L-M,S) plane. To quantify tuning properties, we fit a circular normal function, fc = A0 + A exp((cos(ϕ − ϕ0) − 1)/σ2), to the responses to stimuli in different chromatic directions ϕ in the (L-M,S) plane. For most tuning curves, this method yielded good fits (χ2, 4 d.f., p < 0.15). The tuning curves that did not give good fits (n = 5) were bimodal and therefore could not be described well by a circular normal function. In these cases, the function was fitted to the highest peak of the tuning curve. The fitting procedure served to interpolate the data points by a smooth function to derive tuning parameters like tuning peak direction and tuning width. Using other interpolation functions, like powers of cosine functions or polynomials, yielded similar results.
shows the distribution of tuning peaks as a function of chromatic direction. In accordance with the findings of other studies (Lennie et al., 1990
; De Valois et al., 2000
; Hanazawa et al., 2000
), the distribution is continuous, but it is not uniform. Furthermore, the distribution is highly asymmetric. The peaks in the distribution do not coincide with the coordinate axes, as for cells in the LGN (Derrington et al., 1984
). The main peak of the distribution lies in the fourth quadrant of the (L-M,S) plane, corresponding to the yellow/orange region. There is also a relatively high number of tuning directions in the third quadrant, corresponding to greenish colors. Other distinct peaks are apparent for blue (second quadrant), as well as for purple in the first quadrant (Dow and Vautin, 1987
). The coordinate axes were the directions that tended to have the lowest incidence of tuning peaks.
Chromatic Tuning for Isoluminant Colors
The distribution of tuning widths () is broad and appears bimodal. The peaks of the distribution lie below and above the width of a cosine function, respectively. This indicates nonlinear processing of cone inputs, in agreement with the findings by De Valois et al. (2000)
Effects of Background
In the following, we maintain the term “stimulus” to describe the single color patch stimulating the receptive field of a neuron. To investigate effects of background chromaticity, for each trial it was chosen randomly whether background chromaticity remained neutral gray throughout the trial or changed for the duration of the stimulus presentation. With respect to the gray background, chromatic backgrounds had a cone contrast of 0.1, while stimuli had a cone contrast of 0.15. Tuning curves of 11 neurons for isoluminant stimuli on the gray background and on a chromatic background, respectively, are shown in . We compared chromatic tuning under the two background conditions by testing for differences between responses to the same stimuli. In 72 out of 94 cells (77%), responses to at least one of the stimuli were significantly different (t test, p < 0.01) when presented on the colored background as compared to presentation on the neutral gray background.
Effect of Background Chromaticity on Tuning Curves
The most common type of difference (51 cells, 71%) was a reduction in response magnitude for stimuli in the chromatic direction of the background color or the neighboring directions. In approximately half of the cells with altered tuning (37, 51%), responses to stimuli with directions roughly opposite to the background color were enhanced.
The influence of the background typically appeared early in the time course of the responses (Knierim and Van Essen, 1992
; Li et al., 2000
), as illustrated in . It was strongest around 100 ms after stimulus onset, slightly later than for line stimuli as reported by Li et al. (2000)
. In control conditions where the background changed without a stimulus being presented, i.e., the chromaticity in the region of the receptive field remained gray, direct responses to the background change, with latencies of more than 100 ms (Li et al., 2000
), were observed in 18 cells (19%).
Differences in responses to the same stimuli on different backgrounds suggest that responses are determined not only by the chromaticity of the stimulus, but also to some degree by the chromatic contrast of the stimulus to the background. When a stimulus of a certain chromatic direction (hue) is presented on a background of the same chromatic direction (but weaker saturation), its chromatic contrast is reduced as compared with presentation on the gray background. Correspondingly, in most neurons the response is reduced. To quantify this influence of the background on the responses to color stimuli, we compared the reduction in the neurons’ responses with the reduction in stimulus contrast. We calculated a background modulation index, which measures the difference in responses r
to stimuli in the direction of the background as a fraction of the difference in cone contrast c
between stimulus and background,
are response and cone contrast for the stimulus on the chromatic background, respectively, and r0
are for the stimulus on the gray background, respectively. An index of zero indicates that the neuron is insensitive to background chromaticity, giving same responses for same stimuli presented on different backgrounds. An index of 1 indicates that the reduction of the response matches the reduction of the contrast between stimulus and background. A negative index occurs if the response to the stimulus on the colored background is stronger than the response to the stimulus on the gray background. shows the distribution of this index. The values are broadly distributed, but most values are above zero, indicating a modulating effect of the background. The median of the distribution of 0.69 indicates that this modulation is on average not quite as strong as one would expect if the responses would represent the contrast of the stimulus to the background.
Effect of Background Chromaticity on Response Strength
A complementary view of the background influence is to consider the response differences as a difference in signaled stimulus contrast. shows mean responses as a function of stimulus contrast for both background conditions. The response in the chromatic background condition for our standard stimulus contrast of 0.15 (dashed vertical line) is of a magnitude that would indicate a stimulus of lower contrast (0.085) in the neutral background condition (dotted lines). The response difference corresponds to a contrast reduction of 0.065. Thus, the same stimuli may lead to different responses, whereas different stimuli may elicit the same responses, depending on chromatic context.
Effects of Remote Colors
To test lateral interactions besides the immediate spatial contrast of the stimulus, we presented, in addition to the color stimuli at the receptive field position, 2° color patches at a distance of 4° to 6° from the receptive field. The response to the stimulus was often different when these remote fields were present (). We quantified this difference by the ratio of the response to the stimulus in the presence of the remote fields, rrem, to the response in the absence of the remote fields, r0: ρrem = rrem/r0. shows the distribution of response ratios ρrem for remote fields of the same chromaticity as the stimulus. The distribution is shifted to values lower than 1 (p < 0.001), with a median of 0.88, indicating an average reduction of the response when the remote fields were present. In contrast, the distribution for the responses when remote fields had the opponent color of the stimulus () shows no significant shift. This indicates that, like the effect of the background, the influence of remote color patches is color specific.
Responses Are Influenced by Remote Color Fields
Influence of Remote Color Fields
The appearance of a color stimulus on a colored background can vary depending on the color of the background. Induction effects typically shift the perceived stimulus color away from the background color. Our data show that background color influences responses to chromatic stimuli in primary visual cortex in a qualitatively similar way. If these effects in V1 responses are relevant for color perception, we could expect a quantitative correspondence to the perceptual effects. We therefore compared the magnitudes of the chromatic interactions in the neural responses to induction effects in perception. We used data acquired in psychophysical experiments investigating lateral interactions in color perception (Wachtler et al., 2001a
). In these experiments, observers judged the color of a 2° test field presented on either a neutral gray background or a colored background, with or without 2° remote fields 4.5° from the test field. Chromaticities and presentation times were the same as in the current study. The resulting data were perceptual color shifts, measured in cone contrast, induced by changes in the chromaticities of background or remote color fields.
To make the comparison between neural responses and perceptual effects, we assumed that our measured tuning curves, though individually tuned to different colors, were representative of the population of neurons encoding a single stimulus color after compensation for differences in preferred chromatic directions. We then assumed that perception of a certain color depends mainly on such a population, that is, on the neurons with the strongest responses. Under the further assumption of a linear relation between perceptual color shifts and underlying neural responses, we used the psychophysically measured values to calculate background modulation index ρbg and remote fields response ratio ρrem, respectively. The resulting data for eight human subjects are superimposed on the respective distributions in and . For both indices, the values derived from human psychophysical data cluster around the centers of the distributions for the neural responses. This indicates that the magnitudes of the influences of both background color and remote colors are comparable in responses of V1 neurons and in perception.
For our comparison, we used data from experiments where the distance of the remote fields to the stimulus was similar (4.5° in human psychophysics, 4° to 6° in the physiology experiments). While we found the influences of the remote fields to range over at least 10° in perception (Wachtler et al. 2001a
), occasional tests of neural responses with remote fields at 8° did not yield measurable effects of the remote fields. We did not investigate the spatial extent systematically, but these observations seem to indicate that the spatial range of chromatic interactions is more limited in primary visual cortex than in perception.
Estimating Stimulus Color from Population Responses
For methodological reasons, our quantitative comparison of neural and psychophysical data was restricted to the conditions where background and stimulus were along the same chromatic direction. At a qualitative level, we can investigate further induction effects. The alterations observed in tuning curves when stimuli were presented on chromatic background indicate that the same chromaticity can evoke different responses in V1 neurons. Conversely, a certain response pattern of color-selective neurons in V1 will not correspond to a unique stimulus chromaticity. Similar effects are known in perception and are often associated with strategies for achieving color constancy. Under different illumination, light from the same object will have different spectral composition, but nevertheless the color of the object typically looks similar. This is illustrated in , where two schematic scenes with different backgrounds are depicted, demonstrating interactions between stimulus and background chromaticities. We asked whether V1 neurons may implement some of these chromatic interactions.
Estimation of Stimulus Color from Population Response
To illustrate our approach, we first consider the responses of four neurons () to color patches on different backgrounds. The chromatic background used to determine tuning curves was typically different for different neurons. To mimic identical background conditions, we rotated the tuning curves in the (L-M,S) plane such that all background chromaticities fell on the same direction. Thus, we assume that tuning properties and background effects in the neural population do not depend on chromatic direction. The color patches (a) and (c) in have chromaticities that roughly correspond to 0° (+L-M) and 45° directions in the (L-M,S) plane, respectively. The responses they elicit can be estimated by the corresponding data points on the tuning curve for neutral background. Color patch (b) has the same chromaticity as (c) but is displayed on a bluish background. Therefore, the response it elicits corresponds to the 45° data point on the tuning curves for chromatic backgrounds. The respective responses for the four neurons are plotted in . The response patterns for (a) and (b) are highly similar and are different from the pattern for (c), although patches (b) and (c) are physically identical. This corresponds to the perceptual similarity of patches (a) and (b).
Applying this approach to our population of 94 neurons, we determined for six of our stimuli (open black dots in ) presented on a bluish background, the respective chromaticities on a neutral background that would elicit the most similar responses. Since the tuning curves were obtained for fixed stimulus contrast, we excluded the stimuli in the direction of the background chromaticity and the opposite direction. They would be expected to lead mainly to contrast changes rather than hue changes, the case which has been considered above (). Responses as a function of chromatic direction were estimated from the individual tuning curves obtained by second-order polynomial interpolation of the data, and population responses were represented as 94-dimensional vectors. For each of the six stimuli, we then determined the chromatic direction for which the response vector for the neutral background condition had minimal distance to the response vector for that stimulus on the chromatic background. Vector difference was measured by Euclidean distance, but other measures gave similar results. The obtained chromaticities were shifted from the original stimulus chromaticities in the direction away from the background color, toward the opponent color. This is in close correspondence to induction effects in color perception, where, for example, stimuli on bluish background appear less blue, or more yellow, than on gray background ().