the whole receptive field, thus resulting in a greater degree of opponency than with a smaller stimulus (see below).

Electrophysiological recordings from single cells in the macaque LGN (Zrenner, 1983; Valberg et al., 1985b) has given the following distribution of cell types: DS-L, 10 percent; IM-L, 15 percent; DM-L, 15 percent; IM-S, 3–4 percent; IL-M, 20–25 percent; DL-M, 15 percent. For the rest of the encountered cells the cone inputs could not be sufficiently identified, or they fell between these classes.

Correlates of related and unrelated colors

We have seen that for each type of M/L opponency, ‘L–M’ or ‘M–L’, there are two types of PC cells; a D-cell and an I-cell. Color coding in one of these two opposite directions of color space is divided between I- and D-cells depending on relative luminance. The strongly inhibited D-cells can only transmit information about colors of low relative luminance, for example of surfaces of objects with reflection factors lower than about one. Such reflecting surfaces are the most frequent object surfaces in a natural environment. The color appearance of such surfaces is strongly dependent on the adapting surround, and opponent cells have been demonstrated to adjust their responses and sensitivity to such surrounds (Valberg et al., 1985a).

I-cells give spectrally selective responses for higher luminance ratios, far above a luminance value that completely suppresses the responses of D-cells, albeit with less opponency at the higher luminance ratios. This qualifies I-cells for responding to bright, unrelated colors of self-luminous areas, or isolated reflecting areas in the dark, also called void colors. Because, for a given adaptation, these different physical domains of lightness and brightness together span more than four decades of relative intensity, the need for different coding units seems natural. This is analogous to the sensory temperature scale being divided between ‘warm coding units’ and ‘cold coding units’ (Hensel and Kenshalo, 1969). Combining the responses of I- and D-cells with the same opponency (as in Figure 6.9(c)) allows us to cover the whole range of relative luminance values, from black surfaces to bright light sources.

It has been suggested that only cells with relative larger and coextensive excitatory and inhibitory receptive fields can be involved in color vision processing (Rodieck, 1991), thus excluding the retinal midget ON-ganglion cells and geniculate PC Increment cells with their small receptive field centers and highly spatial selective responses. However, the consequence of limiting the M/L dimension of color vision to processing by the Decrement cells would be to restrict color discrimination to related colors of rather low luminance ratios (see Figures 6.10 and 6.11). In the account of the Bezold–Bru¨cke phenomenon to be presented later, we shall see that the Increment cells are indeed needed in order to explain changes of color strength and hue over a several log unit range of luminance ratios.

Based on psychophysical evidence, we shall further assume that constant hue of a chromatic stimulus is determined by the relative response, or the response ratio of two neighboring cells with different opponency, e.g. the response ratio of ‘L–M’ cells and ‘M–S’ cells. A constant orange hue, perceived to be midway between unique red and unique yellow, will be related to the response ratio between IM-S cells and the summated response of the hypothetical ‘IL-M þ DL-M’ unit. Later, we shall see how these conjectures allow us to account for several perceptive color phenomena and the scaling of color differences.

Antagonistic receptive fields of opponent cells

The concept of receptive fields was introduced in Figure 3.22. Here we shall discuss possible receptive fields structures of opponent cells. Figure 6.12 shows a model of probable spatial sensitivity of the receptive fields of PC-cells. Figure 6.12(a) is for a weakly inhibited IM–L cell (type I in the terminology of Wiesel and Hubel, 1966), and Figure 6.12(b) is for a strongly inhibited DM–L cell (type II with coextensive center and surround fields). Possible spatial sensitivities of the center and surround mechanisms are shown by the thin solid and dashed curves. In a test situation, where the spatial sensitivity is probed with a small spot of light that traverses the receptive field along its diameter, these two sensitivities summate to a resultant sensitivity shown by the solid green curve (see also the Gaussian model in Figures 3.22 and 3.23). In Figure 6.12, the excitatory input from M-cones is restricted to the center while the inhibitory mechanism of the L-cones extends throughout the receptive field, both center and surround. This need not always be the case. In the central fovea, for example, the excitatory center mechanism is likely to consist of only a single cone. To determine the spatial profile of the excitatory center mechanism, the M-cone response must be isolated. This can be achieved by adapting the cell to light of a suitably chosen wavelength that strongly excites and saturates (adapts) the L-cones, but not the M-cones. With the surround mechanism rendered insensitive, the center mechanism can be probed selectively. A corresponding isolation of L-cone responses allows the surround mechanism to be mapped.

In Figure 6.12(a) and (b), the spatial boundaries of the two cone mechanisms are only slightly dependent on stimulus wavelength. However, in the spatial profile of the M–L response, the boundaries of the excitatory center and the inhibitory surround are very much a function of the probing wavelength, as shown by the examples of response profiles for 600 and 530 nm. The greater the relative sensitivity of the center M-cone mechanism to the chosen wavelength, the larger the excitatory center of the corresponding M–L receptive field. In the top panel of Figure 6.12(a), for example, the center is small and the excitation is weak at 600 nm and much larger at 530 nm.

conditions as those used to obtain in Figure 6.10. The different symbols and curves represent different luminance ratios Y of stimulus/adapting background. The responses have been derived from plots like those of Figure 6.10, for different luminance ratios Y ¼ L=Lb (where Lb ¼ 100 cd/m2):

Y¼ 10 ðopen circlesÞ

Y¼ 1 ðcrossesÞ

Y¼ 0:1 ðsolid trianglesÞ

Y¼ 0:01 ðsolid circlesÞ

The responses to white light can differ from cell to cell and, to emphasize the chromatic and luminance response differences relative to the achromatic adaptation stimulus, we have once again subtracted the response to the white adaptation light (for Y ¼ 1) and plotted N NW along the y-axis. The adaptation stimulus is represented by the horizontal line, for which N NW ¼ 0 imp/s (for Y ¼ 1). The responses to achromatic light of the given luminance ratios are shown to the right in each graph. Note that for PC cells, without an S-cone input, the response to white corresponds to that of 571 nm of the same luminance; 571 nm is the PC cells’ spectral neutral point. This means that these cells are tritanopic and cannot distinguish 571 nm from the white adapting light. The fully drawn curves in the graphs are the calculated responses from the simple response equation applied to the results of Figure 6.10.

The neutral wavelength 571 nm represents the transition point in the spectrum between activation and inhibition for cells without S-cone inputs. An ‘L–M’ cell is activated for longer wavelengths, and it is inhibited for shorter. For an ‘M–L’ cell it is the other way around. The blue-sensitive ‘S–L’ cells have a neutral point at about 515 nm, and the ‘M–S’ cells have two neutral points, one at about 600 nm and the other one for short wavelengths near 495 nm.

The same response equation that has been used to calculate the curves in Figure 6.10 and 6.14 has also been used to compute the responses of these cells to colorimetric purity (metric saturation between white and maximum chromaticity) for selected wavelengths in the spectrum. Examples of such responses are given in Figure 6.15, and examples of the combined responses to luminance ratio and purity for an ‘L–M’, I-cell cell are shown in three-dimensional plots in Figure 6.16. Again, the plot is in terms of response difference relative to the adapting background so the value for the white adapting background will therefore be zero.

The results of such computations for an isoluminant plane are shown in Figure 6.17. The color circle in the inset shows the approximate orthogonal directions of yellow (Y), red (R), blue (B) and green (G), with white (W) in the center. Computations for the same cell, and for different luminance ratios, are displayed as one vertical column, and the brightness of the disks illustrates response strength. For the ‘S–L’ cell to the left of the figure, we see that the brightest sector is at the bottom of the disk, centered around 477 nm. For the ‘L–M’ cells in the two right-most columns, maximum activity is in a sector between red and blue, and thus shifted towards purple relative to the

Figure 6.15 Left panels: the data points represent cell responses of an ‘L–M’ Increment cell to the exchange of a white adapting field with a coextensive red (a) or orange (c) test light. The response magnitude is a difference measure, where the response to the white adapting field is subtracted from the response to the test light. For each data set, the ratio, Y, between the test light luminance and the adaptation luminance is constant, while the colorimetric purity of the test varies. Right panels: the prediction of the model for the cell’s response magnitude for the same stimuli.

unique red hue. The approximate hue of maximum response under our adaptive conditions is indicated in the figure by the color of the disks in the column for each cell type (Valberg and Lee, 1992).

‘M–L’ cells show the largest response for blue–green colors. In other words, neither for ‘M–L’ cells nor for ‘L–M’ cells does the response maximum correspond to a unique hue. For the ‘S–L’ cell, the maximum response is not far from unique blue, shifted only slightly to the violet side, and for the ‘M–S’ cells the maximum is close to unique yellow.

The I-cells shown here are activated, to a greater or lesser degree, by white light and by a surprisingly wide range of wavelengths. Because all cell types are activated by a broad spectrum of wavelengths, the discrimination of a color’s hue most likely

Figure 6.16 Model response magnitudes of an ‘L–M’ Increment cell for combinations of colorimetric purity and luminance ratios at four different wavelengths. Such three-dimensional plots summarize the results of Figures 6.10 and 6.15.

depends on the relative responses of at least two opponent cell types from neighboring groups in this figure. We postulate that, when this response ratio is constant and does not change with purity, hue will remain constant [see also Figure 5.32(c) and the Abney effect, p. 327].

Of all the opponent cells (about 1000) recorded in Barry B. Lee’s laboratory at the Max–Planck Institute of Biophysical Chemistry in Go¨ttingen over a 10 year period, between 75 and 80 percent belonged to one of the six groups described above. Among the remaining 20 percent, some cells had so little inhibition that an activation could be elicited by all wavelengths and all luminance ratios. Earlier reports of such cells (Padmos and van Norren, 1975) described how their ‘hidden opponency’ can usually be revealed by selective spectral adaptation. These cells may represent one extreme in

Figure 6.17 A representation of the responses of the six types of opponent cells of Figure 6.10 are given here as the density of bright spots in a polar diagram representing isoluminant color stimuli of different dominant wavelengths (indicated by radial angle) and spectral purity (indicated by distance form the center). Achromatic stimuli are represented at the center of each disk. Brighter areas indicate stronger responses than dark ones. The figure visualizes the neural responses shown in Figures 6.10 and 6.14 (except that the response to the white adapting reference has not been subtracted). I-cells (ON-center cells) fire more strongly to a bright color than D-cells (OFF-center cells) and all cells respond to a relatively broad range of wavelengths. The colors used for each disk indicate the spectral region/hue to which the cell responds best. Luminance ratio, Y ¼ L=Lb, is between stimulus and adaptation background (adapted from Valberg and Lee, 1992). (See also color plate section.)

a continuum of different degrees of inhibition and might be called ‘L–(M)’ or ‘M– (L)’ Increment cells. At the other end of the scale, cells were so strongly inhibited that, for all wavelengths, only decrement responses were elicited. Consequently, they might be called ‘(L)–M’ or ‘(M)–L’ Decrement cells, depending on the dominant cone type. Other cells were hard to classify in terms of three cone inputs, either because their response characteristics were between those of the established groups, or because wavelength and luminance responses did not resemble anything that the model could simulate with a simple combination of cone potentials.

Quantitative simulations aimed at determining the cone inputs to opponent cells have demonstrated a great deal of variation (Derrington et al., 1984; Valberg et al., 1987). For instance, even some of the relatively simple ‘L–M’ and ‘M–L’ cells may have additional weak S-cone inputs (DeMonasterio, 1984; Valberg et al., 1985b). De Valois (1969) used an S–L combination for his ‘B–Y’ cells, and L–S for the ‘Y–B’ cells, whereas Wiesel and Hubel (1966) concluded, as we have done, that the latter cell type received inputs mostly from M- and S-receptors. We have found a