The relationship between spectral sensitivity and spatial sensitivity for the primate r-g X-channel

0042-6989~83 S3.00+ 0.00 Copyright &’ 1983Pergamon Press Ltd

VisionRes. Vol. 23. No. 12, pp. 149s1500. 1983 Printed in Great Britain. All rights reserved

THE RELATIONSHIP BETWEEN SPECTRAL SENSITIVITY AND SPATIAL SENSITIVITY FOR THE PRIMATE r-g X-CHANNEL CARL R. INGLING JR and EUGENIO MARTINEZ-URIEGAS* Division of Sensory Biophysics. and Institute for Research in Vision. The Ohio State University. Columbus, OH 43210. U.S.A. (Received 9 May 1983) Abstract-Which visual channel detects high spatial frequencies during careful fixation? Color vision models based on psychophysical data contradict electrophysiological results. According to electrophysiology, the channel which mediates fovea1 acuity originates in the small. tonic color-opponent r-g units of the X-cell pathway. However, psychophysical models assign acuity to the Vj channel because when acuity is used as a criterion for equating luminosity it is additive. in all opponent-color models the r-g channel is subadditive and hence is excluded from mediating acuity. We show that the r-g channel adds cone signals for high spatial frequencies and subtracts them for low, and conclude that the major achromatic channel for human fovea1 vision originates within the r-g color-opponent channel. Quantitative analysis makes explicit the interaction between the spatial and spectral variables for the simple-opponent cells which predominate in primate fovea1 vision. Spectral sensitivity

Spatial sensitivity

X-channel

Opponent channel

Color vision

The criteria used for equating lights can be divided into two classes: those that assign values to lights Background which when mixed are additive, and those which do not. For example, match (using a given criterion) Color-matching experiments prove that the human light A to a standard light S, and then match light B visual system is trivariant; it has three channels. These three channels originate in three kinds of to S. The criterion produces additive values if mixcones, R, G, B. Recent models of color vision transtures of A and B in proportions which sum to 1 form the signals from these three kinds of cones to match S. By this definition, heterochromatic flicker sum and difference signals before transmitting them photometry, minimization of border distinctness, and to the brain. Electrophysiological recordings from visual acuity are additive (LeGrand, 1972; Boynton many species, from fish to primate, confirm the and Kaiser, 1968; Myers ef al.. 1973; Guth and Graham, 1975). Direct comparison and increment or validity of such models. Figure I shows a typical zone model and the equations which specify the sum and absolute thresholds are not. difference transformations. Theories of this form The Fig. I model explains these results by postuaccount for many visual discrimination functions lating that different criteria tap different visual chan(Hurvich, 1981; Guth, Massof and Benzschawel, nels having additive or non-additive properties. In1980; lngling and Tsou, 1977; Jameson, 1972; Vos spection of the model shows that in general it is not and Walraven, 1971). additive. To make it additive the criterion must Zone models have clarified a problem of great isolate the Vi channel (but see Ingling, 1978 and theoretical and practical interest in vision: the deterparticularly Ingling and Drum, 1973 for alternate mination of the efficiency of differently colored lights interpretations of the acuity papers leading to the to produce vision. Because two patches of light present work). Current opponent theory requires that having different spectral composition can be made detection by the chromatic channels be tagged by equal by many different criteria, the answer to the subadditivity. From the spectral sensitivity curves of the opponent channels, it is clear that one unit of, say, problem depends upon the experimental procedure red light added to one unit of green light not only used to find how much energy is needed at each wavelength for equivalence. Zone models of the type does not produce two of the mixture, it might, shown in Fig. I quantitatively account for the depending upon the wavelength, produce zero units different results obtained when various criteria are of the mixture. That is what is meant by subadditivity, and some models of the Fig. 1 form deduce used to equate spectral lights. the spectral sensitivity of the opponent channels from the subadditivity of mixtures (Guth and Lodge, *Present address: Inst. Inv. Biomedicas. UNAM. DeDarta- 1973). In summary so far, the summing and differencing mento de Biomatematicas, Apdo. postal 70228, -04510 Mexico, D.F. model of Fig. I successfully accounts for the results INTRODUCTION

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studies have focused upon different cell characteristics. there is a high correlation between the properties of cells said to be tonic. Type 1. X. simpleopponent, projecting to the parvocellular layer of LGN. etc. (Lennie. 1980). The problem is with the additivity of mixtures when acuity is used as the criterion. Electrophysiological studies conclude that the acuity system for the primate fovea must be the X-cell channel (De Monasterio. 1981). The primate capacity to see high spatial frequencies during careful fixation must depend upon the small. tonic. color-opponent units of the X-cell channel. Some 90”,, of the cells in the primate fovea are X-cells (Lennie. 1980). However. psychophysical experiments have excluded this channel because acuity is additive, whereas X-cells are color-opponent, and hence subadditive. The chromatically opponent properties of X-cells cannot simultaneously be used to explain subadditivity and also account for additivity without theoretical justification. This is of course the reason why acuity measures have been assumed to isolate the conventional achromatic or flicker channel.

of brightness additivity experiments which use different criteria. Lights are additive when the criterion is detected by the photometrically additive I’, channel, and subadditive if the opponent channels contribute to detection. The prohh

Results from electrophysiological recordings do not corroborate the psychophysical model which attributes acuity to an additive luminance channel. The major conclusion from this literature has been summarized as follows: “The electrophysiologicai studies indicate a structure for the visual system which is composed of two systems: (i) a fast system which responds to stimuli physically, i.e. with transients at on or off, subserved by large neurons having large axons with short conduction times. preferentially sensitive to low spatial frequencies. and predominantly color-blind; and (ii) a slow system which responds tonically with sustained responses. subserved largely by the midget system of the retina and having the smallest receptive fields recorded. showing Iong conduction times to higher centers, preferentially sensitive to high spatial frequencies, and whose receptive fields give color-opponent responses” (lngling, 1978). The two systems go under various names-tonic and phasic, Type I and Type 111,X and Y. sustained and transient, etc. Although different

t

I

r-g.O.%R-I.260

RESC’LTS

Tlwory

The additivity of the r-g channel is spatialfrequency dependent; analysis of the spatial and

I

y-b-O.O3R-0.036

I VI= 0.6R + 0.37G

Fig. I. A conventional opponent diagram showing the transformation from RGB cone sensitivities to r-g. y-b and Vi.channel sensitivities. This diagram applies to only the low spatial frequency signal of the r-g channel. For high spatial frequencies. the signal in this channel resembles the Vi signal. The transformation equations are from Guth ef ~1. (1980).

The relationship

spectral

properties

of

between spectral sensitivity and spatial sensitivity for the primate

simple-opponent

receptive

fields shows that the additivity changes with spatial frequency. Figure 2 shows an idealized representation of a simple-opponent r-g receptive field with an R-cone excitatory center and a G-cone inhibitory surround. This ceil has both spatial and spectral properties. To represent the spatial properties, define

Spatial

frequency

tu)

at 001

I

01 Log

spatial

frequency

Fig. I!. The equations at the top show the square-wave approximation of a simple-opponent r-g (X-cell) receptive field. and illustrate how it is factored by using the identity given in the Appendix. Fourier t~dnsfo~ing the spatial filters (the coefficients of the R, G terms) to the spatial frequency domain illustrates the change in spectral sensitivity of the receptive field from (R-G) at low spatial frequencies to (R + G) at high. The curve at the bottom shows that the r-g cell. generally viewed as a differencing mechanism which computes the r-g signal of Fig. 1, is photometrically additive (i.e. adds rather than subtracts quantum absorptions in the R and G photopigments) at high spatial frequencies. The additivity vs o curve was calculated for a mixture of 520 and 6lOnm lights as shown on the inset.

r-g X-channel

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a unit center spread function, &,,,,,. and a unit surround function,~~“~~~~, of equal area. The spectral properties are given by the R and G cone sensitivities normalized to have equal sensitivity at 580 nm. The first-order spectral and spatial sensitivity of the cell is given by R -fanter + G .fsunound. The conventional response of this cell as a function of wavelength is shown as the r-g opponent-channel spectral sensitivity of Fig. 1. The signal caused by quantum absorptions in G cones is subtracted from the signal caused by quantum absorptions in R cones. This has been the usual view of the behavior of such ceils since their discovery. However, this same cell also transmits a photometrically additive (R + G) signal which has a Vi-like spectral sensitivity. That is, the same ceil, with no alteration of its subtractive wiring diagram, also ad& the signal caused by quantum absorptions in R cones to the signal caused by quantum absorptions in G cones. By substitution into a simple identity (see Appendix) the expression for the spectral and spatial sensitivity given above can be rewritten as foiiows: R.~+~.~=~R+G)~~+~)+~(R-G) (rC-x). (See Fig. 2). Thus, substitution into this identity shows that the first-order response of the simple-opponent r-g ceil is identically equal to the sum of two filter responses. One of these filters is a low-pass filter which has (R-G) opponent spectral sensitivity. The other is a bandpass filter which has (R + G) spectral sensitivity. It is an inherent property of simple-op~nent cells that they produce both differencing and summing signals. The differencing signal is produced at low spatial frequencies and the summing signal at high spatial frequencies. Thus the cell adds quantum absorptions in R and G cones for high spatial frequencies (e.g. gratings, Landolt c’s, small spots) and subtracts them for low spatial frequencies (e.g. uniform patches). Figure 2 (middle) shows the transformations to the frequency domain of the spatial filters (f, +f;) and (f, -f,) shown in Fig. 2 (top) (see Appendix). To illustrate how this cell responds as a function of spatial frequency, we calculate the results of an additivity test which adds a threshold amount of green light to a threshold amount of red light. The answer depends upon the spatial frequency, and must be calculated as a function of w. For the choice of wavelengths shown on the opponent spectral sensitivity curve inset of Fig. 2 (bottom), the result shows complete cancellation at low frequencies and perfect additivity at high. The inset spectral sensitivity curve which shows the wavelengths used in this additivity calcuiation is the conventional r-g opponent spectral sensitivity curve. It is the point of this article and of this calculation in particular that this r-g spectral sensitivity curve is appropriate only for w = 0. As w increases, the inset curve changes shape. At high spatial frequencies it resembles the luminosity curve, VJ, because the w term coefficient of (R-G) shown graphically in Fig. 3 goes to zero at high frequencies,

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while the bandpass term (the R + G coefficient) is tuned to higher frequencies (and is zero for w = 0). Although the additivity curve was calculated from the factored expression for the receptive field. the same result would necessarily have been obtained 5~. anr computational procedure whtch used the un,fuct~red ~eceptiz~e.~eld.The identity makes the spatial frequency-dependent additivity obvious. Given the filters and spectral sensitivities produced by the factoring. the additivity curve can be drawn by inspection. Simply notice that the spectral sensitivities are modified by spatial frequency-dependent weights which shift the spectral sensitivity of the cell from a difference at low frequencies to a sum at high frequencies. It is this obscure property of the simpleopponent receptive field that the factors of the identity make obvious. Although simple-opponent cells are the predominant cell of primate fovea1 retina, and thus perhaps one of the most significant cells known to sensory physiology, this spatial frequencydependent property has been generally ignored in psychophysical analyses and models of channel properties since discovery of the cells some 15 years ago {Wiesel and Hubel. 1966), despite demonstrations of the spatial frequency dependence of r-g cell spectral sensitivity by electrophysiology (e.g. see De Valois and De Valois, 1975. which summarizes several studies by De Valois and coworkers emphasizing this point). DfSCUSSION

Because the above analysis results in a structure for the achromatic channel which departs from the conventional view, it might be well to note some frequently encountered misconceptions. It might be objected that because this conclusion is based upon an identity which can be infinitely manipulated and always reduces to zero = zero. it is physiologically irrelevant. The point is that this particular form makes the behavior of the system transparent, and not only explains how r-g units can be additive at high spatial frequencies, it shows they must be. Because the factoring of the expression for the cell is an identity. what is true for the factors is true for the expression representing the cell. In particular. the additivity curve of Fig. 2 holds for the simpieopponent cell, a result not readily apparent without factoring. A common thought experiment is to try to place a grating on the receptive field in such a way that because of phase relationships and on-off responses the cell becomes additive. The only correct procedure is to convolute the spread function with gratings of various frequencies of fixed wavelength and observe by looking at the modulation of the response that at high frequencies the center and surround signals are summed. Even when great familiarity with convolution procedures has been gained it is not easy to anticipate our result unless the cell is factored into the

terms we have used in our analysis. However. the following might provide some insight into the behavior of the cell: “Consider a yellow grating made up of red and green primary components. moving past an r-g receptive field that is tuned to the frequency of this grating. The antagonism between the redsensitive center and the green-sensitive surround .of this receptive field will be converted to synergism by this red-green stimulus because. when its red component is in phase with the center of the receptive field, its green component is out of phase with the surround. Now shift the spatial phase of either the red or the green primary by I80 degrees. producing a red-green grating of unvarying luminance. This shift of stimulus phase will of course also shift the response phase, so that the response of the center to the red component will now be in phase with the response to the green component. and will cancel. Thus the same spatial frequency at which the receptive field is tuned to luminance contrasts will be very poor at evoking a response to chromatic ones.” (See Acknowledgements.) A frequently suggested thought experiment is: record from microelectrodes placed both in the center and surround of a simple-opponent receptive field. Do we assert that merely because the spatial frequency content of the stimulus changes that the fundamental inhibitory nature of the surround is altered? Again, this experiment derives from a misunderstanding of the nature of convolution. Convolution or its analog in the spatial frequency domain. multiplication of transforms, is the correct method for deriving system response, and the proposed test is not analogous to either. The correct quantity to record is modulation in the cell output. The modulation sensitivity to high spatial frequencies will be as if it were produced by a photometrically additive cell; i.e. with V,,-like rather than conventional r-g spectral sensitivity. E.G. consider a yellow grating which lies at the neutral point of the cell. When a very low frequency or uniform field covers the cell. it has zero output. The (R-G) (lowpass filter) term is zero for a spectral reason: R -G = 0. whereas the (R + G) (bandpass filter) term is zero for a spatial reason: the bandpass jilter is insensitive at low spatial frequencies. For high frequencies. the (R-G) (lowpass filter) term is zero because both terms are zero. However, the highfrequency (R + G) (bandpass filter) term, tuned to these frequencies, now resolves the grating and for this term there is no chromatic cancellation. Consequently the output is modulated. Without decomposing the receptive field into independent factors, this somewhat counterintuitive result is not easy to see. Finally. it should be emphasized that this result does not mean that the cell shifts to a different wiring diagram as a function of spatial frequency, or employs any other physiological or functional switching mechanism. The cell changes spectral sensitivity be-

The relationship between spectral sensitivity and spatial sensitivity for the primate r-g X-channel cause the spatial and spectral characteristics of the r-g receptive field are identically equivalent to a low-pass filter with (R-G) spectial sensitivity and a bandpass filter with approximate Y, spectral sensitivity. This equivalence explains the paradox of how the principal achromatic channel of the primate fovea originates in the r-g color-opponent channel. SUMMARY AND CONCLUSIONS ( 1) Psychophysical models divide the visual system into opponent and luminance. or summing and differen~ing channels. Within this framework the summing channels are photometrically additive, the differencing channels subadditive. (2) This structure explains the results obtained using different criteria for comparing the visual effectiveness of colored lights. Criteria which produce additivity of differently colored lights isolate the additive luminance channel; subadditivity results when the criterion taps the d~fferencing channels. (3) Temporal and acuity criteria yield additive luminosities, implying both are detected by the additive luminosity channel. (4) This result is not congruent with electrophysiology. Electrophysiology suggests that acuity is mediated by the small, tonic receptive fields predominating in primate fovea, but which are coloropponent and ostensibly subadditive. (5) This further suggests, and analysis shows. that for simple-opponent units, photometric additivity is spatial-frequency dependent. At low spatial frequencies, simple-opponent cells are differencing cells; at high spatial frequencies they are summing cells. The color-opponent cells of the primate fovea, classically viewed as encoding and transmitting only information about hue differences as a difference signal, actually form the major ue~romatic pathway of the primate visual system. The principal characteristics of fovea1 vision-the ability to extract high spatial frequency information in careful fixations-have their origin in a photometrically additive signal originating in small. tonic receptive fields of the r-g opponent cell pathway.

Guth S. L. and Lodge H. R. (1973) Heterochromatic additivity. fovea1 spectral sensitivity. and a new color model. 1. opr. Sot. ‘Am. 63, 4W-46i. Guth S. L. and Graham B. V. 119751 Heterochromatjc additivity and the acuity response. Vlsun Res. 15. 317-319. Guth S. L.. Massof R. W. and Benzschawel T. (1980) Vector model for normal and dichromatic vision. J. opr. Sot. Am. 70. 197-212. Hurvich L. M. (1981) Color Vision. Sinauer Associates, Sunderland, MA. lngling C. R. Jr and Drum B. A. (1973) Retinal receptive fields: correlations between psychophysics and electrophysiology. Vi~sion Res. 13, i ISi-I 163. fngling C. R. Jr and Tsou B. H.-P. (19771 Orthogonal combination of the three visual channels. C%orr Re.s. 17. 1075-1082. lngling C. R. Jr (1978) Luminance and opponent color contribut;,lns to visual detection and to temporal and spatial integration: Comment. J. opr. Sot. Am. 68, 1143-l 146. Ingling C. R. Jr and Martinez E. (1983) The spatiochromatic signal of the r-g channel. In Cofour I~kion: Phvsioloxv and P.~;,~hooh~,.~ic.~ (Edited bv Mellon J. D. a& Sharp L. ‘I”.).Acahe&c Press. New’York. Jameson D. (1972) Theoretical issues of color vision. In Handbook of Sensor? Physio1og.v (Edited by Jameson D. and Hurvich L. M.), Vol. VIIIi14, pp. 381-412. Springer. Berlin. Le Grand Y. (1972) Spectral luminosity. In Handbook of Sensory Physiology (Edited by Jameson D. and Hurvich L. M.). Vol. VIII/l4, pp. 413-433. Springer, Berlin. Lennie P. ( 1980) Parallel visual pathways: A Review. Vision Rw. 20. 561-594. de Monasterio F. M. (1981) Functional properties and presumed roles of retina1 ganglion cells df tie monkey.

Paper presented at 28th Int. Gong. Physiol. Sri.. Budapest 1980.in A&. Ph.vsiol. Sci., Vol. 2 Regulatory Functions of rhe CNS Subsvstems (Edited by Szentdgothai J.. Himori J. and Palkovits M.). Adademiai KiadoiPereamon Press. Budapest ( I98 I ). Myers K. J.. lnglinp C. R. Jr and Drum B. A. (1973) Brightness additivity for a grating target. Vision Res. 13, 1165-I 173. Vos J. J. and Walraven P. L. (1971) On the derivation of the fovea1 receptor primaries. V&ion Res. 11, 799-818. Wiesel T. N. and Hubel D. (1966) Spatial and chromatic interactions in the lateral geniculate body of the rhesus monkey. J. Neurophwiol. 29. I 1I5- I 156. Woodward T. N. (1953) Probability and Iqformation Theory, with Applications IO Radar. McGraw-Hill. New York. _

APPENDIX Lineur

AcX-noM,fe~~e~~~enrs-Thisresearch was partially supported by NE1 Grant NO. 5 ROI EY 03236 to C. R. ingling Jr. We thank Dr Karl Komacker for helpful discussions, Dr Stanley Klein for a suggestion which simplifies the presentation. Dr Phillip Russell for a critical readine of the manuscriot. and Referee No. I for the paragraph quoted in the discussion and for suggesting the use of Woodward’s notation in the Appendix. REFERENCES

Boynton R. M. and Kaiser P. K. (1968) Vision: The additivity law made to work for heterochromatic photometry with bipartite fields. Science 161, 366-368. De Valois R. L. and De Valois K. K. (1975) Neural coding of color. In Handbook of Perception V (Edited by Carterette E. C. and Friedman M. P.). Academic Press, New York.

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Most receptive fields can be characterized by the comtrination of a spectral sensitivity and a spatial transfer function. Such a field, or channel. has only 1d.f.; it is univariant. The r-g simple-opponent field, however, requires IH’Ospatial transfer functions, each modified by a different spectral sensitivity. for its description. It is not a univariant channel; it is equivalent to a channel which (apparently) simultaneously transmits information from two classes of cone independently over a single channel, but at different spatial frequencies. This is shown by writing separate expressions for the center and surround (see Fig. 2) and then factoring the resulting sum of products by substitution into the identity (As +&)=&A fB)(x +.v)+d(A - B)(x -y). [This result for the Type I single-opponent cell may be compared to that obtained for Type II and Type III (Wiesel and Hubel, 1966) cells. for which a similar substitution yields only a single product that characterizes the spatial and spectral properties of the cells (Ingling and Martinez, 1983).]

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Approximating the receptive field center and surround with rectangular functions simplities the transformations of the pomt-spread functions to the spatial frequency domain. Using Woodward’s (1953) notation. a rectangular pulse of length 7’ is written rect I ii? where rect I is a pulse of unit width centered on the origin. Letting I, = receptive field center and,/; surround.,l; = 2 met r../+= -frect f:3 - rect rt.

as illustrated m Fig 2 (top). Using these definitions. the two channel filters which result from substitution of the exprcsston for the receptive field into the above identity are then /; -Cf; = 3 rect t - rect I ‘3. and /; - 1, = rect t + rect I 3. Given the transform pair rect 1T-+ T sine u. the shapes of the filters in the frequency domam are readily calculated. as shown in Fig. 2.