JOURNAL OF THIE OPTICAL SOCIETY OF AMERICA

Spatial Characteristics of Metacontrast*

RONALD GROWNEY AND NAOMI WEISSTEIN

Department of Psychology, Loyola University, Chicago, Illinois 60626(Received 14 August 1971)

The spatial extent of lateral interaction was determined for nonoverlapping equal-energy stimuli in ametacontrast design with targets and masks of constant separation but varying width. The weighting func-tions derived from these data are wholly negative. Unlike previous estimates of spatial extent in meta-contrast, based on experiments in which the separation between target and mask was varied, our weightingfunctions subtend only about 10' of visual angle, for both monoptic and dichoptic observations. However,the weighting functions resemble those derived from a wide variety of other psychophysical proceduressuch as sensitization. The differences of estimates of weighting functions are interpreted in terms of twospatial-lateral-interaction systems. One of these systems may depend critically on the proximity of stimuli;the independence of the spatial extent of the system from target size suggests the involvement of an edgemechanism.INDEx HEADING: Vision.

Brightness is not a simple function of luminance'-3

but depends at least in part on the spatial distributionof luminances. One explanation of the spatial inter-action of luminances is that the brightness at any pointis a weighted sum of the luminances about that point. 4

This explanation assumes linearity and is consistentwith a lateral-inhibition hypothesis, in which positiveweights are interpreted as excitation, contributing tobrightness, and negative weights are interpreted asinhibition.

A variety of psychophysical experiments havemeasured the relative magnitude and spatial extentof these weights, particularly for the fovea. For ex-ample, Thomas reported an induction experiment inwhich the apparent brightness of a 3' wide test linewas varied by rectangles that flanked the target.4

Assuming that the brightness of the target correspondsto the output of a detector cell and that the outputof the detector cell is governed by the weighted sumof the retinal illuminance in the cell's receptive field,Thomas computed a weighting function, roughlygaussian in shape, with a central excitatory width of 5'and an inhibitory diameter of 20' of visual angle. Thefiring of each detector cell, R(p), can be characterizedby the convolution of the weighting function, 0(x), andthe stimulus luminances,5 F(x),

r+.R(p) =g} F(x)0(p-x) dx.

-0:

The spatial extent of the weights can also be deter-mined from Westheimer's data.6 For foveal stimuluspresentations, Westheimer found an initial increaseof increment threshold of a 1' angular-diameter targetfor overlapping masking disks up to 5' in diameterand then a decrease of threshold, leveling off for disks20' in diameter or larger. On the basis of a detector-

cell mnodel, the increase of ihCfehleellt tlhehold wouldbe expected for disk sizes within the excitatory regionof the cell's receptive field and a reduction of thresholdwithin the cell's inhibitory region. The results are

consistent, then, with a receptive field of 5' excitatorydiameter and 20' inhibitory diameter.

As an alternative to the detector-cell model, it mightbe assumed that brightness corresponds to the outputof a neural layer with both mildly and maximallystimulated cells contributing information. The ana-lytical prediction of Mach bands by applying a weight-ing function to a step of luminance assumes a neural-layer model. This procedure predicts that the effectiveinhibitory width of the weights yielding the Machbands is the width of one of the bands, about 20',assuming the excitatory width to be small.7 The pro-cedure could also be used with Westheimer's data; theresults would be identical to those obtained above. Inorder to work conveniently with the neural-layermodel, two assumptions about the neural-layer modelmust be made: (1) that the distribution of different-sizecells in a neural layer is in some way homogeneous andadds linearly, so that the neural layer can be charac-terized by just one weighting function; and, (2) thatthe weights characterizing the neural layer can bemeasured about one point. This second assumption isnontrivial if, for example, we assume that brightness isdetermined by interaction at the edges of a stimulus.

Psychophysical experiments have yielded rathersimilar estimates of weighting functions, whether theunderlying model used to derive these weighting func-tions has been a detector cell or a neural layer, that is,the measurements of the weighting functions areapproximately the same: an excitatory center about 5'of visual angle in diameter and an inhibitory surroundof 20'. The excitatory-center estimate is consistentwith the foveal-excitatory-center estimate of 5' ob-tained by Bryngdahl.A These measurements are onlyapproximate because subjects differ, at least for theWestheimer paradigm,9 and the magnitude and spatialextent of the weights increase with increasing retinalilluminance.t But, if we asggume the approximatevalidity for a foveal weighting function with a 5'excitatory and 20' inhibitory width, it is possible thatthe above procedures are measuring the same mecha-

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VOLUME 62, NUMBER 5 MAY 1972

SPATIAL CHARACTERISTICS OF METACONTRAST

nism, perhaps a retinal one. It is also possible that noneof the procedures are measuring a retinal mechanism(that is, chiefly reflecting retinal characteristics), orthat the same-size function characterizes processes atdifferent sites in the visual pathway. Westheimer'sdata6 suggest that the function he measured character-izes a retinal mechanism, because he found no dichoptictransfer of the effect, although dichoptic transfer hasbeen obtained by Markoff and Sturrj' particularly fortransient stimuli.

Metacontrast studies, in which rectangular maskson each side of the target decrease the apparent bright-ness of a target, have obtained much larger estimates ofthe spatial interaction of luminances.12-'4 The diminu-tion of brightness which has been found with increasingdistance between target and mask could correspond to aweighting function with inhibitory effects or negativeweights extending out to a radius of one degree ormore. This difference is particularly interesting ifmetacontrast is interpreted as a cortical interaction 1 5 ;the difference of estimate may characterize mechanismsat different loci of interaction. One masking study,16

however, produced a much smaller estimate of negativeweights; masking of a disk by a ring dropped to zeroat an interstimulus distance of 10'. These data suggestan alternate hypothesis. Differences in estimation ofthe extent of weights may be due to the triggering ofdifferent spatial mechanisms. The larger estimationsof weights were obtained from metacontrast studies inwhich the target and mask were similar in form.Similarity of form is important in metacontrast' 7 8;perhaps similarity of form defines the input for a spatialmechanism which is characterized by the larger weight-ing function. Smaller estimations of weights may bemeasuring a different spatial mechanism which isrevealed when target and mask are dissimilar in form.The critical factor determining the amount of lateralinteraction for this second spatial mechanism may bethe proximity of edges of target and mask. In summary,the conflicting estimates from different studies maybe due either to different loci of interaction (periph-eral vs central) and/or to two different spatialmechanisms.

The following experiment was performed to measurethe magnitude and extent of the weights about a targetin a metacontrast study and to obtain informationabout the mechanism characterized by the weights. Astimulus arrangement similar to that of Thomas4 wasused, where targets and masks of varying sizes werenonoverlapping and separated by a constant, smalldistance. Rectangular targets of varying width wereused with rectangular masks of identical height butvarying width.

METHOD

Three students, observers 1, 2, and 3, with 20/20or 20/20 corrected vision were paid to serve as observers.

The display was presented on a six-channel binoculartachistoscope (Scientific Prototype, model G). Thestimuli were illuminated rectangles against a constantlyilluminated 9-mL background. Stimulus luminance was17 mL, measuring the blank stimulus field. Luminancemeasurements were made with an SEI photometer andluminance flashes were monitored by phototubes placedin each channel; their outputs were displayed on anoscilloscope. All channel sources were set to produce35-mL luminance; luminance was varied for differentconditions by neutral density filters.

The stimuli were slide negatives on Kodak Ortho-Type HII film. All stimuli were 49' visual-angle high.Four targets were used, having widths of 1', 8', 25',and 49'. Each mask consisted of two equal rectanglesflanking the target on each side with a target-maskseparation smaller than 1'. Each set of masks consistedof eleven sizes from 1' to 98' wide. Stimuli were alignedmanually. This could be done accurately owing to thesmall constant distance between target and mask.Exposure duration was 16 ms for target and mask.Stimulus presentations were separated by at least a5-s interval of the uniform background.

A fixation X, crossing the entire visual field, was usedto facilitate alignment of the dichoptic field; the centerof the X served as fixation point. The stimulus displaywas centered one degree below, and to the right of,the fixation point. The observer adapted to the back-ground luminance for 10 min prior to each day'ssession.

The Stevens magnitude-estimation procedure wasused; a modulus of 10 was assigned to the luminanceof the target flash, presented by itself. This standardwas shown to the observer at the beginning of eachtrial. Each observer had 10 h of practice before datagathering was begun. One trial consisted of 17 ISIs(interstimulus interval, measured from extinction ofthe target to the beginning of the exposure of the mask,for positive values, and from extinction of the maskto first appearance of the target for negative values)over the range -100 to 200 ms in 20-ms steps (omitting180). Each target was presented with each maskmonoptically. Only the 25' and 49' targets were pre-sented dichoptically, because fusion could not beobtained with the smaller targets. Each test conditionwas replicated ten times. Target, mask, ISI, and state(monoptic vs dichoptic) orders of presentation wereall randomized, except that each session consisted ofonly one state and one target. The brightness of the 1'target was difficult to estimate (observer's report) andthe data were highly variable; so we dropped the datafor the 1' target from the analysis of the results.

RESULTS

Because magnitude estimations tend to give lognormal distributions,1 9 analyses of variance were per-formed on the logarithms of the data. A four-way

691May 1972

R. GROWNEY AND N. WEISSTEIN

TABLE I. Significant effects for the four-way (observerXtargetXmask widthXISI) analysis of variance (p<0.01).

Main First order Second order

3 23 2344 24

34

analysis of variance (observerXtargetXmask widthXISI) was performed on the monoptic data for the 8',25', and 49' targets; a five-way analysis of variance(observerX target Xmask width X ISI Xstate: monopticvs dichoptic) was performed on the dichoptic data forthe 25' and 49' targets. The results are summarized inTables I and II.

The monoptic data for the three observers for the 25'target are shown in Fig. 1. Each point in each graphis the geometric mean over ten replications. The mostmasking for each mask was at ISIs for which the targetpreceded the mask by 20 to 80 ms. The peak maskingamplitude for each curve increases with increasingmask width, up to 10' to 16'. Both of these effects, themain effects of ISI and mask width, were statisticallysignificant (see Table I). The curves level off for largermask widths (observers 2 and 3) or decrease of ampli-

0-

3-

6-

t 9:

J3 3-

0-

,q6-

9-

-q

- (b)

I | I I i i i ! !-100 -60 -20 SP 20 60 100 140 180 2201 SI- '

I

FIG. 1. Masking amplitude as a function of interstimulus inter-val (1ST) for monoptic presentation of the 25' target. Results areshown for representative masks of width 1' *-*, 3' x-x, 4'[l-El, 8' A-A, 12' o--o, and 74' A--A for the three ob-servers (a) observer 1, (b) observer 2, and (c) observer 3. SP issimultaneous presentation of target and mask (At= 0). Minus ISIindicates forward masking.

6-

9.

: 9.

II

PI'

t (b)

0-I

3-

6

9

-100 -60 -20 SP 20 60 100 140 180 220- lSI ->

FIG. 2. Same as Fig. 1, for dichoptic presentationof the 25' target.

tude (observer 1). Besides this reduction of amplitudefor larger masks, the data of observer 1 differed fromthose of the other observers in that the masking curveswere much narrower; the curves were shaped more likean inverted V than an inverted U. The amplitude-vs-ISI masking curves for the 8' and 49' targets closelyresemble the graphs of Fig. 1 except that (1) the peakmasking amplitudes of the data of observer 1 for the8' target are more like those of the data for observers2 and 3; (2) all three observers showed some forwardmasking for the 8' target, the effect being most pro-nounced for the data of observer 1. The targetXIS1interaction was statistically significant (see Table I).

The dichoptic data for the 25' target are shown inFig. 2. Under monoptic conditions, there was very littlemasking at simultaneous presentation (ISI =SP) of thetarget and mask; the backward-masking curves ap-peared like an inverted U. Under dichoptic conditions,there was appreciable masking at simultaneous presen-

TABLE II. Significant effects for the five-way (observerXtargetXmask widthXISIXstate: monoptic vs dichoptic) analysis ofvariance (p<0.O1).

Main First order Second order

3 23 23534 24535 34545

- -| u ) u^

692 Vol. 62

SPATIAL CHARACTERISTICS OF METACONTRAST

TABLE III. Arithmetic standard deviations of the magni-tude estimations for the peak masking ISI, averaged across masksfor each observer and target.

Monoptic Dichoptic

Observer 1 2.63 1.88 1.97 2.73 2.65Observer 2 1.19 1.42 1.41 2.24 2.34Observer 3 1.60 2.17 1.74 3.08 3.61

tation so that the masking curves appear truncatedfrom an inverted U to an inverted J. This J shape, whichhas been found previously for dichoptic data,' 4" 1

1' seemsdue partly to a leftward time shift of peak maskingfor some of the masks larger than 8' (see Table IV) butdue mostly to a raising of masking amplitude in theregion near simultaneous presentation of target andmask. The maskXstate (35) and ISIXstate (45) inter-actions were both statistically significant (see TableII). The main effect of state (5) was not significant;this is at least partly due to the unusually high monopticpeak masking amplitudes. Previous studies'4 2 0 havereported that monoptic masking is smaller in amplitudethan dichoptic masking. The dichoptic data are alsolike the monoptic data in that peak masking amplitudeincreases with increasing mask width up to widths of12' to 16' (and to 30' for the dichoptic data of the 49'target for observers 2 and 3; this can be seen in Fig. 4).

I-

3-

6-

TI

O_

a

*

CD 6-z

A \=-

(a)

(c)

10 20 30 40 5o 6o 70 do 9o- MASK WIDTH IN MINUTES OF-

VISUAL ANGLE

FIG. 3. Peak masking amplitude as a function of mask width formonoptic presentation of targets of width 8' o-a, 25' A- -A,and 49' [- -E for the three observers (a) observer 1, (b) ob-server 2, and (c) observer 3.

(c)

10 20 30 40 50 60 70 80 90-MASK WIDTH IN MrNUTES OF-'

VISUAL ANGLE

FIG. 4. Same as Fig. 2, for dichoptic presentation of twotargets of width 25' 0-0 and 49' A- -A.

The peak of each amplitude-vs-ISI curve (as in Figs.1 and 2) for each mask width measures the optimalsuppression effect of each mask on the target. Theincrease of peak masking amplitude with increasingmask width for monoptic conditions is shown in Fig. 3.Generally, peak masking amplitude for the data ofobserver 1 decreases for masks larger than 8' to 12';peak masking amplitude for the 8' target in the dataof observer 1 is higher than for the 25' or 49' targets,which accounts in part for the high significance of thetarget Xmask (23) interaction. A plot of the peakmasking amplitudes of the dichoptic data is shown inFig. 4. The chief difference of the dichoptic curves isthe greater increase of masking amplitude of the 4'mask over the 3' mask for observers 2 and 3 and themore gradual increasing slope of the curves for the 49'target.

TABLE IV. ISIs at which peak masking occurred for eachobserver and mask for monoptic and dichoptic presentations. Thevalues are averaged across targets. Mask width is in minutes ofvisual angle.

Mask width 1' 3' 4' 8' 12' 16' 25' 34' 49' 74' 98'

Observer I Monoptic 33 20 20 20 27 20 27 27 27 20 20Dichoptic 10 40 20 20 20 20 10 10 10 10 20

Observer 2 Monoptic 60 40 27 47 47 40 47 33 47 47 40Dichoptic 80 60 40 40 10 30 30 40 30 30 30

Observer 3 Monoptic 47 33 27 40 40 40 47 53 40 33 33Dichoptic 60 30 30 30 50 40 40 40 50 50 40

l l- l l l l l l l l

May 1972 693

R. GROWNEY AND N. WEISSTEIN

Li,I O-

Z 0.2

Erm

i -0.2

I o"

5 10 5 ' 10 15I l 0 15

l I-VISUAL ANGLE IN MINUTES -

FIG. 5. Weighting functions computed from the monopticdata of each observer: observer 1 o-o, observer 2 A-A, andobserver 3 E-[] for the three targets, from left to right, 8', 25',and 49' width.

While not strictly appropriate, the arithmeticstandard deviation for each test condition was com-puted, to show the variability averaged at these peakmasking points. These data are summarized as averagestandard deviations for a particular observer and target,as shown in Table 111.21

The peak masking amplitudes are the data we haveused to construct the weighting functions. These peakamplitudes were not constant for all ISI for eachobserver but vary as shown in Table IV. Because theweight is a number representing the change of brightnessdue to some change of size of the flanking rectangle, theweighting function is essentially the derivative of thepeak masking amplitude-vs-ISI curve.2 2 To computethe weighting function, we assumed that (1) Magni-tude estimations are a power function of luminance.(2) The brightness of the target corresponds to theoutput of a single detector cell. This assumption isnecessary to obtain a unique set of weights about aparticular point. (3) Magnitude estimations are linearlyrelated to the weighted sum of the luminances withinthe receptive field of the detector cell. (4) The detectorcell that determines brightness is at the edge of thetarget. This assumption was made because (a) ourweight for the 1' mask was obtained with reference tothe edge of the target; (b) because there is evidencethat the brightness of an object is a function of theedges of the object,' 23 the reduction of target brightnessin metacontrast may also be a function of the target'sedges. If so, the visual system may create an input to ametacontrast mechanism that resembles an impulsefunction by selecting the edge from the target24 ; (c) thechange of magnitude estimations of the target withchanges of mask width looked the same for each target.This should not have been the case if form similarity werethe basis of the brightness interaction or if the outputof the hypothesized detector cell corresponded to aweighted sum of luminances centered at the middle ofthe target. The latter hypothesis would have predictedmasking that varied with target size, because the larger

the target, the larger should have been the receptivefield of the corresponding detector cell.

The monoptic weighting functions of the threeobservers for each target are shown in Fig. 5. Previousestimates of weighting functions have either hadpositive weights at the center of the function or, atleast, weights which were slightly less negative so thatthe minima of the function occurred about 3' or 4'from the center of the function. Only the functions ofobserver 1 and one function of observer 3 show anyevidence of troughs, that is, minima not located at thecenter of the function. The reason for this is clear fromFig. 3 because for these cases the change of brightnessof the target between the 3' and 4' masks is greaterthan the change caused by the 1' mask. The absence oftroughs in the weighting functions of observer 2 andtwo of the functions of observer 3 means that thegreatest change of brightness of the target occurredwith the 1' mask. This relatively large effect of a smallmask has also been observed when interstimulusdistance between small targets and small masks wasvaried (see Weisstein1 ). The weighting functionsderived from the dichoptic data are shown in Fig. 6.These functions are not as deep as the monoptic func-tions. The dichoptic functions of observer 2 and onedichoptic function of observer 3 are wider than thecorresponding monoptic functions.

Although the double trough seen in three of the sixdichoptic functions might indicate the added operationof a small-width, strictly dichoptic mechanism, thepossibility of blurring of the stimulus pattern due tofusion difficulties or binocular rivalry seems morelikely. Because of the variability of the data, the rela-tive magnitudes of the weights within the 10' radiuscan be considered only tentative. The spatial extentof the weights is more reliable in that, at 10' radius,the magnitude of the weights for both monoptic anddichoptic functions has decreased to 5% of the maxi-mum absolute value. There are individual differencesin the spatial extent of the functions (the monopticfunctions of observer 2 are effectively zero at 4' radius);

I

I-m

c:3

Xir

0.4-

0.2-

5 10 15

-0.2 t-

-0.4t

5 10

- VISUAL ANGLE IN MINUTES -..

FIG. 6. Same as Fig. 3. The functions are computed fromthe dichoptic data for two targets, from left to right, 25' and 49'width.

694 Vol. 62

SPATIAL CHARACTERISTICS OF METACONTRAST

however, the monoptic and dichoptic functions aresimilar, in that the effective magnitude of the weightsis approximately zero at 10' radius.

The J shape describing the dichoptic data may bepartly due to binocular rivalry.2 0 Subtraction of amonoptic curve (Fig. 1) from its corresponding dichopticcurve (Fig. 2) yields functions that peak at the originand decrease to 0-420 ms from simultaneous presen-tation, about the duration of our stimuli exposure.These functions increase in amplitude at the origin asmask width increases, up to widths of 8' to 16'. Thissuggests that the same mask size that gives peak mask-ing also gives maximum target suppression at simul-taneous presentation. Perhaps binocular rivalry isrelated to the characteristics of the edge mechanism.Binocular rivalry has been linked to contour suppres-sion25 ; and these data suggest that for short-exposurestimuli in an experiment where rivalry has had time todevelop, maximal suppression occurs at simultaneouspresentation of stimuli.

Figures 1 and 2 show that wider masks yield broadermasking-amplitude peaks across ISI for mask widthswithin the 10' range, where the negative weights addsignificantly. This supports one of Matteson's hypothe-ses26 for a lateral-inhibition model that follows fromthe postulated addition of longer-latency inhibitionby increasing mask width. This supposition is also thebasis for Matteson's second hypothesis, that widermasks should move the masking peak to smaller ISIs.This hypothesis receives some support from the data,as can be seen in Table IV. Again, within the 10' rangeof negative weights, there is evidence of a shift fromlonger to shorter ISIs (although three points reversethis shift). The statistical significance of these changesof the masking functions with different mask widthsis indicated by the ISIXmask-width (34) interaction,p<0.01 for both monoptic and dichoptic functions (seeTables I and II). The support of the hypothesessuggests that, within the 10' range of effective weights,the weighting mechanism has lateral-inhibitioncharacteristics.

DISCUSSION

Both monoptic and dichoptic data agree with pre-vious small-width estimates of a lateral-interactionmechanism with negative weights extending approxi-mately 10' of visual angle from the edge of a simplestimulus for foveal presentation, regardless of stimulussize. Thus, the difference between small and largeestimates cannot be explained as a difference betweencortical and subcortical interactions (although thelarge-extent estimates may refer to a mechanism at adifferent central locus). Rather, both small and largemetacontrast estimates may refer to cortical processes,because both can be obtained dichoptically. That thesmall estimate of this study refers to central processesdoes not necessarily imply that other small-widthestimates also refer to central processes, but it is

interesting that they agree. The spatial extent of theweights was the same for targets of different sizes; thebrightness of the target depended on the luminance of asmall area, constant in size, immediately adjacent tothe target, which did not change in size with changesof target size. This suggests the activity of an edgemechanism. The lateral-interaction mechanism charac-terized by this small-radius weighting function displaysseveral lateral-inhibition characteristics. Masking in-creases with increasing mask size up to about 10', aswould be expected from a cumulative stimulation of acell's 10' inhibitory radius or of the composite weightingfor 10' radius around some point in a neural layer.Matteson's hypotheses2 6 about the changes of temporalcharacteristics of metacontrast expected from changesof spatial properties of the stimuli due to lateralinhibition were supported by the data.

With the exception of the data of observer 1, maskingamplitude was rather constant for mask widths morethan 10'. A decrease of masking with increasing masksize would be analogous, neurophysiologically, tospatial disinhibition; if the inhibiting surround of adetector cell is itself inhibited, the output of the detectorcell will increase.27 If such a neurophysiological modelwere to account for our psychophysical data, a decreaseof masking might be expected as masks get larger thanthe width of the negative weights. A neural-layermodel with more than one layer would predict no otheroutcome than disinhibition; a detector-cell modelwould predict no other outcome if it is assumed28 thata number of independent, different-size detector cellsabout the edge of a target, perhaps within a 10' radius,fire in response to the edges of a stimulus (also seeWeisstein1 5). Therefore this failure to find disinhibitionis puzzling (but see the data of observer 1 for themonoptic 8' target and the dichoptic 25' target). Onepossibility is that the response saturated at completemasking. Although observers did not report darkeningin the area of the target, which might be expected fromsuch saturation, no provision was made for reports ofbrightness reduction below the level of the backgroundluminance. The failure to observe any disinhibition inthe data of two of the three observers in this experimentseems characteristic of metacontrast2 6 (with theexception of Mayzner et al.29).

There was no evidence of masking peaks for masksizes corresponding to the same target sizes, so similar-form effects were not observed. Although the hypothesisof a form mechanism was not supported by these data,it is unclear just how a form mechanism might interactwith an edge mechanism. There is, at least, evidenceof another lateral-interaction mechanism, which mayor may not be form specific. This second mechanism,which is characterized by large-width 2 '-4 weightingfunctions also displays lateral-inhibition characteristics.Although it may possess the nonlinearity of a form-specific input, masking does decrease for increasingdistance between target and mask"3 ' 4 similar to the

May 1972 695

R. GROWNEY AND N. WEISSTEIN

stimulation of the receptive field of a cell. Further,Alpern"3 found a regular shift of masking peaks tosmaller ISIs as the masks moved farther from thetarget. This shift is one of Matteson's hypotheses 26 fora lateral-inhibition model. Because lateral inhibitionappears at many levels of the visual system, we mightexpect to find evidence of different lateral-inhibitionmechanisms in psychophysical data, depending on thedesign. If there are several different spatial mecha-nisms, then lateral inhibition may be found within aparticular mechanism once the requisite preprocessingfor input to the mechanism has been defined. But thecomplexities of specific connections 3 0 need not hidealtogether the simpler operations of lateral inhibition;within the region of effective weights of the lateral-interaction mechanisms these lateral-inhibition proper-ties should hold, if we properly define the input.

The locus of the spatial mechanisms characterizedby the weighting functions is not established; as acomposite, the weighting function may characterizeseveral processing stages. Although the dichoptic datasuggest that cortical components are involved, it is notinconceivable that the cortex may be involved infeedback to prior stages concerned with brightness,because brightness and patterns (edges) seem verymuch related. The weighting functions need not beinterpreted as characterizing cortical output only, sothat cortical locus of interaction is implied, but ratheras characterizing the composite activity of a systemwithin which the cortex is one processing component.

The shape of the weighting function obtained fromthe data of this study shows little evidence of excitatorycenters but consists mainly of an inhibitory trough.Perhaps the spatial mechanism characterized by thesefunctions is different from the mechanisms measuredby steady-state techniques (see Thomas4 but noticethat one observer in that study also showed no excita-tory center) and may be characterized by a completelynegative function; or perhaps the transient stimuli ofmetacontrast pick out only the negative weights of theweighting function. It seems likely, however, that theseweighting functions characterize a mechanism that isinvolved in pattern processing; in general, the spatialextent of the negative weights obtained from the short-exposure stimuli of metacontrast is similar to thespatial extents indicated by other methods understeady-state conditions. This may indicate that meta-contrast is a function of general pattern-brightnessmechanisms, and that hypotheses based on meta-contrast data may have general applicability.

REFERENCES

* An earlier version of this paper was presented at the May1971 meeting of the Midwestern Psychological Association. Theresearch was supported in part by U. S. Public Health ServiceGrant No. EY00143-03 to the second author.

lV. O'Brien, J. Opt. Soc. Am. 48, 112 (1958).2 T. N. Cornsweet and D. Y. Teller, J. Opt. Soc. Am. 55, 1303

(1965).3 M. Davidson and J. A. Whiteside, J. Opt. Soc. Am. 61, 530

(1971).4J. P. Thomas, Vision Res. 8, 49 (1968).J. P. Thomas, Psychol. Rev. 77, 121 (1970). We have modified

the equation slightly.6 G. Westheimer, J. Physiol. (London) 190, 139 (1967).7 G. von Bekesy, J. Opt. Soc. Am. 50, 1060 (1960).8 0. Bryngdahl, Vision Res. 6, 553 (1966).9 D. Y. Teller and B. Lindsey, Vision Res. 10, 1045 (1970).10 A. S. Patel, J. Opt. Soc. Am. 56, 689 (1966)."'J. I. Markoff and J. F. Sturr, J. Opt. Soc. Am. 61, 1530

(1971).12 G. A. Fry, Am. J. Optom. Arch. Am. Acad. Optom. 25, 162

(1948).13 M. Alpern, J. Opt. Soc. Am. 43, 648 (1953).14 N. Weisstein and R. Growney, Percept. Psychophys. 5, 321

(1969).15 N. Weisstein, in Visual Psychophysics, edited by D. Jameson

and L. M. Hurvich (Springer, Heidelberg, 1972). The hypothesisthat metacontrast is a cortical interaction is supported by thedichoptic transfer of the effect, the time delay for which the maskis most effective, and the dependence of metacontrast on bothtarget and mask as patterns.

16 S. I. Cox, W. N. Dember, and M. F. Sherrick, Psychon. Sci.17, 205 (1969).

17 W. R. Uttal, Percept. Psychophys. 7, 321 (1970).18 M. S. Mayzner and M. E. Tresselt, Psychon. Sci. 17, 77

(1969).19 S. S. Stevens, Percept. Psychophys. 1, 96 (1966).20 P. H. Schiller and M. C. Smith, Percept. Psychophys. 3, 237

(1968).21 What is strictly appropriate for measuring the variability

of a geometric mean is a standard deviation computed with thelog data, analogous to the computation of the geometric mean.The standard deviations computed in this manner are quitesmall, however, and can be misleading in describing the actualvariability of the data; the range of standard deviation is con-siderably compressed.

22 This approximation can be obtained by taking the derivativeof the convolution integral (see introduction) at a particular point,p, at the edge of the target [we assumed 0(-x)=O(x)2. Wesolved for the weighting function so that

O (x) ) dlx

where dR is approximated by the difference between the magni-tude estimations (ME2-MEI) corresponding to the change ofdistance along one dimension, x, and where dx is approximatedby the difference between two successive mask sizes (M2-M1).See Thomas (Ref. 4) for a similar procedure.

2 T. N. Cornsweet, Visual Perception (Academic, New York,1970).

24 On the other hand, the edge mechanism involved in bright-ness might require a smaller target as an impulse function, orgenerally, metacontrast might not be an edge effect at all but afunction of some larger detector cell for brightness. In either case,under the assumption of linearity, as targets get narrower andapproach the width of an impulse, the computed functions shouldapproach the actual weighting function.

25 A. G. Goldstein, Percept. Psychophys. 7, 28 (1970).26 H. H. Matteson, J. Opt. Soc. Am. 59, 1461 (1969).27 F. Ratliff, Mach Bands: Quantitative Studies on Neural

Networks in the Retina (Holden-Day, San Francisco, 1965).28 G. Sperling, Percept. Psychophys. 8, 143 (1970).29 M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T.

Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D.Nilsson, Psychon. Sci. 3, 79 (1965).

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