PSYCHOLOGICAL REVIEWwexler.free.fr/library/files/weisstein (1975) a... · 2020. 7. 29. · Naomi Weisstein State University of New York at Buffalo Gregory Ozog and Ronald Szoc Loyola

PSYCHOLOGICALREVIEWCopyright <0 1975 by the American Psychological Association, Inc.

VOL. 82, No. 5 SEPTEMBER 1975

A Comparison and Elaboration of Two Models of Metacontrast

Naomi WeissteinState University of New York at Buffalo

Gregory Ozog and Ronald SzocLoyola University, Chicago

Metacontrast has been the subject of two neural network simulations byWeisstein and Bridgeman. We compare and elaborate on the two models,correct flaws not inherent in the models' conceptualizations, and discuss theremaining shortcomings. The idea behind how U-shaped metacontrastfunctions are generated is similar in both models, but the assumptions abouthow the visual system is organized are quite different. In one of themodels temporal ringing, combined with a complex and implausible linkinghypothesis, is necessary in order for masking to be obtained; this modelassumes a single spatial and temporal channel. In the other model, mask-ing does not depend on temporal ringing; this model assumes multiplespatial and temporal channels and a simple linking hypothesis. We showthat of the two models only the second adequately predicts empirical meta-contrast functions, and we relate this model to recent evidence that thevisual system contains multiple channels. Sometimes treated as a puzzlingand somewhat singular phenomenon, isolated from the "mainstream" ofvisual data and theory, metacontrast may, on the contrary, turn out to beone of the more interesting manifestations of a multiple-channel visualsystem.

Metacontrast backward masking has been briefly flashed target (generally a disc orthe subject of two neural network simula- rectangle) and a briefly flashed mask (gen-tions in this journal (Bridgeman, 1971; erally an annulus or two rectangles thatWeisstein, 1968). Metacontrast would seem flank the target) are above threshold and ofinnocuous enough as a backward-masking roughly equal energy, the greatest reduc-design, and might not generate such interest tion in apparent brightness of the target willwere it not for the data it produces. If a occur when the mask is presented as much• as 125 msec after the target has been turned

This study was supported in part by grants off (Alpern, 1953). But when the targetPHS EY 00143 (now EY 01330) from the and mask are presented simultaneously, littleNational Eye Institute and CA 06475 from the ... , .r . . . . . . J

National Cancer Institute. lf any reduction in apparent brightness oc-We would like to thank Ronald Growney, curs. This reduction in apparent brightness

Bruno Breitmeyer, Kevin Berbaum, and John with increasing delays between target andTangney for their helpful comments and criticisms. magk ;s illustrated in Figure j It is the \J

Requests for reprints should be sent to Naomi . , . , . . ° , .Weisstein, State University of New York, Buffalo, m thls function that generates such interestNew York 14226. in metacontrast. Why should a target dis-

325

326 N. WEISSTEIN, G. OZOG, AND R. Szoc

appear only if a mask is delayed by some60-125 msec and not before?1

LATE ACTIVITY AS AN EXPLANATIONFOR METACONTRAST

Most theories attempting to explain theU-shaped functions in metacontrast have acommon assumption, namely, that the kindsof masks used in metacontrast suppress oralter the late portion of the response to thetarget, and do not interfere with earlier por-tions. If so, in order for masking to occur,the mask must be delayed until its presenta-tion will interfere with the appropriate(late) portion of the target response.

The response to the target may be dividedinto early and late portions if for no otherreason than that a brief stimulus flash pro-duces neural activity which may last wellover 150-200 msec after the stimulus goesoff (Sturr & Battersby, 1966; measurementof the gross potential).2 In addition, the

1 One way around this puzzle is to assume thatU-shaped functions in metacontrast do not reallyexist (e.g., Eriksen, Becker, & Hoffman, 1970;Lefton, 1973a). However, proponents of thisposition will admit that there is a U-shaped re-duction in apparent brightness of the target(Eriksen et al., 1970; Lefton, 1973b) ; their maincriticism is that detection functions in metacon-trast are not U-shaped. This is generally true(but see Cox & Dember, 1972) ; however, it is anirrelevant argument. There are a number ofsimilar paradigms which demonstrate that detec-tion and apparent brightness do not covary. Corn-sweet and Teller (1965) found that incrementthresholds remained constant even though theapparent brightness of a steadily presented discvaried depending on the brightness of a surround-ing annulus. Few would claim that although theincrement threshold to the disc did not change,simultaneous brightness contrast is not "real":discs do look brighter when surrounded by darkannuli than when surrounded by bright annuli.One simply has to use a response indicator ap-propriate to the phenomenon one wants to measure.

Another approach is to assume a priori thatcomplex phenomena such as metacontrast are notworthy of serious attention (e.g., Sekuler, 1973).However, it would seem that we progress by ex-ploring, rather than evading, that which is puz-zling.

'•> As early as 1966, Sturr and Battersby noticedthe possible relevance of the later portions ofneural activity to backward masking. They hy-pothesized that the entire 150-200 msec of neuralactivity had to occur undisturbed in order for a

early portion of this activity looks differentfrom the later portions. If early and latecorrespond to different perceptual events,then the late-activity explanation for meta-contrast may make sense. In metacontrast,something about the appearance of a targetis affected, while its detectability is generallyunchanged: Its apparent brightness or con-trast decreases, and its contours break up orfragment. The loss in detectability is heldto a minimum by the metacontrast design:Both target and mask are well above thresh-old, and they are adjacent to each otherrather than superimposed on the same reti-nal location. If we suppose appearance tobe connected with the late portion of neuralactivity, then a mask, to be effective in meta-contrast, might have to coincide with thelate portions of neural activity to the target.Hence U-shaped masking functions wouldbe predicted. In somewhat loose terms,then, two adjacent, briefly flashed, above-threshold stimuli might not be able to affecteach other's appearance unless the activityproduced by one of the stimuli "hits" theright portion of the activity produced by theother stimulus; if this portion of activity islate activity, then U-shaped functions will begenerated.

NEURAL MODELS AND VISUAL-SYSTEMORGANIZATION

To tie these ideas down to specific pre-dictions, one may make a model of neuralresponse or visual-system activity. Thismodel should generate metacontrast func-tions, be consistent with what is knownabout mammalian visual-system organiza-tion, and make reasonable linking hypotheses—that is, make reasonable hypotheses abouthow neural response might correspond tothe perceptual data (Brindley, 1970).

Before considering each metacontrast sim-ulation in particular, a few comments are inorder about two somewhat competing viewsof general visual-system organization, the

stimulus to escape masking. This is a somewhatmore general form of the theories developed toaccount for metacontrast; additional assumptions,about what happens when, have to be made inorder to predict U shapes.

Two MODELS OF METACONTRAST 327

((A!)

FIGURE 1. Metacontrast functions for each of three subjects, TJ, BW, and JP, as indicatedon the figure (solid curves) at each of five target-to-mask energy ratios, T/M (functions 1through 5; from Weisstein, 1972). The mask was always a lighted 16 msec, 16 footlambert(54.8 cd/m2) annulus; the target was a lighted, 16 msec disc whose luminance decreasedrespectively from 1 through 5 as follows: 16, 8, 3.2, 2, and 1 footlambert (54.8, 27.4, 10.9,6.8, 3.4 cd/m2). Each point on the solid curves represents a geometric mean of five mag-nitude estimations of the apparent brightness of the disc at each of 27 Afs, beginning withAf = — 100 msec and proceeding in 10 msec increments to Af — 100 msec; thereafter in 25 msecincrements to A£ = 200 msec, and finally, 250 and 300 msec. U shapes are found for each sub-ject for each T/M except the lowest one or two. Dotted vertical lines indicate simultaneouspresentation of target and mask, or A< = 0. If the function falls below the amplitude at thedotted vertical line, then it can be said to be U-shaped. The height of the solid vertical linesrepresents the points predicated by Weisstein's (1972) model. (From "Metacontrast" by NaomiWeisstein, in D. Jameson & L. Hurvich (Eds.), Handbook of Sensory Physiology (Vol. 7,part 4: Visual Psychophysics). Copyright 1972 by Springer-Verlag. Reprinted by permission.)

single-channel view and the multiple-channelview.

Single Channel

A single-channel view assumes that visual-system response can be characterized by oneset of parameters. To put it in terms ofneurons, a single spatial and temporal chan-

nel (or, equivalently, filter) would cor-respond to the assumption that the visualsystem responded as if all single units hadthe same receptive field size and time courseof excitation and inhibition. Then one wouldsimply need one function to describe thevisual system's spatial properties and onefunction to describe the visual system's tern-


poral properties. The single-channel as-sumption is not necessarily contradicted bythe evidence that single units in the visualsystem have different receptive field sizesand different rates and latencies of firing,since all units could contribute to a com-posite size and response rate. (See Nach-mias, 1968, for a discussion of a compositevisual-system spatial response, and seeCornsweet, 1970, for an excellent discussionof how if one assumes a single channel, onecan obtain an overall estimate of the visualsystem's temporal and spatial response byutilizing frequency-response techniques.)

Multiple Channel

A multiple-channel view assumes that tocharacterize visual-system response, familiesof parameters are necessary. Many differ-ent channels may be active in the visual sys-tem, depending on whether a stimulus issmall or large, periodic or aperiodic, transi-ent or sustained. These channels do notcontribute to one composite, overall function;rather, at some stages in the visual systemtheir activities are independent of eachother. Thus, for instance, at threshold itwould not be the sum of the activity of anumber of different channels that determinesthreshold, but the activity of a particularchannel that has reached threshold, activitynot directly influenced by the subthresholdmumblings of other channels that may beactive. (The threshold itself may be low-ered somewhat by subthreshold mumblingdue to probability summation, but this wouldreflect the independent activities of a num-ber of channels rather than the change inactivity of a particular channel as a resultof the activity in another. See Graham,in press, for an excellent discussion.)

An above-threshold view of a multiple-channel model might assume that differentchannels are responsible for different fea-tures of a stimulus—some channels for theedges of the stimulus, for example, andothers for the inside. We will have moreto say about this later. In terms of neurons,a spatial multiple-channel model would as-sume that units with different receptive fieldsizes respond to stimuli that are somewhere

within the range of their field size, and thatwhen a stimulus is too small or too large,the unit will simply not respond. (Spatialmultiple-channel models have usually beenphrased in terms of parallel spatial filters,each responding to a band of spatial fre-quencies, but we prefer, for the moment, touse a somewhat looser notion.) A temporalmultiple-channel model would assume thatunits would respond at different rates, andthis implies that some units might prefertransient stimulation and other units mightprefer sustained stimulation. Again, we willhave more to say about this later. Themultiple-channel model doesn't mean thatonly one channel will respond if only onestimulus is presented; a particular stimulusmay produce response in a number of chan-nels. The important point is that thesechannels are looking at different aspects ofthe stimulus, and they are responding atdifferent rates.

THE Two METACONTRAST SIMULATIONS

Of the two attempts to quantify the hypo-thesis that metacontrast is the suppressionof the late activity or slow portion of visual-system response to a stimulus, one (Weis-stein, 1968, 1972) is a multiple-channelmodel, and the other (Bridgeman, 1971) isa single-channel model. We will examinethe two models to see which one seems themore plausible. Neither model is adequateas it stands, and in considering which modelbetter fits the data, we need to expand andelaborate on both models. First, we willpresent Bridgeman's simulation, which as-sumes a single channel, taking the stepsnecessary for it to generate metacontrastfunctions (this was not done in his paper).As we examine this model, some seriousshortcomings that have previously escapednotice will become apparent. Then we willconsider Weisstein's simulation (1968,1972), which assumes multiple channels,expanding it so that it can deal with spatialinteractions. We will show that two short-comings noted for this model as it was form-ulated may be more apparent than real.Finally, we will present an elaboration ofthis model, which associates the fast and


DISC ALONE

-DISC ON —

240

C 2 I O

£180

§150

S l 2 0

3 90§ 60

i 30te

0 1 2 3 4 5 6 7NUMBER OF CYCLES

-DISC ON -

DISC PLUS ANNULUSAt = 60 msec

< ANNULUS ON-

NUMBER OF CYCLES

FIGURE 2. The activity of Bridgeman's (1971) neural network (the neuralimages) for each of six successive time periods. The top row of Figure 2shows neural images that occur during and after a disc is presented. Thebottom row of Figure 2 shows neural images that occur during and aftera disc is presented, followed by an annulus. The main thing to notice isthat the neural images of cycles 3 through 6 for disc alone (top row) versusdisc plus annulus (bottom row) do not resemble each other: This is thebasis of the metacontrast interaction. Time is a discrete function of num-ber of cycles: This is plotted in the inset.

slow responses assumed by Weisstein withthe recent work on transient and sustainedmechanisms (channels) in the visual system.

Metaconlrast Simulation 1

Bridgeman (1971) hypothesized that meta-contrast occurs because the late neuralactivity to a target followed by a mask dif-fers from what it would be to a target alone.

To obtain a picture of neural activity,Bridgeman uses the one-dimensional neuralnetwork developed by Ratliff and his co-workers (1965), in which each neuron in-hibits and is inhibited by its neighbors at re-current intervals. A neuron in the systeminhibits its neighbors in proportion to its ownactivity and to its distance from its neighbors.In addition, inhibition is subject to time de-lays: Adjacent neurons are inhibited with a


time lag of 30 msec and neighbors one re-moved are inhibited with a time lag of 60msec. To simulate this digitally, Bridgemanuses the Ratliff equations (1965, p. 110),with parameters chosen from Barlow's(1969) study of Limulus. This network issingle channel because it has a single set ofspatial and temporal parameters—a spatialweighting function consisting of a pointexcitation and a spread of inhibition oneither side, and a temporal weighting func-tion that is simply a step for excitationand inhibition from adjacent units, and a stepwith a one-period lag for inhibition fromunits one removed.

The Network

The Ratliff (1965) equations represent adiscrete form of repeated inhibition: Eachrecurrence of inhibition "spreads" a signallaterally so that one by one, units furtherand further removed from the site of stimu-lation become involved. The activity of theneurons in the network, what we may callthe neural image, is shown in Figure 2,during and after stimulation, for each suc-cessive recurrence of inhibition of the net-work. The top row shows a network re-sponding to a target alone, and the bottomrow shows a network responding to a tar-get and then a mask, which is presentedafter the initial response and one cycle ofinhibition of the network. The inhibitiondelay defines time in this network; that is,one cycle means that up to 30 msec havepassed, two cycles means that up to 60 msechave passed, and so forth. This quantiza-tion or "stepping" of time is shown in theinset of Figure 2.s

3 This figure was prepared usitig the output fromour own simulation program, which repeats thecalculations described in Bridgeman (1971). Thefigure agrees with Bridgeman's Figure 3 (p. 533)with two exceptions (see below), and for the sakeof brevity we have left out his third row, whichshows the network response to the annulus alone.Our Figure 2 also differs from Bridgeman's be-cause we adjusted the neural images so that theyeach had the same maximum peak-to-troughamplitude; this way, it is easier to see what theneural images look like for the later cycles wherethe total signal is very small. (Adjusting thepeak-to-trough amplitude, or normalizing these

As shown in Figure 2, when the stimulusis on, the corresponding neural images re-main fairly similar to the physical stimulusthrough successive cycles, that is, throughsuccessive 30 msec intervals at which theinhibition recurs. Each successive recur-rence can be seen to spread the signal, andedges and troughs develop at the borders ofthe stimuli. (Edges and troughs generatedby networks like these are the basis of manyexplanations of Mach bands and relatedeffects.) Bridgeman adopts the term homo-photic from Stigler (1910) to describe theset of neural images during stimulation. Theterm metaphotic describes the set of neuralimages that occur when the stimulus is re-moved. Although the metaphotic imagesno longer resemble the physical stimulus,they are uniquely related to it.

Masking

The set of neural images that occurs whenthe target is presented by itself comprisesthe reference to which all other conditionsare compared. The amount of masking isassumed to depend on the extent to whichthe set of neural images formed when bothtarget and mask are presented differs fromthe set of neural images formed when thetarget is presented by itself. This measure

functions, does not change the measure of simi-larity that Bridgeman used and we have repli-cated, since the measure itself normalizes allfunctions.) While this effectively makes all theneural images the same size, it should be stressedthat by the seventh or eighth cycle, the actualneural image is almost indistinguishable fromnoise.

There are some minor differences between ourtop-row cycles (3 and 4), and Bridgeman's. Be-low, there are some minor differences betweenour similarity function (Figure 3), and Bridge-man's. We have gone through extensive checkingprocedures on our own simulation (followingBridgeman's description of how he did his simu-lation) and are convinced that our calculationsare correct. The differences may be due to thefollowing factors: We used different computers,which could have led to a difference in word size,number of significant digits, rounding errors, plot-ter and plotting routine; and there may have beensome small drafting errors in Bridgeman's figures.In any case, none of these differences are suffici-ently large to affect the arguments that we makein this paper.


of similarity includes the entire neural image,from one end of the network to the other:The activity of every element in the net-work is considered, rather than, for instance,just the activity in and around the targetarea. We shall have more to say aboutthis below. The similarity comparison ismade cycle by cycle, and a similarity func-tion is produced, which gives a value ofsimilarity for pairs of neural images (target,target + mask) for each cycle.4

Bridgeman (1971) divides masking intotwo types: The type associated with thehomophotic neural images (forward andsimultaneous masking) and the type as-sociated with the metaphotic neural images(backward masking and metacontrast). Ac-cording to Bridgeman, homophotic neuralimages allow subjects to make detectiondecisions, while metaphotic neural imageshave to do with the appearance of the tar-get. It is not clear how the visual system isable a distinguish homophotic from meta-photic images; the images themselves can-not provide a unique criterion for whetheror not a stimulus is physically present. Butfor the purposes of argument, let us assumethat this problem can be solved. If we as-sume, then, that the system is somehowable to tell the difference between homopho-tic and metaphotic, in those instances where

4 These similarity comparisons are called cross-correlations, but the reference appears to be to aPearson r. That is, if one computes the actualcross-correlations for the output generated byBridgeman's (1971) network for the 6 cyclesillustrated in Figure 2, they are, in order, 1600,256, -394, 172, 16, and -5. This bears no re-semblance to Bridgeman's Figure 6. Next wetried various variations on our cross-correlations,but none of them got us near Bridgeman's Figure6. We thought perhaps he had normalized thecross-correlations in some way, so we computed a"constant of correlation" (Lathi, 1965) : F(x) *G(x)/F(x)*F(x), where * denotes convolution(for symmetrical stimuli, this is the same ascross-correlation), F (^ f )= the neural image inresponse to the target alone, and G(^)=theneural image in response to the target-plus-mask.Again, these numbers in no way resembledBridgeman's Figure 6. We then computed Pear-son rs [the normalized cross-correlation for thepoints F(0), G(0)], and finally our results agreein all major respects with Bridgeman's Figure 6(for the minor respects in which they do notagree, see footnote 3).

the mask is presented before or simultane-ously with the target, the homophotic imagesof the target are somewhat different fromthose of the target and mask together. Inthis case, detection drops. When the maskis presented later than the target, the homo-photic images are identical, but the meta-photic images of the target alone are differ-ent from those of the target-plus-mask, ascan be seen in Figure 2. Here, then, theappearance of the target—its apparentbrightness—is assumed to change, and onehas the makings of a metacontrast siutation.(Actually, the model predicts that wheneverdetection drops, the appearance of the targetalso changes for those instances where thetarget is detected, since if the homophoticneural images of target and target-plus-maskare dissimilar, so are the metaphotic images.But the important point is that one canhave appearance changes without detectionchanges, and this forms the basis of themetacontrast predictions.)

Thus the appearance of a stimulus is medi-ated by the late neural images (i.e., the lateneural activity), and metacontrast occurswhen these late neural images differ fromwhat they would be if a target had beenpresented alone. How is a metacontrastfunction constructed from this formulation?

Constructing the Metacontrast Function

A metacontrast function is a plot of somemeasure of the change in appearance of thetarget (generally apparent brightness) foreach delay between target and mask (foreach A£). No plots of this kind appear inBridgeman's (1971) simulation. Rather,neural image similarity is computed cycle bycycle for one At in the backward maskingrange, one in the forward masking range,and one at simultaneous masking. Thesimilarity function obtained is different forthese three cases; in particular, for the back-ward masking case the later, metaphoticneural images of the target do not resemblethe corresponding images of the target-plus-mask. This similarity function is shown inFigure 3.

A similarity function is not a metacon-trast function, because it provides informa-


SIMILARITYFUNCTION

FOR At = 60 msec

oencr

2 3 4 5 6 7 8

NUMBER OF CYCLES

FIGURE 3. The similarity function (what Bridge-man, 1971, calls the cross-correlations) for whatis assumed to be the metacontrast or backwardmasking case (actually, this represents only thepoint A( = 60 msec). The points on this functionare Pearson rs for the neural image pairs (discalone, disc-plus-annulus) which occur during thesame cycle. Each column in the top and bottomrow (each cycle) in Figure 2 allows calculation ofanother Pearson r.

tion about only one delay (or value of A£) .But the information from the similarityfunction can be suitably processed to ob-tain a metacontrast function. We can de-cide on an appropriate measure for masking(a measure that computes from the simi-larity function for a particular delay a num-ber that corresponds to target apparentbrightness for that delay) and then we canrepeat this calculation on similarity func-tions for a sufficient number of delays togive us a metacontrast function.

If we take these calculations step by step,we must first decide on what information

to compute from the similarity function.The computation will yield a number, whichwill be assumed to correspond to target ap-parent brightness. One should rememberthat the model assumes that the apparentbrightness of a target is mediated by itsmetaphotic images, and that masking is re-lated to how similar the neural images thatoccur when a target is flashed in conjunc-tion with a mask are to the neural imagesthat occur when a target is flashed alone.However, the set of metaphotic images can-not be a necessary condition for target ap-parent brightness, since a steadily presenteddisc of light has a distinct apparent bright-ness, and therefore homophotic stimulationis sufficient for the perception of apparentbrightness. (This is related to the problemof how the system is able to distinguishhomophotic from metaphotic stimulation inany case.) So a suitable measure of ap-parent brightness for a target for a particularA£ might consider both homophotic andmetaphotic neural images, and simply sumthe similarity values, that is, sum the pointscomputed for the similarity functions for thatA£. The sum would run from the onset ofstimulation (the first cycle) through theseventh or eighth cycle (the just-distinguish-able signal).5 The greater the similarity, thegreater the value of the sum, the brighterthe target, and hence the less the masking.

The results of these calculations are shownin Figure 4. Figure 4a shows calculationsfor three points in the original network; inFigure 4b, we calculated all the other +A*sthat can be generated by the network. Theseare 30, 90, 120, 150, 180, and 210 msec.(The entire set of +A£s is limited to abouteight, due to the quantization of time andthe fact that, at \ts longer than 210, thetarget signal can not be distinguished from

5 It should be noted that we also tried summingvarious other combinations of cycles: threethrough seven (i.e., just the metaphotic cycles),four through six, and so forth. None of thesesums changes the argument. However, one shouldnot restrict measurement to the later cycles, andindeed, measurement should stop at about theseventh or eighth cycle, since after this eventhough the Pearson r may still take on largenegative or positive values, the actual signal isindistinguishable from noise.


-w*

-60

40)

4b) THEORETICALMETACONTRAST FUNCTIONSFOR T/M=I

120 ISO 240 -60 -30 0 30 60 90 120 150 180 210 240At

FIGURE 4. Masking, as computed from Bridgeman's (1971) similarityfunctions. Each point represents the sum of Pearson rs at a particular A<from the first through the seventh cycle. Figure 4a shows what one wouldobtain if attention were restricted simply to the three values of A* thatBridgeman considered; Figure 4b shows the masking functions one obtainswhen one computes the sum of points on each similarity function for all theother A/s that can be generated by Bridgeman's network. The dotted lineshows the masking function obtained when both target and mask are pre-sented for one cycle of the network; the solid line shows the maskingfunction obtained when both target and mask are presented for two cyclesof the network (allowing the network one application of inhibition beforestimulation is removed). These can be thought of, respectively, as a targetand mask presented for durations of 0 < t £ 30, and 30 < t <; 60, where t =duration.

noise.) In addition, we calculated the sameset of A£s for another duration, namely, aduration less than or equal to 30 msec, or thecondition where the network does not havea chance to initiate a second cycle before thestimulus is turned off.

The arrows in Figure 4a suggest thebeginnings of a U. But when one extendsthese calculations to include the completeset of A£s possible in this network, it be-comes apparent that the function reversesitself two or three times (rather than justonce, to produce the U) and thus does notresemble metacontrast functions which areempirically obtained. Let us examine thisproblem, and related temporal problems, ina little more detail.

Shape of the Metacontrast Function

Networks such as the one in Figure 2,with inhibitory feedback occurring after

some short, discrete delay, are subject todamped oscillations or temporal "ringing."That is, a point on the neural image will,with sustained stimulation, first fire at a cer-tain rate; on the next cycle, it will fire less;on the succeeding cycle, it will fire somewhatmore again; and so on. This ringing allowsstrong masking to develop. Pairs of neuralimages (target, target-plus-mask) at par-ticular cycles can become quite dissimilar,with corresponding points on the neuralimage even having differing signs (seeFigures 2 and 4, cycle 6 for instance: ThePearson r for this cycle goes negative). Butringing also results in the metacontrast func-tion itself oscillating a number of times. If,for a given A£, the neural images producedby a target-plus-mask resemble the neuralimages produced by a target alone, then forthe next A*, the neural images of the target-plus-mask will be out of phase with those


of the target alone, and hence metacontrastmasking at successive A£s will first be weak,then strong, then weak again, then strongagain, and so on. But metacontrast func-tions do not oscillate (Alpern, 1953;Growney & Weisstein, 1972; Schiller &Smith, 1966; Weisstein, 1971, 1972; Weis-stein, Jurkens, & Onderisin, 1970). It isunlikely that if metacontrast functions hadtwo or three major troughs and peaks theywould have been missed by the sampling ofA£s utilized by the various studies. Forinstance, Figure 1 shows empirical metacon-trast functions (solid lines) which contain27 A£s, 21 of them spaced in 10 msec incre-ments, from -100 to +100 Af. In the de-sign from which these data are drawn, all theA£s are presented in random order five timesper Ai per target luminance per subject.While there are some ragged edges in Sub-ject TJ's functions, there is no evidence ofthe kind of abrupt reversals shown inFigure 4b.

Other Temporal Properties of the Network

What matters for a metacontrast functionis the ratio of target duration to mask dura-tion (with luminance held constant), whichwe will call T/M. When the durations oftarget and mask are equal, that is, whenT/M = 1, the same U-shaped metacontrastfunction is obtained, no matter what thedurations of target and mask, that is, nomatter what T and M (Kahneman, 1967;Weisstein, 1972; Weisstein & Growney,1969). Thus a target and mask can be pre-sented for 25 msec each or for 125 mseceach, and the difference in the metacontrastfunctions is negligible (Kahneman, 1967).On the other hand, as T/M —> 0, metacon-trast functions change shape (they becomemonotonic, increasing with increase in At,as in Figure 1). Neither of these propertiesof metacontrast is generated by Bridgeman's(1971) network.

Target-to-mask duration ratio approacheszero (T /M—>0) . Time is a discrete func-tion of number of cycles in this network.While there is nothing wrong with approxi-mating time by discrete steps, the assumed

duration of each step is much too large tosimulate the pertinent features of metacon-trast. This is especially true for the first30 msec, when T/M is the most sensitive tovariations in duration. For instance, if onepresents a target for 1 msec and a mask for16 msec, a monotonic function of +Ai willbe obtained; if one presents a target for 16msec and a mask for 16 msec, a U-shapedfunction of +Af will be obtained (Weisstein,1971). This network cannot distinguish be-tween these two cases.

Target and mask of equal duration (T/M= 1). At the jump points of the network—30 msec, 60 msec, 90 msec—the neuralimages change. This means that if oneholds T/M constant at 1, but multiples of30 msec are added to both target and mask(that is, one changes the number of cyclesthe network goes through while each stimu-lus is present), different metacontrast func-tions will be obtained. Figure 4b illustratesthis: The solid line shows a masking func-tion obtained by allowing the network toreceive the target (30 msec) and then re-cycle once while the target is still present,for a total target duration of 30 < t < 60.The dotted line shows the masking functionobtained by allowing the network no recy-cling while the target is on: It simply re-ceives the target (0 < i < 30). In eachcase, the mask is presented for the sameduration intervals as the target. SinceT/M = 1, the masking functions should beidentical. However, as Figure 4b shows,the functions are quite disparate. This con-tradicts a considerable body of empiricalevidence (Weisstein, 1972).

These temporal problems are not cavtsedby the fact that time is quantized in thisnetwork, but rather by the dependence ofthe recurrence of inhibition on the steppingof time. Hence, the problems are not solvedby changing the cycle time, that is, by de-creasing or increasing the duration betweensteps. Making the cycle time longer willproduce masking at A£s which are too greatto correspond to what has been found em-pirically, and it will only increase the dif-ficulties in predicting monotonic functions asT/M —» 0. Making the cycle time shorter

Two MODELS OF METACONTEASX 335

will only translate the metacontrast func-tions leftward and increase oscillation fre-quency. This can be illustrated in Figure4b: Shortening the cycle times, for example,would be equivalent to rescaling the ^r-axis.If this were done, and each cycle time wereassumed 5 msec long (so that the intervalswere —10, -5, 0, +5, +10, and so on) itwould solve neither the problem of oscilla-tion nor the problem of differing metacon-trast functions for T/M = 1 for differenttarget-mask durations. But shortening thecycle time would introduce additional prob-lems : Masking would occur too soon, and,at the delay at which masking should occur,the network would have already gonethrough so many cycles that the signalwould be too damped to be distinguishedfrom noise.

Spatial Properties

The network exhibits spatial as well astemporal ringing. This means that it doesnot predict the spatial properties of meta-contrast either. Empirically, as the separa-tion between target and mask increases,metacontrast decreases monotonically. Thenetwork, on the other hand, produces abruptreversals in masking as the separation be-tween target and mask is increased, unit byunit. So, for instance, masking is greaterat spatial separations of three neural unitsbetween target and mask than it is at sepa-ration of two units.8 These abrupt reversalsare again a function of the ringing of thenetwork, especially at the edges of the targetand mask; when these neural images are inphase, masking is slight; when they areout of phase, masking is heavy.

The Linking Hypothesis: Correlation as anIndex of Apparent Brightness

Even if the temporal and spatial proper-ties of metacontrast were better predicted by

8 The sum of Pearson rs for Ai = 60 msec(Bridgeman's condition, 1971) for seven cyclesat a separation of two units between targetand mask is 3.75; at a separation of three unitsbetween target and mask it is 2.94. If one in-spects the metacontrast function for this condition(solid lines in Figure 4b), it is clear that relativeto the rest of the points, this is a large difference.

this network, the way neural image simi-larity is measured cannot be justified. Foreach cycle, a Pearson r is computed for theneural images obtained in response to thetarget alone versus those obtained in re-sponse to the target-plus-mask. What thismeans is that the value of each element inthe network for a target neural image at aparticular cycle is multiplied by the sameelement in the network for a target-plus-mask neural image at that cycle, and thenthe products are summed across the entirenetwork and normalized. Consequently, themeasure will produce masking no matterwhat is added to the target, as long as it ispresented somewhere else in the network(and, at least until the cycles spread theneural image to the location in the networkwhere the additional stimulus is located, itdoesn't matter ivhere else in the network theadditional stimulus is presented). That is,for this measure, the magnitude of maskingis not affected by the separation betweentarget and mask until the signal is spreadfar enough. Thus, within some finite num-ber of cycles one could simply add a secondstimulus at the very edge of the network, orsome place in the middle, and the sameamount of masking would be produced. In-deed, one could add two, three, many stimuliat the edges of the network and producelower and lower correlations.

This does not agree with the evidence.Adding flanks in metacontrast only decreasesthe apparent brightness of a target when theflanks are close to it (Alpern, 1953; Weis-stein & Growney, 1969). As the spatialseparation between target and mask in-creases, masking declines sharply. Further-more, when disc and annulus are presentedsimultaneously at the same luminance andduration, enhancement may occur (Mat-thews, 1974).

It might be more reasonable to inspect thechange in neural activity only for those unitsin and around the location of the target.7

7 It could be argued that the information aboutthe target might not be restricted to a retinallylocalized area. Such distributed encoding schemesare discussed by Weisstein (in press). Distribu-tion of target information over an extensive re-tinal area may be a possibility, but then, generally,


When this is done, the correlations remainnear 1.00 for both the simultaneous condi-tion and for 60 msec A£. Cycle by cycle,for 60 msec M, they are 1.0, 1.0, 1.0, .97,.932, .997, .999. This hardly constitutes areduction in similarity.

Summary oj Metacontrast Simulation 1

This model fails to simulate a metacon-trast function, and it predicts neither thespatial nor the temporal properties of meta-contrast. In addition, masking is predictedonly by the use of an implausible linkinghypothesis.

Many of these flaws have specifically todo with the way in which this particularsimulation is constructed and the assump-tions behind it. But some of the difficultiesmight beset any single-channel network,which essentially repeats the physical stimu-lus (with some modification). Such a net-work preserves information, but it canhardly be thought of as processing informa-tion. That is, different features of a stimu-lus, which might provide some basis fordeciding what kind of stimulus has been pre-sented and when that stimulus has beenpresented, are not independently represented,at least at the level where the network isstill single channel.

We can use Bridgeman's (1971) networkas an example of the problems this maycreate. In Bridgeman's network, apparentbrightness is distinguished from detection bya stimulus-dependent event—the stimulus isturned off. But this assumption is unten-able for two reasons. First, with a singlechannel alone, it is not possible to distin-guish which is the homophotic and which isthe metaphotic signal. Second, the assump-tion that metaphotic activity results in ap-parent brightness contradicts the obviousfact that if a stimulus is left on long enoughfor a subject to make a response to it, thesubject will respond that it has a distinctapparent brightness. However, makingthings stimulus-dependent may be one of thefew ways one can distinguish between differ-

more than one channel is assumed, and one mustuse a more plausible linking hypothesis to relatesuch distributed encoding to perceptual events,

ent stimulus properties while preserving thenotion of a single channel.

It is entirely possible that a more con-vincing single-channel model can be con-structed that will overcome some of theseproblems. Meanwhile, however, it might beworthwhile to turn attention to the othermetacoHtrast simulation (which assumesmultiple channels and a rather straight-forward linking hypothesis) and see if thissimulation does any better.

Metacontrast Simulation 2

The other metacontrast simulation (Weis-stein, 1968, 1972) assumes that there ismutual inhibition between fast- and slow-responding neural populations. In particu-lar, for metacontrast it assumes that unitswhose response is fast inhibit units whoseresponse is slower. Hence, one must delaythe stimulus for the fast-responding units inorder to have them interfere with a priorstimulus.

Quantification and Criticisms

These assumptions were worked outquantitatively in a neural network incorpor-ating Rashevsky-Landahl two-factor neurons—neurons whose temporal response is acombination of excitation and inhibition(Weisstein, 1968, 1972). This networksuccessfully predicted a number of propertiesof metacontrast, such as (a) the shape ofthe metacontrast function and its change ofshape as T/M changes (as in Figure 1) ;(b) the reappearance of the target whentarget and mask are repeatedly presented atappropriate A/s (as in Schiller & Smith,1966) ; and (c) for 34 out of 35 data pointsthat appeared in the metacontrast literature,the Af at which the minimum of the U oc-curred. This model is continuous, so anycombination of target and mask luminance,duration, and At can be simulated.8 It does

8 Inspection of the predictions from Weisstein's(1968, 1972) model in Figure 1 might, at firstglance, seem to indicate that the same type ofquantization of time applies to her model as well.But this is not the case. Weisstein's network wassimulated on an analog computer, and within theresolution of the computer, any duration and AJcan be simulated,


SI

MASK

FIGURE S. Expanded version of Weisstein's (1968, 1972) model, whichclarifies the spatial symmetry implicit in that model. The subscriptedneurons are those which also appear in Weisstein (1968, 1972). Neuronn-n responds faster than ni2; therefore, stimulation for n& must arrive laterthan stimulation for nia in order that the response of nM be suppressed. Ifone traces responses in the unlabeled neurons, it is clear that an identicaleffect will occur for the bottom neuron similar to n« if the stimulus in thetop row is delayed. Thus one can interchange target and mask and pro-duce the same result.

not depend on temporal ringing to producemasking, and thus it is not subject to thesame temporal difficulties as the networkconsidered earlier. In addition, the measureof target apparent brightness is proportionalto the frequency of firing of the unit desig-nated as carrying information about thetarget, so the linking hypothesis is not quiteso problematic as it is in Bridgeman's (1971)network.

However, there are two criticisms of thissimulation. One has to do with what areassumed to be the spatial constraints im-posed by the model, and the other with atemporal assumption behind some of theparameters chosen for individual neurons.

Spatial Interaction

The criticism here has been that "thesimulation will not work if target and maskare interchanged" (Bridgeman, 1971, p.530). This seems to us easily solved. Weis-stein's diagram for the metacontrast inter-action (1972, p. 248) is not symmetric, butsymmetry is implicit, and it is easily ob-tained without making any additional as-

sumptions. Figure 5 depicts the following:Somewhere, some place in the central ner-vous 'system, two neurons receive the sameexcitatory input. The response of one ofthese neurons is faster than the response ofthe other, and there is cross-inhibition fromthese fast responders. That is, the neuronsthat are responding faster inhibit their suc-cessive neighbors. Because their responseis fast, inhibition will be effective only if thestimulus for these fast responders is delayed.Working through the various combinations,it is immediately obvious that the networkis symmetrical: All that is required for onestimulus to suppress response to another isthat it follow the other. (Although theschematic shows only one line of units re-sponding to target and one line of units re-sponding to mask, it is assumed that therewill be a collection of units responding toany stimulus.)

The Assumption of Fast Inhibition

Consider now the temporal assumption.Weisstein chose rate constants for the in-hibitory factors in most of the neural units


that were faster than the rate constants forthe excitatory factors. Since the inhibitoryand excitatory rate constants are supposedto correspond to inhibitory postsynaptic po-tentials (IPSPs) and excitatory postsynapticpotentials, (EPSPs), respectively, thisamounted to an assumption that IPSPs werefaster than EPSPs. Although there is someevidence for fast IPSPs (Creutzfeldt & Ito,1968), in general the assumption of IPSPsbeing faster than EPSPs appears tenuous.

However, there are other ways to pro-duce fast and slow responses. With two-factor neurons, the particular rate and shapeof the neural temporal response dependsmost critically on the relationship betweenthe ratios of excitatory gain to excitatoryrate constant versus inhibitory gain to in-hibitory rate constant, and only secondarilyon the rate constants themselves. One canproduce a fast response in a neuron — that is(as illustrated by n22 in Figure 5), a re-sponse in which firing freqviency reachessome criterion amplitude rapidly after stim-ulus onset and decreases to some criterionamplitude rapidly with stimulus offset, sothat the latency of response is short, and thetemporal resolution is high — by adjustingthe gains in that neuron (A, B), the rateconstants (a, b), or both. This can be seenby solving Equations 2 and 3 in Weisstein(1972), which would give the functions forc and /, that is, for the excitatory and in-hibitory factors that combine to give theneural temporal response. The solutions fora step function input, setting initial condi-tions to zero, are the familiar exponentials,

Response = c(t) — j(f) = [ ( A / a )

where A is the gain and a is the rate con-stant for the excitatory factor, and B is thegain and b is the rate constant for the in-hibitory factor, and e — 2.718. Now, if oneassumes, for instance, that a >>> b (that is,EPSPs that are considerably faster thanIPSPs), and A » B, such that A/a isslightly larger than B/b, a fast, sharp transi-ent excitatory response will be produced,which will then die down to some minimal

firing slightly above spontaneous level foras long as a stimulus is maintained.

On the other hand, if one assumes a > b,and A > B, such that A/a > B/b, a slower,more sustained response will develop. Sincea number of afferent orders are assumed tobe traveled before the metacontrast inter-action, one could enhance these differencesby further convolution (the fast responsewould get somewhat slower; the slow re-sponse would get a great deal slower). Thus,there are a number of different choices ofparameters that will give fast and slow re-sponses. But one does not even have toadjust parameters relative to each other toproduce Weisstein's results. One could ob-tain fast and slow responses simply by as-suming slower conduction times in the slowerresponding neurons. Either (or both) ofthese alternate ways of producing a fast re-sponse would only minimally affect the pre-dictions from the Weisstein network, sincethe narrowing of the functions and theirshift towards the origin, with T/M —»0,as well as the other temporal properties ofmetacontrast that were predicted, are duenot so much to the temporal shapes of theslow and fast neurons (responses that areinfluenced by the rate constants), but to theneurons' nonlinearity (Weisstein, 1972,Equation 4, p. 246) and to the fact that theresponse to a stimulus, even if it were transi-ent, would nevertheless smear out somewhatin time when the energy of the mask is high.

The nonlinearity means that the functionswill first be wide and then narrow as maskenergy increases; the "smearing" of themask in time means that one will not haveto delay presentation of the mask as much,as its energy increases, in order to have itinterfere with the target, and thus the meta-contrast functions will shift their minimatoward the origin, as in Figure 1.

In short, alternate ways of producing afast response are easily available; the focuson fast IPSPs, or "fast inhibition" (Weis-stein, 1972), obscures the main point thatthe only thing that has to be fast in Weis-stein's model is a fast excitatory response,which then inhibits a slow excitatory re-sponse. To construct this, one can choose


parameters in several ways, only one ofwhich involves choosing faster IPSPs.

One could decide on one or another ofthe alternative ways of producing a fast re-sponse by drawing on the accumulating dataabout the properties of transient and sus-tained neural populations in the visual sys-tem (see below), and the equations for thetwo-factor neurons could be revised in lightof this evidence. However, for now, sincealternate constructions will yield roughlythe same results, we prefer simply to notethe equivalence of the different ways oflooking at what was called fast inhibition.

Further Elaboration oj Metacontrast Simu-lation 2

Edges and blobs. The main assumption inthis model is that more than one temporalweighting function is needed to characterizevisual system response (i.e., fast versusslow response). So the simulation involvesmultiple temporal channels, two classes ofwhich are assumed to interact. But thereare spatial assumptions as well. Weisstein(1968, 1971, 1972, 1973) proposed that theunits that mediated detection of a stimulushad different time constants than the unitsthat carried information about contour oredge. She assumed, as Werner had sug-gested (1935) that the basis of metacontrastwas the suppression of edges or contourinformation, and that apparent brightnessdecreased as some function of the suppres-sion of edges. Edges have long been knownto play a critical role in the perception ofapparent brightness (e.g., Cornsweet, 1970;Land & McCann, 1971; O'Brien, 1958;Shapley & Tolhurst, 1973).

If apparent brightness is largely dependenton edges, then "edgeless" stimuli should bemore resistant to metacontrast masking.This seems to be the case: Growney (inpress) has shown that one obtains negligibleamounts of metacontrast masking when thesharp edges of a target are blurred. Mask-ing is not as negligible when the target edgesare sharp and the edges of the mask areblurred. Thus relatively "edgeless" stimuli(they are not completely edgeless, especiallyif one analyzes edges in terms of the amount

of high spatial-frequency components theycontain) do not get masked very much.0

The slow response in Weisstein's model(1968, 1972) was assumed to have some-thing to do with contour or edge. Evidencehas since accumulated that high and lowspatial frequencies may be processed by dif-ferent temporal channels (e.g., Kulikowski& Tolhurst, 1973), and that these differenttemporal channels may respond with dif-ferential speed and resolution (e.g., see dis-cussion by Breitmeyer, in press; Breitmeyer,Love, & Wepman, 1974; and Breitmeyer,Note 1; also see Hood, 1973). A highspatial-frequency response may be thoughtof (very roughly) as a response to edges,and a low spatial-frequency response maybe thought of (just as roughly) as a responseto non-edges—blobs, or large, blurredshapes, as in a defocused picture.10 Thus,given a single stimulus, the response to itsedges may be slower than the response to its"blob presence." Hence, both an edge re-sponse and a non-edge response may be tiedto the accumulating evidence for the pres-ence in the visual system of channels thatrespond to transient, low spatial-frequencystimuli, and channels which respond to su-stained, high spatial-frequency stimuli. (Thisdirect association of fast and slow responsesin metacontrast with transient and sustainedchannels was first suggested by Breitmeyer

9 Growney (in press) has presented quite inter-esting evidence that the specific type of edge inmetacontrast in both target and mask can changethe amount of masking obtained. While some ofthis is easily explained by the edge-blob schemediscussed below, some of this may require furtherelaboration.

10 Actually, both edges and blobs will have lowfrequency components, but edges will also containmore high frequency components. Edges andblobs can be specified much more precisely, ofcourse—for any given edge or any given blob, onecan calculate its spatial frequency or Fourierspectrum. Similarly, the units sensitive to edgesand blobs can be denned by the spatial frequenciesto which they respond. But until we know con-siderably more about these units' spatial frequencyresponse—bandwidth, channel density, variation oftemporal response with center frequency (seeGraham, in press, for an elegant summary of ourignorance on these matters, and an excellent dis-cussion of how to overcome it)—we lose nothingin precision by talking about edges and blobs, andwe may gain in comprehensibility.


et al., 1974, and Breitnieyer, Note 1. Adifferent approach to the relationship be-tween masking and activity in the sustainedand transient channels has been suggestedby Matin, 1974, and Matin, Notes 2 and 3.)

It should be noted that transient responsesdo not necessarily imply speed, nor do sus-tained responses imply delay; however,there is evidence that the higher spatial-frequency channels may require a longerintegration time than low spatial-frequencychannels (e.g., see Breitmeyer, in press;Hood, 1973; Breitmeyer, Note 1), andthere is neurophysiological evidence that thelatencies and conduction velocities of neuralpopulations that prefer transient, low spatial-frequency stimuli are faster than the latenciesand conduction velocities of those neuralpopulations that prefer sustained, highspatial-frequency stimuli (the Y and X cells,respectively—Enroth-Cugell & Robson,1966. For evidence concerning conductionvelocity and latency of these populations, seeCleland, Dubin, & Levick, 1971, and Fukada,1971; for evidence that these populationsmay mutually inhibit each other, see Singer&Bedworth, 1973).

Breitmeyer also has gathered independentevidence from reaction times, which suggeststhat edges may be processed more slowlythan blobs or non-edges (Breitmeyer, inpress). He reported that reaction times tohigh spatial-frequency sinusoidal gratingsare greater than reaction times to sinusoidalgratings of lower spatial frequency. Thesereaction-time data may reflect processingtimes for edges versus non-edges, since edgescontain more high spatial frequencies.

Masking in General

The association of slow and fast responseswith the accumulating evidence for sustainedand transient, high and low spatial-frequencychannels, which we will call the edge-blobscheme, has enormous integrating potential.It may make it possible to explain maskingphenomena that have not yet adequatelybeen treated; and it may help explain therelation between apparent movement andmetacontrast (see also Breitnieyer et al.,

1974; Kahneman, 1967, 1968; Weisstein &Growney, 1969; Matin, Notes 2 and 3, fordiscussions) .J1

As long as channels are near enough toeach other to inhibit each other, the edge-blob scheme works for metacontrast, asstated: U-shaped backward masking occursbecause the fast part of the response to themask inhibits the slow part of the responseto the target. This can be easily extendedto nonmetacontrast designs, where U-shapedmasking functions are also obtained (Pur-cell & Stewart, 1970; Weisstein, 1971; Tur-vey, 1973), that is, designs where the targetand mask partially or completely superim-pose on the same retinal areas. Separatechannels are assumed mutually inhibiting;as they approach each other's retinal loca-tions (including superimposition), inhibitionwill become stronger or remain the same,depending on one's specific spatial-frequencyassumptions (e.g., Weisstein, in press). Forforward masking, a U shape would be pre-dicted if the slow part of the response to themask inhibited the fast part of the responseto the target.

Here, one might assume that since thetarget blob response would be inhibited(rather than the target edge response, as inbackward masking), the forward analog ofmetacontrast—paracontrast, where the maskprecedes the target—would not be as greatas metacontrast, since it is the edges of a

11 It should be noted that although the schemegeneralizes beyond typical metacontrast backwardmasking, it does not (nor is it meant to) accountfor masking that is thought to be more peripheral—masking that decreases detection, depends pri-marily on overlap of the target and mask, pro-duces montonic functions, and so forth (seeKahneman, 1968, and Weisstein, 1972, for a re-view of the different types of masking). Thatis, although blobs might play a role in the de-tectability of the target, the edge-blob distinctiondoes not commit the blobs to target detection, asmight be assumed from the earlier model (Weis-stein, 1968, 1972) where the basic distinctionwas between contour interactions and detection.Rather, masking that involves simple detectionmay occur as a result of different mechanisms thanthe ones suggested here; in any case, at the levelof processing we are considering, we assume thatboth blobs and edges play a role in target ap-pearance.


stimulus rather than its blob presence thatseem to play such an important role indetermining apparent brightness and theother features of the appearance of the tar-get which get disrupted in metacontrast.On the other hand, if the appearance of thetarget is even minimally dependent on blobsas well, then, although one might not expectmuch paracontrast until the mask becamequite strong, when the mask did becomestrong, forward U shapes would be expected.Finally, if the mask produced a responsethat was much greater than the target re-sponse, one might predict the same kind ofshift of the bottom of the U that one findsin backward masking. This seems to bewhat happens. In Figure 1, the forward Uis either absent or appears as a minor dipcompared to the backward U when T/M •=•1. It only reaches a respectable size asT/M decreases substantially; then, withfurther decreases in T/M, the bottom of theU begins to shift towards the origin. So,the edge-blob scheme might be able to ac-count both for forward and backward Us,and for their asymmetry.

Finally, there has always been the naggingsuspicion (see footnote 1) that metacon-trast does not really exist. In a metacon-trast design, while it is clear that target ap-parent brightness decreases, it is also clearthat there is something going on in the loca-tion of the target, and indeed, detectionmeasures rarely produce U-shaped metacon-trast functions. Also, apparent movementis generally noticed in metacontrast, evenwhen the target apparent brightness is neg-ligible. The edge-blob explanation couldaccount for both of these things: If onlythe edges of a target are suppressed, some-thing indeed remains. That somethingwould be the target blob. But since blobsproduce a stronger response in the transientchannels, those which prefer moving stimuli,there is reason to suppose that the continuedactivity of these channels during metacon-trast masking would lead to the impressionof movement.

CONCLUSION

A stimulus produces prolonged neuralactivity. The notion that different perceptual

events are associated with different portionsof this activity is intriguing, and it lies atthe basis of all of the theories of metacon-trast discussed in this paper. The majordifference in the various theories has to dowith assumptions about visual system organ-ization. Here, Bridgeman's (1971) modelappears to fail in important respects, whereasWeisstein's (1968, 1972) model does not.While much of this may be due to theparticulars of the way Bridgeman set up hismodel, some of the failure does appear inti-mately connected to the general notion thata single spatial and temporal channel de-scribes visual system activity. On the otherhand, Weisstein's model (with subsequentelaboration) not only offers the prospectof simulating many of the relevant spatialand temporal aspects of metacontrast, butagrees with much current investigation in-dicating both the presence in the visualsystem of multiple spatial and temporal chan-nels (Campbell & Robson, 1968; Graham &Nachmias, 1971; Kulikowski & Tolhurst,1973; Pantle, 1971), and also (for spatialchannels at least) their mutual inhibition(Tolhurst, 1972). It is possible that by con-ceptualizing metacontrast in terms of mul-tiple spatial and temporal channels, we mayget a clearer idea of the variety of perceptualfunctions served by these different channels.

REFERENCE NOTES

1. Breitmeyer, B. G. Implications of reactiontim-e to sinusoidal gratings for contour formingoperations in human vision. Unpublished manu-script, 1974. (Available from the Departmentof Psychology, University of Houston, Houston,Texas 77004.)

2. Matin, E. The two-transient (masking) para-digm. Paper presented at the meeting of theAssociation for Research in Vision and Oph-thalmology, Sarasota, Florida, May 1975.

3. Matin, E. The two-transient (masking) para-digm. Manuscript submitted for publication,1975.

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(Received December 16, 1974)

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PSYCHOLOGICAL REVIEWwexler.free.fr/library/files/weisstein (1975) a... · 2020. 7. 29. · Naomi Weisstein State University of New York at Buffalo Gregory Ozog and Ronald Szoc Loyola