JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Propagation Velocity of Lateral Interaction in the Human Visual System*

ROBERT A. SMITH AND WinnTmAx RICHARDS

Massachusetts Institute of Technology, Department of Psychology, Cambridge, Massachusetts 02139

(Received 7 February 1969)

Interactions between line stimuli include luminance-threshold effects that are delayed in time, with thedelay depending upon the spatial separation between the contours. These delayed effects can be accountedfor by lateral interactions that propagate with a velocity of about 0.65 deg/sec.

INDEx HEADING: Vision..

A direct test for a slowly propagating lateral interactionis to examine the luminance-threshold changes thatoccur in a single center line flanked by two lines thatcan be turned on suddenly (Fig. 1). When the twoflanking lines appear, the effects of lateral interactionshould begin moving inwards, like a wavefront, con-verging upon the inner line at some later time. Oncethis effect impinges upon the central test line, itsincrement threshold should be altered. If the interactionis not essentially instantaneous, then there will be adelay between the onset of the flanking lines and thischange of increment threshold. In particular, if inter-actions propagate with a measurable velocity, this delaywill be linearly related to the propagation distance.

In order to determine the relationship between thepropagation distance and the time delay, three differentsets of line stimuli were used, each having a differentspatial distance over which the interaction must propa-gate. The line stimuli were all 0.8-deg high, and 0.05-degwide. The three experimental conditions (denoted A,B, and C) correspond to lateral separations betweenthe flanking and test lines of 0.126, 0.175, and 0.260deg, respectively. For each of these separations, theflanking lines always appeared for 1.0 sec every 2.5 sec,while the test line remained on continuously, as shownin Fig. 2.

THE WINK

The increment threshold for the central test line wasmeasured by varying the amplitude of a short, negativeincrement (referred to as a wink) in the center line. Inextensive preliminary tests, we found that the mostsensitive indicator of delayed interactions was a winkhaving the waveform shown in Fig. 3. The amplitudeof this wink could be continuously adjusted so thatthresholds could be measured in terms of modulation.Modulation was defined as the ratio of the maximumamplitude of the wink to the resting luminance of thetest line. The threshold of the wink was determinedfor various delays, I, with respect to the onset of theflanking lines. These delays varied by 40 msec stepsfrom -80 to 520 msec.

* Author RAS was supported by N. I. H. training grant5-TOI-GM01064, awarded to Prof. H.-L. Teuber, Chairman,Department of Psychology. Supplementary support was receivedby WR under AFOSR contract F44620-67-C-0085 and NASAand NIMH grants NsG 496 and MH 05673, the last two awardedto Prof. H.-L. Teuber.

For each delay, I, thresholds were obtained on atleast three separate trials. Additional measurements,up to a total of seven, were taken at data points thatseemed to deviate from adjacent points or whichshowed an unusually large variability. As a result,most mean values, including all of those in significantregions of the curves, represent an average of four ormore settings. Occasional deviant settings were notdiscarded (approximately one in twenty), but, rather,additional measurements were taken to minimize theerror, by averaging. Each session generally lasted 142hours, but in some cases a session was terminatedearlier, when the settings became erratic or when thesubject became tired.

MEASUREMENTS

All threshold measurements were made by two sub-jects, WR (one of the authors) and LH (a naive ob-server). The subjects were first dark-adapted for 5 min,then given several practice trials. During these andsubsequent trials, the subjects found their thresholdsby adjusting a knob which controlled the modulationof the wink. The delay, I, on each trial was set by theexperimenter in a pseudo-random order. On odd-numbered trials the subject fixated the upper blackdot, located 1" above the center of the stimulus; thelower dot was fixated during even trials. This alterna-tion improved the reliability of the threshold measure-ments, presumably because Troxler's fading was greatlyreduced. (There were no apparent systematic differ-ences between upper and lower fixation conditions.)As a further aid to reducing variability attributable to

Xi'730 6.50

FIG. 1. The configuration of the stimulus. (The central testline is shown as dotted for clarity.) The two dots above andbelow the test line are fixation points.

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FIG. 2. Time relations between the flank and test stimuli.

fading, most threshold judgments were made within30 sec.

CRITERION

The criterion used by the subject was a crucialfactor. Over the complete range of delays used (-80-520 msec), the appearance of the wink varied, depend-ing upon the delay. At some delays, for example, therewas a very distinct double flash. The procedure eachsubject finally used was first to set the wink at 100%modulation, noting the appearance of the wink. Themodulation was then reduced so that the wink was nolonger visible. By gradually increasing the modulation,eventually a modulation was reached which produceda supra-threshold effect similar to that seen at 100%modulation. This modulation was taken as the threshold.

APPARATUS

The experimental apparatus was a maxwellian-viewsystem for use with the right eye; the observer's headwas stabilized by a bite board. This apparatus hasbeen described in detail elsewhere.' Briefly, the opticalsystem provided two independently controlled stimuluschannels, plus a background. The background wasapproximately 62O in diameter, and was formedjby atungsten source with a Kodak Wratten number 99filter. The dominant wavelength of this 64° field wasabout 554 nm, with an equivalent luminance of 15cd/in 2 .

The flanking lines were illuminated by a tungsten-iodine source with a Wratten number 99 filter, and hadan equivalent luminance of 100 cd/M2 . The test line

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FIG. 3. Oscilloscope tracing showing the waveform of the teststimulus, designated as a wink. The modulation is defined tobe a/Jo.

1 G. Wasserman, J. Opt. Soc. Am. 56, 242 (1966).

was produced by light from a B & L monochromatorset at 555 nm, with a half-band width of 4.4 nm. Thiswas matched in color and brightness to the flankinglines.

The timing of thestimuli was controlled by a Hewlett-Packard 203A-function generator, which produced asquare wave with a period of 2.5 sec. This oscillatorhas two outputs, whose relative phase is continuouslyvariable. The first of these outputs triggered a timerwhich emitted a 1-sec pulse. This pulse operated ashutter in the light path of the flanking lines. Thesecond oscillator output was amplified and then passedthrough a simple RC network, which converted thesquare wave into 40-msec positive pulses (the negativepulses were eliminated by a diode). This pulse trainwas voltage divided by a potentiometer, which servedas the modulation control, and then operated a

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FIG. 4. Relative threshold vs interstimulus interval (t), forsubject WR. The standard error of the mean of each point isindicated by the bar on the abscissa.

D'Arsonval shutter. The arm of the shutter was fittedwith a piece of polarized acetate (Polaroid, HN32),and was placed adjacent to a stationary polarizer inthe light path of the test line. The polarizers wereoriented so that the light beam was reduced by apositive pulse, the amount of reduction depending onthe pulse amplitude, which was, in turn, dependentupon the potentiometer setting. The waveform of theresultant wink is shown in Fig. 3. Thus, the timeinterval, i, was controlled by the relative-phase adjust-ment of the oscillator, and the modulation by thepotentiometer. The data were recorded on an X-Yplotter. The oscillator phase control was mechanicallylinked to a voltage divider, which drove the X axis of

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the plotter. Similarly, the potentiometer was gangedto a voltage divider which drove the Y axis. When thesubject had achieved a satisfactory setting of thethreshold, it was recorded as a point on the paper.

RESULTS

The relative thresholds at each delay, t, are presentedin Figs. 4 and 5; the separate portions of each figurerepresent the three stimuli in order of increasing sepa-ration between the test and flanking lines. The lengthsof the lines at the base of each graph indicate the meandeviation associated with each measurement. It is clearfrom these figures that there are at least two types ofthreshold effects. First, there is a large elevation ofthreshold at about t=0. Secondly, there is a smallerrise in threshold beginning at about t = 100 msec. Thissecond rise is quite sharply defined in Fig. 4a, andbecomes less so as separation increases in Figs. 4b and4c. In Fig. 5a it is either absent, or has been obscuredby the initial rise. Note that, for each figure, the peakof this second rise shifts systematically with increasingseparation between the test line and the two flankinglines. This second, delayed rise of threshold appearsto be the effect of a slowly propagating interaction.

The data of Figs. 4 and 5 provide an estimate of thevelocity of this interaction. In theory, the velocitywould be the slope of a plot of line separation vs thetime delay before the onset of the increase of threshold.As a measure of this time delay, we have taken thevalue of i that corresponds to the maximum of thedelayed rise of threshold. The maximum was chosenbecause it is well defined, whereas the onset is not.Figure 6 shows the relationship between the delay ofthe second rise of threshold and the spatial separationbetween the centers of the test and flanking lines. Theslopes of the two lines, one for each observer, yieldestimates of 0.6 and 0.7 deg/sec for the velocity of thepropagated wave.2

DISCUSSION

The interpretation of the threshold changes shown inFigs. 4 and 5 is not entirely clear. The elevation that issimultaneous with the onset of the outer lines appearsto be analogous to threshold changes previously re-ported3 and suggests that the major portion of the

2 Note that the lines in Fig. 6 do not pass through the origin,which would be expected for a true velocity. The most likelyexplanation is that in Fig. 6 we have plotted the separationbetween the centers of adjacent lines; it could reasonably beargued that the separation between the inside edges of adjacentlines is the appropriate distance. If the curves are displaceddownward by 0.05 deg to compensate for this, most of the dis-crepancy disappears.

3 Much of the extensive literature on masking is relevant tothis point. See, for example, G. Sperling, J. Opt. Soc. Am. 55,541 (1965); P. H. Schiller, Percept, & Psychophys. 1, 161 (1966);R. M. Boynton and J. B. Siegfried, J. Opt. Soc. Am. 52, 720(1962); W. S. Battersby and I. H. Wagman, J. Opt. Soc. Am.49, 752 (1959); and B. H. Crawford, Proc. Roy. Soc. (London)B134, 283 (1947).

OF LATERAL INTERACTION

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FIG. S. Same as Fig. 4; observer LH.

neural-summation process is not dependent upon thespatial distribution of the stimuli. Part of this primarythreshold rise may be attributable to scattered light.Other interfering effects might include an involuntary

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FIG. 6. Time delay for the secondary rise of threshold vsstimulus separation. The slopes of these lines represent thepropagation velocity. (a) Observer LH; slope=0.6 deg/sec. (b)Observer WR; slope=0.7 deg/sec.

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7R. A. SMITH AND WHITMAN RICHARDS

distraction of attention, rather than lateral interactionsin the usual sense.

Distraction of attention and scattered light seem notto be responsible for the delayed rise of threshold,however. Neither of these effects would explain theobserved influence of the separation between the testand flanking lines on the time course of the secondarythreshold rise. For the same reason, we also feel thatany explanation based upon eye movements4 is elimi-nated. For example, if saccades elevate the thresholdIthen eye movements must not only be correlated withthe appearance of the flanking lines, but must also bedelayed according to the spatial separation between thetest and flanking lines. For a spatial increase of 0.13°,this delay must change by 100 msec-an unreasonableassumption.

Thus, the linear relationship between the spatialseparation and the delayed appearance of the secondarythreshold rise strongly suggests to us that a lateralinteraction has propagated with a functional velocity.By a functional velocity, we mean simply that theeffects of lateral interaction are felt after a delay thatis proportional to the spatial separation. We cannotconclude from this experiment that the functionalvelocity necessarily represents a physical propagation,though this is certainly a possible explanation.

In addition to the above, several other reservationsmust be made regarding the interpretation of Figs. 4and 5. It is possible that the significant portion of thedata is not the secondary rise, but rather the dip thatfalls between the two rises, and that this dip representsthe delayed effect. In this case, the propagation ve-locity would be faster by about a factor of two. InFig. 4, in particular, it appears to be the rise in thresh-old, rather than the dip, that is moving to progressivelylonger delays, but to be sure of this we would have toemploy still longer delays and greater separations. Un-fortunately, there was no clear effect with greaterseparations, presumably because the range of the inter-actions was exceeded.

A further difficulty in interpreting the delayed riseof threshold is that this effect is considerably dependentupon the choice of waveform. Pilot experiments sug-gested that a negative increment gave a higher signal-to-noise ratio than a positive increment. In addition, asmooth waveform was found to be superior to a squarewave, which seemed to produce strong visual transient.At present, however, we have no proper theory thatjustifies the selection of the smooth negative pulse.

There are points of theoretical interest underlyingthis study, which have not been made explicit. It is

4 D. H. Kelly, J. Opt. Soc. Am. 50, 1115 (1960).6 See bibliography inl W. Richards, J. Opt. Soc. Am. 59, 617

(1969).

commonly believed that the observed fall-off of visualcontrast sensitivity at low spatial frequencies is dueto the antagonism of center and surround in visualreceptive fields.6' 7 Some authors have suggested thatthis mechanism could also explain the observed fall-offof contrast sensitivity at low temporal frequencies, ifit is assumed that the surround antagonism acts onlyafter a short delay.'' 0 One of the present authors"has advanced the specific hypothesis that this delaymight result from the slow propagation of lateralinteractions; this experiment is, in part, a direct testof that hypothesis. While the present data are notconclusive, they certainly suggest the presence of aslowly propagated effect, with a velocity of about 0.65deg/sec. This is in reasonable agreement with Smith'stheoretical prediction of 0.85 deg/sec.

The suggestion that there is a fundamental connec-tion between spatial and temporal contrast sensitivityhas been tested in a number of other studies. Commonly,this has been done by measuring sensitivity to astanding-9 12J3 or traveling-wave' 4 stimulus, one that issinusoidally modulated in both time and space. Underthese conditions, the velocity hypothesis would predictresonance-like interactions between spatial and tem-poral frequencies. However, no interaction at all isobserved, except at low frequencies, for which there isa gradual change of the shape of the contrast-sensitivityfunction. In view of the present study, this absence ofinteractions is disturbing. A possibility that has notbeen explored is that eye movements may blur theseinteractions at high frequencies, because the eye doesnot remain stationary during the propagation of long-range effects. A more acceptable hypothesis may bethat only inhibition from the antagonistic surrounddisplays a propagation velocity. This assumption wouldreconcile the observation of a velocity with the factthat spatial-temporal interactions occur only at lowfrequencies, for which the effect of the surround isimportant; but it contradicts the assumptions by whichSmith" predicted the numerical value of the propaga-tion velocity. Obviously, further studies are needed toclarify the relationships between spatial and temporalcontrast sensitivity and the functional organization ofthe receptive field.

6 0. H. Schade, J. Opt. Soc. Am. 46, 721 (1956).7 J. G. Robson and C. Enroth-Cugell, J. Physiol. (London)

187, 517 (1966).8 D. H. Kelly, J. Opt. Soc. Am. 49, 730 (1959).9 J. G. Robson, J. Opt. Soc. Am. 56, 1141 (1966).0 J. Levinson, Doc Ophth., XVIII, 16 (1957).11 R. A. Smith, J. Opt. Soc. Am. 57, 1425A (1967).12 D. H. Kelly, J. Opt. Soc. Am. 56, 1442A (1966).13 D. H. Kelly, J. Opt. Soc. Am. 56, 1628 (1966).14 F. L. van Nes, J. J. Koenderink, H. Nas, and M. A. Bouman,

J. Opt. Soc. Am. 57, 1082 (1967).

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