Ellemberg et al. Vol. 15, No. 7 /July 1998 /J. Opt. Soc. Am. A 1733

Apparent contrast and spatial frequencyof local texture elements

Dave Ellemberg and Frances Wilkinson

Department of Psychology, McGill University, Montreal QC, Canada H3A 1B1

Hugh R. Wilson

Visual Sciences Center, University of Chicago, Chicago, Illinois 60637

A. Serge Arsenault

Department of Psychology, McGill University, Montreal QC, Canada H3A 1B1

Received November 12, 1997; revised manuscript received March 16, 1998; accepted March 16, 1998

We measured the apparent contrast and spatial frequency of a parafoveal Gabor signal located at the center ofan array of Gabor signals as a function of both element density and the direction of contrast and spatial fre-quency of the surrounding elements. The target Gabor appeared lower in contrast and higher in spatial fre-quency when the elements were in close proximity, regardless of the direction of contrast and spatial frequencyof the surrounding elements. Overall, the evidence suggests that the appearance of a parafoveal target isstrongly affected by its visual context. These findings provide additional support for the existence of spatialinteractions among neurons implicated in textural processing. © 1998 Optical Society of America[S0740-3232(98)01307-6]

OCIS codes: 160.2120.

1. INTRODUCTIONThe perception of a local visual feature is greatly influ-enced by its surroundings. Ejima and Takahashi1 re-ported that the apparent contrast of a central strip ofsine-wave grating flanked by similar peripheral gratingsdecreases when peripheral-grating contrast is higherthan the central strip and increases when peripheral-grating contrast is lower than the central strip. Chubbet al.2 found a similar pattern of results by modulatingthe contrast of a random-noise texture surrounding apatch of similar random texture. The apparent contrastof the central disk was reduced in the presence of ahigher-contrast texture surround and enhanced in thepresence of a lower-contrast texture surround. However,not all studies demonstrate that such an induction effectis dependent on the direction of the peripheral array’scontrast. Apparent contrast reductions were reported byCannon and Fullenkamp3 in a series of experiments inwhich a central grating patch was surrounded by a grat-ing of either higher or lower contrast than the centralpatch.

Comparable effects have also been measured in thespatial-frequency domain. MacKay4 established severalvariants of the simultaneous shift in the apparent spatialfrequency of broadband patterns near discontinuities intexture density. Klein et al.5 further investigated theshift in the apparent spatial frequency of a target sinu-soidal grating surrounded by an annular grating. Theyreported that when the inducing grating had a lower spa-tial frequency than the target, the spatial frequency of thetarget grating appeared elevated. On the other hand,

0740-3232/98/071733-07$15.00 ©

when the inducing grating had a higher spatial frequencythan the target, they found that the target appearedlower in frequency.

One notable feature of all the studies of apparent con-trast and apparent spatial frequency described above isthat the stimulus about which the judgment was madewas viewed foveally, typically covering an area of 0.5°–2°in diameter. Whether the percept of peripheral targets issimilarly affected by their surroundings is unknown.

In recent work in our laboratory we have been examin-ing the lateral interactions that occur among elementsthat make up texture strings in the near periphery.6 Wehave reported marked elevations in the threshold for de-tecting a change in the contrast, spatial frequency, or ori-entation of a two-dimensional Gabor element when it isflanked by a string of similar elements. The strength ofthis threshold elevation diminishes with increased inter-element spacing. In agreement with previous lateralmasking studies7–9 we found that this effect disappears atthe fovea. In a separate study we measured the criticalcoherence limit—the inter-element spacing at which anarray of individual elements is perceptually grouped andgenerates the percept of a texture.10,11 When bandpasselements were used we found that the coherence limitwas a power-law function of the size (space constant) ofthe elements.

The present study was designed to investigate themanner in which texture coherence influences the appar-ent contrast and the apparent spatial frequency of a tar-get element in parafoveal vision. Using a one-dimensional array of Gabor patches, we report that the

1998 Optical Society of America

1734 J. Opt. Soc. Am. A/Vol. 15, No. 7 /July 1998 Ellemberg et al.

appearance of these two properties is strongly affected atelement densities previously shown to produce strong tex-ture coherence.11 Contrary to the previous foveal stud-ies, this parafoveal effect is not dependent on the relativecontrast or spatial frequency of its surround; the appar-ent contrast was always reduced and apparent spatial fre-quency always increased under the conditions we havestudied.

2. EXPERIMENTAL METHODSA. SubjectsTwo of the authors (DE and SA) along with two naıve ob-servers, unaware of the issues being examined partici-pated in the experiment. All had 20/20 Snellen acuity,and none had any known visual disorders.

B. StimuliIn successive experiments we measured the apparent con-trast and the apparent spatial frequency of a Gabor patchembedded in a one-dimensional array of similar patchesby use of a matching paradigm in which the target ele-

ment in the array is compared with a single Gabor patchappearing in the same spatial location. In referring tothe stimuli, we have adopted the terminology of Cannonand Fullenkamp.3 The array containing the flanked tar-get Gabor will be termed the comparison stimulus, andthe single Gabor element will be referred to as the teststimulus. In the matching paradigm the value of the teststimulus is varied to determine a perceptual match to thetarget element of the comparison stimulus, which re-mains fixed.

The comparison stimulus array (Fig. 1) consisted of onerow of equally spaced two-dimensional Gabor patchescentered 1.9° above a fixation cross. The string of micro-patterns had a horizontal extent of ;9.5°, and the targetelement was always located at the center of the array.

The Gabor elements are vertically oriented sine-wavegratings multiplied by Gaussians in the horizontal (sx)and orthogonal (sy) dimensions and are given by the fol-lowing equation:

G~x, y ! 5 L@1 1 C exp~2x2/sx2!

3 exp~2y2/sy2!sin~2pfx !#, (1)

Fig. 1. Example of the stimulus configuration. The stimulus consists of an array of equally spaced Gabor signals with a horizontalspace constant of 0.19°, spatial frequency of 3.3 cpd, and contrast of 40%. Viewed from a distance of 98 cm, the spacing between theelements is 0.57° and the width of the array is 9.5°. The element string is centered 1.9° above the fixation point. The target Gabor wasalways the central element. In the schematic its position is delimited by the dashed ellipse; however, its position was not indicated inany way during the experimental procedure.

Ellemberg et al. Vol. 15, No. 7 /July 1998 /J. Opt. Soc. Am. A 1735

where L is the mean luminance of the pattern, f is thespatial frequency of the sine wave, C is the contrast of thestimulus, and (sx) and (sy) are, respectively, the horizon-tal and the vertical space constants (the distance from theelement’s center at which its amplitude envelope de-creases to 1 /e). Each Gabor element had a vertical spaceconstant (sy) of 0.57° and a horizontal space constant(sx) of 0.19°. Unless otherwise specified, the Gaborpatches had a contrast (C) of 40% and a vertical carrierfrequency (v) of 3.3 cycles per degree (cpd).

The stimuli were generated on a Macintosh IIvx com-puter and were displayed on an Apple monochrome moni-tor with a frame rate of 67 Hz and a pixel resolution of640 3 480. The display subtended a visual angle of;12° 3 9° at a viewing distance of 98 cm. The stimuliwere produced by means of a linearized subset of 151 grayvalues. Mean screen luminance was maintained at 70cd m22.

C. ProcedureObservers viewed the screen from a distance of 98 cm in adimly illuminated room. In all conditions a chin- andforehead-rest was used to minimize head movements.Subjects were instructed to fixate a small cross at the cen-ter of the uniformly illuminated screen. In consecutiveexperiments apparent contrast and spatial frequencywere measured by means of a two-alternative temporalforced-choice paradigm and the method of constantstimuli.

The observer initiated each trial with a key press. Thecomparison stimulus and the test stimulus were each pre-sented for 100 ms in random order, separated by a 500-msinterval during which the screen returned to the mean lu-minance. Each interval was marked by a tone. Depend-ing on the condition being tested, subjects indicated bymeans of one of two key presses which interval containedthe higher-contrast central patch or the lower-spatial-frequency central patch. Five test values spanning thepsychometric function were presented in each run.Twenty-five trials were run for each test value, with theorder of presentation randomized in each run.

Apparent contrast and apparent spatial frequency wereexamined as a function of two contextual variables:

1. Element density: Inter-element spacing in thecomparison stimulus was varied over a range of 0.57° to3.8° (or 1.8 to 12.6 cycles of the Gabor carrier, where eachcycle is 18.2 arc min).

2. Reltive contrast and spatial frequency of the sur-rounding elements: The effect of the direction of the sur-rounding elements’ contrast on the apparent contrast ofthe target was assessed by setting the contrast of the sur-rounding elements either higher than (80%), equal to(40%), or lower than (20%) the central target’s contrast of40%. The effect of the direction of the surrounding ele-ments’ spatial frequency on the apparent spatial fre-quency of the target was assessed by setting the spatialfrequency of the surrounding elements either higher than(4.4 cpd), equal to (3.3 cpd), or lower than (2.2 cpd) thecentral target’s spatial frequency of 3.3 cpd. In separateruns the subjects were tested for each surround conditionthree times at each inter-element spacing (i.e., three sur-round contrast conditions at four inter-element spacings,

and three surround spatial-frequency conditions at fourinter-element spacings). There were three experimentalruns per subject per condition.

Psychometric functions were fitted to each data setwith a Quick12 or a Weibull13 function from which we es-timated the 50% probability level, or the point of percep-tual equality. Since it could be argued that a cumulativenormal fit might be more appropriate in these circum-stances, as it is a symmetric distribution on linear axeswhereas the Quick function is symmetric on a log plot, wereanalyzed a random subset of our data in this manner.In all cases the estimated points of subjective equalitywere reduced by ,0.5%, far less than the size of a symbolin the figures. Therefore we are confident that in thepresent circumstances, in which the test values cover aquite restricted range, the Quick function provides an ac-curate estimate of the point of subjective equality. Weexamined the slope parameters of the Quick functionsand found no consistent pattern of variation with increas-ing element spacing.

3. RESULTSA. Contrast InductionThe effect of the presence of surround elements on theperceived contrast of the target is illustrated in Fig. 2,where apparent contrast is plotted as a function of inter-element spacing. In each panel open circles representthe condition in which the actual contrast of the surroundelements is identical to that of the target (40%). The re-sults are quite similar across the three subjects. Wefound that the apparent contrast of the target was judgedto be nearly equal to that of the single test element (`) atlarge spacings but decreased abruptly when the inter-element distance was reduced to 0.95°. Apparent con-trast underwent a further reduction at the inter-elementdistance of 0.57°. The apparent contrast of the centralGabor target at the smallest spacing ranged from 29% to32% contrast (i.e., a contrast reduction of 20%).

The effect of the relative contrast of the surrounding el-ements on the target’s apparent contrast is also presentedin Fig. 2. The different curves in each graph, 20% /40%,40% /40%, and 80% /40%, respectively, signify that thesurrounding elements’ contrast is lower than, equal to,and higher than that of the target. All three curves fol-low a similar pattern for each subject. At the smallestinter-element spacings the apparent contrast of the targetdecreases regardless of the direction of the surroundingelements’ contrast. The reduction in apparent contrastis most pronounced in all subjects when the target is sur-rounded by elements of higher contrast. However, thereis no consistent ordering for targets surrounded by ele-ments of equal or lower contrast.

B. Orientation Tuning of Contrast InductionIn the previous experiment the carrier of all the Gabor el-ements in the arrays had the same orientation. To ex-amine whether the apparent contrast-induction effectmeasured above is tuned for orientation, we carried outan experiment in which the orientation of the carrier ofthe surrounding Gabors was made orthogonal to the car-

1736 J. Opt. Soc. Am. A/Vol. 15, No. 7 /July 1998 Ellemberg et al.

rier grating of the target Gabor. The distance betweenthe elements was held constant at 0.57°, the spacing atwhich the largest effect was measured above. However,to carry out this experiment we had to modify one of theparameters of the basic paradigm. In the original arraythe space constants of the Gabors had a 3:1 aspect ratio,making them vertically elongated. This second orienta-tion cue was eliminated by changing the aspect ratio ofthe Gaussian windows to 1:1, thus making the Gabors cir-cular while preserving the orientation cue provided bytheir carrier grating. All other stimulus parameters andtesting procedures were the same as in the experimentpresented above.

One of the original subjects (DE) and a new subject(SA) were tested on this task. Their data (Fig. 3) are pre-sented as the percent reduction in apparent contrast to avertical target surrounded by either vertical elements

Fig. 2. Apparent-contrast data for the three subjects tested onthe three directions of contrast. The abscissa is the center-to-center distance between the elements in degrees of visual angle.Subjects SM and MO were tested on four of the five inter-elementspacings.

Fig. 3. Percent reduction in the apparent contrast of central tar-gets surrounded by flankers of identical (vVv) or orthogonal(vHv) orientation.

Fig. 4. Apparent-spatial-frequency data for three subjects plot-ted against inter-element spacing. Each subject was tested onthe three spatial-frequency surround conditions.

Ellemberg et al. Vol. 15, No. 7 /July 1998 /J. Opt. Soc. Am. A 1737

(vVv) or horizontal elements (hVh). The resulting pat-terns are similar for the two subjects.

First, it is important to note that reductions in appar-ent contrast for these circular Gabors (vVv) were similarto those found for the elongated Gabors used in the firstexperiment. However, when the orientation of the sur-round was orthogonal to that of the target, there was nochange in the apparent contrast of the target, thus indi-cating that apparent contrast induction is tuned for ori-entation.

C. Spatial-Frequency InductionThe 3.3/3.3-cpd curve in each panel of Fig. 4 shows the ap-parent spatial frequency of the target as a function ofinter-element spacing when target and surround haveidentical spatial frequencies. We found an increase inapparent spatial frequency at the smallest inter-elementspacing. A marked shift to higher spatial frequencies oc-curs at the inter-element distance of 0.57° for SM andMO and at 0.95° for DE. The shift in apparent spatialfrequency ranged from 0.5 to 0.8 cpd (mean spatial-frequency reduction 520%).

As was the case for contrast, the relative spatial fre-quency of the surround elements did not affect the direc-tion of the perceived shift in spatial frequency. Filledand open squares in Fig. 4 represent the cases in whichthe surround elements have higher (4.4 cpd) and lower(2.2 cpd) spatial frequencies than the target. The resultsare essentially identical for all subjects. Regardless ofthe direction of the surrounding elements’ spatial fre-quency, the target’s apparent spatial frequency increasesat small inter-element spacings. The largest shift in ap-parent spatial frequency consistently occurs when thetarget is surrounded by elements of equal spatial fre-quency. However, there is no particular trend for targetssurrounded by elements of lower or higher spatial fre-quencies.

Figure 5 compares the spatial extent of the contrast in-duction and the spatial-frequency induction. Each pointrepresents the percent change in apparent contrast andapparent spatial frequency for the central target, aver-aged over the three subjects. The curves demonstratethat there is a close relation between the spatial extent ofthe two phenomena.

D. Spatial-Frequency Tuning of Spatial-FrequencyInductionWe also examined the spatial-frequency tuning of spatial-frequency induction. Spatial-frequency tuning was mea-sured for targets of 3.3 and 6.6 cpd by use of surroundspatial frequencies that varied in approximately half-octave steps from one octave above to one octave belowthe target’s spatial frequency. Inter-element distancewas held constant at 0.57°, the spacing at which the larg-est effect was measured above. The results for the 3.3-and 6.6-cpd targets are shown in the top and bottom pan-els, respectively, of Fig. 6. The data are presented as thepercent increase in apparent spatial frequency as a func-tion of the spatial frequency of the surround. Each datapoint represents the mean of three test runs. All sub-

jects showed quite similar results for both 3.3- and 6.6-cpd targets. The largest shift occurs when the center andthe surround are of identical spatial frequencies. How-ever, when the spatial frequency of the surround was 1octave higher or lower than the spatial frequency of thetarget, there was little if any change in the apparent spa-tial frequency of the target, thus suggesting that appar-ent spatial-frequency induction is tuned for spatial fre-quency.

Fig. 5. Percent change in the apparent contrast and apparentspatial frequency of the target Gabor as a function of inter-element spacing, when the surrounding elements had the samecontrast and spatial frequency as the target.

Fig. 6. Spatial-frequency-tuning functions of the shift in appar-ent spatial frequency of targets of 3.3 cpd (top panel) and 6.6 cpd(bottom panel). The abscissa is the spatial frequency of the sur-rounding elements.

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4. DISCUSSIONIs the perception of local information within a restrictedregion of a textural surface dependent on its visual con-text? The data presented above indicate that the appear-ance of a Gabor signal is influenced by the presence ofclosely neighboring Gabors; however, the simultaneous-induction effect declines steeply in strength as the dis-tance between the elements increases. Moreover, con-trast induction and spatial-frequency induction areindependent of the direction of the surrounding elements’contrast and spatial frequency, respectively.

A. Spatial Relationship between SimultaneousInduction and the Texture-Coherence LimitCannon and Fullenkamp14 found that the apparent con-trast of a Gabor pattern decreased as the distance be-tween the central target and surround Gabors decreased.However, the widest inter-element spacing tested was0.75° (or 6 cycles, where each cycle is 7.4 arc min), a dis-tance at which they still found a strong induction effect.Further, in their study the target stimulus was presentedfoveally, and the flanks had an annular surround configu-ration.

As mentioned in Section 1, it has been reported10,11

that the percept of a texture breaks down abruptly as thedistance between elements exceeds a clear limit. This co-herence boundary was found to be related to the elements’size (space constant) by a power-law function.11 This ledus to wonder whether the critical spacing defining both ofthese phenomena is comparable. Wilkinson andWilson11 found that under experimental conditions simi-lar to those of the present study the texture-coherencelimit of a string of Gabors with the same space constantwas 0.72°. Averaged over all three subjects, the datapresented here show that apparent contrast and apparentspatial frequency undergo a sudden shift at inter-elementspacings below 1° (Fig. 5). Thus, at nearly the sameinter-element distance at which the appearance of the el-ements shifts, the elements also give rise to the percept ofa textured surface.

Wilkinson et al.6 and others15,16 have suggested thatpooling performed by a second-order filtering stage is akey element of texture processing. Wilkinson et al. alsosuggested6 that cortical complex cells may provide theneural substrate for the psychophysically measured pool-ing, as complex cells summate inputs in a nonlinear fash-ion from across their receptive fields and are thereforephase insensitive. In the present case the orientationand the spatial-frequency tuning of the effects we havedescribed would be consistent with the receptive-field or-ganization of complex cells as described by Movshonet al.17 However, we use the term complex cell with cau-tion, as we have no direct basis on which to relate our psy-chophysical findings to complex cells in a particular corti-cal lamina or even in a particular cortical region.

Wilkinson and Wilson11 proposed that the spacingthreshold for texture coherence represents the thresholdactivation of complex cells. Applying this to our data, wepropose that when simple cell activity underlies the vi-sual percept, the apparent contrast and apparent spatialfrequency of the target are unchanged; however, where

the threshold for complex cell activation is met, at thetexture-coherence limit, there is a shift in the apparentcontrast and apparent spatial frequency of the target.

It could be argued that our findings result from limita-tions on selective attentional processes. That is, as thedistance between the elements is reduced, it may becomemore difficult to locate the target stimulus accurately.This in turn could bias judgments of apparent contrastand apparent spatial frequency. However, there are twosources of evidence from this study that strongly argueagainst this position. First, the subjects’ judgments werequite reliable, as indicated by the small standard errors.Second, if subjects were confused as to the location of thetarget, the judgments would have been affected differen-tially by the higher and lower contrast and spatial-frequency surround conditions, and this was not the case.

B. Effect of the Relative Contrast and SpatialFrequency of the Surrounding Elements on theAppearance of the TargetFor well over a century, evidence has shown that the per-cept of a region of fixed luminance can be made to appeardifferent in lightness by varying the luminance of its im-mediate surround.18–20 A key feature of the classicalbrightness-induction phenomenon is that objects appearbrighter when the luminance of their background islower, and darker when the luminance of their back-ground is higher. Similar effects were found for gratinginduction when a grating’s apparent contrast and appar-ent spatial frequency were shifted in the direction oppo-site to their background’s contrast and spatial frequency,respectively.1,5 On the other hand, our experiments re-vealed a different pattern of results. The apparent con-trast of the central Gabor appeared lower than its physi-cal contrast, whether it was flanked by elements of equal,greater, or lower contrast; and the apparent spatial fre-quency of the central Gabor appeared higher than itsphysical frequency, whether it was flanked by elements ofequal, lower, or higher spatial frequency. An importantdistinction between our study and the ones describedabove is that we investigated the appearance of a singleelement within a textured surface, whereas the previousstudies measured the appearance of an extended texturedpattern. Thus the main effect that we see could be onethat they are not measuring. Another important distinc-tion between our study and the ones described above isthat our target stimulus was viewed parafoveally,whereas theirs was viewed foveally. The one exceptionin the previous literature is the work of Cannon andFullenkamp3 (experiment 3, Fig. 8), who also reported re-ductions in the apparent contrast of a target grating sur-rounded by a lower-contrast grating; unlike our findings,these reductions were consistently smaller than thosefound for a target grating surrounded by a higher-contrast grating.

Cannon and Fullenkamp14 also reported reductions inthe apparent contrast of a target Gabor pattern. In theirstudy, however, the target was always flanked by Gaborsin an annular surround configuration, and the flankingelements always had at least twice the contrast of the tar-get. The authors proposed a feed-forward divisive gaincontrol to explain the reductions they found in the appar-

Ellemberg et al. Vol. 15, No. 7 /July 1998 /J. Opt. Soc. Am. A 1739

ent contrast of the central Gabor target. Although wehave not yet developed a full model for our findings, ourdata on contrast also suggest a divisive gain control thatwe would see operating on the complex cells. One inter-pretation of the apparent spatial-frequency shifts wouldbe that the complex cells pool subunits of a single spatialfrequency over a moderate spatial range and that the di-visive gain control pools both a wider spatial range andacross a wider range of spatial-frequency-tuned channelsthat are not weighted equally. The data suggest that thestrength of the gain control diminishes as complex-cellpeak spatial frequency increases and augments ascomplex-cell peak spatial frequency decreases. This pu-tative gain control may provide an explanation for the ef-fects we have reported.

5. CONCLUSIONWe have demonstrated that the apparent contrast andspatial frequency of a Gabor element is dramatically in-fluenced by its visual context. Because of the close rela-tion between the texture-coherence limit and the spatialextent of our effect, the present paper conjectures thatthis form of simultaneous induction may result from theactivity of cortical complex cells, as does the percept ofgrouping that characterizes visual textures. Our resultson the spatial-frequency selectivity of apparent spatialfrequency also provide additional evidence that corticalcomplex cells implicated in second-order texture percep-tion are tuned to spatial frequency.21

ACKNOWLEDGMENTSThis research was supported by the Natural Sciences andEngineering Research Council (Canada) (grantOGP0007551 to FW) and by the National Institutes ofHealth (grant EY02158 to HRW).

Address correspondence to Frances Wilkinson, Depart-ment of Psychology, McGill University, 1205 Penfield Av-enue, Montreal QC, Canada H3A 1B1. FrancesWilkinson’s e-mail address is fran@hebb.psych.mcgill.ca.

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