effect of background components on spatial-frequency masking

J. Yang and S. B. Stevenson Vol. 15, No. 5 /May 1998/J. Opt. Soc. Am. A 1027

Effect of background components on spatial-frequency masking

Jian Yang and Scott B. Stevenson

College of Optometry, University of Houston, Houston, Texas 77204

Received August 6, 1997; revised manuscript received December 16, 1997; accepted December 22, 1997

Previous studies of spatial-frequency masking and adaptation have shown that the contrast-detection thresh-old elevates maximally when the test spatial frequency is the same as the masking (or adapting) frequency butchanges only slightly when they are separated by two or more octaves. At low spatial frequencies, however,the peak of the threshold-elevation function does not obey this rule: there is a well-established peak shift inthe threshold-elevation functions toward higher spatial frequencies. We investigated whether this shiftmight be due to the masking effects caused by the background field, which contributes energy at the very lowend of the spectrum. We first measured the effect of a 3-cycles/deg (c /deg) mask on detection of a range of testfrequencies, compared with unmasked detection thresholds. We then measured the combined effect of a 2-c /deg and a 3-c /deg mask on detection, compared with detection with just the 2-c /deg mask. The comparison inthe second case still tests the effect of the 3-c /deg mask, but the presence of the hidden 2-c /deg mask causesthe peak masking effect to shift toward higher frequencies. This result provides a proof of concept for thehypothesis that the peak shift at low spatial frequencies is caused by the low-frequency energy in the back-ground field, which is present in both masked and unmasked conditions. A five-parameter quantitative modelof frequency masking is presented that describes the pure contrast-detection function, the frequency-maskingfunctions at mask frequencies of 0.25, 0.5, 2, and 3 c /deg, and the peak-shift phenomenon. © 1998 OpticalSociety of America [S0740-3232(98)02205-4]

OCIS codes: 330.1800, 330.4060, 330.5510, 330.7320, 330.6110, 330.2630.

1. INTRODUCTIONThe work of Campbell and Robson1 in 1968 suggestedthat the human visual system processes spatial patternsaccording to their spatial-frequency components. Sincethen, it has been generally agreed that the visual systemcontains relatively independent channels selectivelytuned to different spatial frequencies.2–11 The neuralsubstrate for such spatial-frequency selectivity is widelyidentified with cells in the striate cortex.12–17

One line of psychophysical evidence came from experi-ments on frequency adaptation: after adaptation to agrating, the contrast threshold for detecting a grating el-evated significantly when the test frequency was thesame as the adapting frequency but changed only slightlywhen the test and adapting frequencies were separatedby two or more octaves.2,18 The curve of threshold eleva-tion versus test frequency peaked at the adapting fre-quency. When the adapting frequency was very low,however, the peak of the threshold-elevation curve shiftedto test frequencies higher than the adaptingfrequency.2,19,20 The suggestion was made that this peakshift might be due to a lack of spatial channels tuned tovery low frequency. However, Stromeyer et al.21 pointedout that the threshold elevation at the adapting frequencyshould remain high if the visual system simply lackedvery low channels: the detection of low-spatial-frequencypatterns would be determined by channels centered at ahigher spatial frequency, but so would the adaptation.Stromeyer et al.21 suggested that the peak shift might in-stead be explained by assuming that very-low-frequencychannels exist but for some reason are not as adaptable.The phenomenon of peak shift is complicated; studieshave also shown that the amount of peak shift varies with

0740-3232/98/051027-09$15.00 ©

the size of viewing field and temporal properties of thestimuli.20,21 It remains unclear why very-low-spatial-frequency channels are not adaptable and the low-fre-quency peak shift changes with experimental conditions.

In the adaptation paradigm, the observer looks at thedesensitizing stimulus, i.e., the adapter, for up to a fewminutes before the presentation of a test pattern. In themasking paradigm, the desensitizing stimulus, i.e., themasker, is presented simultaneously with the test pat-tern. It has been reported that the effects of frequencyadapting and frequency masking are quite similar.22–26

The connection between the underlying desensitizingmechanisms has been debated,4 but recent evidence27

suggests that contrast adaptation at the cortical level ismanifested as tonic activation, not unlike a masking ef-fect. Adaptation and masking paradigms provide thecentral evidence for the existence of spatial-frequencychannels in human vision and provide similar estimatesof channel bandwidth. In this paper we make qualitativecomparisons across the two experimental paradigms onthe basis of an assumption that adaptation and maskingcan probe the same frequency filters in human vision.

In masking experiments investigators usually havekept the test frequency constant and measured thethreshold elevation by varying the masking frequency.The curve of the threshold elevation versus masking fre-quency showed a low-frequency peak shift, as had beenfound with the adaptation paradigm. When test fre-quency was very low, the maximum threshold elevationwas located at masking frequencies that were higher thanthe test frequency and the peak shift was taken to inferthat human vision lacks very-low-frequency sustainedchannels.6,11,28–30

Although the effects of frequency adapting and fre-

1998 Optical Society of America

1028 J. Opt. Soc. Am. A/Vol. 15, No. 5 /May 1998 J. Yang and S. B. Stevenson

quency masking are similar, it is not obvious that theytell the same story. In the first instance, the curves wereplotted as threshold elevation against test frequency; andin the second instance, the curves were plotted as thresh-old elevation against mask frequency. The conclusionfrom the masking experiments was that the human visualsystem lacked very-low-spatial-frequency sustainedmechanisms.11,28,29 The conclusion from the adaptationexperiments, however, was that the very-low-spatial-frequency mechanisms do exist but are not adaptable. Itis desirable, therefore, to seek further explanations of thepeak shifts.

A recently proposed masking model31–33 suggests thatpeculiar behaviors identified at low spatial frequenciesare often caused by masking that is due to the back-ground luminance (zero and near-zero frequency) compo-nent that is inherently a part of any grating stimulus, aphenomenon referred to as implicit masking. The energyof the background field concentrates at very low spatialfrequencies, so the effect of implicit masking is to attenu-ate visual sensitivities at low spatial frequencies. It maybe noted that the background component might act asboth an adapter and a masker, but here we use the termmasking in reference to its effect on pattern detection.We use the term explicit masker to refer to stimulus com-ponents that are explicitly added to a test pattern to as-sess their effects on detectability of the test.

Yang et al.32 hypothesized that the peak shift awayfrom low frequencies in threshold elevation functions isdue to implicit masking; at very low spatial frequenciesthe baseline sensitivities are already masked by theoften-ignored background component; thus the addition ofan explicit masker may not be as effective in elevating thecontrast threshold as it would be at higher spatial fre-quencies. This suggestion provides a natural answer tothe question of why very-low-spatial-frequency channelsare not adaptable, and it is compatible with empiricalfindings that the adaptability of the visual system is in-versely related to its sensitivity.34 If this hypothesis iscorrect, it should apply to higher spatial frequencies aswell: including a background grating to both baselineand test conditions should cause a peak shift in the mask-ing function away from the background grating fre-quency. To test this hypothesis, we first measured amasking function with a mask frequency of 3 cycles/deg(c /deg) in the conventional way and then measured thesame masking function with an extra background gratingof 2 c /deg added to both baseline and masked conditions.The prediction is that in the first case the masking func-tion will show a peak at the mask frequency of 3 c /deg butin the second case the masking function will show a peakshift to a frequency higher than 3 c /deg.

In this paper we first present experimental data toshow the peak shift of the threshold elevation against testfrequency produced by a masker of 3 c /deg in conditionsin which a background grating of 2 c /deg was present.We then present a quantitative model of grating contrastsensitivity (modified from a previously publishedversion32) that encompasses both implicit and explicitmasking effects to account for experimental data reportedhere and elsewhere.28,32 Finally, we compute the mask-ing functions as defined by threshold elevation against

mask frequency based on the obtained model parametersand compare them with new experimental data run underthe same experimental settings.

2. METHODSA. StimuliVisual stimuli were horizontal gratings, as expressed by

s~ y ! 5 L$1 1 sin~2pvt !@SCm cos~2pfmy !

1 C cos~2pfy !#%, (1)

where s is the luminance profile of the stimulus, with Lits mean luminance of 110 cd/m2. Cm and fm are the con-trast and frequency of a mask component, respectively,and the summation is over different mask components.C and f are the contrast and spatial frequency of the testcomponent, respectively. The value of v was set to 1 Hz.With the display duration of 500 ms, the contrasts werefaded in and faded out within each interval following thefirst half period of the 1-Hz sine wave. Both the test andthe mask components were in cosine phase with respectto a fixation target. Pilot data did not show reliable ef-fects of random relative phase.

All stimuli were generated with a Cambridge ResearchSystems VSG 2/3 board and displayed on an Image Sys-tems monitor at a frame rate of 130 Hz. The display areawas rectangular with a width of 6.1° and a height of 6.0°at viewing distance of 200 cm. There were 720 horizon-tal lines, corresponding to a line width of 0.5 arc min. Itwas dark outside of the display area. The gray level ofthe video screen was gamma corrected with a CRS Opti-cal™ tool and had an effective 12-bit luminance resolu-tion. The mask and the test targets were displayed in al-ternate frames, so the effective frame rate was reduced byhalf to 65 Hz. This technique allowed the test contrast tobe varied on a trial-by-trial basis through lookup-tablemanipulations, avoiding the requirement of recomputingthe combination of masks and test for each trial. Thehigh frame rate obscured any flickering between test andmask components. Observers viewed the display binocu-larly with natural pupils and were stabilized by a chin-and-head rest. Three observers, QW, SBS, and JY, withcorrected vision, participated in the experiments.

B. Psychophysical ProceduresThe purpose of experiment I was to obtain the curves ofthreshold elevation versus test frequency. The frequencyof the mask or masks was fixed within an experimentalsession, and each block in the session had a constant testfrequency. The purpose of experiment II was to obtainthe curves of threshold elevation versus mask frequency.The test frequency was fixed within a session, and eachblock in the session had a constant mask frequency.These two experiments represent complementary ways ofsampling all the possible combinations of mask frequencyand test frequency; previous investigations have used oneor the other but usually not both. At the beginning ofeach block, the test grating was shown by itself at highcontrast so that the observers would know what to lookfor. Contrast thresholds were measured with a forced-choice procedure with two 500 ms stimulus intervals,


separated by 500 ms of a uniform field of the same meanluminance. The observers responded by pressing one oftwo buttons to signal which interval appeared to containthe target component. A fixation cross was displayed be-fore and after each stimulus interval, which was demar-cated by a beep. The contrast of the test component oneach trial was determined by a QUEST procedure,35

which searched for the contrast at which the interval con-taining the test component was correctly identified on84% of the trials. Auditory signals informed the observerabout the correctness of the preceding response. The tri-als were terminated by a x2 test with a 95% confidenceinterval of 60.1 log contrast. Individual data reportedhere are geometrical means over five sessions run mostlyon different days.

3. RESULTS OF EXPERIMENT 1A. Peak Shift Due To Explicit MaskingYang et al.32 suggested that contrast sensitivity at verylow spatial frequencies is desensitized by low-frequencycomponents in the background, causing the peak shifts inthe threshold-elevation curves. As implicit masking af-fects only low frequencies, owing to its frequency selectiv-ity to nearby spatial frequencies, visual sensitivity athigh spatial frequencies is basically not affected by im-plicit masking. Therefore the suggested peak shift doesnot apply to medium and high spatial frequencies. Thefirst purpose here was to test the notion that the presenceof an extra mask frequency can shift the peak of thethreshold-elevation curve obtained with a medium mask-ing frequency. We measured the elevation curve with amask grating of 3 c /deg. The solid curve in Fig. 1 showsthe mean threshold elevation produced by this maskerplotted against test frequency. The peak of thethreshold-elevation curve due to the masker of 3 c /degpeaks at the test frequency of 3 c /deg, in general agree-ment with literature reports on masking and adaptation,although the shape of the masking function is not sym-

Fig. 1. Masking by a 3-c /deg grating of 15% contrast. Thresh-old elevation is plotted against test frequency for observers QW,SBS, and JY. Error bars represent 11 standard error of thedata and are shown in just one direction for clarity. The solidcurve represents geometrical mean over the three observers.The arrow points to the mask frequency.

metrical. The baseline for calculating the threshold el-evation is the detection threshold where no explicitmasker was presented. Numerically, the threshold el-evation equals the ratio between the contrast thresholdmeasured in the presence of the masker and the contrastthreshold measured in the absence of the masker.

When a background grating of 2 c /deg was presentedas the baseline in both intervals, as shown in Fig. 2, thethreshold elevation due to the 3 c /deg masker is reducedsharply at frequencies near 2 c /deg (i.e., the frequency ofthe extra masker) from ;0.6 log unit to less than 0.2 logunit. As a consequence, the peak of the curve shifts to ahigher frequency (;3.6 c /deg). This effect is most pro-nounced for subjects JY and QW but is still evident forsubject SBS, as can be seen by comparing individual sub-ject data in Figs. 1 and 2. The threshold elevation asshown in Fig. 2 is the ratio between the threshold mea-sured in the presence of the 3-c /deg explicit masker andthe 2-c /deg background grating and the threshold mea-sured in the presence of the 2-c /deg background grating.(See Fig. 5 below for the raw contrast sensitivities.)

The results shown in Fig. 2 indicate that the extramasker of 2 c /deg substantially reduced the masking ef-fect of the 3 c /deg masker in the neighborhood of 2 c /deg.As a by-product, the peak of the masking function isshifted to a frequency that is higher than 3 c /deg, al-though the amount of peak shift is small (;0.6 c /deg).The presence of the background grating reduced the over-all threshold elevation compared with the explicit-onlycase (Fig. 1 versus Fig. 2). In the following, we check theamount of peak shift for the threshold-elevation curves at0.25 and 0.5 c /deg, which according to Yang et al.32 iscaused by the implicit masking effect of the backgroundluminance.

B. Peak Shift Due To Implicit MaskingThe threshold-elevation curves with mask frequency of0.25 and 0.5 c /deg are shown in Figs. 3 and 4, respec-

Fig. 2. Masking by a 3-c /deg grating of 15% contrast in the casein which both masking and baseline conditions had an extrabackground grating of 2 c /deg and 20% contrast. Threshold el-evation is plotted against test frequency for observers QW, SBS,and JY. Error bars represent 11 standard error of the mean foreach subject. The solid curve represents the geometric meanover the three observers. The arrows point to the mask frequen-cies.


tively. The peak shift is most evident in the 0.25-c /degdata (Fig. 3), but there is a small shift in the 0.5 c /degdata as well (Fig. 4). These shifts are generally smallerthan those reported previously in the literature,2,20 al-though some investigators have reported little or noshift.21 Additionally, the overall threshold elevation isless for the 0.25-c /deg mask (Fig. 3) than for the 0.5-c /degmask (Fig. 4).

So far, the elevation curves have been compared by vi-sual examination of the figures. In the following, we fitcurves to the data using a modification of the quantitativemodel developed by Yang et al.32

4. FREQUENCY-MASKING MODELA. Model of Yang et al.32

By considering the energy spreads of the background lu-minance (dc component) and of the explicit masker at the

Fig. 3. Masking by a 0.25-c /deg grating of 15% contrast.Threshold elevation is plotted against test frequency for observ-ers QW, SBS, and JY. Error bars represent 11 standard errorof the mean for each subject. The solid curve represents the geo-metric mean over the three observers. The arrow points to themask frequency.

Fig. 4. Masking by a 0.5-c /deg grating of 15% contrast.Threshold elevation is plotted against test frequency for observ-ers QW, SBS, and JY. Error bars represent 11 standard errorof the mean for each subject. The solid curve represents the geo-metric mean over the three observers. The arrow points to themask frequency.

test frequency and a nonlinear thresholding at the detect-ing stage, Yang et al.32 developed a masking model to cal-culate the contrast threshold for detecting a grating. Therationale and underlying assumptions of the model arediscussed in Ref. 32. Here we discuss those parts of themodel that are relevant to this paper. With luminancefixed, the Yang et al. equation [Ref. 32, Eq. (11)] relatingcontrast threshold to mask and test stimuli simplifies to

Cth 5 exp~af !~N 1 E0 1 Em! 2 rmG~ f, fm!, (2)

where f is the test frequency, fm is the explicit mask fre-quency, a is a spatial-frequency constant related to thelow-pass property of the visual system, N is a noise term,and E0 is a contribution from the dc component to the testfrequency, in the form of

E0 5 h0s02/~ f 2 1 s0

2!, (3)

where h0 is the masking strength and s0 the half-width ofthe frequency spread of the zero frequency component.The higher the test frequency, the smaller the effect of thebackground luminance. Em is a contribution from an ex-plicit masker to the test frequency in the form of

Em 5 Cm exp~2afm!hmG~ f, fm!, (4)

where G( f, fm) is the frequency spread from fm to f, mod-eled as

G~ f, fm! 5 sm2/@~ fm 2 f !2 1 sm

2#. (5)

The last term of Eq. (2) is a contribution from subthresh-old summation, by addition of the subthreshold test andmask contrasts with some weights, and with

rm 5 CmG~ f, fm!C02/@Cm

2G~ f, fm!2 1 C02#, (6)

where C0 is the detection threshold in the absence of ex-plicit maskers, and according to Eq. (2) we have

C0 5 exp~af !~N 1 E0!. (7)

B. Refinements of the ModelThe model [Eq. (2)] was derived by considering mainlythree stages of visual processing: low-pass filtering, fre-quency spreading, and nonlinear thresholding for condi-tions where up to one explicit mask frequency was pre-sented. We can extend the model to more-general cases,where many mask frequencies may be involved, by a sumof related components:

Cth 5 exp~af !~N 1 E0 1 SEm! 2 SrmG~ f, fm!; (8)

here the summations are over different mask frequencies.It should be emphasized that the model components asdescribed by Eqs. (3)–(6) were obtained empirically to fitexperimental data. Therefore the exact shapes of thesecomponents are subject to refinements as more experi-mental data are available. One obvious modificationcalled for is the expression for the frequency spread func-tion [Eq. (5)]. Figure 1 shows that the masking functionis not symmetrical, which indicates that the frequencyspread function should be nonsymmetrical as well. Inthe search of a replacement, we found that the expression

G~ f, fm! 5 ~ fm /f !0.5sm2/@~ fm 2 f !2 1 sm

2# (9)

provides an appropriate fit to the experimental data.


It has been suggested previously2,36,37 that spatial-frequency channels have a bandwidth that is roughly pro-portional to their peak frequency. This relationship can-not strictly hold for very low frequencies, however,because bandwidth would approach zero. Equation (10)was formulated to allow for a proportional bandwidthover most of the range but finite bandwidth at very lowfrequencies:

sm 5 s0 1 kfm , (10)

where s0 is the half-width of the frequency spread of thebackground field that peaks at 0 c /deg and has been at-tributed to the field truncation and retinal inhomogene-ities. Yang and Makous38 approximated it with an em-pirical relationship,

s0 5 0.042 1 0.64/field–size. (11)

Note that the Eqs. (2) and (5) have been replaced by cor-responding new Eqs. (8) and (9), respectively. The modi-fied model contains a total of five free parameters: a, N,h0 , hm , and k. The optimal values of the parameters ob-tained by fitting Eq. (8) to the averaged sensitivity data(see data points in Fig. 5) are shown in Table 1. The sixsmooth curves in Fig. 5 are fitted simultaneously with thesame parameter values, accounting for 95.5% of the vari-ance in the data.

Figure 6 shows the theoretical threshold-elevationcurves computed with the model equations and the ob-tained parameter values. One can see that the theorypredicts a nice upward peak shift for mask frequency of0.25 and 0.5 c /deg but not for mask frequencies of 2 or 3c /deg. When both the baseline and masked data includethe 2-c /deg masker, however, the peak of the masking by3 c /deg also shifts to a frequency higher than 3 c /deg.

It would be undesirable if the modified equations couldfit only the current data but not also the original data of

Fig. 5. Mean contrast sensitivity functions for unmasked (filledsquares) and in the presence of a mask frequency of 0.25 c /deg(open circles), 0.5 c /deg (filled triangles), 2 c /deg (open dia-monds), 3 c /deg (open squares), and both 2 and 3 c /deg (filledcircles). The mask contrast was 15% for all but the 2-c /degmasker, which had a contrast of 20%. Error bars represent 11standard error of the mean over three observers. The solidcurves are the model fits. The data for 2-c /deg masking (opendiamonds) served as the baseline function for the threshold el-evations plotted in Fig. 2 and the solid curve (3 1 2) in Fig. 6.For all other cases, the unmasked data (filled squares) were usedfor the baseline.

Yang et al.32 Thus we compared the quality of the fits bythe modified equations with the quality of the fits by theoriginal model in terms of percentage of the variance inthe data that is accounted for by the model. The originalmodel, which included eight free parameters, accounts for98.4% of the variance in the averaged data across thethree observers in the study of Yang et al.32 As discussedabove, two of the parameters (g and s0) were eliminatedfor the current version of the model. Yang et al.32 dis-cussed that the slope of the low-pass filter of the whole vi-sual system tended to be steeper as luminance decreased,for which we made a rough correction here by replacingthe slope a with a 1 d/L1/2, where L is the mean retinalilluminance in trolands. In comparison with Eq. (8), onemore parameter was included to describe the noise depen-dence on mean luminance. In summary, the modifiedmodel to account for the data of Yang et al.32 containsseven free parameters, i.e., one less than that in the origi-nal model, and accounts for almost the same amount ofthe variance as the original one does: 98.7% of the vari-ance in the averaged data from Yang et al.32 The corre-sponding parameters, in addition to the four shown inTable 1, are N0 5 0.022 td, b 5 0.0034 td1/2, and d5 0.10 deg td1/2. We emphasize here that when themean luminance in the experiment is constant as in cur-rent study, only five free parameters are required for themodel equation.

C. Change of Threshold-Elevation Curve by ImplicitMaskingTolhurst20 reported no peak shift in the threshold-elevation curve when the test stimuli were drifting grat-

Fig. 6. Model-based threshold-elevation curves with mask fre-quency of 0.25, 0.5, 2, 3, or 2 and 3 c /deg. The contrast of themask was 15% except for the 2-c /deg masker which had a con-trast of 20%. The arrows point to the mask frequencies.

Table 1. Estimated Model Parametersa

Studya

(deg) N h0 hm k

Current 0.17 0.0024 0.058 0.12 0.49Yang et al.32 0.23 — 0.061 0.24 0.33

a Parameters N, h0 , hm , and k are scaling factors without a physicalunit.


Fig. 7. Simulation of the change in peak shift by (a) varyingmasking strength or (b) varying the half-width of the zero-frequency spread. Parameter values, other than that shown inthe figure, were the same as those shown in Table 1 of the cur-rent study. The arrows point to the mask frequencies.

ings, and he attributed this phenomenon to the existenceof low-frequency transient channels. The peak shift ob-served with static gratings was attributed to a lack of low-frequency sustained channels. However, Stromeyeret al.21 argued that one needs to have low-frequency chan-nels that are not adaptable but that can mediate the de-tection of static low-frequency gratings to account for thepeak shift. It is not clear how the transient low-frequency channels can meet the two requirements.

Implicit masking from the background field, on theother hand, provides a natural account of both peak shiftfor static gratings and no peak shift for moving gratings.According to Eq. (3), the effect of the background lumi-nance is determined by the masking strength h0 and thezero-frequency spread half-width s0 under a fixed meanluminance. The masking strength is dependent on thetemporal modulation of the stimuli.31,39 When the lumi-nance of the background field is temporally modulated insynchrony with the test component, the masking strengthis the greatest. If the two components are modulatedquite differently, such as counterphase-modulated ormoving gratings against a steady background, the mask-ing strength is reduced. Figure 7(a) shows the modelsimulation with h0 being 0.029, 0.058, and 0.12 at a maskfrequency of 0.25 c /deg. The decrease of the maskingstrength from the implicit masking effect of the back-ground leads to an increase of the threshold elevationthat is due to the explicit masker, especially at low spatialfrequencies. As a consequence, the peak of the curvesmoves closer to the explicit mask frequency. In otherwords, the smaller the value of h0 , the more adaptablethe low-frequency channel.

Tolhurst20 also showed that the size of the viewing fieldhad an effect on the peak shift: the larger the field size,the smaller the shift. Yang and Makous38 indicated thatthe half-width of the frequency spread from the back-ground field, the spectrum of which peaks at 0 c /deg, canbe determined by field truncation and retinal inhomoge-neities and decreases as field size increases. These ef-fects are captured in Eq. (11) by the reciprocal relation-ship between the spread parameter s0 and field size.Figure 7(b) simulates the effect on masking of changes infield size. When s0 is increased from 0.075 to 0.298 c /deg, the threshold-elevation curve with a mask of 0.25 c /deg is greatly reduced at lower frequencies, and the peakshifts upward.

Several investigators21,40 found the peak shift, if therewas any, to be much less than what was reported byTolhurst.20 In these experiments, observers adapted tobandpassed dynamic random dots before the presentationof a static test grating. The current masking data withlow frequencies (see Figs. 3 and 4) also show relativelysmall peak shifts. A possible source of this inconsistencyacross studies may be experimental settings that affectthe degree of implicit masking, such as mean luminance,temporal properties, and field size.

5. COMPARISON OF MODEL PREDICTIONSWITH OTHER DATAA. Results of ExperimentWith the values of the model parameters established (seeTable 1), one can compute the threshold-elevation curves


for fixed test frequencies. The purpose of this experi-ment was to measure the function of threshold elevationversus mask frequency at several fixed test frequencies inthe same experimental settings as in experiment 1 and tocheck the accuracy of the model predictions.

Both experimental data and theoretical predictions areshown in Fig. 8. The masking functions with test fre-quency of 0.25 and 0.5 c /deg showed peak shifts, in agree-ment with data reported in the literature. From this fig-ure, one can see that the model captures the general

Fig. 8. Geometrically averaged experimental data over threesubjects (symbols) and the model predictions (curves) ofthreshold-elevation curve versus mask frequency for test fre-quency of 0.25 c /deg (open circles, dotted curve), 0.5 c /deg (filledtriangles, dashed curve), 3 c /deg (open squares, dotted–dashedcurve) and 3 c /deg with an extra masker at 2 c /deg (filled circles,solid curve). The contrast of the maskers was 10% except forthe extra masker, which had a contrast of 5%. Error bars rep-resent 11 standard error of the mean over three observers. Thearrows point to the test frequencies.

Fig. 9. Comparison of the model predictions (curves) and themasking data (symbols) of Legge (Fig. 7 of Ref. 28), for test fre-quency of 0.125 c /deg (open squares, dotted–dashed curve), 0.25c /deg (filled circles, solid curve), 1 c /deg (stars, long-dashedcurve), 4 c /deg (open circles, short-dashed curve), and 16 c /deg(open triangles, dotted curve) c /deg. The contrast of themaskers was 19%, and the field size was 13 deg for test frequen-cies of 1 c /deg and below and 3.25 deg for test frequencies of 4and 16 deg. The predictions were based on the same five param-eter values as those used in Fig. 8. The threshold elevation iscalculated as the ratio between the contrast thresholds obtainedwith and without a masker, which is slightly different from thedefinition used in the Legge paper.

trends of the masking functions in terms of absolutethreshold elevations at given contrast value and maskfrequencies. The main discrepancy is that the amount ofthreshold elevation found experimentally for the test at0.25 c /deg was greater than predicted. Most importantfor the current study, the model accurately predicted thespatial frequencies that produced the peak elevation.

B. Monocular Data of Legge28

In Ref. 28, Legge reported threshold-elevation curves fortest frequencies of 0.125, 0.25, 1, 4, and 16 c /deg. In hisexperiment, the field size was 13 deg for test frequenciesof 1 c /deg and below and was 3.25 deg for other test fre-quencies. The contrast of the maskers was fixed at 19%.Other experimental settings, such as mean luminance(200 cd/m2) and stimulus duration (200 ms), were close tothose used in the current experiments. Therefore wecompared the masking function of Legge that was mea-sured monocularly with the model predictions by usingthe same five parameter values obtained above. Thecurves in Fig. 9 are the model predictions, and the sym-bols are data points scanned from Fig. 7 of Ref. 28. Theaccuracy of the model prediction is similar to that shownin Fig. 8.

6. SUMMARY(a) The quantitative model of masking presented de-scribes the basic trend of a broad range of experimentaldata on contrast sensitivity for up to two explicit maskingfrequencies being presented. Five parameters are re-quired for a fixed mean luminance, and two more are re-quired to handle cases in which mean luminance is also avariable. The model fitted most of the data well, with thebiggest departures being at low spatial frequencies and incases with two explicit maskers. The model predictionfor a test frequencies of 0.25 c /deg in Fig. 8 and the onefor a test frequency of 0.125 in Fig. 9 are lower than cor-responding experimental data, although the peak posi-tions are more or less consistent. These deviations mayreflect the limitation of the approach of pure frequencyanalysis,41,42 and it is suggested that spatial-domainanalysis should be included for a more accurate descrip-tion of visual sensitivities. In this study our subjectswere aware of some local cues which may have aided thedetection of the test pattern in some conditions more thanothers, perhaps accounting for some of the variability inthe data. Overall, the frequency-based analysis pre-sented here has captured the trend of our data quite well,further demonstrating the generality of this approach instudies of visual processing (e.g., Refs. 13 and 43).

(b) The current study demonstrated that a backgroundgrating added to both baseline and masked conditions canshift the peak of a masking function toward higher fre-quencies. This result supports the hypothesis that theupward peak shift in the curve of threshold elevation ver-sus test frequency in the presence of a low-frequencymask is due to the effect of the static background field.On the other hand, the upward peak shift in the curve ofthreshold elevation versus masking frequency (Fig. 8) isdue to a strong masking effect of a higher spatial fre-quency on a lower spatial frequency: that is, a high fre-


quency masks a low frequency more than vice versa in thelow-to-medium-frequency range. Further research is re-quired for understanding the reason for this asymmetri-cal effect of frequency masking.

(c) The model used here to compute masking functionscould, in principle, apply to contrast adaptation as well.This application requires several further assumptionsabout the effect of adaptation on sensitivity, however, andis beyond the scope of this paper. Nevertheless, qualita-tively the results of the current study are consistent withthe suggestion of Stromeyer et al.21 that the peak shifts ofthe threshold-elevation curves at low spatial frequenciesare caused by the fact that low-frequency channels arenot as adaptable as higher-frequency channels. Our sug-gestion is that this resistance to adaptation at low fre-quencies is a consequence of a saturating effect from im-plicit masking by the low-frequency-dominated back-ground field energy.

ACKNOWLEDGMENTSThis work was supported by National Eye Institute grantEY-10531. We thank Alan Wang for serving as an ob-server and two anonymous reviewers for helpful sugges-tions.

REFERENCES1. F. W. Campbell and J. G. Robson, ‘‘Application of Fourier

analysis to the visibility of gratings,’’ J. Physiol. (London)197, 551–566 (1968).

2. C. Blakemore and F. W. Campbell, ‘‘On the existence ofneurones in the human visual system selectively sensitiveto the orientation and size of retinal images,’’ J. Physiol.(London) 203, 237–260 (1969).

3. N. Graham, ‘‘Spatial frequency channels in the human vi-sual system: effects of luminance and pattern drift rate,’’Vision Res. 12, 53–68 (1972).

4. N. V. S. Graham, Visual Pattern Analyzers (Oxford U.Press, Oxford, 1989).

5. N. Graham and J. Nachmias, ‘‘Detection of grating patternscontaining two spatial frequencies: a comparison of single-channel and multiple-channels models,’’ Vision Res. 11,251–259 (1971).

6. R. F. Hess and R. J. Snowden, ‘‘Temporal properties of hu-man visual filters: number, shapes and spatial covaria-tion,’’ Vision Res. 32, 47–59 (1992).

7. L. A. Olzak and J. P. Thomas, ‘‘Seeing spatial patterns,’’ inHandbook of Perception and Human Performance, Vol. 1,Sensory Processes and Perception, K. R. Boff, L. Kaufman,and J. P. Thomas, eds. (Wiley, New York, 1986), Chap. 7.

8. C. F. Stromeyer III and S. Klein, ‘‘Evidence against narrow-band spatial frequency channels in human vision: the de-tectability of frequency modulated gratings,’’ Vision Res.15, 899–910 (1975).

9. J. P. Thomas, ‘‘Model of the function of receptive fields inhuman vision,’’ Psychol. Rev. 77, 121–134 (1970).

10. A. B. Watson and J. G. Robson, ‘‘Discrimination at thresh-old: labelled detectors in human vision,’’ Vision Res. 21,1115–1122 (1981).

11. H. R. Wilson, D. K. McFarlane, and G. C. Phillips, ‘‘Spatialfrequency tuning of orientation selective units estimated byoblique masking,’’ Vision Res. 23, 873–882 (1983).

12. R. L. De Valois, D. G. Albrecht, and L. G. Thorell, ‘‘Spatialfrequency selectivity of cells in macaque visual cortex,’’ Vi-sion Res. 22, 545–559 (1982).

13. R. L. De Valois and K. K. De Valois, Spatial Vision (OxfordU. Press, Oxford, 1988).

14. L. Maffei and A. Fiorentini, ‘‘The visual cortex as a spatialfrequency analyser,’’ Vision Res. 13, 1255–1267 (1973).

15. J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, ‘‘Spatialand temporal contrast sensitivity of neurones in areas 17and 18 of the cat’s visual cortex,’’ J. Physiol. (London) 283,101–120 (1978).

16. R. Shapley and P. Lennie, ‘‘Spatial frequency analysis inthe visual system,’’ Ann. Rev. Neurosci. 8, 547–583 (1985).

17. M. S. Silverman, D. H. Grosof, R. L. De Valois, and S. D.Elfar, ‘‘Spatial-frequency organization in primate striatecortex,’’ Proc. Natl. Acad. Sci. USA 86, 711–715 (1989).

18. A. Pantle and R. Sekuler, ‘‘Size-detecting mechanisms inhuman vision,’’ Science 162, 1146–1148 (1968).

19. M. W. Greenlee, S. Magnussen, and K. Nordby, ‘‘Spatial vi-sion of the achromat: spatial frequency and orientation-specific adaptation,’’ J. Physiol. (London) 395, 661–678(1988).

20. D. J. Tolhurst, ‘‘Separate channels for the analysis of shapeand movement of a moving visual stimulus,’’ J. Physiol.(London) 231, 385–402 (1973).

21. C. F. Stromeyer III, S. Klein, B. M. Dawson, and L. Spill-mann, ‘‘Low spatial-frequency channels in human vision:adaptation and masking,’’ Vision Res. 22, 225–233 (1982).

22. J. M. Foley and Y. Yang, ‘‘Forward pattern masking: ef-fects of spatial frequency and contrast,’’ J. Opt. Soc. Am. A8, 2026–2037 (1991).

23. J. M. Foley and G. M. Boynton, ‘‘Forward pattern maskingand adaptation: effects of duration, interstimulus inter-val, contrast, and spatial and temporal frequency,’’ VisionRes. 33, 959–980 (1993).

24. M. A. Georgeson and J. M. Georgeson, ‘‘Facilitation andmasking of briefly presented gratings: time-course andcontrast dependence,’’ Vision Res. 27, 369–379 (1987).

25. J. Ross and H. D. Speed, ‘‘Contrast adaptation and contrastmasking in human vision,’’ Proc. R. Soc. London, Ser. B246, 61–69 (1991).

26. J. Ross, H. D. Speed, and M. J. Morgan, ‘‘The effects of ad-aptation and masking on incremental thresholds for con-trast,’’ Vision Res. 33, 2051–2056 (1993).

27. M. Carandini and D. Ferster, ‘‘A tonic hyperpolarizationunderlying contrast adaptation in cat visual cortex,’’ Sci-ence 276, 949–952 (1997).

28. G. E. Legge, ‘‘Sustained and transient mechanisms in hu-man vision: temporal and spatial properties,’’ Vision Res.18, 69–81 (1978).

29. G. E. Legge, ‘‘Spatial frequency masking in human vision:binocular interactions,’’ J. Opt. Soc. Am. 69, 838–847(1979).

30. D. H. Peterzell and D. Y. Teller, ‘‘Individual differences incontrast sensitivity functions: the lowest spatial fre-quency channels,’’ Vision Res. 36, 3077–3085 (1996).

31. J. Yang and W. Makous, ‘‘Spatiotemporal separability incontrast sensitivity,’’ Vision Res. 34, 2569–2576 (1994).

32. J. Yang, X. Qi, and W. Makous, ‘‘Zero frequency maskingand a model of contrast sensitivity,’’ Vision Res. 35, 1965–1978 (1995).

33. J. Yang and W. Makous, ‘‘Modeling pedestal experimentswith amplitude instead of contrast,’’ Vision Res. 35, 1979–1989 (1995).

34. R. J. Snowden, ‘‘Adaptability of the visual system is in-versely related to its sensitivity,’’ J. Opt. Soc. Am. A 11,25–32 (1994).

35. A. B. Watson and D. G. Pelli, ‘‘QUEST: a Bayesian adap-tive psychometric method,’’ Percept. Psychophys. 33, 113–120 (1983).

36. N. Brady and D. J. Field, ‘‘What’s constant in contrast con-stancy? The effects of scaling on the perceived contrast ofbandpass patterns,’’ Vision Res. 35, 739–756 (1995).

37. A. B. Watson, ‘‘Efficiency of a model human image code,’’ J.Opt. Soc. Am. A 4, 2401–2417 (1987).

38. J. Yang and W. Makous, ‘‘Implicit masking constrained byspatial inhomogeneities,’’ Vision Res. 37, 1917–1927 (1997).

39. J. Yang and W. Makous, ‘‘Three theories of the low fre-quency cut,’’ Invest. Ophthalmol. Visual Sci. (Suppl.), 37,S733 (1996).

40. C. F. Stromeyer III and B. Julesz, ‘‘Spatial frequency mask-


ing in vision: critical bands and spread of masking,’’ J.Opt. Soc. Am. 62, 1221–1232 (1972); M. A. Webster and E.Miyahara, ‘‘Contrast adaptation and the spatial structureof natural images,’’ J. Opt. Soc. Am. A 14, 2355–2366(1997).

41. H. Akutsu and G. E. Legge, ‘‘Discrimination of compound

gratings: spatial-frequency channels or local features?’’Vision Res. 35, 2685–2695 (1995).

42. J. Nachmias, ‘‘Masked detection of gratings: the standardmodel revised,’’ Vision Res. 33, 1359–1365 (1993).

43. W. L. Makous, ‘‘Fourier models and loci of adaptation,’’ J.Opt. Soc. Am. A 14, 2323–2345 (1997).

effect of background components on spatial-frequency masking

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