Spatial-Frequency Masking in Vision: Critical Bands and Spread of Masking

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Spatial-Frequency Masking in Vision: Critical Bands and Spread of Masking*

CHARLES F. STROMEYER IIIt AND BELA JULESZ

Bell Laboratories, AiMrray Hill, New Jersey 07974

(Received 12 April 1972)

Vertical sinusoidal gratings were viewed in masking noise consisting of vertical stripes spread alongthe horizontal direction. Masking functions were obtained while varying the grating frequency relativeto various one-octave-wide bands of noise. These functions closely resemble curves derived from previous

experiments on adaptation to gratings. Masking was also measured as a function of the width of a bandof noise centered on the grating frequency. Masking increased as the band was widened up to approxi-

mately 41 octave; masking did not increase further when the band was widened beyond this range. The

results demonstrate that a grating is masked only by noise whose spatial frequencies are similar to the

grating frequency. The experiments provide further indication of the existence of channels in the visual

system that are selectively tuned to different spatial frequencies.

INDEX HEADINGS: Vision; Gratings.

For more than a century it has been known that theear analyzes irregular sound waves into simple spectralcomponents'; indeed, any good listener can perceiveindividual tones in a complex chord. Recently it hasbeen suggested that the visual system performs ananalogous process of spectral decomposition in thespatial domain.2 The idea that the visual system de-composes a visual scene into a set of sinusoidal gratingsoi specific spatial frequencies, orientations, phasepositions, and contrasts is contrary to our introspection:We do not typically see the grating components.Nevertheless, this idea is consistent with several studieswhich use simple gratings as stimuli.

The existence of visual channels, each selectivelysensitive to a limited range of spatial frequencies, wasfirst proposed by Campbell and Robson3 in an in-vestigation of the visibility thresholds of gratings ofdifferent wave forms (e.g., sine wave, square wave).Recently, Graham and Nachmias4 have shown that agrating consisting of two superimposed sinusoids offrequencies f and 3f is detected when either sinusoidreaches its own independent threshold. Similarly,Sachs et al.' have shown that the sinusoidal componentsof a complex grating (consisting of the sum of twosinusoids) are detected independently at threshold,provided that the components are separated by oneoctave. However, for gratings below 2.8 cycles/deg alarger separation is needed. This suggests that inde-pendent spatial-frequency channels may exist in man,and that the output of those channels are detectedindependently.

The existence of independent spatial-frequencychannels is also suggested by the aftereffects producedby either colored gratings 6 (McCollough effects) orluminance-modulated gratings. 2' 7' 8 Prolonged viewingof a high-contrast, luminance-modulated grating bothraises the threshold for detecting gratings of similarorientations and spatial frequencies2 and produces ashift of the apparent frequency of gratings of neigh-boring frequencies away from the frequency of theadapting grating.' 9 (Similar effects may be demon-strated in audition.'0 ) The threshold-elevation effect

falls to one-half of its peak value for test gratingsslightly more than 0.5 octave either side of the adaptingfrequency,2 and the apparent frequency shift is strongestfor test gratings 0.5-1 octave either side of the adaptingfrequency.8.9 However, both aftereffects influence testgratings extending from 2 octaves below to 1.5 octavesabove the adapting frequency.

Electrophysiological studies on single units in thevisual system of the cat" and monkey" reveal neuronswith antagonistic center and surround receptive fieldsthat are sensitive to the width of spots and bars. Thesemechanisms might extract information about spatialfrequency. Indeed, single units have been found in thecat'3' 4 and monkey' that respond to continuouslymoving gratings whose spatial frequencies lie within alimited range; the range is different for different cells.The tuning of these units, however is quite broad, andthe number of cycles over which the receptive fieldintegrates remains almost entirely unexplored. A studyon the evoked potential in man also suggests theexistence of channels selectively sensitive to spatialfrequency.'6

In the present experiments, spatial-frequency selec-tivity is studied by measuring the threshold for de-tecting vertical gratings presented in a masking noisethat consists of rapidly changing patterns of stripesfiltered so as to present selected bands of spatialfrequencies. The experiments are analogous to severaltechniques that have been used to study the criticalband in hearing-a concept that Fletcherl7",8 introducedto characterize the narrow band of frequencies withina broad band of noise that alone masks a tone in thecenter of the band.

Several studies have investigated the visibility ofgratings presented in masking noise. Campbell andKulikowskil studied orientation sensitivity by maskinga grating with one-dimensional narrow-band noise, butthey did not examine frequency sensitivity. Pollehnand Roehrig2' did examine frequency sensitivity; theyused two-dimensional (spot) noise to mask one-dimen-sional sinusoidal gratings. Two-dimensional noise,however, may not always provide a good mask for

1221

VOLU-ME 62, NUMBER 10 OCTOBER 1972

C. F. STROMEYER III AND B. JULESZ

(a) (b) (C)

(d)

(e) (f) (g)FIG. 1. Demonstration of frequency-specific masking. (d) shows a one-octave-wide band of masking noise. (a), (b), and (c) show

gratings whose spatial frequencies lie, respectively, 1.5 octave below the band, in the middle of the band, and 1.5 octave above theband [i.e., the spatial frequencies in (a) and (c) are, respectively, 4 and 4 times the frequencies in (b)]. (e), (f), and (g) show thegratings superimposed on the noise band of (d). The grating in the middle of the band is completely masked, whereas the gratingsfalling outside the band are visible through the noise.

one-dimensional patterns, because the visual systemcan readily integrate along one dimension. Perhaps thisintegrative capacity accounts for the poor masking theyobserved with low-frequency noise.

In the present experiments, various strategies wereused to investigate frequency-selective masking. Grat-ing thresholds were measured under three conditions:(i) The grating frequency was held constant and thefrequency of either high-pass or low-pass noise wasvaried relative to the grating; (ii) the grating frequencywas varied relative to various one-octave noise bands;(iii) the grating frequency was held constant and thewidth of a band of noise centered on the grating wasvaried. Masking was produced by a limited range offrequencies surrounding the test grating.

The reader can gain an idea of our technique byexamining Figs. 1 and 2. It must be emphasized thatthe figures can give only an impression of our technique,for in the actual experiments the noise was dynamicwith a 60-Hz frame rate, whereas the noise shown inthe figures is a still picture of one frame. In addition,

the reproduction process used to print the figures mayproduce considerable nonlinear distortion of the stimuli.

Figure 1 shows that a relatively narrow band ofnoise masks a grating whose frequency falls in themiddle of the band, but exerts little masking effect ongratings whose frequencies are 1.5 octaves either sideof the band. Figure 1 (d) shows a one-octave-wide bandof masking noise. Figures 1(a)-1(c) show gratingswhose spatial frequencies lie, respectively, 1.5 octavesbelow the band, in the middle of the band, and 1.5octaves above the band. Figures 1(e)-i(g) show thesegratings superimposed on the noise band of Fig. 1(d).The grating whose frequency is in the middle of theband [Fig. 1(f)] is completely masked, whereas thetwo gratings whose frequencies are outside the band[Figs. 1(e) and 1(g)] are still visible through the noise.A more dramatic demonstration may be produced bymaking transparencies of these stimuli and superim-posing the gratings and noise field by two projectors.The relative contrasts of the gratings and noise may bemanipulated by varying the relative intensities of the

1222 Vol. 62

October1972 CRITICAL BANDS IN SPATIAL-FREQUENCY MASKING

projectors. The demonstration is largely unaffected ifone of the overlapping images is jiggled.

Figure 2 shows that only noise within a limitedfrequency band surrounding the frequency of thegrating is effective in masking the grating. The gratingin Fig. 2(a) falls in the center of a band of noise -E 1octave wide (with grating contrast just comfortablyabove the threshold for most viewers). Figure 2(b)shows the same grating when the band of noise iswidened to ± 2 octaves. Widening the band increasesthe average noise contrast, but it does not appear toincrease the masking. The results are not substantiallyaffected by the absolute retinal spatial frequencies ofthe gratings and noise, as the reader can verify byvarying his viewing distance for each demonstration.

METHODS

A. Apparatus

The stimuli were displayed on a high-resolutionvideo monitor with electrostatic deflection (Hewlett-Packard 1300 A x-y Display). The monitor had a P4white phosphor, and a 60-Hz frame rate. The sweeplasted 8 ms and repeated once every 16 ms. The decaytime of the phosphor was sufficiently rapid so that eachframe was independent: The luminance fell to approxi-mately zero in 200 5s. The space-average luminancewas 5 mL at all times. All stimuli were varied in lumi-nance only in the horizontal direction. The spot wasdeflected vertically by a 3.5-MHz sine wave. A masklimited the visible part of the screen to an area 6.5 cmhigh and 17 cm wide. The raster was swept verticallybeyond this area in order to eliminate the bright edgeswhere the sinusoidal sweep reversed direction. Sincethe stimuli were one dimensional, the apparatus couldbe restricted to standard acoustical equipment with a20-kHz bandwidth. For most of the experiments, theviewing distance was 4 m, and hence the stimulus fieldwas 10 high and 2.50 wide. The field had a dark sur-round, and the room was dark.

Vertical gratings of sinusoidal waveform were gener-ated on the monitor by a sine-wave generator. Thegratings were stabilized on the screen by first lettingthe oscillator reach a constant temperature and thenadjusting the oscillator so that the desired number ofbars appeared within the stimulus field without driftingacross the field. The modulation voltage was passedthrough an amplifier whose characteristics were theinverse of the CRT grid characteristics, in order thatthe contrast would be a linear function of the modu-lation voltage. The contrast was measured with anilluminometer and found to be proportional to themodulation voltage at least up to 0.48 contrast. Thegrating contrast was controlled with a 1-dB-stepattenuator.

Noise consisting of vertical stripes could also bedisplayed on the monitor. The noise was produced by arandom-noise generator, which gave an approximately

(a)

( b)FIG. 2. Demonstration that only noise within a limited fre-

quency band surrounding the grating is effective in masking thegrating. The grating in (a) falls in the center of a band of noise±1 octave wide, and the contrast is set so that the grating is justcomfortably visible. (b) shows the same grating when the band iswidened to ±42 octaves. Widening the band increases the averagenoise contrast, but it does not appear to increase the masking.

flat spectrum up to 20 kHz. (20 kHz corresponds to aspatial frequency of 54 cycles/deg at the 4-m viewingdistance.) The probability distribution of the noiseluminance was gaussian. Each frame of the noise wasgenerated independently and displayed at a frame rateof 60 Hz (which is the standard field rate of broadcasttelevision with interlace). This rate is comfortablyabove flicker fusion and yet is slow enough to portraymasking noise as dynamic noise. At much higher framerates, the noise would appear as a homogeneous smear.Under 60 Hz, the masking could become more effective;however, the flicker of the grating and noise mayintroduce some undesirable effects. Before this noisewas displayed on the screen, it was passed through afilter (Spectrum Analog Filter type LH-42D) that felloff 42 dB/octave from the 3-dB-attenuation points.The filter had a bandwidth extending from zero to 200kHz. Broad bands of this noise contain gratings ofindefinitely many spatial frequencies, which are pre-sented at a rapid rate at different levels of contrast andin different phase positions. The noise gives the im-pression of many stripes of different widths, which moveabout rapidly. Narrow bands of the noise look muchlike a sinusoidal grating whose contrast and positionchange rapidly.

B. Definitions

Lo is the mean luminance of the grating, i.e.,

Lmax+Lmiin/2,

1223


-

tozw

U)

100

10

-F -- I I

-

I I I I I I . I I

0.05 0.1 0.50AVERAGE NOISE CONTRAST

FIG. 3. Contrast sensitivity of vertical gratings as a functionof the average noise contrast of uniform broad-band noise con-sisting of vertical stripes of spatial frequency up to approximately54 cycles/deg. * * grating frequency 1.77 cycles/deg,X- - -X 5.0 cycles/deg, o ao 10.0 cycles/deg. Verticalbars indicate +1 S.E. of the mean (n=3). The straight diagonallines represent a function of exponent - 1 for the idealized casewherein contrast sensitivity (reciprocal of grating contrast) varieslinearly with the average noise contrast. Upper panel: subjectRAP. Lower panel: subject CFS.

or the space-time-average luminance of thenoise.

Grating contrast is Lnac-Lmin/ 2 Lo.Contrast sensitivity is the reciprocal of the contrast

of a grating at the threshold of visibility.Average noise contrast is lL/LO, where L is the noise

luminance with a gaussian distribution, and UL is the

-I . .- .

. . . . . . . . . .

1224 Vol. 62

standard deviation of this distribution. To determinethe voltage level at which the average noise contraststayed within the linearity range of the CRT 95% ofthe time, we applied the following procedure. We firstmeasured the Vyms (root-mean-square voltage) of asinusoidal grating whose contrast was the highestobtainable without exceeding the linearity range. Afactor v2 times this Vrms is the peak voltage of thesinusoidal grating. The Vlrm (standard deviation)2 ' ofthe noise was set to one-half of this peak voltage, whichyielded an average noise contrast of 0.24. This assuredthat the noise stayed within the linearity range 95%of the time. Other values of average noise contrast werethen easily determined, since the average noise contrastis a linear function of the noise Vrms.

Filter cutoff: All cutoff values of the noise filters arespecified at the 3-dB-attenuation points.

Spatial frequency is the number of cycles of arepetitive pattern per degree of visual angle.

Relative threshold elevation: The elevation in thegrating threshold produced by the masking noise isdefined as the ratio of contrast sensitivity for a gratingviewed with and without masking noise, minus 1.0. Noadaptation would be represented by a ratio of 1.0.Thus, to express adaptation as increments above zero,1.0 is subtracted from the ratio. This definition is alsoused by Blakemore and Campbell.2

C. General Procedure

Vertical gratings were displayed on the monitoreither with or without masking noise consisting ofvertical stripes. The noise was either uniform broad-band noise or noise that was filtered in various ways, asdescribed in the results. The subject adjusted thegrating to threshold with a 1-dB-step attenuator. Thesubject attempted to bracket the adjustment, i.e., bysetting the contrast of the grating too high and too lowbefore reaching the final adjustment. The grating wasdisplayed continuously; however, the subject had atwo-position switch that could be used to turn thegrating either off or on. In each session, thresholdsettings were made with and without the maskingnoise to determine the relative threshold elevationproduced by the noise. Each data point, for eachsubject, was based on three settings. The screen wasviewed binocularly at a distance of 4 m. For someexperiments, the viewing distance was shortened.

D. Subjects

Three subjects participated in various phases ofthese experiments. Subjects CFS and RAP were awareof the general goals of the experiments, whereas MHWwas not informed concerning them. All subjects hadnatural or corrected acuity of 20-20 or better, and theywere highly practiced in judging gratings in noisebefore the data-taking experiments were begun.

l


RESULTS

A. Masking with Uniform Broad-Band Noise

In the present experiment, gratings were maskedwith uniform broad-band noise at different levels ofaverage noise contrast. The experiment provides abase line to which we can compare masking with filterednoise. Gratings of 1.77, 5, and 10 cycles/deg were setto threshold in the presence of uniform broad-bandnoise consisting of vertical stripes whose spatial fre-quencies extended up to approximately 54 cycles/deg.Figure 3 shows the threshold contrast sensitivity foreach grating as a function of the average noise contrast.The straight diagonal lines represent a function ofexponent - 1 for the idealized case wherein contrastsensitivity (i.e., the reciprocal of the grating contrast)varies linearly with the average noise contrast. Thedata are approximately parallel to these diagonal lines.

The ear demonstrates comparable behavior in itsresponse to tones masked with auditory noise.'7 Toobtain uniform masking throughout the spectrum, thespectrum level of the noise must be adjusted to approxi-mately the shape of the audiogram measured withoutmasking noise. When the intensity of this entire noisespectrum is then increased uniformly, masking increasesby an amount proportional to the increase of the noiselevel.

B. Masking with Low-Pass or High-Pass Noise

In this experiment, gratings of a constant spatialfrequency were masked with either low-pass noise(noise falling below the grating frequency) or with

,10 lilili I ,,I, I i1111I

II 7'U IN

0 E

0.1 fM.0

1.0 10 1.0 10

UPPER CUT-OFF, fMAX. OF LOW-PASS NOISE (cycles/deg)

Fro. 4. Relative threshold elevation of vertical gratings as afunction of the upper cutoff, fmax, of low-pass noise consisting ofvertical stripes (see inset). The relative threshold elevation isdefined as the ratio of the contrast sensitivity of a grating viewedwith and without noise minus 1. A -A grating frequency2.5 cycles/deg, U U 5.0 cycles/deg, * * 10.0cycles/deg. Vertical bars indicate 41 S.E. of the mean (n=3).The average noise contrast was maintained at 0.15 when fmarwas varied. Left panel: subject RAP. Right panel: subject CFS.

II 1 , ,I

VE

'ZLL 4 FREC

0.1 1

I

1.0 10 1.0 10LOWER CUT-OFF, fU,,OF HIGH-PASS NOISE %vIes/Ceg)

FIo. 5. Relative threshold elevation of vertical gratings as afunction of the lower cutoff, m of high-pass noise consisting ofvertical stripes (see inset). A A grating frequency 2.5cycles/deg, * U 5 cycles/deg. Vertical bars indicate 41S.E. of the mean (n=3). The average noise contrast was main-tained at 0.15 when fmin was varied. Left panel: subject RAP.Right panel: subject CFS.

high-pass noise (noise falling above the grating fre-quency). The cutoff frequency of the noise was variedrelative to the grating. The object of the experimentwas to see how masking decreases as the noise cutofffrequency is moved away from the grating frequency.The grating was set to threshold with the noise cutofffrequency at different positions, starting at the gratingfrequency and progressing further away in 0.5-octavesteps. The low-pass noise and high-pass noise wereobtained by varying, respectively, the upper and lowercutoff frequencies of the uniform-broad-band noise (upto approximately 54 cycles/deg). The average noisecontrast was maintained at 0.15 at all times; at thislevel the noise stayed within the linearity range 99.7%of the time. The experiment is analogous to an auditoryexperiment by Webster et a1.2- which showed that themasked threshold for a tone dropped sharply as thetone was moved away from the edge of a band of eitherhigh-pass or low-pass noise.

Figure 4 shows the relative threshold elevation ofgratings of 2.5, 5, and 10 cycles/deg as a function ofthe frequency of the upper cutoff, fmaxi of low-passnoise. (The relative threshold elevation was defined asthe ratio of the contrast sensitivity for a grating viewedwith and without noise, minus 1.0.) Figure 5 shows therelative threshold elevation of gratings of 2.5 and 5cycles/deg as a function of the frequency of the lowercutoff, fin, of high-pass noise. (A 10-cycles/deg gratingwas not used in this latter experiment, because the eyeis relatively insensitive to high-frequency noise ofaverage noise contrast 0.15.)

The curves in each figure are approximately parallel,which shows that the masking decreases in a consistentmanner as the noise cutoff is moved away from thegrating frequency in 0.5-octave steps. Masking typically

1225


10

1.0

0.1

10

1.0

0.1-J I- I II1.0 10

SPATIAL FREQUENCY (cycles/deg)

FIG. 6. Relative threshold elevation of vertical gratings pro-duced by various 1-octave-wide bands of noise consisting ofvertical stripes. * - noise of 2.5-5 cycles/deg, averagenoise contrast 0.042; o--- - o noise of 5-10 cycles/deg, contrast0.059; X )X noise of 10-20 cycles/deg, contrast 0.074. Thevertical bars indicate 41 SLE. of the mean (n=3). Upper panel:subject MHW. Lower panel: subject CFS.

falls to one-half of its maximum value when the noisecutoff is moved 0.5-0.75 octaves away from the gratingfrequency.

An objection can be raised against this method ofvarying the spectral composition of the noise. The eyeis most sensitive to gratings in the range of 2.5 to 10cycles/deg.23 Thus, removing components of the noisein this range may reduce the masking effectiveness ofthe noise. This may in part account for the declineobserved in the relative threshold elevation curves.For this reason, in the next experiment the noise bandwas maintained constant, and the frequency of the testgrating was varied relative to the noise.

C. Masking with Band-Pass Noise

1. One-Octave-Wide Noise Bands

Various one-octave-wide bands of noise were usedfor masking. The grating frequency was varied relativeto the band. Each band was simply selected from theuniform-broad-band noise, which was maintained atan average noise contrast of 0.15. Since the energyspectrum of the broad-band noise was approximatelyflat, each higher-octave band has approximately twicethe energy or v2 times the average noise contrast ofthe next-lower-octave band (since energy is proportionalto the square of voltage, and average noise contrast isa linear function of voltage). The noise bands and theirmeasured average noise contrasts were 2.5-5 cycles/deg,0.042; 5-10 cycles/deg, 0.059; and 10-20 cycles/deg,0.074. Gratings spaced at 0.5-octave intervals were setto threshold in the presence of each of these noisebands. The technique in part resembles Greenwood's2 4

experiments on the auditory critical band, in whichcomplete masked audiograms were obtained for noisebands of a given width.

Figure 6 shows the relative threshold elevationvalues. The same data are shown normalized for spatialfrequency in Fig. 7-the points for gratings extendingin frequency above and below the noise bands have beenshifted along the abscissa, so that all points at the lowercutoffs of the noise bands fall at 0 octave on the left-hand half of the figure, and all points at the uppercutoffs fall at 0 octave on the right half. The octavescale thus shows how far away the gratings are fromthe noise bands (measured from the noise-band cutoffs).

The continuous curves in Fig. 7 represent the function[Fef2-e-(2) 2]', taken from Blakemore and Campbell.2They found that this simple but arbitrary function pro-vided a good fit to data describing the relative thresholdelevation (i.e., the ratio of contrast sensitivity of agrating before and after adaptation, minus 1.0) pro-duced by adapting gratings having spatial frequenciesbetween 3 and 14 cycles/deg. In their study, the curvedescribes the elevation of threshold contrast of testgratings whose spatial frequencies diverge from theadapting frequency which is designated 0 octaves,whereas, in the peseiLt study, the curve describes theelevation of threshold contrast of gratings whose spatialfrequencies diverge from the noise-band cutoffs, alsodesignated 0 octaves. The curves in Fig. 7 were fitted

1226 Vol. 62


by eye so that the peaks pass through the data pointsat 0 octaves. Because our effects were stronger thanBlakemore and Campbell's, their curves have beenscaled upward for easy comparison. The function pro-vides a reasonably good fit to the data. The divergenceof the data from the curves for gratings far removedfrom the noise bands may in part be due to the limitedrate of decrease with frequency of our noise filters.(The average noise contrast in the present experiment

10

z0

LUJ

-_J

0

LUJa:C

LUJ

Ht

2 1 0 0 1 2

SPATIAL FREQUENCY (OCTAVES)

FIG. 7. Relative threshold elevation data of Fig. 6 normalizedfor spatial frequency. Data points for gratings extending inspatial frequency above and below the noise bands have beenshifted along the abscissa, so that all points at the lower cutoffsof the noise bands fall at 0 octave on the left half of the figure, andall points at the upper cutoffs fall at 0 octave on the right half.The octave scale thus shows how far away the gratings are fromthe noise bands (measured from the noise-band cutoffs). Thecontinuous curve represents the function [ef 2 -e12f)l]2, whichwas fitted by eye so that the peaks pass through the data pointsat 0 octaves. The curve is from Blakemore and Campbell's (Ref.2) study on the effects of adapting to gratings. Upper panel:subject MHW. Lower panel: subject CFS.

z0

-JWw

20-J

I-W

-J

LLI

0.1 1.0SPATIAL FREQUENCY (cycles/deg)

10

FIG. 8. Relative threshold elevation of vertical gratings pro-duced by I-octave-wide band of low-frequency noise consistingof vertical stripes. A - - - noise of 0.625-1.25 cycles/deg,average noise contrast 0.095, stimulus field 200 wide from 50-cmviewing distance. A A noise of 1.25-2.5 cycles/deg, averagenoise contrast 0.059, stimulus field 100 wide from 100-cm viewingdistance. Vertical bars indicate 41 S.E. of the mean (n=3).Upper panel: subject MHW. Lower panel: subject CFS.

was quite low. If the noise level were increased, themasking curve would most likely have to be scaledupward still more, because the first experiment withbroad-band noise showed that the threshold contrastof the test grating varies linearly with average noisecontrast.)

To investigate the masking behavior of very-low-frequency gratings, we repeated the experiment with a

1227


2C

I--JL'

nuJ-J0XV0wa:

I--

-_J

rLJ

2 1 0 0 1 2SPATIAL FREQUENCY (OCTAVES)

FIG. 9. Relative threshold elevation data of Fig. 8 normalizedfor spatial frequency in the same manner as Fig. 7. Upper panel:subject MHW. Lower panel: subject CFS.

much larger stimulus field. The viewing distance wasreduced to either 50 cm, so that the field was 8° highby 200 wide, or 100 cm so that the field was 4° by 10°.The masking noise consisted of one-octave-wide bands-0.625-1.25 cycles/deg for the 50-cm viewing distanceand 1.25-2.5 cycles/deg for the 100-cm distance. Theaverage noise contrast of each band was 0.059.

Figure 8 shows the relative threshold elevation ofgratings, spaced at 0.5-octave intervals, which wereviewed in each of these noise bands. In Fig. 9 the dataare shown normalized for spatial frequency in the samemanner as in Fig. 7. Again, the curves are the functionthat Blakemore and Campbell2 used to describe the

effects of adapting to gratings in the middle range ofspatial frequencies, between 3 and 14 cycles/deg.Clearly the present masking effects are frequencyselective, even for gratings as low as 0.15 cycles/deg.However, the spread of masking for the lowest-fre-quency gratings is somewhat broader than the data forthe higher frequencies shown in Fig. 7. Also note thatthe spread for the 0.625--1.25-cycles/deg noise band isslightly broader than the data for the 1.25-2.5-cycles/deg band.

2. Variable-Width Bands

In this experiment, masking is measured as a functionof the width of a band of noise centered on the gratingfrequency. The experiment is analogous to a techniqueused by Fletcher'8 to measure the critical band inhearing. He observed that a tone was most effectivelymasked by noise falling in a limited band of frequenciessurrounding the tone; widening the band beyond thiscritical bandwidth did not produce greater masking.25

In the present experiment, the bands of maskingnoise were selected from the uniform-broad-band noise,which was maintained at an average noise contrast of0.15. The energy in each band was proportional to thebandwidth measured on a linear frequency scale, andthus the average noise contrast was proportional to thesquare root of the width. The grating frequency wasplaced at the geometrical center of the noise band, andthe width of the band was varied symmetrically in0.25-octave steps about the center, from a width of±0.5 to ±2 octaves. The spatial frequency of thegrating and noise was changed by varying the viewingdistance. For a grating of 10 cycles/deg, the viewingdistance was 400 cm and the stimulus field was 10 highby 2.5° wide. For gratings of lower frequency (5, 2.5,and 1.25 cycles/deg), the viewing distance was pro-portionally shorter and the stimulus field was propor-tionally larger. This method of varying spatial fre-quency assured that the average noise contrast fornoise of a given octave bandwidth was constant for allspatial frequencies of the test grating. The measuredvalues of the average noise contrast for different band-widths are specified in Table I.

If masking were insensitive to the noise frequency,then we might expect the grating threshold to increase

TABLE I. Measured values of average noise contrast.

Noise bandwidth(octaves, centered ongrating frequency) Average noise contrast

*0.50 0.067*0.75 0.088*1.00 0.099*1.25 0.11141.50 0.12041.75 0.128*2.00 0.134

1228 Vaol. 62

October 1972 CRITICAL BANDS IN SPATIAL- FEUNYMSIG12

monotonically as the noise band is widened, sincewidening the band increases the average noise contrast.Figure 10 shows that masking increases as the noiseband is widened from ±+0.75 to -4-1.5 octaves, where-upon masking reaches a peak. On the average, the peakis reached at approximately ±1 octave (mean of allpeaks). Further widening of the band at times slightlyreduces masking below the peak level. (This effect wasalso noted in measurements made on subject RAP.)

The experiment thus shows that masking does notincrease when the noise band is widened beyond acritical width of approximately =E 1 octave (althoughwidening the band does increase the average noisecontrast). This result cannot be accounted for by simplyassuming that masking reaches an asymptote at a givenlevel of average noise contrast, for the experiment withuniform-broad-band noise showed that masking in-creased linearly with average noise contrast (measuredfor average noise contrast as high as 0.34).

When the band of masking noise was widened beyondthe critical width of approximately -± 1 octave, maskingof ten decreased slightly from the peak level. Severalfactors might account for this decrement. The subjectmay adopt a different criterion for judging gratings innarrow-band vs broad-band noise. When the gratingwas masked with relatively narrow-band noise from±+0.5 to 4-1 octaves, the noise and grating appearedquite similar, and thus the threshold setting was, inpart, a determination of the difference limen of contrast.When the noise band was widened beyond approxi-mately ±L 1 octaves, the grating appeared quite differentfrom the noise. Perhaps the threshold was raised slightlydue to the difficulty of discriminating the grating innarrow-band noise.

The masking, decrement that is observed when thenoise band is widened beyond the critical width mightalso be caused by disinhibition. Components of thenoise far from the grating frequency might exert aconsiderable masking effect on noise components thatare nearer the grating frequency and which do maskthe grating, while exerting little masking effect on thegrating itself. Thus, widening the noise band beyondthe critical width might reduce the masking effective-ness of noise within the critical band. Disinhibitionhas been demonstrated in studies on backward mask-ing"6 and simultaneous brightness contrast2 " and inelectrophysiological recordings from the Limulus eye-"'

DISCUSSION

In these experiments, several strategies were usedto investigate the masking of vertical sinusoidal gratingsby filtered noise consisting of vertical stripes. In oneexperiment, the grating frequency was held constantand the cutoff frequency of either low-pass or high-passnoise was varied relative to the grating frequency,while the average noise contrast was held constant.Masking typically decreased to half when the noise-

I I . . . . . .I . . . I

G11NOIS-

I I I I I I I I I I I I It O., ±I.O ±l.5±2.0O±O.+,.O± ,.S±.

WIDTH OF NOISE RND 8 IOCTAVE1SI

FIG. 10. Relative threshold elevation of vertical gratings as afunction of the bandwidth of noise (consisting of vertical stripes)which is centered on the grating frequency (see inset). X -- Xgrating frequency 1.25 cycles/deg, A -- -- A 2.5 cycles/deg,* -U 5 cycles/deg, * --- 10 cycles/deg. The noisecomprising the variable width bands was selected from theuniform broad-band noise, which was maintained at an averagenoise contrast of 0.15. The average noise contrast of the variable-width bands varied in proportion to the square root of their widths,measured on a linear frequency scale. Since spatial frequency wasvaried only by varying the viewing distance in this experiment,the average noise contrast of a given octave bandwidth wasconstant for all spatial frequencies of the test gratings. The mea-sured values of average noise contrast were :1:0.5 octave, 0.067;-1-0.75 octave, 0.088; 4-1 octave, 0.099; dJ=.25 octave, 0.111;4:1.5 octave, 0.120; 4d1.75 octave, 0.128; 41:2 octave, 0.134. Thevertical bars indicate 4-I S.E. of the mean (n=3). Left panel:subject MHW. Right panel: subject CFS.

cutoff frequency was changed from the grating fre-quency 0.5 to 0.75 octave away. In a second experiment,the grating frequency was varied relative to variousone-octave noise bands. Masking again decreased tohalf when the grating frequency was changed from thefrequency limit of the noise band to a frequency 0.5 to0.75 octave from the band. These masking data agreereasonably well with Blakemore and Campbell's2 dataon the effects of adapting to gratings. In a third experi-ment, masking was measured as a function of the widthof a band of noise centered on the grating frequency.Masking increased as the band was widened, up to acritical width of approximately 4h 1 octave, and did notincrease further when the band was widened beyondthis range.

The close agreement between our results and Blake-more and Campbell's 2 data on the effects of adaptingto gratings is surprising in that we used dynamicmasking noise and they used periodic adapting gratings.Blakemore et al.9 emphasize the unnatural nature of a

FREQUENCY MASKING 1229

I . I . I I I 1 I I I I I I

W

1.

5

C. F. STROMEYER 111 AND B. JULESZ

periodic grating, for they conjecture that a periodicgrating acts like a "stabilized cortical image": Whereverthe gaze is directed on the pattern, the same class ofcortical neurons is stimulated. It is thus not surprisingthat a grating produces rather specific aftereffects. Thedynamic masking noise may appear very different froma periodic grating. Broad bands of this noise give theimpression of many stripes of different widths, whichmove about rapidly.

The present masking technique has several advan-tages over other methods used to investigate frequencyselectivity of the visual system. The detection studies3 -5

employ only low-contrast threshold stimuli, whereasthe masking technique permits the use of both high-and low-contrast stimuli to determine whether thesystem remains linear at different contrast levels. Inaddition, the masking technique has several advantagesover adaptation studies2' 7-9 that employ high-contrast,luminance-modulated gratings: The threshold elevationmay be considerably higher; dynamic masking noiselargely eliminates the effects of afterimages, whichmight inadvertently occur in adapting to periodicgratings29 ; and the threshold settings for gratings viewedin noise are relatively stable, whereas the aftereffectsdue to adaptation change rapidly and it is thereforedifficult to track their fading time course.

A. Critical Bands vs Spread of Masking

The last experiment showed that only noise withina band approximately ± 1 octave wide either side ofthe grating was effective in masking a grating whosespatial frequency is in the center of the band, formasking did not increase when the band was madewider. However, noise at frequencies beyond thiscritical bandwidth might produce weak masking effectsif noise within the critical band were not also present.Indeed, in the experiment in which the grating fre-quency was varied relative to various one-octave noisebands, weak masking effects were observed when thedistance between the grating and noise cutoff fre-quencies was as great as two octaves. These measure-ments of spread of masking should be distinguishedfrom measurements of critical bandwidth, because thetwo types of measurement provide different estimatesof the distance over which masking occurs.

Several factors might account for the spread ofmasking (beyond the critical bandwidth) in the presentexperiments: harmonic distortions in the stimuli,harmonic distortions in the response to the stimuli, thelimited rate of frequency decrease of the filters, and thesmall size of the stimulus field. First, consider non-linearities in the stimuli. When the noise exceeds thelinearity range, harmonic components are introducedin the noise, which might contribute to spread ofmasking. However, in all of the experiments withfiltered noise, the average noise contrast never exceeded0.15; at this level the noise exceeded the linearity range

only 0.3% of the time. The gratings themselves werekept within the linearity range at all times.

Next, consider harmonic distortion in the visualresponse to the stimuli. If the spatial-frequency re-sponse of the visual system were both nonlinear andasymmetrical (with respect to luminance), then theresponse might produce odd and even harmonics notpresent in the original stimulus, and these harmonicsmight cause spread of masking. Considerable evidencesuggests that a nonlinear transformation may occur asearly as the retinal receptor level.30 However, no effectsof harmonic distortion were observed in various experi-ments on the detection and discrimination of gratings3

and in adaptation experiments. 2 9 A single function, forexample, was found to describe the aftereffects pro-duced by adapting gratings covering a large range ofcontrast. 2'9 Kelly,3' however, has shown an effect ofapparent spatial-frequency doubling with sine-wavegratings in counterphase flicker, which may be due toa nonlinear brightness response.

The limited decrease with spatial frequency of thenoise filters (42 dB/octave) may have contributed tothe spread of masking. Let us assume, for example,that only noise falling within the critical bandwidth(± 1 octave) contributes to masking. Spread of maskingwas observed when the grating frequency was twooctaves below the lower cutoff of a one-octave-widenoise band. Under these conditions, the noise at theedge of the critical bandwidth (1 octave from thegrating frequency) is attenuated 38 dB below the noiseat the cutoff. In this case, at least, very little noisewould fall within the critical band. However, as thedifference between the grating frequency and the noiseband is reduced further, more and more noise fallswithin the critical band.

The limited size of the stimulus field might also causespread of masking. A small field or aperture producesspreading of the spatial-frequency content of thestimuli. The effect becomes especially significant forlow-frequency stimuli. For example, consider a gratingat 2.5 cycles/deg. When this grating is convoluted withan aperture 2.50 wide (the field size used in most of thepresent experiments), many side bands of frequenciesare produced on either side of 2.5 cycles/deg." This side-band contrast of the frequency component at 1.5 octavebelow the grating frequency of 2.5 cycles/deg is attenu-ated only 23 dB with respect to the contrast at 2.5cycles/deg. The aperture would have to be increasedhorizontally almost 10 times for the aperture to behavelike a filter that is comparable in steepness with theelectronic noise filters. The aperture factor becomesstill more significant for lower frequencies. The smallaperture may thus produce some spread of masking byspreading the spatial-frequency content of the gratingsand noise; however, this effect would be hard to evaluatequantitatively. The effect of a small aperture can beeliminated by using a larger stimulus field, but this

1230 Vol. 62

October1972 CRITICAL BANDS IN SPATIAL-FREQUENCY MASKING 1231

introduces additional problems due to well-knownvariations of visual functions that occur at differentretinal eccentricities.

Measurements of spread of masking thus may besensitive to the limited spatial-frequency rate of attenu-ation of the electronic filters and especially sensitive tothe small aperture effect. Critical-band experiments areprobably less sensitive to these limiting factors; for thisreason, they may be preferable for estimating the widthof spatial-frequency-selective masking functions.

B. Critical Band vs Difference Limen for Frequency

Both our masking results and Blakemore andCampbell's adaptation results show that the frequency-selective process in vision is broadly tuned, by com-parison with the auditory critical band, which isapproximately 0.25 octave wide.33 Nevertheless, thecritical bands in vision and audition are of comparablewidth when each is expressed in units that reflect thedifferential sensitivity of each sense modality, i.e., thedifference limen for frequency. Zwicker et al.33 showedthat there are approximately 30 frequency-differencelimens in each critical band in hearing. (The differencelimen was determined by measuring the detectablerange of frequency modulation when the modulationrate was about 4/s.) Campbell et al.3 4 measured theability to discriminate the spatial frequency of gratingsand found that for a large range of frequencies thedifference limen was approximately 4-6%. (The grat-ings were presented successively with more than 2 sbetween presentations.) If we assume that the criticalband in vision is Lt 1 octave (either side of the centerfrequency), then there are approximately 25-35 dif-ference limens in each critical band. Thus each criticalband, both in audition and vision, contains a similarnumber of difference limens.

C. Masking at Low Spatial Frequencies

Masking was found to be frequency specific forgratings of low spatial frequencies. For example, thecritical bandwidth of masking noise for a grating of1.25 cycles/deg was similar to the critical bandwidthfor gratings of higher spatial frequencies. It was alsoshown that a single curve approximately fitted maskingdata for various one-octave-wide bands of maskingnoise-bands as low as 0.625-1.25 cycles/deg and1.25-2.5 cycles/deg. A large stimulus field was used inthese experiments.

These results are interesting in light of failures toobtain adaptation effects specific to low-frequencygratings. Blakemore and Campbell2 found that low-frequency gratings produced a threshold-elevationcurve that peaked at 3 cycles/deg. And similarly,Blakemore et al.9 found that low-frequency gratingsproduced an apparent frequency shift away from 3.5cycles/deg. Reducing the adaptation frequency reduced

the strength of both aftereffects, but did not changetheir spatial frequency. Both studies employed a smallstimulus field, and the authors suggest that, in fovealvision, there are no adaptable channels with peaksensitivity less than 3 cycles/deg. However, a smallfield produces considerable side bands, so as to distortthe stimulus spectrum considerably.

Perhaps aftereffects specific to low spatial frequenciescan be produced with gratings of large field size.Channels sensitive to low frequencies may predominatein the periphery of the retina. Indeed, the peak of thecontrast-sensitivity curve3 and the peak of a curvethat describes sensitivity to suprathreshold contrast3

both shift to lower frequencies in the periphery.Responses specific to low-frequency gratings have beenshown in studies on frequency discrimination,3 4 thedetection of complex gratings,5 and aftereffects pro-duced by large-field square-wave gratings.7

CONCLUSION

Our results show that a critical band exists in spatialvision. The results provide further indications of theexistence of channels in the visual system that areselectively tuned to different ranges of spatialfrequencies.

ACKNOWLEDGMENT

We gratefully acknowledge the assistance of R. A.Payne, who both prepared the electronic equipmentand served as an observer.

REFERENCES

* Some of this work was presented at the annual meeting ofthe Psychonomic Society, November 1970; at the 1971 springmeeting of the Association for Research in Vision and Ophthal-mology. See also B. Julesz, "Critical Bands inVision andAudition,"in Proceedings of the 7tht International Congress on Acoustics(Akademiai Kiado, Budapest, 1971), pp. 445-448, and B. Julesz,Foundations of Cyclopean Perception (University of ChicagoPress, Chicago, 1971).

t Present address: Department of Psychology, Stanford Uni-versity, Stanford, Calif. 94305.

' G. S. Ohm, Ann. Phys. Chem. 135, 497 (1843).2 C. Blakemore and F. W. Campbell, J. Physiol. (London) 203,

237 (1969).3 F. W. Campbell and J. G. Robson, J. Physiol. (London) 197,

551 (1968); see also J. G. Robson and F. W. Campbell, in Pro-ceedings of the Symposium on the Physiological Basis of FormDiscrimination (Laboratory of Psychology, Brown University,Providence, R. I., 1964); F. W. Campbell and J. G. Robson, J.Opt. Soc. Am. 54, 581 (1964).

4 N. Graham and J. Nachmias, Vision Res. 11, 251 (1971).M. B. Sachs, J. Nachmias, and J. G. Robson, J. Opt. Soc. Am.

61, 1176 (1971).6 C. S. Harris, Psychon. Sci. 21, 350 (1970); C. S. Harris, J.

Opt. Soc. Am. 61, 689A (1971); C. F. Stromeyer III, Vision Res.12, 717 (1972).

7 A. Pantle and R. Sekuler, Science 162, 1146 (1968).8 C. Blakemore and P. Sutton, Science 166, 245 (1969).9 C. Blakemore, J. Nachmias, and P. Sutton, J. Physiol.

(London) 210, 727 (1970).l0 von B6k6sy has shown that listening for 2 min to an 800-Hz

tone at a sound pressure of 10 dynes/cm 2 both reduces the loud-ness of subsequently heard tones near 800 Hz and produces apitch shift, so that tones higher than 800 Hz seem still higher and

1231


lower tones seem still lower. [G. von Bek6sy, Physik Z. 30, 115(1929); reprinted in G. von Bekesy, Experizments in Hearing,edited by E. G. Wever (McGraw-Hill, New York, 1960), pp.354-368.]

11 S. W. Kuffler, J. Neurophysiol. 16, 37 (1953).12 D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 195, 215

(1968).23 C. Enroth-Cugell and J. G. Robson, J. Physiol. (London)

187, 517 (1966).14 F. W. Campbell, G. F. Cooper, and C. Enroth-Cugell, J.

Physiol. (London) 203, 223 (1969).16 F. W. Campbell, G. F. Cooper, J. G. Robson, and M. B.

Sachs, J. Physiol. (London) 204, 120-121P (1969).16 F. W. Campbell and L. Maffei, J. Physiol. (London) 207,

635 (1970).17 H. Fletcher and W. A. Munson, J. Acoust. Soc. Am. 9, 1

(1937).18 H. Fletcher, Rev. Mod. Phys. 12, 47 (1940).19 F. W. Campbell and J. J. Kulikowski, J. Physiol. (London)

187, 437 (1966).20 H. Pollehn and H. Roehrig, J. Opt. Soc. Am. 60, 842 (1970).21 W. B. Davenport, Jr. and W. L. Root, An Introduction to the

Theory of Randomi Signals and Noise (McGraw-Hill, New York,1958), p. 49.

22J. C. Webster, P. H. Miller, P. 0. Thompson, and E. W.Davenport, J. Acoust. Soc. Am. 24, 147 (1952).

23 F. W. Campbell and D. G. Green, J. Physiol. (London) 181,576 (1965).

24 D. D. Greenwood, J. Acoust. Soc. Am. 33, 484 (1961).21 Fletcher's original measurements using this method were

quite variable. However, Scharf, in reviewing recent studies onthe critical band in audition, concludes that, "Despite theapparent confusion of intensity discrimination and masking,masking by narrow-band noise can provide adequate estimates ofcritical bandwidth, as evidenced by the overall agreement ofGreenwood's, Hamilton's, and van der Brink's measures withall the other measures of the critical band." Pp. 167-168 in B.

Scharf, in Foundations of Modern Auditory Theory, Vol. 1, editedby J. V. Tobias (Academic, New York, 1970), pp. 157-202.

26 D. N. Robinson, Science 154, 157 (1966).27 M. Alpern and H. David, J. Gen. Physiol. 43, 109 (1959).28 H. K. Hartline and F. Ratliff, J. Gen. Physiol. 40, 357 (1957).29 C. S. Harris and A. R. Gibson, Science 162, 1506 (1968).30 L. E. Lipetz, Vision Res. 9, 1205 (1969)31 D. H. Kelly, J. Opt. Soc. Am. 56, 1628 (1966).32 If a sinusoidal grating Lo[1+m cos(27rfox+0)] does not

extend to infinity in the x direction, but is truncated by anaperture of width A, such that

f (x) = [mn cos (27rfox+4)] rect (x/A),

when the constant term is neglected, where

rect (x) = 1 for=0 for

I xX >xI2,

then F(f), the Fourier transform of f (x), will be the convolutionof the Fourier transform of the grating and aperture functions,yielding

F(f) mAfeio sin7rA (- fo)+e io sinirA (f+fo)i2 7rA (f-o) 7rA (f+fo)

If A =N/fo, where N is the number of cycles of the grating thatfell in aperture A, then at f= fo/3 (i.e., 1.5 octave below fo) for4=0, fo=2.5 cycles/deg, and A =2.5 deg; N=6.25 and

F (f)/F (fo) =-23 dB.For other references, see D. H. Kelly, J. Opt. Soc. Am. 60, 98(1970).

33 E. Zwicker, G. Flottorp, and S. S. Stevens, J. Acoust. Soc.Am. 29, 548 (1957).

34 F. W. Campbell, J. Nachmias, and J. Jukes, J. Opt. Soc. Am.60, 555 (1970).

35 J. M. Daitch and D. G. Green, Vision Res. 9, 947 (1969).38 0. Bryngdahl, Vision Res. 6, 553 (1966).

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Spatial-Frequency Masking in Vision: Critical Bands and Spread of Masking