contrast dependence of the oscillatory motion threshold across the visual field

Vol. 9, No. 10/October 1992/J. Opt. Soc. Am. A 1663

Contrast dependence of the oscillatory motion thresholdacross the visual field

Wolfgang Wesemann

Hdhere Fachschule fur Augenoptik K6in, Bayenthalguertel 6-8, 5000 Cologne 51, Germany

Anthony M. Norcia

Smith-Kettlewell Eye Research Institute, 2232 Webster Street, San Francisco, California 94115

Received August 5, 1991; revised manuscript received May 29, 1992; accepted June 3, 1992

Observer sensitivity to oscillatory step displacements of sine-wave gratings was investigated at various loci inthe visual field (0-30°) as a function of contrast. Detection thresholds at 10 Hz and high grating contrastswere -11-15 arcsec in the fovea and 37-47 arcsec at 30° eccentricity. At any given contrast, threshold displace-ment increases linearly with eccentricity. The data provide evidence against an interpretation based on corti-cal magnification, because the slope and the scale-free x intercept of the eccentricity function vary stronglywith contrast. While foveal thresholds for high-contrast gratings are in the range of the hyperacuities, theoscillatory motion threshold falls off an order of magnitude more slowly than the traditional hyperacuities.Rather than conceiving of the oscillatory motion threshold as a spatial acuity limited by cortical magnification,we suggest an alternative approach that is based on a form of contrast discrimination. Oscillatory motion canbe decomposed into the sum of a modulating counterphase grating and a static masking grating, both of whichare in spatial quadrature (i.e., 90° out of phase). At low grating contrast, oscillatory motion can be detectedwhen the counterphase component exceeds a constant contrast value. Above a critical contrast value of thestatic component Ccrit, threshold rises as a power function of contrast with a slope near 1.0. The critical con-trast value CBCrit increases linearly with eccentricity, indicating that oscillating gratings observed with theperipheral visual field are less easily masked compared with foveally fixated gratings.

1. INTRODUCTION

Foveal threshold values for the detection of abrupt dis-placements or the detection of oscillatory motion can be assmall as 10-14 arcsec.1-3 These values are smaller thanthe intercone spacing on the retina and are comparable topositional hyperacuity thresholds and thresholds for rela-tive motion. 4

Wright and Johnston2 studied the eccentricity behaviorof oscillatory motion detection and found that thresholddisplacement fell off at a rate similar to that for gratingacuity. Wright and Johnston concluded that oscillatorymotion sensitivity scaled according to the cortical magni-fication function proposed by Rovamo and Virsu.5 Virsuet al.6 used the Wright-Johnston data as further evidencefor a single cortical magnification factor for virtually allpsychophysical tasks.

The Wright-Johnston eccentricity function differs fromthat observed by other groups who studied both relativeand unreferenced motion. McKee and Nakayama4 andLevi et al.7 ', have shown that referenced motion acuity,i.e., detection of motion in the presence of a static target,declines more rapidly toward the periphery than doesgrating acuity, at a rate similar to that for vernier andLandolt ring acuity. On the other hand, thresholds formotion in the absence of a stationary reference have beenreported to fall off more slowly than does grating acuity.7 ' 0

We have studied the eccentricity dependence of the os-cillatory motion threshold as a function of contrast. Wefound that the rate at which the oscillatory motion thresh-old increases in the periphery is highly dependent on

stimulus contrast. This result indicates that the eccen-tricity dependence of the oscillatory motion thresholdcannot be explained by a single magnification factor(M scaling) as suggested by Wright and Johnston2 andVirsu et al.6

We offer an interpretation of the contrast dependence ofthe oscillatory motion threshold in the periphery that isbased on a form of contrast discrimination. Oscillatorymotion is decomposed analytically into two compo-nents: a counterphase grating at the temporal frequencyof the oscillation and a static component that is in spatialquadrature. Reformulation of our data in this contextsuggests that there are qualitative as well as quantitativedifferences in oscillatory motion processing between thefovea and the periphery.

2. METHODS

A. ObserversThree normal observers have been studied in detail. Thebasic findings were replicated on several other subjects.All subjects had normal or corrected-to-normal vision(HIW OD and OS: 0.0 D, visual acuity 20/12.5; AMN OD-4.25 = +1.75 X 109, OS -3.00 = +1.25 X 95, visualacuity 20/15; WFW OD and OS: -2.5 D, visual acuity20/20). The subjects observed the grating binocularlywith natural pupils.

B. Stimulus PresentationVertical sine-wave gratings were displayed on the face of adc-coupled video monitor. The gratings were generated

0740-3232/92/101663-09$05.00 © 1992 Optical Society of America

W Wesemann and A. M. Norcia

1664 J. Opt. Soc. Am. A/Vol. 9, No. 10/October 1992

by gating a sine-wave generator in synchrony with thehorizontal lines of the video raster. The spatial fre-quency and the contrast of the grating were continuouslyadjustable under computer control. The luminance re-sponse function of the monitor was linearized by a diode-resistor network in the input stage so that gratings withhigh contrast were virtually free of higher harmonics.Oscillatory step displacement of the grating was accom-plished by means of special-purpose hardware that incor-porated a 256-step digital delay line (PDU 13256-1). At aviewing distance of 167 cm, which was used at an eccen-tricity of 5 in experiment I, the displacement step sizewas 0.61 arcsec. The size of the screen was 24.1 17.5 cm, corresponding to a visual angle of 8.2° X 6 at167 cm. The constant mean luminance was 80 cd/in2 .Grating contrast was varied between 4.7% and 76%. Lu-minance and contrast of the grating were calibrated be-fore each session by a Pritchard Spectra spot meter. Thesurround was dimly illuminated.

In the experiments presented here, oscillatory displace-ment sensitivity was investigated at a temporal frequencyof 10 Hz. Each presentation of the oscillatory step dis-placement started with a tone signal followed by anabrupt onset of the oscillation -0.2 s later. The durationof the oscillatory movement was 1 s. The mean position ofthe oscillating grating was kept identical to the position ofthe static grating in order to avoid positional cues.

Before each measurement session, a test location inthe visual field was selected, and the monitor was posi-tioned at the appropriate viewing distance. The series ofthreshold measurements started with the lowest contrastcondition.

The gratings were presented in the central and lowervisual fields. In the foveal viewing condition, the observ-ers fixated the center of the screen. No fixation markwas provided. All other eccentricity values refer to theangular distance from the upper edge of the grating to afixation mark on a line above the middle of the screen.The fixation marks contained sufficient detail for stimu-lating accurate accommodation. The extent of the visualfield and the spatial frequency of the grating were variedwith eccentricity by changing the viewing distance ac-cording to the scaling procedure described in Sub-section 2.D. During all the experiments, the grating wascontinuously visible. The monitor was not occluded witha limiting aperture.

C. Psychophysical Threshold MeasurementThresholds were measured with an adaptive staircase pro-cedure developed by Tyler." The procedure started withthe method of adjustment to estimate the approximatethreshold-the displacement amplitude was increasedfrom below threshold until the oscillatory movement ofthe grating was two or three steps above threshold. Theend value of the initial adjustment was then used as thestarting value for the staircase. The staircase step sizewas 5-8% of the starting value.

The staircase procedure differed from conventionalstaircase procedures in several ways: (1) 50% no-signaltrials were randomly interleaved during the procedureso the percentage of correct responses could be monitored.(2) The decision to decrease or increase the stimulus in-tensity was derived from the percentage of correct re-

sponses within the last presentations ±1 step from thecurrent stimulus intensity. If the percentage of correctresponses exceeded 75%, the stimulus intensity was (a) notchanged or (b) increased every second time. (3) The fol-lowing stopping criteria were used: the responses duringthe last 20 trials had to pass 3 successive stopping criteriabefore the staircase came to an end: (a) the last stimulusintensity tested had to be within 0.8 step from the meanstimulus intensity; (b) the slope of the regression linethrough the last 20 trials was not allowed to exceed 1/20of a step; (c) the percentage of correct responses acrossthe last 20 trials had to lie between 65% and 85% correct.Since the staircase started from a near-threshold value,the staircase stopped with these criteria after fewer than30-40 presentations.

In addition, a number of measurements have been per-formed by using a conventional two-alternative forced-choice procedure (method of constant stimuli), which wasused as a yardstick for the accuracy of the forced-choicestaircase. The results of the forced-choice staircase pro-cedure were found to be in close agreement with the 75%threshold of the method of constant stimuli.

All the observers were given intensive practice beforethe actual trials started, especially with regard to observ-ing and detecting the oscillating grating in the far periph-ery. A large number of initial trials were rejected untilthreshold values no longer improved.2"3

D. Rationale for the Scaling ProcedureSince the present study aims at comparing the visual per-formance of the fovea with that of the periphery, it is im-portant to scale the visual stimuli appropriately. We wereinterested in studying the minimum displacement ofsuprathreshold gratings that could be detected at severallevels of contrast. We wanted to ensure that these supra-threshold gratings were equally detectable in terms of theirdistance above contrast threshold at all eccentricities soas not to confuse detectability of the grating with motionsensitivity. To accomplish this, we scaled the spatial fre-quency and the field size to match the decrease of gratingacuity and contrast sensitivity with eccentricity.7 "4 '16

There are two alternative scaling procedures currentlyused by different laboratories. Virsu and co-workers6 6

argue that the performance of almost all visual func-tions-from motion detection to vernier acuity-can bescaled with a single nonlinear magnification function (Mscaling). Levi et al.,7', on the other hand, argue that dif-ferent tasks have different eccentricity functions. Theyshow that a large body of data 783-15720 gives evidence infavor of at least three functionally different, linear eccen-tricity functions, the intercept of which depends on therespective task.

For all the measurements described here, we adoptedthe scaling factor M = 1/2.5° preferred by Levi andKlein7 3"9 in order to equalize contrast sensitivity andgrating acuity at all peripheral loci. Thus all spatial fre-quencies and the viewing distances were calculated fromthe equation P(E) = Pf0 V/(1 + E/2.5), where E is the ec-centricity in degrees and Pfa, is the value of the respectiveparameter (spatial frequency or viewing distance) forfoveal fixation. Spatial frequencies and viewing distanceswere 8 cycles/deg and 167 cm at 0, 2.7 cycles/deg and167 cm at 50, 1.6 cycles/deg and 100 cm at 100, 1.14 cycles/



deg and 71.4 cm at 150, 0.89 cycles/deg and 55.5 cm at 200,0.72 cycles/deg and 45.5 cm at 25°, and 0.62 cycles/deg and38.5 cm at 300. The viewing distance for foveal measure-ments was the only exception to the above rule, because ofthe length of the room.

3. RESULTS AND DISCUSSION

A. Experiment I: Eccentricity FunctionsIn the first experiment, the threshold for oscillatory stepdisplacements was measured as a function of eccentricityand contrast. Figure 1 shows the results for subjectsHIW, WFW, and AMN, obtained at a temporal displace-ment rate of 10 Hz. At any given contrast value, thresholddisplacement (TD) increases with increasing eccentricityE in a well-defined, linear manner. The data were fittedby a linear regression line

TD(E) = TDf0 v(l + E/E2), (1)

which relates the threshold displacement at eccentricity Ewith the foveal threshold value TDfo, and an eccentricityfactor E2.'9 E2 is the eccentricity in degrees at which thethreshold reaches twice the foveal value. All regressionlines fitted through the data points have correlation coef-ficients greater than r = 0.97.

At high contrast values of 76% and 46%, we find fovealthreshold displacements of 11-18 arcsec, values that aresimilar to previously published threshold data."2 Sur-prisingly, the periphery is also remarkably good at highgrating contrasts. At 30° eccentricity and 46% contrast,e.g., we obtained threshold displacements of 37 arcsec forHIW, 49 arcsec for AMN, and 47 arcsec for WFW

Threshold displacements at 76% and 46% contrast werealmost equal. The threshold values, however, increasewith decreasing contrast but with a different pace at dif-ferent eccentricities. As a consequence, the slope of theeccentricity function changes (Fig. 1).

A convenient way of describing the characteristicchanges in visual performance with eccentricity is to cal-culate the intercept of the linear regression line with theeccentricity axis.7'8 This allows one to characterize the

increase in threshold with eccentricity by a single num-ber. The modulus of the x intercept is identical to E 2[Eq. (1)] and specifies the eccentricity at which the respec-tive visual function doubles its threshold with respect toits optimal value in the fovea. For the detection of oscil-latory step displacements of sine-wave gratings, we findthe x intercepts listed in Table 1.

The eccentricity functions are extremely shallow athigh grating contrasts and yield x intercepts that are un-precedentedly large (see Refs. 7 and 21). All three ob-servers listed in Table 1 exhibited x intercepts larger than-15° at contrasts larger than 46%. A fourth observer ob-tained a -11.4° intercept without prior practice. Themean value of -18.4° is -7.5 times larger than the x inter-cept for grating acuity. At lower grating contrasts, theeccentricity function steepens considerably, dropping tovalues as small as -1.8° at 8.5% contrast.

B. Oscillatory Motion Detection Interpreted as a Form ofContrast DiscriminationAn oscillating sine-wave grating can be decomposed intotwo orthogonal components (Fig. 2), namely, into a staticgrating with a modulation amplitude Ctat and an alternat-ing grating with a modulation amplitude Calt that under-goes a phase reversal of 1800 (pattern reversal) and isoffset by 90° spatial phase. A similar decomposition hasbeen suggested by Nakayama and Silverman.22 Given anoscillating grating of contrast C0, the modulation ampli-tude of these two components can be derived from the for-mulas

Ctat = C0 cos(,), C1 t = Co sin(4)), (2)

where 20 represents the change in spatial phase at thresh-old. These two components are commonly looked at ascontrast values, although this is not true in a strict sense(see Appendix A). This decomposition allows one to in-terpret the perceptual task of oscillatory motion detectionas a task in which a grating that is periodically jumpedthrough a phase angle of 180° (signal) has to be detectedin the presence of a stationary grating (mask) that is inspatial quadrature.

- HIW%C

4.7

8.5

WFW%C

8.5

15

264676

0 10 20 30 0 10 20 30 0

AMN

8.5

15

25

46

10 20 30

Eccentricity (deg)Fig. 1. Threshold values for the detection of oscillatory step displacement of sine-wave gratings versus eccentricity. Grating contrast isvaried parametrically between 4.7% and 76%. Oscillation frequency is 10 Hz. Each datum is the mean of at least 6 independent trials(3-4 for AMN). Threshold displacement increases linearly with eccentricity. The slope of the regression lines fitted through the datapoints steepens considerably with decreasing contrast.

250

200 C)

0

150

100

50

L



Table 1. Modulus of the X Intercept in DegreesaContrast (o)

Subjects 76 46 26 15 8.5 4.7

HIW 25.40 20.00 11.50 4.4 3.20 2.40WFW 13.70 15.20 9.20 3.20 1.80AMN 17.60 4.40 4.60 1.80

'(=Eccentricity factor E2 ) of the eccentricity function versus gratingcontrast. Threshold displacement doubles at the specified angle.

+ Cait

C stat

- Cait

Fig. 2. During a step displacement, the sine-wave grating withcontrast C0 jumps through a phase angle of 24. The static com-ponent Ctat does not change. The alternating component Caltchanges its sign, indicating a pattern reversal.

Figure 3 replots the data from Fig. 1. The magnitudeof the alternating component Cast at motion threshold isshown as a function of the magnitude of the static compo-nent Ctat at motion threshold for subjects HIW and WFWThe Cast curve can be divided into two functionally differ-ent regions. At low values of the static component Ctat,oscillatory motion can be detected once the alternatingcomponent Cat exceeds a certain minimal threshold value.This constant value is denoted as Ctmin throughout thepaper. At high Ctat values, the visual system cannotmaintain its performance quality, i.e., an increasinglyhigher Calt value is required for detection. The flat partof the Cdt function gives way to a Weber-like, rising partat a critical Ctat value that depends strongly on eccentric-ity. For subject HIW this critical Ctat value lies at amodulation of -7% for foveal viewing and increases to29% at 30° eccentricity. Below the critical Cat value, de-tectability of the alternating component is not affected bythe presence of the static component.

The magnitude of the critical Cat value, which is de-noted by C0 0 rit, was calculated from the intersection of theflat part of the Calt function and the straight lines fittedthrough the rising part. When it is plotted as a functionof eccentricity (Fig. 4), we find that the critical modula-tion Cscrit increases linearly with eccentricity.

C. Experiment II: Oscillatory Displacement Detectionin the FoveaIt is important to verify that the increasing resistance tomasking is actually a property of the periphery and not anexperimental artifact introduced by our scaling proce-dure. In our scaling procedure, we reduced the spatial

frequency of the test grating from 8 cycles/deg at 00to 0.62 cycles/deg at 300 in order to maintain equalvisibility.

We evaluated the effect of spatial frequency on the criti-cal value for masking Crit in a second series of experi-ments by measuring threshold displacements in the foveaas a function of spatial frequency and contrast. The re-sulting threshold displacements for foveal fixation weresubjected to the same decomposition into alternating andstanding components as described above. In order toallow for a larger summation area at lower spatial frequen-cies, we have measured the results presented in Fig. 5by using a shorter viewing distance (137 cm at 1-8 cycles/deg, corresponding to a visual angle of 10° X 7.3°, and68.5 cm at 0.5 cycles/deg = 19.4 x 14.30). The resultsare depicted in Fig. 5. Similarly to Fig. 3, the thresholdmodulation of the alternating grating Calt shows a flat anda Weber part. Consistent with the well-known shape ofthe contrast sensitivity function at a reversal rate of10 Hz,23 the minimal value of Calt decreases from 8 to2 cycles/deg. In the increasing Weber part, Ct growswith a slope close to 1.0.

Considered in terms of absolute displacement, the dis-placement threshold versus contrast functions we havemeasured are similar to those in the literature (see Fig. 4of Ref. 2). Foveal displacement thresholds at high and

Deg.I 010 HIW

3

0

5

0.3

0.1

- WFW,Deg.

/0/5, 10- 15P30

1 3 10 30 100 1 3 10 30 100

Cstat (%)

Fig. 3. Modulation depth of the alternating grating componentCast at the detection threshold for oscillatory motion. The x axisdepicts the modulation depth of the static grating componentCtt. Eccentricity is varied parametrically between 00 and 30°.

40WFW

(.°300

n 20 -o HIWE

.2 10

0 10 20 30Eccentricity (deg)

Fig. 4. Lower threshold for masking Ccit versus eccentricity.Ccrit denotes the limiting value of the static grating componentabove which the alternating component is being masked by thepresence of the static component.


1

I


10r

3

0

0.3

o.1 I I I1 3 10 30 100 1

Cstat (%)

Fig. 5. Alternating versus static compcmotion detection threshold. Similar to Ftion. Spatial frequency is varied parame8 cycles/deg (HIW) and between 1 and 4

401

301

200

10

0

0

.

0

4

3

2

1

HIW

M IZFI

0.25 0.50 1 2

Spatial frequencyFig. 6. Upper panel: lower threshold fspatial frequency. Foveal fixation (filledfixation (open symbols). The peripheraleccentricities of 30°, 15°, 100, and 5, reELower panel: the ratio Ccrit (peripherywith decreasing spatial frequency (increconverges toward a constant value of from

intermediate contrasts were typicallyject WFW and 17-25 arcsec in subie

Fwf ^ 4. GENERAL DISCUSSION

A. Oscillatory Motion Thresholds Are Not Related toCortical MagnificationThe basic finding of the present study is that oscillatorymotion detection has an extremely shallow eccentricityfunction at high contrast values that steepens consider-ably with decreasing contrast. This result helps to solve adiscrepancy found in the literature. Wright and Johnston2

3 10 30 100 measured threshold displacements for sine-wave gratingsin the range of 0-7.5° eccentricity at moderate contrast

- a values of 0.1 and 0.3 and concluded that oscillatory motionMeent at the oscillatory'ig. 3 but for foveal fixa- sensitivity scales according to the magnification functiontrically between 0.5 and of Rovamo and Virsu.5 Levi et al.,7 however, describedcycles/deg (WFW). x intercepts for unreferenced motion from -5.6° to -14°

(see also Refs. 10 and 21). Wright and Johnston2 workedat low contrast values, whereas Levi et al.7 used high con-trast targets. The slope of our eccentricity functionschanges with contrast, and so do the x intercepts. Thevisual system exhibits its optimal performance at highcontrast values, leading to x intercepts of as high as -25°,but its performance deteriorates faster in the peripherywith decreasing contrast compared with the fovea. Natu-rally, even in our data set, a contrast value could be pickedat which the eccentricity function resembles the Rovamo

WFW and Virsu5 magnification function. For our experimentalconditions, this contrast value lies between 8.5% and 15%(see Table 1 and Ref. 24). However, our findings demon-

HIW strate that it is inadmissible to use the Wright-Johnston 2

data as evidence for the assumption that oscillatory mo-tion detection scales according to the magnification func-tion of Rovamo and Virsu5 and Virsu et al.6 Since theslope of the eccentricity function changes with contrast,our data indicate that there is not a unique eccentricitydependence (i.e., magnification) for the detectability of os-

5 10 cillatory step displacements. While foveal thresholds forcpd) high contrast gratings are in the range of the hyper-r masking Cscrit versus acuities, the oscillatory motion threshold falls off an ordersymbols) and eccentric of magnitude more slowly than the traditional hyper-

curves were obtained at acuities (see, e.g., Ref. 8).Lding from left to right. Unreferenced unidirectional and oscillatory motion at)/Ccrit (fovea) increases low temporal frequencies are known to fall off slowly to-easing eccentricity) andl2 (WFW) to2.5 (HIW). ward the periphery.7 ' 9"0' 2' However, none of the studies

cited above found, as we did, threshold values smaller than1 arcmin in the periphery. Crucial for an optimal detec-

11-15 arcsec in sub- tion threshold seems to be a rapid step displacementect HIW The lowest (>5 Hz) instead of slow gradual transitions.

threshold values for both observers were normally ob-tained not at the highest grating contrasts but at inter-mediate contrasts slightly above the location of the kneepoint Cscrit. The near-Weber law performance at highercontrasts reflects an almost constant value of the actualdisplacement threshold in this range. The contrast abovewhich the threshold no longer improves depends on bothspatial frequency and eccentricity and can be determinedfrom the values of Cscrit. This value ranges from 5% to15% (Fig. 5).

The foveal Cscrit value is fairly constant between 2 and8 cycles/deg but increases for lower spatial frequencies(Fig. 6). However, the critical value Ccrit measured in theperiphery at the same spatial frequency is always larger.The difference amounts to a constant factor of 2.0-2.5 atspatial frequencies lower than 2 cycles/deg.

B. Foveal Oscillatory Motion Detection Versus ContrastDiscrimination with Static TargetsWe have modeled the detection of oscillatory motion as thediscrimination of a high temporal frequency test from astatic mask. In a conventional contrast discriminationtask, a contrast increment AC has to be detected in thepresence of a masking grating with pedestal contrast C, ofthe same temporal frequency.2 5 26 The alternating compo-nent, Cat, of our experiments may be compared with thecontrast increment AC of a contrast discrimination task;the static, masking component, Ctat, may be comparedwith the pedestal contrast C. However, the present dataindicate a number of differences between oscillatory mo-tion detection and contrast discrimination tasks as men-tioned above.

rl | W ,


1


1. Exponent of the Power LawIn our formulation for motion detection, the rising part ofthe CatCstat function (Figs. 3 and 5) can be fitted by apower function (a straight line on log-log coordinates).The exponent N of the power function

CaIt = k (Ctt)N (3)

is obtained from the slope of the regression lines on log-log coordinates. A similar analysis has been applied inconventional contrast discrimination studies. Some havefound Weber's law behavior, but the majority of contrastdiscrimination studies (see Refs. 25 and 27 for reviews) areconsistent with a slope of from 0.6 (at 2 cycles/deg) to 0.7(at 8 cycles/deg). The slope of the contrast discriminationfunction tends to be somewhat steeper at high spatial fre-quencies but is in general fairly insensitive to changes inthe experimental procedure and the state of adaptation.2 5

The foveal data for oscillatory motion detection presentedhere (Fig. 5) show a steeper CaitCstat function, althoughfairly low grating frequencies of 0.5-8 cycles/deg havebeen used. The slope is consistent with Weber's law. Nvaried from 0.88 to 1.12 in subject HIW and from 0.95 to1.06 in WFW

2. No Pedestal EffectContrast discrimination functions generally show a pedes-tal effect, i.e., the presence of the masker facilitates signaldetection at low contrast values.26' 28 Although we did notinvestigate the low contrast region of the dipper in detail,the CaIt-Cstat functions found in oscillatory motion detec-tion seem to show no facilitation. The pedestal effect incontrast discrimination has a narrow frequency selectiv-ity and disappears when test and mask are of differentspatial frequencies.2 6 This has been interpreted as a con-sequence of the varying phase relationship between themask and the test, resulting in an inability of the mask todrive the accelerating nonlinear transducer function to anoperating point with a steep slope.26 29 Following thisphase argument a facilitation is not to be expected in os-cillatory motion detection, since alternating and staticcomponents are presented 90° out of spatial phase and atdifferent temporal frequencies (see also the discussion inSubsection 4.0).

3. Location of the Knee PointContrast discrimination and oscillatory motion maskingfunctions differ in the location of the knee point that sepa-rates the flat part at low masking contrast values fromthe power-law region. Contrast increment thresholds,AC, rise almost immediately after the pedestal gratingexceeds its detection threshold and starts to act as amasker.2 5 28" 0 Displacement detection, on the other hand,is not masked below a fairly large critical contrast value,Cscrit. For foveal viewing, the detection threshold of thealternating component Calt of the oscillating grating staysat its minimal threshold value, Caltmin, until the maskingstatic grating component reaches a contrast well abovethreshold (Cscrit = 7-19%). In the periphery, the kneepoint, Cscrit, is shifted toward even higher contrast values(Ccrit = 10-40%; see Fig. 6).

C. Oscillatory Motion Detection versus ContrastModulation Detection

1. Shape of the Threshold versus Contrast FunctionOur hypothesis that oscillatory step displacement detec-tion may be a form of contrast discrimination is supportedby the results of Bodis-Wollner and Hendley" and Pantle.'2

Bodis-Wollner and Hendley measured the detectability ofan 8-Hz contrast modulation at different mean contrastlevels. Similarly to our experiments, the observer's taskwas interpreted as the detection of a counterphase gratingin the presence of a static grating; however, in their ex-periment, the static and alternating components were inthe same spatial phase. The contrast modulation stimu-lus can be expressed as

I = Io[l + Co cos(2irfx) ± CoM cos(27rf,)], (4)

where C0 denotes the mean contrast and M denotes themodulation amplitude. By comparison with our results[see Appendix A, Eq. (A2)] we find a static component ofC.,at = C0 and an alternating component of Calt = CoM.

When we replot the Bodis-Wollner and Hendley data inour format (Fig. 7), we find functions that are similar tothose in our Fig. 5. First, modulation detection is almostindependent of C.tat at low contrasts of the static maskerbut rises as a power function at high Cgtat values. Second,unlike in the static contrast discimination tasks,2 6 theknee point is located at fairly large masking contrasts (2%at 3 cycles/deg, -3% at 6 cycles/deg, and 8% at 12 cycles/deg). Third, a dipper is not readily apparent.

Pantle"2 studied simultaneous masking of a gratingwith spatial frequency f by a second grating at 3f Testand masking gratings were independently either static ormodulated at 5 Hz. His basic findings (Figs. 2 and 3) aresimilar to ours and to the Bodis-Wollner-Hendley data asplotted in Fig. 7. In addition, he found that, when bothtest and mask were static, the knee point of the thresholdversus contrast function (Cncrit) occurred at low contrasts(1.9% at 2 cycles/deg), but, when the test alternated at5 Hz on a steady background, the knee point was shiftedto higher contrasts (-13% at 2 cycles/deg) under other-wise identical conditions.

30 r

10

03

0.3

cpd

' 12

1 6D 3

0 3 1 3 10 30 100

Cstat (%)

Fig. 7. Contrast modulation sensitivity at 8 Hz. Data trans-formed and replotted from the Bodis-Wollner and Hendley"Figs. 2 and 5 (observer DB's data are plotted for 3, 6, and12 cycles/deg; observer OW, for 6 and 12 cycles/deg). Note thatpower-law behavior begins only at relatively high Cstat values andthat facilitation at low contrasts is not apparent.

l



A similar shift in the location of the knee point Cscrit canbe found by comparing Fig. 3 in Ref. 33 with Fig. 3 inRef. 34. Hess and Snowden333 4 measured the contrast ofa mask necessary to extinguish the visibility of a probe(see also Subsection 4.E). For a probe stimulus at 0.8 Hzand a masking stimulus at 8 Hz, the knee point of themasking function was found at a contrast of -1.7% in thefovea. At 30° eccentricity, the critical contrast for mask-ing was shifted to 6.5%. The factor of 3.8 between thesetwo values is larger than what we have found, but betteragreement may not be possible because of the substantialdifferences in the design of the experiments and the factthat Hess and Snowden did not scale their stimuli in orderto compensate for cortical magnification.

2. Possible Role of AdaptationDuring our threshold measurements the grating was con-tinuously visible. This may have reduced the visibility ofthe static grating because of pattern adaptation. Theeffects of adaptation in our experiment are not likely tobe large given previous observations on the effects ofcontrast adaptation on contrast modulation detectionand contrast discrimination. Bodis-Wollner and Hendleyadapted observers to a 70% contrast grating for 3 min be-fore one of their series of threshold measurements. Theyfound a strong effect of adaptation on the shape of the Caltversus Cstat function. After adaptation, the functionsceased to show a power-law exponent near one-the expo-nent in fact fell to near zero when plotted as in Fig. 7.The detectability of the alternating component was re-duced at low Cgat values and facilitated at high Qtat values.Overall, the detection of the modulating component be-came independent of the contrast of the masking grating.

Similar changes in the slope of the threshold versus con-trast function have been observed in contrast discrimina-tion tasks. After prolonged inspection of a high contrastgrating, the observer's ability to discriminate subse-quently presented gratings was impeded at low contrastsand facilitated at contrast above 0.4-0.5.3" Discrimi-nation threshold for a 0.8 background contrast was ap-proximately a factor of 2 lower following adaptation (Fig. 3of Ref. 26).

The relative steepness of our functions thus arguesagainst a large role for pattern adaptation. However, thisinterpretation is not entirely straightforward. In theBodis-Wolner-Hendley unadapted condition, the gratingwas also continuously visible, as in our experiments.Therefore it is possible that their curves and ours reflectpartial adaptation. In their experiment, the effect ofadaptation was to reduce the slope of the discriminationfunction. Smith and Swift found a similar effect in con-ventional contrast discrimination-adapted slopes were inthe neighborhood of 0.3, much lower than ours. If any-thing, our power-law slopes might be underestimated ifpartial adaptation occurred during our measurements.

D. Behavior in the PeripheryContrast discrimination in the periphery was investigatedby Bradley and Ohzawa37 and by Legge and Kersten.3 0

The latter used small 2-cycles/deg grating patches at reti-nal loci of as high as 20° eccentricity and did not scale thefield size and the spatial frequency of their gratings butnormalized the increment and pedestal contrast by the re-

spective contrast sensitivity. Thus the comparabilitywith our present data may be limited. Legge andKersten3 0 found that properties of contrast discriminationare qualitatively and quantitatively similar in the foveaand the periphery. The location of the knee point and thedipper was unchanged. The exponent of the power func-tion was similar to the foveal datum. The present dataindicate that the power law governing oscillatory motiondetection in the periphery may have a shallower slopecompared to the fovea. The slope of the regression linesdrawn in Fig. 5 varied from 0.72 to 0.79 for HIW and from0.75 to 0.83 for WFW However, because of the variabil-ity, these values are not statistically discriminable from aslope of 1.0. [In fact, the slope of the power functiontends to increase toward the high end of the contrastrange (46-76%).]

E. Physiological InterpretationIt is generally assumed that temporal sensitivity is sub-served by at least two but not more than three relativelybroadly tuned channels.38 '3 9 The low-frequency filter hasa low-pass shape, while the mid- and high-frequency rangeis served by bandpass filters with optimal sensitivity at-10 Hz.38 A recent study by Snowden and Hess34 foundmaximal sensitivity for the first and second bandpassfunctions to be at 8.4 and 14 Hz, respectively. Each ofthe three filters should be capable of detecting both thestatic and alternating components of oscillatory motion,but the bandpass channels would be relatively more sensi-tive to the alternating component and the low-pass chan-nel would be more sensitive to the static component.

The data presented here have demonstrated differencesin foveal and peripheral sensitivity to the alternating com-ponent in the presence of a static component. These dif-ferences suggest that the detectability of the alternatingcomponent in the periphery is less affected by the pres-ence of the static masking component. As a consequence,the location of the critical contrast for masking Ccrit isshifted to higher values in the periphery. This increasedresistance to masking could come about in several ways:

(1) It might be a consequence of a reduced sensitivity ofthe low-pass channel relative to the sensitivity of the band-pass channel(s) in the periphery.

(2) It might be a consequence of changes in the responsecharacteristics of the temporal filters operating at dif-ferent eccentricities since a shift in center frequenciestoward higher temporal frequencies or an increasing mag-nitude of the low-frequency rolloff as a function of eccen-tricity would also result in decreasing sensitivity to thestatic mask.

(3) Alternatively, our findings might be interpreted in afundamentally different framework, such as that sug-gested by Nakayama and Silverman,22 which posits con-trast saturation in motion detection. Saturation may beless in the periphery than in the fovea.

Our data do not provide conclusive evidence in favorof one of these possibilities. However, the recent resultsof Hess and Snowden33

,34 provide support for the first hy-

pothesis. Hess and Snowden studied the tuning of thetemporal channels with a masking paradigm in which thevisibility of a Gabor patch that was contrast modulated at


.1670 J. Opt. Soc. Am. A/Vol. 9, No. 10/October 1992

a temporal frequency f was decreased by a maskingstimulus alternating at f2. According to their findings,the sensitivity of the low-pass filter was reduced relativeto that of the bandpass filters in the periphery. At aneccentricity of 300, the contribution of the temporal low-pass channel could no longer be detected, and the resultswere consistent with the existence of only one bandpasschannel centered at -10 Hz. Snowden and Hess (Ref. 34,p. 69) argued that "the peripheral field is not merely alower spatial frequency replication of the foveal field, butthe sensitivities of mechanisms with different temporalproperties change at different rates with respect to eccen-tricity, making the peripheral field qualitatively differentfrom the foveal field." A conceivable physiological basisfor this change may be found in the increasing proportionof fast-conducting M-cell input to slow P-cell input towardthe periphery such as that which has been found in themacque visual system.40

Our detection thresholds may be interpreted as anincreased resistance to masking that is contingent onchanges in the mix of temporal channels operating at dif-ferent eccentricities. In the fovea, all three temporal fil-ters can contribute to the detection of the alternatingcomponent of the oscillating grating because each channelhas relatively high sensitivity at 10 Hz. Each channelhas some sensitivity to the static mask, although the low-pass mechanism would have greatest sensitivity to thestatic component. It seems reasonable to assume that theoverall performance of the visual system depends on thecombined outputs of the available temporal filters. Fromthe Hess-Snowden results3 3 it appears that the low-passfilter in the fovea has similar sensitivity at both 0 and10 Hz, which should make this filter relatively nonselec-tive for detection of the alternating component. Its con-tribution may, in fact, reduce the available signal-to-noiseratio, because this mechanism strongly signals the pres-ence of the static component. This potentially counter-productive contribution of the low-pass channel maydiminish in the periphery as the sensitivity of the low-pass channel declines with increasing eccentricity. Onthe other hand, the bandpass channel(s) have little sensi-tivity to the masking component, and their performancewould not be as affected by the presence of the standingcomponent.

APPENDIX A: DECOMPOSITION INSTANDING AND ALTERNATINGCOMPONENTS

The intensity distribution of a sine-wave grating of con-trast C0 that oscillates between two spatial positions canbe described by

11,2 = Io[1 + C0 sin(2rfx ± )], (Al)

where Io is the mean intensity, f., is the spatial frequency,and the magnitude of the grating displacement is ex-pressed in terms of its phase angle 20. The oscillation ofa grating through an angle of 24 can be decomposed intothe sum of a static grating and a grating that undergoespattern reversal. After elementary transformationsEq. (A2) yields

I1,2 = IO[ + Cstat sin(27rf.) ± Cast cos(2rf.)], (A2)

where the abbreviations

Cstat = Co cos(O)),Ca = C0 sin(+)

(A3)

(A4)

represent the modulation amplitudes of the standing andthe phase-alternating grating components.

These two modulation amplitudes Cstat and Calt are com-monly understood as contrast values.2 2 However, this isnot strictly correct. The quantity contrast is not a vectorthat can be decomposed into components (see Fig. 2).Contrast is instead, according to its original definition byMichelson, a scalar derived from scalar intensities. Aninterpretation of the modulation amplitudes Cstat and Caitas grating contrasts is possible only when both compo-nents are detected independently. This requires that themechanism that sees Qtat be blind to Calt and vice versa.

It might be argued that, on time average, the oscillatingcomponent ±Calt cos(2'irfxx) in Eq. (A2) vanishes and thusis invisible to the mechanism that detects the static con-trast component. It might also be argued that displace-ment detection is carried out by a transient mechanismthat detects the alternating grating of contrast Calt but isunable to see the static component.

However, the assumption of a completely independentdetection of Ctt and Calt is obviously wrong, since inter-action (masking) is observed. Therefore it is physicallycorrect to denote the two components as modulation am-plitudes and not as contrast values.

ACKNOWLEDGMENTS

We thank the reviewers for helpful suggestions and S. A.Klein and S. F Bowne for helpful discussions and for pro-viding unpublished details of research. W Wesemann wassupported by the Fogarty International Center, NationalInstitutes of Health, under grant 1FO5 TW033830-01.

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contrast dependence of the oscillatory motion threshold across the visual field

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