effects of spatial frequency, duration, and contrast on discriminating motion directions

J. Yang and S. B. Stevenson Vol. 14, No. 9 /September 1997 /J. Opt. Soc. Am. A 2041

Effects of spatial frequency, duration, and contraston discriminating motion directions

Jian Yang and Scott B. Stevenson

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

Received October 7, 1996; revised manuscript received March 21, 1997; accepted March 31, 1997

The minimum speed required for discriminating the direction of drifting gratings was measured at a variety ofspatial frequencies, display durations, and contrasts. As was reported previously, speed thresholds were rela-tively constant for middle and high spatial frequencies, but speed threshold was found to be almost inverselyproportional to spatial frequency in the range of 0.25 to 1.0 c/deg. Speed threshold was also found to be in-versely proportional to duration between 73 and 400 ms. These results at low frequencies and short durationsare shown to be consistent with limits set by the spread of energy in the stimuli, producing velocity uncer-tainty. A quantitative model of temporal filtering is presented that largely accounts for results at all spatialfrequencies and durations by the inclusion of constant positional noise. A discussion includes the possibleroles of magnocellular and parvocellular mechanisms in mediating speed thresholds. © 1997 Optical Societyof America [S0740-3232(97)03809-X]

1. INTRODUCTIONKulikowski1 reported that when the contrast of a station-ary grating was alternated or displayed on–off repeat-edly, the grating appeared to move laterally. He calledthis phenomenon apparent movement. When the grat-ing contrast was at or near threshold, apparent move-ments were observed only at frequencies below 6.6 c/deg.1

This motion perception, together with flicker perception(see, e.g., Ref. 2) at low spatial frequencies, led investiga-tors to propose two distinct subsystems in processing spa-tiotemporal visual information: a sustained one for pat-tern and form detection and a transient one for flickerand motion detection.2–5 More recently, physiologicalsubstrates for transient and sustained channels havebeen suggested to be magnocellular and parvocellularpathways, respectively (for a review see Ref. 6).

In preliminary observations we found that if a station-ary low-spatial-frequency grating is presented for a shortduration (say, 200 ms), observers report a strong motionpercept. The perceived motion is disorganized in thesense that the direction is unclear or inconsistent. Thisphenomenon seems similar to that reported byKulikowski1 and was associated particularly with verylow spatial frequencies of less than 1 c/deg. The phenom-enon prompted us to ask two questions: (1) Since thephenomenon is most evident at low spatial frequencies, isthere a corresponding difference in motion sensitivityacross the spatial-frequency spectrum? (2) What are theplausible candidates for the mechanisms that underliethis motion perception?

To address the first question we measured speedthresholds for discriminating the direction of a driftinggrating at different spatial frequencies, durations, andcontrasts. The speed threshold, which has often beencalled the lower threshold of motion,7–9 reflects the limitof the visual system’s ability to discriminate moving fromstationary stimuli. Previous studies (e.g., Refs. 7 and 8)showed that speed threshold did not vary with the spatial

0740-3232/97/0902041-08$10.00 ©

frequency of gratings. However, in those studies the low-est spatial frequencies used were ;2 c/deg for foveal con-ditions, where the disorganized motion perception maynot be manifest. Therefore the aim of our first experi-ment was to extend the examined spatial frequency rangeto 0.25 c/deg to see whether there are any effects of spa-tial frequency on speed threshold.

To answer the second question we consider two ap-proaches: sustained–transient dichotomy and motionenergy sensors. In sustained–transient theory, patternor form perception is associated with sustained channels,which are most sensitive to high spatial and low temporalfrequencies. Motion perception is associated with tran-sient channels, which are most sensitive to low spatialand high temporal frequencies. This equation of motionperception and transient channel activity provides a con-venient explanation for the perceived motion: a low-spatial-frequency grating with a short display durationwould generally excite transient channels. Furthermore,as transient channels are associated with motion detec-tion, the excitation of the transient channels would leadto the perception of motion. Although investigators (e.g.,Stromeyer et al.10 and Green11,12) have shown that high-spatial-frequency channels, which are generally catego-rized as sustained, can signal motion information, thepossibility that motion detection at low spatial frequen-cies is determined by transient channels is not ruled out.Experimental data presented in this paper provide evi-dence that transient channels cannot explain minimummotion thresholds at low spatial frequencies either.

Investigators13–15 have also proposed that visual mo-tion extraction is accomplished by motion sensors or en-ergy filters in a spatiotemporal frequency domain. Fordrifting gratings the physical speed can be expressedas13,16

v 5 v/f, (1)

where v represents the speed in degrees per second, vrepresents temporal frequency in hertz, and f is the spa-

1997 Optical Society of America

2042 J. Opt. Soc. Am. A/Vol. 14, No. 9 /September 1997 J. Yang and S. B. Stevenson

tial frequency of the grating in cycles per degree. Figure1 sketches a simplified set of motion energy sensors thatextract velocity information. The gray circles representoverlapping visual filters in the spatiotemporal frequencydomain. When a filter is paired with another filter thatis 180° away and at the same distance from the origin(e.g., the two dark circles in Fig. 1), the two filters to-gether constitute a single motion detector (Refs. 13 and14). If only one motion detector is excited, the velocity ofthe motion is signaled by the labeled motion detector, orfunctionally, the visual system computes the slope of theline connecting the two circles in signaling the velocitymagnitude of the motion. In the case when many motiondetectors are excited by the motion energy of a movinggrating (e.g., the two white ellipses in Fig. 1), the optimalspeed estimation can be based on the slope of the solidline that joins the two ellipses, which might be computedfrom a weighted average of the excited sensors.16

When a static grating is displayed with a short dura-tion t, the energy of the grating has considerable spreadin temporal frequency17 (Fig. 2) of magnitude Dv } 1/t.The range of temporal frequencies covered by this spreadis independent of spatial frequency, but by substitutioninto Eq. (1) we find that the velocity spread is inverselyproportional to spatial frequency: Dv } 1/(t f ), whichcan be thought of as a noise or an uncertainty embeddedin the nominal drifting velocity. Thus the sametemporal-frequency spread that is due to a brief exposureresults in much more velocity noise at low spatial fre-quencies than at high, providing another explanation forthe perception of a disorganized motion at low spatial fre-quencies. For measuring speed thresholds, the task canbe thought of as discriminating the labeled detectors ex-cited by a static grating from those excited by a movinggrating. The velocity spread here produces uncertaintyabout the motion signal. Consequently, the speedthreshold for briefly presented gratings should be higherat low spatial frequencies because of this temporal-frequency domain noise.

Experiment 2 was designed to measure the speedthreshold at a variety of display durations and spatial fre-

Fig. 1. Simplified diagram of velocity detection. The graycircles represent visual sensors in the spatiotemporal domain,and the two ellipses represent the motion energy of a movinggrating. The optimal velocity is estimated by the slope of theline, which is computed with the motion sensors excited by themotion energy.

quencies to check whether the velocity spread, as shownin Fig. 2, is a limiting factor in motion detection. Notethat this analysis of the spread does not assume anyvariation in visual system sensitivity across spatial andtemporal frequency. Any such inhomogeneity in sensi-tivity could have additional effects beyond the limitationsby the spread.

In the past decade, the distinction of motion perceptionfrom pattern perception has been connected to magnocel-lular (M) and parvocellular (P) pathways. Manyinvestigators6,18–20 suggest that motion is processedmainly by the M pathway, although the P pathway con-tributes some to motion processing. Furthermore,Shapley19 and Kaplan and Shapley21 showed that thecontrast responses of M cells saturate at a relatively lowgrating contrast but the responses of P cells keep increas-ing with grating contrast. If M cells mediate the detec-tion of motion at threshold, one would expect that speedsensitivity would saturate at a low contrast value.22 Psy-chophysically, Johnston and Wright8 showed that con-trast had little effect on speed threshold for contrast val-ues higher than 0.05 for the gratings that they used (2 to16 c/deg). Muller and Greenlee23 further showed thatspeed threshold was basically constant over a contrastrange from 0.01 to 0.3 at a spatial frequency of 1.6 c/deg.Visual performance on similar tasks, such as displace-ment threshold,24 coherence threshold for discriminatingthe direction of moving random dots,25,26 and speeddiscrimination,27 has been reported to saturate at low

Fig. 2. Simplified diagram of speed threshold for motion detec-tion. The gray circles represent visual sensors in the spatiotem-poral domain. For a given spatial frequency f1 , the energy of astatic grating is represented by the three white ellipses centeredat 2f1 , 0, and f1 . The height of the ellipses represents the en-ergy spread in temporal frequency, which is inversely propor-tional to the duration of the test grating. For example, whenthe duration is doubled, the grating is represented by the twoless-elongated concentric ellipses (gray). As the grating moves,the centers of the ellipses would shift away from the f axis, withone, e.g., at f1 , moving up and the one at 2f1 moving down. Ifthe spread of the stimulus energy in this spatiotemporal-frequency domain determines the discrimination between the setof sensors excited by a moving grating and those excited by astatic grating, speed threshold will be proportional to the heightof the ellipse (comparing the slopes of the solid and the dashedlines) or inversely proportional to duration t. Furthermore, bycomparing the slope of the dashed line (for f1) and the slope ofthe dotted line (for f2), one can see that speed threshold will beinversely proportional to spatial frequency.


contrasts. There have also been reports that motion sen-sitivity declines at high contrast.9,17,28 Thus much of thedata in the literature are consistent with the contrast re-sponse of the M pathway. However, none of the studieson direction discrimination examined the relatively low-spatial-frequency range where the M system might be ex-pected particularly to dominate. Experiment 3 here wasthus designed to measure speed threshold as a function ofcontrast over a larger range of spatial frequencies thanhad previously been examined.

2. METHODSA. StimulationVisual stimuli were vertical gratings moving leftward orrightward, as expressed by the formula

s~x, t ! 5 L$1 1 C sin@2p~ fx 2 vt !#%, (2)

where s is the luminance profile of the stimulus and L isthe mean luminance of the stimulus, 62 cd/m2, C is thecontrast, f is the spatial frequency, and v is the temporalfrequency of the grating. For a static grating the value ofthe temporal frequency v is zero.

All stimuli were generated with a Cambridge ResearchSystems VSG 2/3 board and displayed on an Image Sys-tems monitor at 150 Hz, which gives 11 frames at theshortest display duration (73 ms) used in the experiment.The display area was a rectangular viewing field of width9.1° and height 6.5° at a distance of 200 cm. There were1024 pixels in a single horizontal line, corresponding to apixel size of 0.538 at the mentioned viewing distance.For the highest spatial frequency used in the experi-ments, which was 12 c/deg, one cycle of the grating hadapproximately nine horizontal samples on the video dis-play. It was dark outside the viewing window. The graylevel of the video screen was gamma corrected with theCRS OptiCal tool and had an effective 12-bit luminanceresolution. Drifting gratings were implemented withlook-up table animation. Periodic ramps were drawninto video memory, which had a fundamental frequencythe same as the frequency of the desired grating. A sinu-soidal profile of the desired contrast was written into thelook-up table, and shifts of this sinusoid produced motionof the displayed grating. The minimum step size of thedrifting grating was 1/256 of a period of the grating.Across all our conditions the actual step size at thresholdwas never more than 1/25 of the grating period, so the mo-tion was not ambiguous from one frame to the next. Ob-servers viewed the stimulus binocularly, in direct viewwithout artificial pupils. Three observers, QW, JY, andSBS, participated in the experiments. All had vision cor-rected to 20/20 or better.

B. Psychophysical ProceduresIn each stimulus interval the motion direction was ran-domly set to be either left or right. The initial phase ofthe grating was randomized from trial to trial. The ob-server responded by pressing one of two buttons to signalperceived leftward or rightward motion. A fixation tar-get was displayed before and after the stimulus interval,which was demarcated by a beep. The fixation targetwas a circular Gaussian with standard deviation of 5.38

and a peak contrast of 10% at the center of a uniform fieldof mean luminance. The observer’s task was to indicatein which direction (left or right) the grating was drifting.The speed of the grating on each trial was determined bya QUEST procedure that searched for the speed at whichthe direction of motion was correctly identified on 84% ofthe trials.29 Auditory signals informed the observerabout the correctness of the preceding response. Thetrials were terminated by a x2 test with a 95% confidenceinterval of 62 dB. In the experiments, speed thresholdswere measured at a variety of spatial frequencies, displaydurations, and contrasts. For a given session, stimuliwith different spatial frequencies were interleaved, withother variables fixed. The data reported here are arith-metic means from at least four repetitions of the samecondition run on different days.

C. Calibration of Grating VisibilityExcept where indicated otherwise, grating contrast ineach condition was set to five times the contrast thresholdfor detecting a stationary grating of the same durationand spatial frequency. Contrast thresholds were mea-sured before the main experiments. Figure 3 shows con-trast thresholds for detecting static gratings, at stimulusdurations of 73 to 1600 ms, for the three observers.

A model equation modified from one developed by Yanget al.30 was used to fit the experimental data. The vari-able t, i.e., the display duration, which was not explicitlyconsidered in the original model, is implemented in thefollowing expression for calculating contrast threshold:

Ct 5 exp~af !$N0 1 bt1/2

1 h@1 2 exp~2t/l!#ts 2/~ f 2 1 s 2!%/t, (3)

where Ct is the contrast threshold; a, N0 , b, h, l, and sare free parameters; and t is

t 5 tt0 /~t 1 t0!, (4)

where t is the display duration and t0 is a free parameter.The smooth curves in each panel are the fits of Eq. (3) toall the data points simultaneously. The free parametersobtained for the three observers are shown in Table 1.The model fit for each subject was then used to provide anestimate of five times contrast threshold for those combi-nations of spatial frequency and duration used in speedthreshold measurements.

In the calculation, the physical units of the stimulusvariables were cycles per degree for spatial frequency fand milliseconds for duration t.

3. RESULTSA. Experiment 1: Effect of Spatial Frequency onSpeed ThresholdsIn the first experiment, speed thresholds for discriminat-ing the direction of a drifting grating were measured atspatial frequencies ranging from 0.25 to 12 c/deg. Grat-ing display duration was 400 ms, and a uniform field ofthe same mean luminance was displayed in the absence ofthe grating. The contrast of the gratings was five timesthreshold.


Fig. 3. Contrast threshold for detecting static gratings at stimulus durations of 73 to 1600 ms. The smooth curves are the fits of Eq.(3) to data at durations of 73 (thick solid), 200 (dashed lines), 400 (dotted-dashed), 800 (dotted), and 1600 (thin solid) ms. The fits wereused to determine contrast values of equal visibility across spatial frequencies to be used in the subsequent experiments.

Table 1. Estimated Model Parameters for the Three Subjects

Subject

Parameter

a (deg) N0 (ms) b (Ams) h s (c/deg) l (ms) t0 (ms)

QW 0.159 0.145 0.005 0.024 0.27 166 180JY 0.187 0.101 0.015 0.039 0.28 284 284SBS 0.170 0.132 0.003 0.189 0.34 1477 154

The resulting speed thresholds for the three observersare shown in Fig. 4(a). Error bars represent 62 stan-dard errors. The speed threshold is plotted on a linearscale to facilitate comparison with earlier studies of lowerthreshold of motion, but the spatial frequency is on a logscale to provide details at low frequencies. All three sub-jects showed little change in threshold between 2 and 12c/deg, consistent with similar studies reported in theliterature.7,8,31

However, when spatial frequency decreases below 2c/deg, as shown in Fig. 4(a), the speed threshold increasesrapidly. This property, which has not been reported inthe literature to our knowledge, is similar to thefrequency tuning in velocity discrimination reported byMcKee et al.27

The attribute considered in Fig. 4(a) is the speed of themoving grating. Another attribute often reported in theliterature on motion detection is the temporal frequencyv. Figure 4(b) shows temporal frequency at threshold,which was converted by the formula v 5 vf, plottedagainst spatial frequency. The threshold in temporal fre-quency is relatively constant for low spatial frequenciesand then increases with spatial frequency above 1 or 2c/deg.

The results of experiment 1 indicate that speed thresh-olds rise considerably at low spatial frequencies, consis-tent with a constant temporal-frequency limit. Such alimit could be due to the spread of energy in the temporal-frequency domain that occurs whenever stimuli are pre-sented briefly, so in experiment 2 we manipulated the du-

ration of stimulus exposure as well to see whetherthreshold depends systematically on duration.

B. Experiment 2: Effect of DurationFigure 5 shows speed threshold for discriminating motiondirection plotted against spatial frequency for stimulusdurations of 73 to 800 ms. Contrasts were again fivetimes the detection thresholds for static gratings of thesame duration. Error bars represent 62 standard er-rors. Figure 5 shows the elevation of speed threshold at

Fig. 4. (a) Speed threshold for discriminating motion directionplotted against spatial frequency for subjects QW, JY, and SBS.Contrasts were five times the detection thresholds for static grat-ings. Stimulus duration was 400 ms. Error bars represent 62standard errors. (b) Same data plotted as temporal frequency atthreshold, converted by the formula v 5 vf.


low spatial frequency for all display durations. For eachcurve, motion sensitivity initially improves with spatialfrequency and then levels off at higher spatial frequency.Speed threshold on the vertical axis is now plotted on alog scale against log spatial frequency, for comparisonwith a line of slope 21, which represents inverse propor-tionality between velocity and spatial frequency and isthe predicted slope if threshold is determined by thespread of temporal frequency. Although the plot of speedthreshold against spatial frequency for a given durationdoes not fit a straight line, at low spatial frequencies (upto 1 c/deg) the slopes of the curves are close to 21 (dottedlines).

Figure 6 shows the data replotted as speed thresholdversus duration for spatial frequencies of 0.25 to 8 c/deg.The threshold value decreases as duration increases andis consistent with the study of Boulton,9 in which an in-verse proportionality was observed between speed thresh-

old and durations of 200 to 500 ms for foveal viewing. Astraight line with a slope of 21 in the log–log plot isshown as the dotted lines, indicating a reciprocity be-tween speed threshold and duration. The slopes of thecurves in the three panels, for subjects QW, JY, and SBS,are close to the slope of the straight line for durations upto ;400 ms, although they tend to be steeper for thehigher spatial frequencies. Thus, for low spatial frequen-cies and short durations, speed thresholds are consistentwith a temporal-frequency limit imposed by the spread ofenergy associated with brief exposures. This pattern ofresults is limited to spatial frequencies below ;1 c/degand durations less than ;400 ms. For higher spatial fre-quencies there appears to be a different regime wherethreshold is constant in terms of velocity. For presenta-tions longer than ;400 ms, duration has a somewhat re-duced influence. All three subjects follow this generaltrend but with some individual differences.

Fig. 5. Speed threshold for discriminating motion direction plotted against spatial frequency at stimulus durations of 73 to 800 ms forsubjects QW, JY, and SBS. Contrasts were five times the detection threshold for static gratings. The dotted-line slope of 21 in thelog–log plot is the predicted slope for a system limited by the velocity spread. Error bars represent 62 errors.

Fig. 6. Speed threshold versus stimulus duration, at spatial frequencies of 0.25 to 8 c/deg, for subjects QW, JY, and SBS. Contrast wasfive times the detection threshold for static gratings. The dotted-line slope of 21 in the log–log plot is the predicted slope for a systemlimited by the velocity spread. Error bars represent 62 standard errors.


The third experiment was designed to determine the ef-fect of grating contrast on speed threshold.

C. Experiment 3: Effect of ContrastIn the third experiment, speed thresholds for discriminat-ing the direction of a drifting grating were measured atspatial frequencies ranging from 0.25 to 8 c/deg. Gratingdisplay duration was 400 ms, and grating contrast was0.05, 0.2, and 0.8. Data were collected for two observers,QW and JY. Data at five times contrast threshold fromexperiment 1 are included in Fig. 7.

Figure 7 shows speed thresholds plotted against the ra-tio of grating contrast to contrast threshold for subjectsQW and JY. A strong interaction between spatial fre-quency and contrast is immediately evident. Speedthresholds varied little with contrast for spatial frequen-cies higher than 2 c/deg. This result is consistent withmany of the reports in the literature.8,23 However, atspatial frequencies lower than 2 c/deg, speed thresholddecreased with grating contrast up to ;100 times con-trast threshold. The overall effect of this is that speedthresholds are relatively constant across spatial fre-quency when contrast is high, and the spatial-frequencydependence shown in the results of experiments 1 and 2 ispredominantly a low-contrast phenomenon.

This phenomenon is illustrated more directly in Fig. 8,which shows speed thresholds measured at a contrast of0.2, considerably higher than the 53 threshold values

Fig. 7. Speed threshold versus ratio of grating contrast to con-trast threshold at frequencies of 0.25 to 8 c/deg. Stimulus dura-tion was 400 ms. Error bars represent 62 standard errors.

Fig. 8. Speed threshold versus spatial frequency at stimulus du-rations of 73 to 400 ms. Contrast was 0.2. The dotted-lineslope of 21 in the log–log plot is also shown. Error bars repre-sent 62 standard errors.

used in the second experiment. Results are shown for arange of spatial frequencies and for stimulus durationsfrom 73 to 400 ms. It is apparent that the spatial-frequency dependence for speed threshold here is muchless than that shown in Fig. 5. The dotted lines have aslope of 21 in the log–log plots, indicating as before areciprocity between velocity and spatial frequency. Theslopes of the curves in the two panels are much shallowerthan this. The effect of duration is similar to that forlow-contrast data, however.

4. QUANTITATIVE MODELThe temporal-frequency spreading produced by a brief ex-posure can be thought of as some external noise in the ve-locity domain:

A~v, v0 , t! 5 sin@p~v 2 v0!t#/@p~v 2 v0!#, (5)

where v is the temporal frequency in hertz and t is theduration in seconds. Equation (5) is a sinc function andrepresents the Fourier transform of the rectangular waveform of duration t. Figure 9 shows the squaredtemporal-frequency distribution function for a driftinggrating presented for 200 ms and is similar to an analysisby Derrington and Goddard.17 If the spatial frequency ofthe grating is 0.5 c/deg, the amount of peak shift v0 awayfrom 0 Hz shown in Fig. 9 corresponds to a drifting veloc-ity of 2.5 deg/s. For a comparison, the actual speedthreshold averaged over three subjects in this case was;0.23 deg/s. Thus threshold-level stimuli have consider-able energy in both positive and negative temporal fre-quency, corresponding to rightward and leftward motion.

Applying the notion that the minimum motion detec-tion task involves the combined action of many spatiotem-porally tuned filters, and particularly a comparison of ac-tivity in channels tuned for opposite directions ofmotion,14,32 we develop here a quantitative model thatcompares the integrated energy for leftward motion sen-sors with that for rightward motion sensors. The modelparticularly includes the effect of temporal-frequencyspread that accompanies brief presentations and also in-cludes position domain noise of the kind that might arisefrom fixation jitter.

The effective temporal-frequency spectrum of a brieflypresented grating is considered to be determined by three

Fig. 9. Relative power distribution in the temporal-frequencydomain for a drifting grating with a display duration of 200 ms, aspatial frequency of 0.5 c/deg, and a temporal frequency of 1.25Hz, which give a speed of 2.5 deg/s.


basic factors: the physical spread of energy, the overallenvelope of human temporal-frequency sensitivity, andthe channel bandwidth of temporal-frequency filters (e.g.,the light gray circles in Fig. 2). Similar to those of a con-trast sensitivity model,30 these factors are described, re-spectively, by the spread function A(v, v0 , t) from Eq.(5), a low-pass filter M(v), and a Gaussian filter profileG(v). The overall spectrum is found by multiplying thespread function by the sensitivity envelope and then con-volving the result with the filter profile. Thus the spec-trum in a later stage is expressed by

e~v, v0 , t! 5 @A~v, v0 , t!M~v!# * G~v!, (6)

where * denotes convolution. The integrated energy forrightward motion is simply

ER 5 E0

1`

e~v, v0 , t!2dv 1 N, (7)

and for leftward motion is

EL 5 E2`

0

e~v, v0 , t!2dv 1 N, (8)

where N is a position noise term, as might arise for ex-ample from eye-movement noise. Because these equa-tions are expressed in terms of temporal frequency butthe noise arises from position uncertainty, the noise hasan increasing effect for higher-spatial-frequency gratingsand is modeled here by N 5 2pbft, where b is the freeparameter.

Direction discrimination is assumed to depend on theratio of rightward energy, ER , to leftward energy, EL ;

r 5 ER /EL . (9)

In the calculation we used a low-pass function: M(v)5 exp(2v/12) as estimated by Yang and Makous.33 Theprofile of high-temporal-frequency filters has little effecton the r value; thus the temporal filter was modeled asshift invariant with a Gaussian G(v) 5 exp(2v2/2s2)/A(2p)s. This model then has three free parameters:the threshold ratio r, the filter size s, and the magnitudeof a position noise b. The fit of model equation (9) withthe averaged data across three subjects is shown in Fig.

Fig. 10. Comparison of the fits (solid curves) and the averageddata across three subjects for the durations shown (milliseconds).

10, with the obtained parameters r 5 1.059, s51.04 Hz,and b 5 2.6 min. The quality of the fit shown in Fig. 10is moderate, but in general this model accounts for the ef-fects of both spatial frequency and duration on speedthreshold in this minimum motion task. Contrast is nota factor in this model, and it is not immediately obvioushow to include it.

5. DISCUSSIONThe data from experiments 1 and 2 show that the percep-tion of disorganized motion that accompanies briefly pre-sented low-spatial-frequency gratings is not associatedwith unusually high sensitivity in a direction discrimina-tion task. Quite the opposite, speed sensitivity was low-est at low spatial frequency, where the disorganized mo-tion was strong. The overall pattern of results suggeststhat motion thresholds at low spatial frequencies (and lowcontrasts) are limited by the spread of energy that accom-panies brief presentations, and the disorganized motionphenomenon may be a consequence of this spread. Atlow spatial frequency the temporal-frequency spreadtranslates to relatively high velocities, perhaps account-ing for the greater salience of the phenomenon in thisrange. At higher spatial frequencies, speed sensitivity islimited to a particular velocity that we have suggestedmay be due to fixation jitter, but any source of uncer-tainty in the position of the grating might produce thesame effect.

Motion processing is often linked with the magnocellu-lar (M system) information stream in the primate visualsystem,18–20 but the results presented here for minimummotion detection seem inconsistent with reported proper-ties of M cells. M cells have their greatest sensitivity atlow spatial frequencies and show saturating responseswith increasing contrast,19 but experiment 1 has shownthat speed threshold increases as spatial frequency de-creases, and experiment 3 has shown that high spatialfrequencies exhibit contrast saturation in the motion taskand that low spatial frequencies do not. The experimen-tal results do not strictly rule out M-cell mediation ofthresholds, of course, since the response of a population ofcells may differ from the response of individual cells. Forexample, the lack of saturation at low frequencies may re-flect recruitment of more and more cells, even though in-dividual cells may show contrast saturation. This phe-nomenon still would not explain the contrast saturationthat is found for high spatial frequencies. Thus it is pos-sible that a population model of just M-cell responsescould account for our minimum motion detection results,but it is not immediately obvious how this would work.

It is known that both the M and the P pathways play arole in motion processing. Merigan et al.34 showed thatM-pathway lesions in monkeys did not affect either direc-tion discrimination at low velocity or speed discrimina-tion. In a review paper, Merigan and Maunsell35 furthersuggested that ‘‘the M pathway is not specialized for mo-tion perception, but is specialized for the transmission ofmiddle and high velocity stimuli... .’’ Many authors (e.g.,see Ref. 20) share a similar view that both pathways canprocess low velocities. Our experimental results do notconclusively point to the action of M cells, P cells, or both,


but what can be concluded here is that visual perfor-mance on motion detection cannot be obtained from theproperties of individual M cells without an elaboratemodel of how the cells combine.

Model equation (9) does not depend on grating contrast,and it was developed to account for low (5 3 threshold)contrast data. Although the data from higher contrastdo not show the same spatial-frequency effect, the dura-tion effect is similar and follows the uncertainty predic-tion fairly well. Our emphasis on the low-contrast datafollows from the notion that lower-contrast stimuli pro-vide better isolation of particular spatiotemporal filters.The spreading of energy at high contrast allows for the in-creased possibility of off-frequency detection, contrastnonlinearities, and other effects that render the stimuliless specific to a particular spatiotemporal band. Theprincipal difference between the data in Fig. 8 (0.2 con-trast) and the data in Fig. 5 (5 3 threshold) is the im-provement in performance at low spatial frequencies.The shallow slope of these speed-threshold-versus-spatial-frequency curves in Fig. 8 could well be due to theaction of higher-spatial-frequency mechanisms, stimu-lated by the greater spread of energy at this higher con-trast.

ACKNOWLEDGMENTSThis work was supported by National Eye Institute grantEY-10531-02. We thank Harold Bedell for helpful dis-cussion and suggestions and Alan Wang for serving as anobserver.

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effects of spatial frequency, duration, and contrast on discriminating motion directions

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