Is motion processing unitary?

2836 J. Opt. Soc. Am. A/Vol. 16, No. 12 /December 1999 Simpson et al.

Is motion processing unitary?

William A. Simpson and Velitchko Manahilov

Vision Sciences Department, Glasgow Caledonian University, Cowcaddens Road, Glasgow G4 0BA, Scotland

Melissa S. Mair

Psychology Department, University of Winnipeg, 515 Portage Avenue, Winnipeg MB, Canada R3B 2E9

Received March 9, 1999; accepted June 22, 1999; revised manuscript received July 21, 1999

Motion discrimination space is conventionally categorized into motion detection, speed discrimination, and di-rection discrimination tasks. But an ideal observer uses a unitary motion mechanism that is affected only bythe noise level and the difference in speed (or displacement) between two stimuli. We tested whether humanperformance in the various motion tasks showed the working of a unitary mechanism or the combined outputsof more than one mechanism. We examined the whole motion discrimination space, using random dots thatunderwent a sudden jump or displacement. The discriminability was measured as a function of the standardand comparison displacements. Both the ideal observer model and a nonideal observer model that containsadditive internal noise predict a planar response surface. When the dot motion was noiseless, the planar sur-face fitted well except for much higher than expected sensitivity for motion detection. This is consistent witha purely temporal mechanism that uses flicker or a purely spatial mechanism that uses the length of time-averaged streaks. It is also consistent with a Weber’s law device. When motion noise was added to the dis-plays, the planar response surface again fitted well, although the residuals showed the presence of a speedenergy mechanism. We conclude that a unitary motion mechanism exists (nonideal observer model), althoughits performance may be supplemented by other mechanisms whose main impact is on discrimination of speedsnear zero. © 1999 Optical Society of America [S0740-3232(99)00212-4]

OCIS codes: 330.4150, 330.5510, 330.4060.

1. INTRODUCTIONHuman motion sensitivity can be measured by severaldifferent sorts of experiment. In a motion detectionexperiment1 the observer discriminates moving and sta-tionary displays. In a speed discrimination experiment,the observer discriminates a larger and a smaller speed,both in the same direction.2 Finally, in a direction dis-crimination task, the two speeds have the same magni-tude but opposite directions.3 Do all these tasks tap oneand the same mechanism?

To an ideal motion observer all the tasks are alike.The ideal observer’s performance depends only on theamount of noise and the size of the speed or displacementdifference. In our experiments we use a sudden jump ordisplacement. A random dot field that jumps rightwardby 2 arcmin can be described as delivering either a posi-tional step of 2 arcmin or a speed of 2 arcmin s21 (since animpulse is in units of s21). To an ideal observer a right-ward jump of 2 arcmin and a leftward jump of 2 arcmin(direction discrimination) would be as discriminable as arightward jump of 4 arcmin and a stationary display (mo-tion detection), which in turn would be as discriminableas a rightward jump of 2 arcmin and a rightward jump of6 arcmin (speed discrimination); in all cases the displace-ment difference is 4 arcmin. We shall develop the idealobserver model in detail shortly.

The ideal observer model uses a unitary motion-sensing mechanism. However, in a real observer, thevarious motion tasks may tap several distinct mecha-nisms. The whole response surface could be a patch-work, with each patch being contributed by a different

0740-3232/99/122836-09$15.00 ©

mechanism. Motion detection stimuli, which containnonmotion cues, could tap a position-based mechanism.4

Direction discrimination stimuli may tap an opponent-motion mechanism, and this mechanism may not work forspeed discrimination stimuli that move in the same direc-tion. Thus the shape of the response surface may dependon factors other than just the speed (or displacement) dif-ference.

We compared the performance of observers in the dif-ferent motion tasks. The experimental layout is shownin Fig. 1. Each cell of the figure corresponds to one ex-perimental condition. In each condition, the standardand the comparison jumps were presented, and the ob-server’s ability to discriminate them was measured withthe signal-detection-theory index d8. The various mo-tion tasks fall in patches of the experimental matrix.When the standard or comparison jump is zero, we have amotion detection task. When the jumps have equal mag-nitudes but are in opposite directions, we have a directiondiscrimination task. When both jumps are in the samedirection but have different magnitudes, we have an ordi-nary speed discrimination task. When the jumps differin both direction and magnitude, we call it a ‘‘combo’’ taskbecause it combines aspects of the direction discrimina-tion and speed discrimination tasks.

By adding motion noise to the displays, we were alsoable to measure the efficiency of the observer in discrimi-nating the stimuli in the various tasks. If motion pro-cessing is unitary, we might expect the efficiency to be thesame regardless of the task. Conversely, if multiplemechanisms process the motion, we expect a pattern of ef-

1999 Optical Society of America

Simpson et al. Vol. 16, No. 12 /December 1999 /J. Opt. Soc. Am. A 2837

ficiencies that reveals these mechanisms. The efficiencywas found by comparing the performance of the real ob-servers to that of an ideal observer. Let us now derivethe performance of an ideal observer.

2. IDEAL-OBSERVER ANALYSISThe situation that we analyze is known as a ‘‘multiplesample binary communication system.’’ 5 There are twospeed signals to be discriminated: the vectors s0 and s1(each consisting of m time samples). At each instant asample of normal N(0, s2) noise, nk , is added to the sig-nal. The ideal observer knows the two signal waveformsexactly and performs the discrimination by cross correlat-ing the received (signal 1 noise) waveform with each ofthe two signals. The discriminability of the standardand comparison speeds is given by

d8 5

F(k51

m

~s1k 2 s0k!G 1/2

s. (1)

This equation holds for any pair of signals. In our ex-periments the speed signals were

s0k 5 a0dk2T 5 H a0 if k 5 T

0 if k Þ T, (2)

s1k 5 a1dk2T 5 H a1 if k 5 T

0 if k Þ T. (3)

Each signal is a Kronecker delta function6: The speed iszero except for an impulsive jump having a speed (or dis-placement) a0 or a1 at time T. The discriminability ofthese signals is

d8 5@~a1 2 a0!2#1/2

s5

ua1 2 a0u

s. (4)

Fig. 1. Each cell in the diagram shows an experimental condi-tion: a pair of standard and comparison displacements to be dis-criminated, in arbitrary units. Detectability d8 for discriminat-ing each pair was measured.

For each pair of comparison and standard speeds (dis-placements) we measured the discriminability. Accord-ing to the ideal observer analysis, the d8 points should lieon the surface of a tilted plane that passes through theorigin. (The surface is actually V shaped, but in our ex-periments we looked at just one of its two symmetricalplanes.)

An ideal observer would discriminate noiseless displaysperfectly, with infinite d8. We can model the results fornoiseless displays if we suppose that the observer’s visualsystem contains motion noise. The noise would likely bedue to variability in the observer’s fixation as well as inthe output of neurons coding the displacement. Thenonideal-observer model prediction is also Eq. (4), butnow we interpret s as representing the standard devia-tion of the internal noise. In the case of a noisy display,s is the square root of the sum of internal and externalnoise variances. This nonideal observer model predictsthat the detectability surface will be a tilted plane pass-ing through the origin.

In our experiments we presented only horizontal mo-tion. In general, motion has a vertical component aswell. If both components were present, the ideal and thenonideal observer models would discriminate the dis-placement or velocity vectors a0 and a1 .

3. METHODA. ObserversThe authors, WS, VM, and MM, served as observers. VMhas normal vision; MM and WS have corrected-to-normalvision.

B. ApparatusThe displays were presented on a Tektronix 608 oscillo-scope with P15 phosphor. The oscilloscope was con-trolled by a point-plotting memory buffer developed at theUniversity of Alberta.7 Viewing was binocular from achin rest placed 86 cm from the face of the oscilloscope.A button box collected responses.

C. StimuliThe stimulus consisted of bright (202 cd/m2) moving ran-dom dots on a black (0.001 cd/m2) background. Therewere 990 random dots and a fixation cross at the centermade up of 10 dots; thus there were 1000 dots in total.Since the dots were plotted at a rate of one per microsec-ond, the refresh rate of a frame was 1000 Hz. The ran-dom dots filled a 4.1-deg-square region. Each dot was 2.8arcmin in diameter.

Two versions of the experiment were run. In thenoiseless experiment, the display was a two-frame hori-zontal motion sequence with wraparound. Each framewas displayed for 200 ms. Several displacements wereused in the range 61.92 arcmin. Given the properties ofthe Dirac delta function, the speed was in the range61.92 arcmin s21. The average speed over the durationof the display was 64.80 arcmin s21.

The noisy experiment was similar, with a single hori-zontal jump as the signal (displacements in the range63.84 arcmin), but horizontal-motion noise was superim-posed on the display. The display used 80 frames, each


displayed for 5 ms. It is easiest to describe the display byseparating the signal and noise components. The signalwas a single horizontal jump, generated by moving eachdot i from position xi on frames 1–40 (200 ms), to positionxi 1 D on frames 41–80 (200 ms). A new sample of nor-mal random noise with mean zero and standard deviation0.3 arcmin was added onto each dot’s horizontal positionon each frame. The noise added on each frame was thesame for all the dots. This gave the display a rigid jitter-ing similar to fixation noise.8 Since the average speed ofthe noise was zero, the average speed of the display wasthe same as in the noiseless case (in the range 64.80arcmin s21).

D. ProcedureIn a block of trials the observer was presented with twostimuli: the standard and the comparison jumps. Eachtrial contained either the standard or the comparison,and the observer indicated by a button press which hadoccurred. The standard and the comparison were pre-sented in random order. A block with a given standardand comparison consisted of 100 trials. Five blocks of tri-als were run for each stimulus pair for the noiseless con-dition, and four blocks were run for the noisy condition.

At the beginning of a block of trials, the observer wasfamiliarized with the standard and comparison stimuli byseeing them presented in alternation three times each.When ready, the observer then initiated the experimentproper. Each response was categorized as a hit (responseof ‘‘standard’’ when standard was presented), miss (re-sponse of ‘‘comparison’’ when standard was presented),false alarm (response of ‘‘standard’’ when comparison waspresented), or correct rejection (response of ‘‘comparison’’when standard was presented). Auditory feedback fol-lowed each incorrect response.

4. RESULTS AND DISCUSSIONWe presented pairs of standard and comparison jumpsand measured their discriminability d8. These discrimi-nations were performed for displays with and without su-perimposed motion noise. The data form a surface whoseshape we can compare to an ideal motion observer thatuses a unitary mechanism. The data from the noisy dis-plays allow us to evaluate the efficiency of motion process-ing, which sheds light on the unitary motion processingissue as well as being of intrinsic interest.

A. Unitary Motion Sensing?If motion sensing uses a unitary mechanism, the idealand the nonideal observer models predict a detectabilitysurface that is a tilted plane passing through the origin.The models are unitary in that the discriminability of apair of jumps should depend only on the difference in thesizes of their displacements and the noise level. Our ap-proach is to fit the ideal and the nonideal observer modelsto the data and then to look at the errors (residuals). Ifmotion sensing is unitary and is well described by theideal or the nonideal observer model, then the error sur-face will be flat with random deviations. On the otherhand, if each task—motion detection, speed discrimina-tion, direction discrimination, combo—taps a different

mechanism, we will expect a surface with bumps or dipsthat deviate from the plane. The errors will not be ran-dom; the error plot will have a systematic nonflat surface.A systematic error surface indicates the presence of extramechanisms operating in addition to the ideal or the non-ideal observer mechanism. The logic is simple. Wehave data 5 fit 1 error, where the fit is due to the idealor the nonideal observer model. In the case in which theideal or the nonideal observer model fits well, the error isdue to sampling or measurement. We explain the databy one mechanism, the ideal or the nonideal observermodel. In the case where there are systematic bumps ordips in the error surface, the error term does not repre-sent sampling error but instead represents the contribu-tion of another mechanism (or mechanisms). Each ob-served d8 is the sum of the d8 output by the ideal observermechanism and the d8 output by an additional mecha-nism.

1. Noiseless DisplaysFigure 2 shows the measured d8 surfaces for the noiselessdisplays. The ideal observer model cannot be fitted ifthere is no noise in the display, so we fitted the nonidealobserver model [Eq. (4)] by using least squares. The non-ideal observer model predicts that the detectability sur-face will be a tilted plane passing through the origin.

Fig. 2. Detectability d8 of the difference between the standardand comparison displacements (arcmin) for observers MM andWS. The display is noiseless.


The obtained surface has more or less the appearance of atilted plane, but for both observers the plane has a super-imposed ridge, which will discuss shortly. The nonidealobserver model has only one parameter, the standard de-viation of the noise inside the observer’s visual system.For observer MM the 95% confidence interval for the in-ternal noise standard deviation is 0.76 6 0.07 arc min,and for observer WS the estimate is 0.65 6 0.05 arc min.

The nonideal observer model does not completely de-scribe the data. There is an L-shaped ridge that is madevery clear by the residual plot in Fig. 3. The residualplot shows the difference between the obtained d8s andthose predicted by the best-fitting nonideal observermodel. The ridge corresponds to the motion-detectiontask: If the standard or the comparison is zero (station-ary), performance is much higher than predicted by themodel.

Fig. 3. Error—difference between observed and best-fitting val-ues of d8 with use of Eq. (4)—as a function of the standard andcomparison displacements (arcmin) for observers MM and WSand a device that obeys Weber’s law. The display is noiseless.In this and subsequent figures the region where the surface wasnot measured is given a height of zero to serve as a visual refer-ence.

We conclude two things from Figs. 2 and 3. First, thenonideal observer model is good as a first approximation.It is able to describe the results from the direction dis-crimination, speed discrimination, and combo tasks quitewell—the residual plot is flat for these conditions. How-ever, and this is the second conclusion, the performance ofthe real observer is much better for the motion detectiontask than we would predict from the nonideal observermodel. The response surface is the sum of the plane dueto the nonideal observer mechanism and the ridge due toanother mechanism. The nonideal observer mechanismis always at work, but an extra mechanism is recruitedwhen one of the sequences being discriminated is station-ary.

Our analysis so far has been at a high level of abstrac-tion. We have stated that a nonideal observer mecha-nism and a mechanism specialized for static displays ex-ist, but we have given no details about how thesemechanisms extract information from the stimuli. Letus first consider how the nonideal observer mechanismmight extract the needed information. A traditionalidea9 is that the position of an object is found at succes-sive instants, and the difference is taken to find the dis-placement. This idea does not spell out how the positionof the object is computed; this information has to be ex-tracted from the time-varying luminance distributionL(x, y, t) delivered to the retina. Other sorts of mecha-nisms that extract the motion from L(x, y, t) have beenproposed.10,11 Any mechanism that extracts the speed ordisplacement is compatible with the nonideal observermodel.

What is the basis of the mechanism specialized forstatic displays? One possible mechanism is based ontime averaging.12 The mechanism works like a long-exposure photograph of a moving scene (Fig. 4). If thedots are static, the output of the mechanism is a set ofdots. If the dots move, the output is a set of streaks. Sothe observer’s rule is, if streaks, say ‘‘motion’’; if dots, say‘‘static.’’ Such a mechanism will work well for motion de-tection and not at all for direction discrimination. Thetime averager is a purely spatial mechanism. A purelytemporal mechanism based on flicker could also be atwork. Any given point in the static display is constantover the display period, whereas for the moving dots, in-dividual locations flicker on and off. The mechanism willsimply test for the presence of flicker to perform motiondetection. This flicker mechanism’s performance will notdepend on the displacement. The ridge in the residualplot (Fig. 3) has a constant height regardless of the dis-placement, and so the flicker mechanism seems plausible.A final possibility is that the ridge is produced by amechanism that obeys Weber’s law.2 In an experimentin which a0 is varied and the value of a1 just discrim-inable from a0 is measured, Weber’s law can be written as

ua0 2 a1u 5 s 1 ua0us1 , (5)

where s is the standard deviation of the internal noise or,in other words, the motion detection threshold, and s1 isthe Weber fraction. If instead a1 is varied and the valueof a0 just discriminable from a1 is measured,

ua0 2 a1u 5 s 1 ua1us1 . (6)


We eventually want an expression for the discriminabilityof the pair a0 and a1 , so we need to combine Eqs. (5) and(6) in some way. One way to do it (using the idea of sepa-rable functions) is

ua0 2 a1u 5 ~ s 1 ua0us1!~ s 1 ua1us1!. (7)

Since d8 5 1 at threshold, we have

d8 5ua0 2 a1u

~ s 1 ua0us1!~ s 1 ua1us1!. (8)

This surface is shown at the bottom of Fig. 4, and it can beseen that the Weber’s law prediction matches the residu-als quite well. So a simple account of the data is thatthey are the combined output of a nonideal (noisy) ob-server and a Weber’s law device.

The logic of our analysis attributes deviations from thenonideal observer models to a secondary mechanism.Could our response surfaces instead be revealing a singlemechanism? Could a single mechanism produce both theplane and the ridge? The answer depends on what onecalls a mechanism. In our view, a mechanism is a func-tional unit that is defined by how it extracts informationfrom the stimulus needed to perform some task. Thetask in our experiments is to discriminate two signals,and the best possible information extraction mechanismfor this task is the ideal observer. The ideal observer is anatural and nonarbitrary starting point in constructing a

Fig. 4. Time-averaging mechanism giving an output like that ofa long-exposure photograph. This mechanism can perform mo-tion detection by comparing the output for static random dots(top) with the streaks obtained for moving random dots (bottom).

functional decomposition of the system. The planar partof the response surface corresponds to the ideal observer(with additive internal noise). The ridge does not corre-spond to the ideal observer and so is due to some othermechanism. Suppose a single motion sensor was con-structed that produced the response surface that we ob-serve. We would say that regardless of the details of theconstruction, such a motion sensor consists of two func-tional parts: one part that acts as a nonideal observerand another that exhibits Weber’s law behavior.

2. Noisy DisplaysThe pattern of results is similar for displays that haveadded motion noise. As shown in Fig. 5, the detectability

Fig. 5. Detectability d8 of the difference between the standardand the comparison displacements (arcmin) for observers MM,VM, and WS. The display has motion noise. Note the differentd8 scale on each observer’s plot.


surface is somewhat planar and tilted upward, as Eq. (4)would predict. The 95% confidence interval for the fittedstandard deviation of the noise for MM’s data is 2.886 0.52 arc min; for VM it is 4.76 6 0.33 arc min; and forWS it is 2.02 6 0.25 arc min. The standard deviation ofthe motion noise in the display was 0.3 arcmin. Sincethe confidence intervals for the noise standard deviationdo not include 0.3, all observers are clearly nonideal, theirvisual systems having additive noise with a standard de-viation of approximately 4.5, 2.6 and 1.7 arcmin, respec-tively. In the noiseless experiment we found the internalnoise standard deviation to be ;0.7 arcmin. So the stan-dard deviation of the internal noise grows as the standarddeviation of the external noise increases. The same ef-fect has been found in the luminance domain.13 Thereare many possible explanations. One simple idea is thatthe observer tries to cope with the noisy stimulus by am-plifying it, and the gain of this internal amplifier in-creases as the standard deviation of the display noise in-creases. The results of our study and the luminancedomain study clash with those of Watamaniuk,14 whoused a form of motion stimulus where each dot performeda two-dimensional random walk. He found that theinternal-noise standard deviation did not depend on thestandard deviation of the external noise. Perhaps thedifference in Watamaniuk’s result and our own is relatedto the form of noise used. In Watamaniuk’s experiments,on each frame every dot received a different value ofnoise. In our experiments, on each frame every dot re-ceived the same value of noise. Our display was a rigid(though jittering) translation; Watamaniuk’s was non-rigid.

The nonideal observer model’s tilted plane fits the re-sponse surface quite well: The residuals (Fig. 6) areabout half as big as they were for the noiseless displays.By adding motion noise to the displays, we have changedthe residual plots dramatically. In the noiseless displaysboth observers’ residual plots showed abrupt L-shapedridges corresponding to better-than-predicted perfor-mance for motion detection. But now, with noisy dis-plays (Fig. 6), these ridges are absent or have a differentform. The residuals for MM are small and show no pat-tern, indicating that the nonideal observer model fitswell. We explained the ridge in MM’s noiseless data asbeing due to the action of a time-averaging or flickermechanism. Since the ridge is now absent, the mecha-nism has been rendered inactive by the addition of motionnoise. This result is consistent with the time-averagingidea, since motion noise will make the time-averaged out-put for both a static and a moving display consist ofstreaks (Fig. 4), resulting in poor performance. Motionnoise would also inactive a flicker-based mechanism,since both static and moving displays with motion noisecontain flicker.

For VM and WS the residuals show a broad peak: Per-formance is higher than predicted from the nonideal ob-server model for motion when one of the displacements isclose to zero. The residual surface’s broad peak is unlikethe abrupt ridge found with the noiseless displays. Weattributed the noiseless displays’ ridge of high motion de-tection sensitivity to a time-averaging or flicker or We-ber’s law device. Perhaps such mechanisms are also

partly behind the broad peak found with the noisy dis-plays. However, we think that now a speed energy de-vice has been engaged. A speed energy device squaresand integrates the displacement or speed waveform deliv-ered to it. Several previous results have pointed to sucha speed energy device: the elliptical threshold loci foundin a two-impulse temporal summation experiment,1 thepedestal effect for speed discrimination,15 and the shapeof directional tuning curves.16 (Note that speed energy isunrelated to Adelson and Bergen’s10 motion energy.)

We now derive the predicted detectability surface froma speed energy mechanism. If the observer’s visual sys-tem squares and sums the motion stimulus, the resulting

Fig. 6. Error (difference between observed and fitted d8) as afunction of the standard and the comparison displacements (arc-min) for observers MM, VM, and WS. The display has motionnoise. Note the different error scale on each observer’s plot.


random variable is distributed as noncentral chi-squared.When signal s0 is delivered, the mean is n 1 a0

2 where n isthe number of samples and the variance is 2(n 1 2a0

2);when signal s1 is delivered, the mean is n 1 a1

2 and thevariance is 2(n 1 2a1

2). For a large number of samples(as we used), the noncentral chi-squared distribution iswell approximated by the normal. The measure d8 is de-fined only for normal distributions with equal variances.However we could measure de8 , which uses the average ofthe standard deviations, giving

de8 5ua1

2 2 a02u

~2n 1 2a02 1 2a1

2!1/2. (9)

The output of this energy device is plotted in Fig. 7. Notethe strong similarity between this plot and the residualplots of VM and WS in Fig. 6. It appears that in VM andWS an energy device is operating in parallel with a noisybut otherwise optimal detector (nonideal observer).

We have argued that motion noise abolishes the actionof a supplementary time averaging or flicker mechanism.This occurs in all observers. We proposed that an energydevice accounts for the residuals in observers VM andWS. Why is it not active in observer MM? There aretwo possible explanations. The first possibility is thatfurther experimental trials would reduce the noise inMM’s response surface and we would be able to observean energy device’s output in her residuals. The secondpossibility is that the deployment of any mechanism, in-cluding a speed energy mechanism, depends on the ob-server. We do not think that visual mechanisms arerigid, fixed, and universal to all observers. The observerdevelops the required mechanisms during the course ofthe experiment (perceptual learning) and chooses andcombines mechanisms to produce the best performance.According to this point of view, MM either did not developthe speed energy mechanism or chose not to use it.

B. Efficiency of Motion SensingWe measured the motion sensing efficiency of our observ-ers on an absolute scale. The efficiency F, is defined17,18

Fig. 7. Output of an energy detection mechanism as a functionof the standard (a0) and comparison (a1) displacements. Thismodel seems to explain the residual plots for VM and WS inFig. 6.

as

F 5 S dobserved8

d ideal8D 2

(10)

where d ideal8 is given by Eq. (4). The ideal observer addsno noise to the received stimulus, so if the stimulus isnoiseless, then s in Eq. (4) is zero. Thus in the noiselesscase d ideal8 is infinite and the efficiency cannot be com-puted. By adding noise to the stimulus motion we areable to compute the efficiency surfaces for both observers(Fig. 8). For WS the maximum efficiency is near 9%, forMM it is about 2%, and for VM it is about 1%. We at-tribute the low efficiencies to internal noise added by the

Fig. 8. Efficiency (F, the squared ratio of observed to ideal d8)as a function of the standard and comparison displacements (arc-min) for observers MM, VM, and WS. The display has motionnoise. Note the different efficiency scale on each observer’s plot.


observer to the stimulus (nonideal observer model). An-other source of inefficiency is likely the extraction of thespeed or displacement from the spatiotemporal luminancewaveform (this extraction occurs perfectly in the ideal ob-server). Our efficiencies are similar to those ofWatamaniuk,14 who compared data from real and idealobservers in an experiment where the random dots had atwo-dimensional directional noise added onto their paths.

Now consider the shape of the efficiency surface. Theideal observer’s efficiency is a flat plane at 100%, and anonideal observer with additive internal noise would havea flat planar efficiency surface at some level below 100%.The efficiency surfaces of VM and WS have a distinctivetwin-peak shape. This shape is similar to that seen inFig. 7; we attribute it to the operation of a speed energymechanism. MM’s surface is irregular and tilted up-ward. This upward tilt implies that proportionately lessnoise is generated in MM’s visual system for the largerdisplacements. This effect has been found in the lumi-nance domain, where the observer’s internal noise de-clines as retinal illuminance increases.19,20 We agreewith Burgess21 that these seemingly low-level discrimina-tion and detection tasks reveal high-level (cognitive) pro-cessing in the brain. If this is true, the sort of stimulipresented—luminance flashes or motion jumps—will notaffect the operation of the information extraction and de-cision mechanisms that we are measuring, and we willfind similar effects across stimulus domains. Whyshould such a noise-reduction-with-increasing-stimulus-magnitude effect be found in any domain? One possibil-ity is that when the stimulus magnitude is increased, ob-server uncertainty about the signal’s waveformparameters (time of the jump and its amplitude) is re-duced. Observer uncertainty about a waveform thatshould ideally be known exactly makes the task one of de-tecting a signal with random parameters.

It is interesting to note that the direction discrimina-tion task, studied widely in the Dmax literature,3 is thetask humans are least efficient at.

5. CONCLUSIONSWe initially wondered whether human motion sensingwas unitary, using one basic mechanism to discriminatemoving displays, or whether instead it used a patchworkof mechanisms, each corresponding to one of the conven-tional motion tasks (motion detection, speed discrimina-tion, and direction discrimination). Our data show thatone basic mechanism, an ideal observer with added inter-nal motion noise, accounts for most of human motion per-formance. This mechanism is unitary in that it caresonly about the speed or displacement difference; the con-ventional motion task categories mean nothing to it.However, we also found evidence for other mechanismsthat operate in parallel with the nonideal observermechanism. The contribution of these other mechanismsis relatively small. When the display is noiseless, thesecondary mechanism could be a Weber’s law device orone that uses purely spatial (time-averaging) or temporal(flicker) information in the displays. When the displayhad added motion noise, we observed a secondary mecha-nism that computes the speed energy. This speed energy

mechanism is unitary and makes a small contribution toperformance over the whole range of conventional motiontasks.

We derived an ideal observer model for the conven-tional motion tasks. Human performance differs fromthe ideal in two ways. First, the human visual systemcontains additive motion noise. This noise is likely dueto variability in the outputs of the speed (or displacement)sensing neurons in the brain and to fixation variability.The standard deviation of the internal noise depends onthe amount of external noise. Second, humans use ancil-lary mechanisms in addition to those used by an ideal ob-server.

ACKNOWLEDGMENTSThis work was supported by a grant from the Natural Sci-ences and Engineering Research Council of Canada.

Send all correspondence to William Simpson at the ad-dress on the title page or by e-mail: [email protected].

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Is motion processing unitary?