psychonomic bulletin & review 2004 (in press why is it...

PROLOGUEIn the year 1997, October 10 was the day on which

citizens of Alaska received their annual oil dividend ofapproximately $1,500 per person. Perhaps it was tocelebrate this event that four young hoodlums decidedto hit the streets of Fairbanks for a Clockwork-Orange-style evening of vicious attacks on random individuals.When the night was over, a teenage boy identified as“L.H.” lay dead, and an older man, Franklin Dayton,

was seriously injured as a result of the gang’s maraud-ing.

Fairbanks Alaska is not a town that takes violentevents in stride: The public responded in outrage, andpolice reaction was swift. Within days, four suspectswere arrested and locked up. Eventually, they weretried for the crimes.

At trial, the prosecutor introduced various kinds ofevidence bearing on the defendants’ guilt. However, theprosecutor had no smoking gun, literal or metaphorical,and the centerpiece of his case was an eyewitness ac-count provided by one Arlo Olson. Mr. Olson testifiedthat while standing in the doorway of Eagles Hall indowntown Fairbanks, he watched in horror as a groupof men, whom he later identified as the defendants,accosted and savagely beat Mr. Dayton in a parking lota couple of blocks away.

Of some note is that “a couple of blocks away”—thedistance from Olson’s vantage point to the parking

Psychonomic Bulletin & Review2004 (in press)

Why is it easier to identify someoneclose than far away?

GEOFFREY R. LOFTUSUniversity of Washington

andERIN M. HARLEY

University of California, Los Angeles

It is a matter of common sense that a person is easier to recognize when close than when far away. Apossible explanation for why this happens begins with two observations. First, the human visual sys-tem, like many image-processing devices, can be viewed as a spatial filter which passes higher spatialfrequencies, expressed in terms of cycles/degree, progressively more poorly. Second, as a face ismoved further from the observer, the face’s image spatial frequency spectrum expressed in terms ofcycles/face scales downward in a manner inversely proportional to distance. An implication of thesetwo observations is that as a face moves away, progressively lower spatial frequencies, expressed incycles/face—and therefore progressively coarser facial details—are lost to the observer at a rate that islikewise inversely proportional to distance. We propose what we call the distance-as-filtering hypothe-sis, which is that these two observations are sufficient to explain the effect of distance on face proc-essing. If the distance-as-filtering hypothesis is correct then one should be able to simulate the effect ofseeing a face at some distance, D, by filtering the face so as to mimic its spatial-frequency composi-tion, expressed in terms of cycles/face, at that distance. In four experiments we measured face percep-tion at varying distances that were simulated either by filtering the face as just described, or byshrinking the face so that it subtended the visual angle corresponding to the desired distance. The dis-tance-as-filtering hypothesis was confirmed perfectly in two face-perception tasks: assessing the in-formational content of the face and identifying celebrities. Data from the two tasks could be accountedfor by assuming that they are mediated by different low-pass spatial filters within the human visualsystem that have the same general mathematical description, but that differ in scale by a factor of ap-proximately 0.75. We discuss our results in terms of (1) how they can be used to explain the effect ofdistance on visual processing, (2) what they tell us about face processing, (3) how they are related to“flexible spatial scale usage” as discussed by P. Schyns and colleagues, and (4) how they may be usedin practical, e.g., legal settings to demonstrate the loss of face information that occurs when a person isseen at a particular distance.

This research was supported by NIMH Grant MH41637 toG. Loftus. We thank Keri Carlsen and Jacquie Pickrell forassistance in data collection. We thank Davida Teller fordetailed and very useful comments on two earlier drafts. Foradditional insights and comments, we also thank Larry Ma-loney, Cathleen Moore, John Palmer, Denis Pelli, andGillian Rhodes. Correspondence concerning this articleshould be addressed to Geoffrey R. Loftus, Box 351525,University of Washington, Seattle, WA 98195-1525 (e-mail:[email protected]).

2 LOFTUS AND HARLEY

lot—was determined to be approximately 450 feet. Inresponse to this and related issues, the defense flew inan expert witness from Seattle—a psychologist whosejob was to educate the jury about various pitfalls ofhuman perception and memory. Part of the expert’s taskwas to provide information about a witness’s ability toperceive and acquire, from a distance of 450 feet, suffi-cient information about an assailant's appearance thatwould allow him to accurately identify the assailantlater on.

The eyewitness, Mr. Olson, testified that he had astrong memory of the defendants. Furthermore, he wasquite certain that his strong memory came about be-cause he had had a good view of the defendants as hewatched the mayhem unfold in the parking lot. Theexpert did not dispute Mr. Olson’s strong memory, andentertained several hypotheses about how Mr. Olsonmay have acquired it. But contrary to Mr. Olson’sclaim, none of these hypotheses involved the proposi-tion that his memory had been formed during the actualevent. The main reason for the expert’s skepticism wasthat 450 feet is simply too far away for a witness to beable to accurately perceive the features that constitute aperson’s facial appearance. In his trial testimony, theexpert tried to convey this difficulty to the jury bypointing out that seeing someone from 450 feet away iswhat you’re doing when you’re sitting hgh in the cen-ter-field bleachers of Yankee Stadium, looking acrossthe ballpark at another individual sitting in the standsbehind home plate.

On his way back to Seattle, the expert pondered howhe might better convey the effect of distance on visualinformation acquisition. He felt that the Yankee Sta-dium example may have sufficed for the somewhatextreme circumstances of this particular case. But inother instances, a witness may have viewed a criminalfrom a distance of 200 ft or 100 ft or 50 ft. How, theexpert wondered, could a jury or anyone else be pro-vided a clear intuition for the information loss that re-sults from seeing someone at successively greater dis-tances, beyond the bland and relatively uninformativeassertion that, “because of acuity limitations, one’sability to perceive something gets worse as distanceincreases”? Perhaps, he thought, some kind of visualrepresentation of such information loss could be de-vised.

And thus were sown the seeds of the research to bedescribed in this article. The general idea we propose isthat the effect of distance on face perception can beconstrued as the visual system’s inability to perceiveand encode progressively coarser-grained facial detailsas the face moves further away. The research reportedin the remainder of this paper has two purposes. Thefirst is to develop and test formal theory incorporatingthis idea and to determine empirically whether it makessense. The second is to begin to develop quantitativetools for demonstrating the loss of facial detail that cor-responds to any specified distance.

DISTANCE, VISUAL ANGLE,AND SPATIAL FREQUENCIES

The proposition that “the visual system is less able toperceive and encode progressively coarser-grained fa-cial details as the face moves further away” is vague. Itneeds to be expressed more precisely before it can beused to explain the effect of distance on perception. Inthis section, such precision is developed. We begin bynoting the relation between distance and visual angleand progress from there to the relation between distanceand spatial frequency. The section ends with a specific,quantitative hypothesis called the distance-as-filteringhypothesis that is suitable for experimental test.

Distance and Visual Angles

If you ask someone why a face is harder to recognizewhen it is further away, most people will answer, “be-cause it gets smaller.” This is obviously true in thesense that as a face is moved further from an observer,it shrinks from the observer’s perspective; i.e., its visualangle and retinal size decrease in a manner that is in-versely proportional to distance. So if one wanted todemonstrate the effect of distance on perception, onecould do so by appropriately shrinking a picture. This isdone in Figure 1, which shows the size that Julia Rob-erts’s face would appear to be, as seen from distancesof 5.4, 43, and 172 feet.

The Figure-1 demonstration of the effect of distanceon perception is unsatisfying for several reasons. Froma practical perspective, it is unsatisfying because (1) itsquantitative validity depends on the viewer’s being aspecific distance from the display medium (in this in-stance, 22” from the paper on which Figure 1 is printed)and (2) the graininess of the display medium can differ-entially degrade the different-sized images—for in-stance, if one is viewing an image on a computermonitor, an image reduction from, say, 500 x 400 pixelsrepresenting a 5-ft distance to 10 x 8 pixels representinga 250-ft distance creates an additional loss of informa-tion, due to pixel reduction, above and beyond that re-sulting from simply scaling down the image’s size (andthis is true with any real-life display medium: Lookingat the bottom image of Figure 1 through a magnifyingglass, for instance, will never improve its quality to thepoint where it looks like the top image). From a scien-tific perspective, the Figure-1 demonstration is unsatis-fying because reducing an image’s size is simply ge-ometry. That is, apart from the basic notion of a retinalimage, it does not use any known information about thevisual system, nor does it provide any new insight abouthow the visual system works.

Spatial Frequencies

An alternative to using variation in an image’s size torepresent distance is to use variation in the image’s

DISTANCE AND SPATIAL FREQUENCIES 3

spatial-frequency composition. It is well known thatany image can be represented equivalently in imagespace and frequency space. The image-space represen-tation is the familiar one: It is simply a matrix of pixelsdiffering in color or, as in the example shown in Figure1, gray-scale values. The less familiar, frequency-spacerepresentation is based on the well known theorem thatany two-dimensional function, such as the values of amatrix, can be represented as a weighted sum of sine-wave gratings of different spatial frequencies and ori-entations at different phases (Bracewell, 1986). One canmove back and forth between image space and fre-quency space via Fourier transformations and inverseFourier transformations.

Different spatial frequencies carry different kinds ofinformation about an image. To illustrate, the bottompanels of Figure 2 show the top-left image dichoto-mously partitioned into its low spatial-frequency com-ponents (bottom left) and high spatial-frequency com-

ponents (bottom right). It is evident that the bottom leftpicture carries a global representation of the scene,while the bottom-right picture conveys informationabout edges and details, such as the facial expressionsand the objects on the desk. Figure 2 provides an exam-ple of the general principle that higher spatial frequen-cies are better equipped to carry information about finedetails. In general, progressively lower spatial frequen-cies carry information about progressively coarser fea-tures of the image.

Of interest in the present work is the image’s contrastenergy spectrum, which is the function relating contrastenergy—informally, the amount of “presence” of somespatial-frequency component in the image—to spatialfrequency. For natural images this function declines,and is often modeled as a power function, E = kf-r,where E is contrast energy, f is spatial frequency, and kand r are positive constants; thus there is less energy inthe higher image frequencies. Figure 2, upper rightpanel shows this function, averaged over all orienta-tions, for the upper-left image (note that, characteristi-cally, it is roughly linear on a log-log scale). Below, wewill describe contrast energy spectra in more detail, inconjunction with our proposed hypothesis about therelation between distance and face processing.

Absolute Spatial Frequencies and Image SpatialFrequencies. At this point, we explicate a distinctionbetween two kinds of spatial frequencies that will becritical in our subsequent logic. Absolute spatial fre-quency is defined as spatial frequency measured in cy-cles per degree of visual angle (cycles/deg). Image spa-tial frequency is defined as spatial frequency measuredin cycles per image (cycles/image). Notationally, wewill use F to denote absolute spatial frequency (F incycles/deg), and f to denote image spatial frequency (fin cycles/image).

Note that the ratio of these two spatial frequencymeasures, F/f in image/deg, is proportional to observer-stimulus distance. Imagine, for instance, a stimulusconsisting of a piece of paper, 1 meter high, depicting10 cycles of a horizontally-aligned sine-wave grating.The image frequency would thus be f = 10 cy-cles/image. If this stimulus were placed at a distance of57.29 meters from an observer, its vertical visual anglecan be calculated to be 1 deg, and the absolute spatialfrequency of the grating would therefore be F = 10 cy-cles/1 deg = 10 cycles/deg, i.e., F/f = (10 cy-cles/deg)/(10 cycles/image) = 1 image/deg. If the ob-server-stimulus distance were increased, say by a factorof 5, the visual angle would be reduced to 1/5 = 0.2deg, the absolute spatial frequency would be increasedto F = 10 cycles/0.2 deg = 50 cycles/deg, and F/f =50/10 = 5 image/deg. If, on the other hand, the distancewere decreased, say by a factor of 8, the visual anglewould be increased to 1 x 8 = 8 deg, the absolute spatialfrequency would be F = 10 cycles/8 deg = 1.25 cy-cles/deg, and F/f = 1/8 image/deg. And so on.

5.4 ft

43 ft

172 ft

Figure 1. Representation of distance by reduction ofvisual angle. The visual angles implied by the threeviewing distances are correct if this page is viewed froma distance of 22”.

4 LOFTUS AND HARLEY

Filters, Modulation-Transfer Functions, and Con-trast-Sensitivity Functions. Central to our ideas is theconcept of a spatial filter, which is a visual processingdevice that differentially passes different spatial fre-quencies. A filter’s behavior is characterized by amodulation-transfer function (MTF) which assigns anamplitude scale factor to each spatial frequency. Theamplitude scale factor ranges from 1.0 for spatial fre-quencies that are completely passed by the filter to 0.0for spatial frequencies that are completely blocked byit.

The human visual system can be construed as con-sisting of a collection of components—e.g., the opticsof the eye, the receptive fields of retinal ganglion cells,and so on—each component acting as a spatial filter.This collection of filters results in an overall MTF inhumans whose measured form depends on the particu-lar physical situation and the particular task in whichthe human is engaged.

What do we know about the human MTF? In certain

situations, the MTF can be described by a contrast-sensitivity function (CSF) which is the reciprocal ofthreshold contrast (i.e., contrast sensitivity) as a func-tion of absolute spatial frequency. A “generic” CSF,shown in Figure 3 reasonably resembles those obtainedempirically under static situations (e.g., Campbell &Robson, 1968; van Nes & Bouman, 1967). As can beseen, it is band-pass; that is, it best represents spatialfrequencies around 3 cycles/deg, while both lower andhigher spatial frequencies are represented more poorly.It is the case however, that under a variety of conditionsthe CSF is low-pass rather than band pass. These con-ditions include low luminance (e.g., van Nes & Bou-man, 1967), high contrast (Georgson & Sullivan, 1975),and temporally varying, rather than static stimuli (e.g.,Robson, 1966).

Thus, the form of the CSF under a variety of circum-stances is known. However, measurements of the CSFhave been carried out using very simple stimuli, typi-cally sine-wave gratings, under threshold conditions,and its application to suprathreshold complex stimuli

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Figure 2. Decomposition of a naturalistic scene (top left) into low spatial-frequency components (bottom left)and high spatial-frequency components (bottom right). The top right panel shows the contrast energy spectrumof the top-left picture.


such as faces is dubious. One of the goals of the presentresearch is to estimate at least the general form of therelevant MTF for the face-processing tasks with whichwe are concerned.

Acuity. While measurement of the CSF has been atopic of intense scrutiny among vision scientists, prac-titioners in spatial vision, e.g., optometrists, rely mainlyon measurement of acuity. As is known by anyone whohas ever visited an eye doctor, acuity measurement en-tails determining the smallest stimulus of somesort—“smallest” defined in terms of the visual anglesubtended by the stimulus—that one can correctlyidentify. Although the test stimuli are typically letters,acuity measurements have been carried out over thepast century using numerous stimulus classes includingline separation (e.g., Shlaer, 1937), and Landolt C gapsize (e.g., Shlaer, 1937). As is frequently pointed out(e.g., Olzak & Thomas, 1989, p. 7-45), measurement ofacuity essentially entails measurement of a single pointon the human MTF, namely the high-frequency cutoff,under suprathreshold (high luminance and high con-trast) conditions.

The issues that we raised in our Prologue and the re-search that we will describe are intimately concernedwith the question of how close a person must be—thatis, how large a visual angle the person must sub-tend—to become recognizable. In other words, we areconcerned with acuity. However, we are interested inmore than acuity for two reasons. First our goals extendbeyond simply identifying the average distance atwhich a person can be recognized. We would like in-stead to be able to specify what, from the visual sys-tem’s perspective, is the spatial-frequency compositionof a face at any given distance. Achievement of suchgoals would constitute both scientific knowledge neces-sary for building a theory of how visual processing de-pends on distance and practical knowledge useful forconveying an intuitive feel for distance effects to inter-ested parties such as juries. Second, it is known that

face processing in particular depends on low and me-dium spatial frequencies, not just on high spatial fre-quencies (e.g., Harmon & Julesz, 1973).

Distance and Spatial Frequencies. Returning to theissue of face perception at a distance, suppose that therewere no drop in the MTF at lower spatial frequen-cies—below I will argue that, for purposes of the pre-sent applications, this supposition is plausible. Thiswould make the corresponding MTF low-pass ratherthan band-pass.

Let us, for the sake of illustration, assume a low-passMTF that approaches zero around F = 30 cycles/deg (avalue estimated from two of the experiments describedbelow); that is, absolute spatial frequencies above 30cycles/deg can be thought of as essentially invisible tothe visual system. Focusing on this 30 cycles/deg upperlimit, we consider the following example. Suppose thata face is viewed from 43 feet away, at which distance itsubtends a visual angle of approximately 1 deg1. Thismeans that at this particular distance, image frequency f= absolute frequency F, and therefore spatial frequen-cies greater than about f = 30 cycles per face will beinvisible to the visual system; i.e., facial details smallerthan about 1/30 of the face’s extent will be lost. Nowsuppose the distance is increased, say by a factor of 4 to172 feet. At this distance, the face will subtend ap-proximately 1/4 deg of visual angle, and the spatial-frequency limit of F = 30 cycles/deg translates into f =30 cycles/deg x 1/4 deg/face = 7.5 cycles/face. Thus, ata distance of 172 feet, details smaller than about(1/30)x4 = 2/15 of the face’s extent will be lost. If thedistance is increased by a factor of 10 to 430 feet, de-tails smaller than about (1/30)x10 = 1/3 of the face’sextent will be lost And so on. In general, progressivelycoarser facial details are lost to the visual system in amanner that is inversely proportional to distance.

These informal observations can be developed into amore complete mathematical form. Let the filter corre-sponding to the visual system’s MTF be expressed as,

A = c(F) (1)

where A is the amplitude scale factor, F is frequency incycles/deg, and c is the function that relates the two.Now consider A as a function not of F, absolute spatialfrequency, but of image spatial frequency, f. Because43 ft is the approximate distance at which a face sub-tends 1 deg, it is clear that f=F*(43/D) where D is theface’s distance from the observer. Therefore, the MTFdefined in terms of cycles/face is,

1 In this article, we define face size as face height because our stimuli

were less variable in this dimension than in face width. Other studieshave defined face size as face width. A face’s height is greater thanits width by a factor of approximately 4/3. When we report resultsfor other studies, we transform relevant numbers, where necessary,to reflect face size defined as height.

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Figure 3. Band-pass approximation to a humancontrast-sensitivity function for a low-contrast, high-luminance, static scene.

6 LOFTUS AND HARLEY

†

A = c(f ) = c 43FD

Ê

Ë Á

ˆ

¯ ˜ (2)

Simple though it is, Equation 2 provides, as we shallsee, the mathematical centerpiece of much of what fol-lows.Distance Represented by Filtering. This logic impliesan alternative to shrinking a face (Figure 1) as a meansof representing the effect of distance. Assume that oneknows the visual system’s MTF for a particular set ofcircumstances, i.e., that one knows the “c” in Equations1-2. Then to represent the face as seen by an observer atany given distance D, one could remove high imagefrequencies by constructing a filter as defined by Equa-tion 2 and applying the filter to the face.

Figure 4 demonstrates how this is done. Considerfirst the center panels in which Julia Roberts is assumedto be viewed from a distance of D=43 feet away (atwhich point, recall, F = f). We began by computing theFourier transform of the original picture of her face.The resulting contrast energy spectrum, averaged overall orientations, is shown in the top center panel (againroughly linear on a log-log scale). Note that the top-row(and third-row) panels of Figure 5 have two abscissascales: absolute frequency in cycles/deg, and imagefrequency in cycles/face. To provide a reference point,we have indicated the region that contains between 8and 16 cycles/face, an approximation of which has beensuggested as being important for face recognition (e.g.,Morrison & Schyns, 2001). Because at D=43 feet theface subtends, as indicated earlier, 1 deg of visual an-gle, 8-16 cycles/face corresponds to 8-16 cycles/deg.The second row shows a low-pass filter: a candidatehuman MTF. We describe this filter in more detail be-low, but essentially, it passes absolute spatial frequen-cies perfectly up to 10 cycles/deg and then fallsparabolically, reaching zero at 30 cycles/deg. The thirdrow shows the result of filtering which, in frequencyspace, entails simply multiplying the top-row contrast-energy spectrum by the second-row MTF on a point-by-point basis. Finally, the bottom row shows the result ofinverse-Fourier transforming the filtered spectrum (i.e.,the third-row spectrum) back to image space. The re-sult—the bottom middle image—is slightly blurredcompared to the original (Figure 1) because of the lossof high spatial frequencies expressed in terms of cy-cles/face (compare the top-row, original spectrum to thethird-row, filtered spectrum).

Now consider the left panels of Figure 4. Here, Ms.Roberts is presumed to be seen from a distance of 5.4feet; that is, she has moved closer by a factor of 8 andthus subtends a visual angle of 8 deg. This means thatthe Fourier spectrum of her face has likewise scaleddown by a factor of 8; thus, for instance, the 8-16 cy-cles/face region now corresponds to 1-2 cycles/deg. Atthis distance, the MTF has had virtually no effect on the

frequency spectrum; that is, the top-row, unfilteredspectrum and the third-row, filtered, spectrum are virtu-ally identical and as a result, the image is unaffected.Finally, in the right panel, Ms. Roberts has retreated to172 feet away, where she subtends a visual angle of0.25 deg. Now her frequency spectrum has shifted upso that the 8-16 cycles/face corresponds to 32-64 cy-cles/deg. Because the MTF begins to descend at 10cycles/deg, and obliterates spatial frequencies greaterthan 30 cycles/deg, much of the high spatial-frequencyinformation has vanished. The 8-16 cycles/face infor-mation in particular has been removed. As a result, thefiltered image is very blurred, arguably to the point thatone can no longer recognize whom it depicts.

Rationale for a Low-Pass MTF. To carry out the kindof procedure just described, it was necessary to choosea particular MTF, i.e., to specify the function c inEquations 1-2. Earlier, we asserted that, for presentpurposes, it is reasonable to ignore the MTF falloff atlower spatial frequencies. As we describe in more detailbelow, the assumed MTFs used in the calculations tofollow are low-pass. There are three reasons for thischoice.

Suprathreshold Contrast Measurements. Althoughthere are numerous measurements of the visual sys-tem’s threshold CSF, there has been relatively littleresearch whose aim is to measure the suprathresholdCSF. One study that did report such work was reportedby Georgeson and Sullivan (1975). They used amatching paradigm in which observers adjusted theperceived contrast of a comparison sine-wave gratingshown at one of a number of spatial frequencies to theperceived contrast of a 5 cycles/deg test grating. Theyfound that at low contrasts, the resulting functions re-lating perceived contrast to spatial frequency werebandpass. At higher contrast levels (beginning at acontrast of approximately 0.2) the functions were ap-proximately flat between 0.25 and 25 cycles/deg whichwere the limits of the spatial-frequency values that theauthors reported.

Absolute versus Image Frequency: Band-Passed Facesat Different Viewing Distances. Several experimentshave been reported in which absolute and image spatialfrequency have been disentangled using a design inwhich image spatial frequency and observer-stimulusdistance—which influences absolute spatial fre-quency—have been factorially varied (Parish & Sper-ling, 1991; Hayes, Morrone, and Burr 1986). Generallythese experiments indicate that image frequency is im-portant and robust in determining various kinds of taskperformance, while absolute frequency makes a differ-ence only with high image frequencies.

To illustrate the implication of such a result for theshape of the MTF, consider the work of Hayes et al.who reported a face-identification task: Target faces,


Distance: 5.4 ft: 8.0 deg Distance: 43 ft: 1.0 deg Distance: 172 ft: 0.25 degRe

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Figure 4. Demonstration of low-pass filtering and its relation to distance. The columns represent 3 distances rang-ing from 5.4 to 172 ft. Top row: contrast energy spectrum at the 3 distances (averaged across orientations). Secondrow: Assumed low-pass MTF corresponding to the human visual system. Third row: Result of multiplying the filterby the spectrum: With longer distances, progressively lower image frequencies are eliminated. Bottom row: Filteredimages—the phenomenological appearances at the various distances—that result.

8 LOFTUS AND HARLEY

band-passed at various image frequencies were pre-sented to observers who attempted to identify them.The band-pass filters were 1.5 octaves wide and werecentered at one of 5 image-frequency values rangingfrom 4.4 to 67 cycles/face. The faces appeared at one oftwo viewing distances, differing by a factor of4—which, of course, means that the corresponding ab-solute spatial frequencies also differed by a factor of 4.Hayes at al. found that recognition performance de-pended strongly on image frequency, but depended onviewing distance only with the highest image-frequencyfilter, i.e., the one centered at 67 cycles/face. This filterpassed absolute spatial frequencies from approximately1.7 to 5.0 cycles/deg for the short viewing distance andfrom approximately 7 to 20 cycles/deg for the longviewing distance. Performance was better at the shortviewing distance corresponding to the lower absolutespatial-frequency range, than at the longer distance,corresponding to the higher absolute spatial-frequencyrange. The next highest filter, which produced verylittle viewing-distance effect passed absolute spatialfrequencies from approximately 0.9 to 2.5 cycles/degfor the short long viewing distance and from approxi-mately 3.5 to 10 cycles/deg for the long viewing dis-tance.

These data can be explained by the assumptions that(1) performance is determined by the visual system’srepresentation of spatial frequency in terms of cy-cles/face and (2) the human MTF in this situation islow-pass—it passes absolute spatial frequencies per-fectly up to some spatial frequency between 10 and 20cycles/deg before beginning to drop. Thus, with thesecond-highest filter the perceptible frequency rangewould not be affected by the human MTF at eitherviewing distance. With the highest filter, however theperceptible frequency range would be affected by theMTF at the long, but not at the short viewing distance.

Phenomenological Considerations. Suppose that thesuprathreshold MTF were band-pass as in Figure 3. Inthat case, we could simulate what a face would looklike at varying distances, just as we described doingearlier using a low-pass filter. In Figure 5, which isorganized like Figure 4, we have filtered Julia Roberts’face with a band-pass filter, centered at 3 cycles/deg. Itis constructed such that falls to zero at 30 cycles/degjust as does the Figure-4 low-pass filter, but also falls tozero at 0.2 cycles/deg. For the 43- and 172-ft distances,the results seem reasonable—the filtered images areblurred in much the same way as are the Figure-4, low-passed images. However, the simulation of the face asseen from 5.4 ft is very different: It appears band-passed. This is, of course, because it is band passed, andat a distance as close as 5.4 ft, the band-pass nature ofthe filter begins to manifest itself. At even closer dis-tances, the face would begin to appear high-passed, i.e.,like the Figure-2 bottom-right picture. The point is thatsimulating distance using a band-pass filter yields rea-sonable phenomenological results for long simulated

distances, but at short simulated distances, yields im-ages that look very different than actual objects seenclose up. A low-pass filter, in contrast, yields imagesthat appear phenomenologically reasonable at all virtualdistances.

The Distance-As-Filtering HypothesisWe will refer to the general idea that we have been

describing as the distance-as-filtering hypothesis. Spe-cifically, the distance-as-filtering hypothesis is theconjunction of the following two assumptions.1. The difficulty in perceiving faces at increasing dis-tances comes about because the visual system’s limita-tions in representing progressively lower image fre-quencies, expressed in terms of cycles/face, causes lossof increasingly coarser facial details.2. If an appropriate MTF, c (see Equations 1-2 above)can be determined, then the representation of a faceviewed from a particular distance, D, is equivalent tothe representation acquired from the version of the facethat is filtered in accord with Equation 2.

The Notion of “Equivalence”. Before proceeding, wewould like to clarify what we mean by “equivalent.”There are examples within psychology wherein physi-cally different stimuli give rise to representations thatare genuinely equivalent at any arbitrary level of thesensory-perceptual-cognitive system, because the in-formation that distinguishes the stimuli is lost at thefirst stage of the system. A prototypical example is thatof color metamers—stimuli that, while physically dif-ferent wavelength mixtures, engender identical quan-tum-catch distributions in the photoreceptors. Becausecolor metamers are equivalent at the photoreceptorstage, they must therefore be equivalent at any subse-quent stage.

When we characterize distant and low-pass filteredfaces as “equivalent” we do not, of course mean thatthey are equivalent in this strong sense. They are notphenomenologically equivalent: One looks small andclear; the other looks large and blurred; and they areobviously distinguishable. One could, however, proposea weaker definition of “equivalence.” In past work, wehave suggested the term “informational metamers” inreference to two stimuli that, while physically and phe-nomenologically different, lead to presumed equivalentrepresentations with respect to some task at hand (seeLoftus & Ruthruff, 1994; Harley, Dillon, & Loftus, inpress). For instance Loftus, Johnson, & Shimamura(1985) found that a d-ms unmasked stimulus (that is astimulus plus an icon) is equivalent to a (d+100)-msmasked stimulus (a stimulus without an icon) withrespect to subsequent memory performance across awide range of circumstances. Thus it can be argued thatthe representations of these two kinds of physically andphenomenologically different stimuli eventually con-verge into equivalent representations at some point priorto whatever representation underlies task performance.


Similarly, by the distance-as-filtering hypothesis wepropose that reducing the visual angle of the face on theone hand, and appropriately filtering the face on the

other hand lead to representations that are equivalent inrobust ways with respect to performance on varioustasks. In the experiments that we report below, we con-

Distance: 5.4 ft: 8.0 deg Distance: 43 ft: 1.0 deg Distance: 172 ft: 0.25 degRe

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8 32 256 512 20482 c/face

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Figure 5. Demonstration of band-pass filtering and its relation to distance. This figure is organized like Figure 4 ex-cept that the visual system’s MTF assumed is, as depicted in the second-row panels, band-pass rather than low-pass.

10 LOFTUS AND HARLEY

firm such equivalence with two tasks.

Different Absolute Spatial-Frequency Channels?A key implication of the distance-as-filtering hypothe-sis is that the visual system’s representation of a face’simage frequency spectrum is necessary and sufficient toaccount for distance effects on face perception: That is,two situations—a distant (i.e., small retinal image) un-filtered face and a closer (i.e., large retinal image)suitably filtered face will produce functionally equiva-lent representations and therefore equal performance.

Note, however that for these two presumablyequivalent stimuli, the same image frequencies corre-spond to different absolute frequencies: They are higherfor the small unfiltered face than for the larger filteredface. For instance, a test face sized to simulate a dis-tance of 108 ft would subtend a visual angle of ap-proximately 0.40 deg. A particular image spatial fre-quency—say 8 cycles/face—would therefore corre-spond to an absolute spatial frequency of approximately20 cycles/deg. A corresponding large filtered face,however, subtends, in our experiments, a visual angleof approximately 20 deg, so the same 8 cycles/facewould correspond to approximately 0.4 cycles/deg.

There is evidence from several different paradigmsthat the visual system decomposes visual scenes intoseparate spatial frequency channels (Blakemore &Campbell, 1969; Campbell & Robeson, 1968 Graham,1989; Olzak & Thomas, 1986; De Valois & De Valois,1980; 1988). If this proposition is correct it would meanthat two presumably equivalent stimulus representa-tions—a small unfiltered stimulus on the one hand anda large filtered stimulus on the other—would issue fromdifferent spatial frequency channels. One might expectthat the representations would thereby not be equivalentin any sense, i.e., that the distance-as-filtering hypothe-sis would fail under experimental scrutiny. As we shallsee, however, contrary to such expectation, the hy-pothesis holds up quite well.

General Prediction. With this foundation, a generalprediction of the distance-as-filtering hypothesis can beformulated: It is that in any task requiring visual faceprocessing, performance for a face whose distance issimulated by appropriately sizing it will equal perform-ance for a face whose distance is simulated by appro-priately filtering it.

EXPERIMENTSWe report four experiments designed to test this gen-

eral prediction. In Experiment 1, observers matched theinformational content of a low-pass-filtered comparisonstimulus to that of a variable-sized test stimulus. In Ex-periments 2-4, observers attempted to recognize pic-tures of celebrities that were degraded by either low-pass filtering or by size reduction.

Experiment 1: Matching Blur to SizeExperiment 1 was designed to accomplish two goals.

The first was to provide a basic test of the distance-as-filtering hypothesis. The second goal, given reasonableaccomplishment of the first, was to begin to determinethe appropriate MTF for representing distance by spa-tial filtering. In quest of these goals a matching para-digm was devised. Observers viewed an image of a testface presented at one of six different sizes. Each sizecorresponded geometrically to a particular observer-face distance, D, that ranged from 20 to 300 ft. For eachtest size, observers selected which of 41 progressivelymore blurred comparison faces best matched the per-ceived informational content of the test face.

The set of 41 comparison faces was constructed asfollows. Each comparison face was generated by low-pass filtering the original face using a version of Equa-tion 2 to be described in detail below. Across the 41comparison faces the filters removed successively morehigh spatial frequencies and became, accordingly, moreand more blurred. From the observer’s perspective,these faces ranged in appearance from completely clear(when the filter’s spatial-frequency cutoff was high andit thereby removed relatively few high spatial frequen-cies) to extremely blurry (when the filter’s spatial-frequency cutoff was low and it thereby removed mostof the high spatial frequencies). For each test-face size,the observer, who was permitted complete, untimedaccess to all 41 comparison faces, selected the particu-lar comparison face that he or she felt best matched theperceived informational content of the test face. Thus,in general, a large (simulating a close) test face wasmatched by a relatively clear comparison face, while asmaller (simulating a more distant) test face wasmatched by a blurrier comparison face.Constructing the Comparison Faces. In this section,we provide the quantitative details of how the 41 filterswere constructed in order to generate the corresponding41 comparison faces.

We have already argued that a low-pass filter is ap-propriate as a representation of the human MTF in thissituation and thus as a basis for the comparison picturesto be used in this task. A low-pass filter can take manyforms. Somewhat arbitrarily, we chose a filter that isconstant at 1.0 (which means it passes spatial frequen-cies perfectly) up to some rolloff spatial frequency,termed F0 cycles/deg, then declines as a parabolic func-tion of log spatial frequency, reaching zero at somecutoff spatial frequency, termed F1 cycles/deg, and re-maining at zero for all spatial frequencies greater thanF1. We introduce a constant, r > 1, such that F0=F1/r.Note that r can be construed as the relative slope of thefilter function: lower r values correspond to steeperslopes.

Given this description, for absolute spatial frequen-cies defined in terms of F, cycles/deg, the filter is com-pletely specified and is derived to be,


c(F) =

†

1.0 for F < F0

1- log(F/F0)log(r)

È

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˘

˚ ˙

2

for F0 £ F

0.0 for F > F1

Ï

Ì

Ô Ô

Ó

Ô Ô

£ F1(3)

Above, we noted that image spatial frequency ex-pressed in terms of f, frequency in cycles/face, isf=(43/D)*F where D is the observer’s distance from theface. Letting k=(43/D), the Equation-3 filter expressedin terms of f is,

c(f, d) =

†

1.0 for f < kF0

1- log(f/kF0)log(r)

È

Î Í

˘

˚ ˙

2

for kF0 £ f £ kF1

0.0 for f > kF1

Ï

Ì

Ô Ô

Ó

Ô Ô

(4)

In Equation 4, kF0 and kF1 correspond to what we termf0 and f1 which are, respectively, the rolloff and cutofffrequencies, defined in terms of cycles/face.

Because this was an exploratory venture, we did notknow what value of r would be most appropriate. Forthat reason, we chose two somewhat arbitrary values ofr: 3 and 10. The 41 comparison filters constructed foreach value of r were selected to produce correspondingimages having, from the observer’s perspective, a largerange from very clear to very blurry. Expressed in termsof cutoff frequency in cycles/face (f1), the ranges werefrom 550 to 4.3 cycles/face for the r=10 comparisonfilters, and from 550 to 5.2 cycles/face for the r=3 com-parison filters. Each comparison image produced by acomparison filter was the same size as the original im-age (1,100 x 900 pixels).

To summarize, each comparison face was defined bya value of f1. On each experimental trial, we recordedthe comparison face, i.e., that value of f1 that was se-lected by the observer as matching the test face dis-played on that trial. Thus, the distance corresponding tothe size of the test face was the independent variable inthe experiment, and the selected value of f1 was thedependent variable.Prediction. Given our filter-construction process, acandidate MTF is completely specified by values of rand F1. As indicated, we selected two values of r, 3 and10. We allowed the cutoff frequency, F1, to be a freeparameter estimated in a manner to be described below.

Suppose that the distance-as-filtering hypothesis iscorrect—that seeing a face from a distance is indeedequivalent to seeing a face whose high image frequen-cies have been appropriately filtered out. In that case, atest face sized to subtend a visual angle correspondingto some distance, D, should be matched by a compari-

son face filtered to represent the same distance. Asspecified by Equation 2 above, f1 = (43F1)/D, or

†

D =43F1

f1

(5)

which means that,

†

1f1

=1

43F1

Ê

Ë Á Á

ˆ

¯ ˜ ˜ D (6)

Equation 6 represents our empirical prediction: Themeasured value of 1/f1 is predicted to be proportional tothe manipulated value of D with a constant of propor-tionality equal to 1/(43F1). Given that Equation 6 isconfirmed, F1—and thus, in conjunction with r, theMTF as a whole—can be estimated by measuring theslope of the function relating 1/f1 to D, equating theslope to 1/(43F1), solving for F1, and plugging the re-sulting F1 value into Equation 3.Method

Observers. Observers were 24 paid University of Wash-ington students with normal or corrected-to-normal vision.

Apparatus. The experiment was executed in MATLABusing the Psychophysics Toolbox (Brainard, 1997; Pelli,1997). The computer was a Macintosh G4 driving two Apple17” Studio Display monitors. One of the monitors (the nearmonitor), along with the keyboard, was placed at a normalviewing distance, i.e., approximately, 1.5 ft from the observer.It was used to display the filtered pictures. The other monitor(the far monitor) was placed 8 ft away and was used to dis-play the pictures that varied in size. The resolution of bothmonitors was set to 1600 x 1200 pixels. The far monitor’sdistance from the observer was set so as to address the reso-lution problem that we raised earlier, i.e., to allow shrinkageof a picture without concomitantly lowering the effectiveresolution of the display medium: From the observer’s per-spective, the far monitor screen had a pixel density of ap-proximately 224 pixels per deg of visual angle thereby ren-dering it unlikely that the pixel reduction associated withshrinking would be perceptible to the observer.

Materials. Four faces, 2 males and 2 females, created us-ing the FACES “Identikit” program were used as stimuli.They are shown in Figure 6. Each face was rendered as a1,100 x 900 pixel grayscale image, luminance-scaled so thatthe grayscale values ranged from 0 to 255 across pixels. Foreach of the 4 faces, six test images were created. They weresized such that, when presented on the far monitor, their vis-ual angles would, to the observer seated at the near monitor,equal the visual angles subtended by real faces seen from 6test distances: 21, 36, 63, 108, 185, and 318 ft.

Design and Procedure. Each observer participated in 8consecutive sessions, each session involving one combinationof the 4 faces x 2 filter classes (r=3 and r=10). The 8 faces xfilter class combinations occurred in random order, but werecounterbalanced such that over the 24 observers each combi-nation occurred exactly 3 times in each of the 8 sessions. Each


session consisted of 10 replications. A replication consistedof 6 trials, each trial involving one of the 6 test distances.Within each replication, the order of the 6 test distances wasrandomized.

On each trial, the following sequence of events occurred.First the test picture was presented on the far screen where itremained unchanged throughout the trial. Simultaneously, arandomly selected one of the 41 comparison faces appearedon the near screen. The observer was then permitted to movefreely back and forth through the sequence of comparisonfaces, all on the near screen. This was done using the left andright arrow keys: Pressing the left arrow key caused the ex-isting comparison image to be replaced by the next blurrierimage, whereas pressing the right arrow key produced thenext clearer image. All of the 41 comparison faces were heldin the computer’s RAM and could be moved very quickly inand out of video RAM, which meant that moving back andforth through the comparison faces could be done veryquickly. If either arrow key was pressed and held, the com-parison image appeared to blur or deblur continuously, and totransit through the entire sequence of 41 comparison facesfrom blurriest to clearest or vice-versa took approximately asecond. Thus, the observer could carry out the comparisonprocess easily, rapidly, and efficiently.

As noted earlier, the observer’s task was to select the com-parison stimulus that best matched the perceived informa-tional content of the test stimulus. In particular, the followinginstructions were provided: “On each trial, you will see whatwe call a distant face on the far monitor (indicate). On thenear monitor, you will have available a set of versions of thatface that are all the same size (large) but which range in clar-ity. We call these comparison faces. We would like you toselect the one comparison face that you think best matcheshow well you are able see the distant face.” The observer was

provided unlimited time to do this on each trial, could roamfreely among the comparison faces, and eventually indicatedhis or her selection of a matching comparison face by pressingthe up arrow. The response recorded on each trial was thecutoff frequency, f1 in cycles/face, of the filter used to gener-ated the matching comparison face.

Results. Recall that the prediction of the distance-as-filtering hypothesis is that 1/f1 is proportional to size-defined distance, D (see Equation 6). Our first goal wasto test this prediction for each of our filter classes, r=3and r=10. To do so, we calculated the mean value, of1/f1, across the 24 observers and 4 faces for each valueof D. Figure 7 shows mean 1/f1 as a function of D forboth r values, along with best-fitting linear functions. Itis clear that the curves for both r values are approxi-mated well by zero-intercept linear functions, i.e., byproportional relations. Thus the prediction of the dis-tance-as-filtering hypothesis is confirmed.

Given confirmation of the proportionality prediction,our next step is to estimate the human MTF for eachvalue of r. To estimate the MTF, it is sufficient to esti-mate the cutoff value, F1. which is accomplished bycomputing the best-fitting zero-intercept slope2 of eachof the two Figure-7 functions, equating each of theslope values to 1/(43F1), the predicted proportionalityconstant, and solving for F1 (again see Equation 6).These values are 52 and 42 cycles/deg for measure-ments taken from stimuli generated by the r=10 and r=3filters respectively. Note that the corresponding esti-mates of the rolloff frequency F0—the spatial frequencyat which the MTF begins to descend from 1.0 enrouteto reaching zero at F1—are approximately 5 and 14

2 It can easily be shown that the best-fitting zero-intercept slope of Y

against X in an X-Y plot is estimated as SXY/SX2. In this instance,the estimated zero-intercept slopes were almost identical to the un-constrained slopes.

F1 F2

M1 M2

Figure 6. Faces used in Experiment 1.

0.000

0.033

0.067

0.100

0.133

0.167

0.200

0 100 200 300

r=10r=3

1/f 1 (f

ace/

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15.0

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les/

face

)

∞

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30.0

Figure 7. Experiment-1 results: Reciprocal ofmeasured f1 values (left-hand ordinate) plottedagainst distance, D. Right-hand ordinate shows f1 val-ues. Solid lines are best linear fits. Each data point isbased on 960 observations. Error bars are standarderrors.


cycles/deg for the r=10 and r=3 filters.Is there any basis for distinguishing which of the two

filters is better as a representation of the human MTF?As suggested by Figure 7, we observed the r=3 filter toprovide a slightly higher r2 value than the r=10 filter(0.998 versus 0.995). Table 1 provides additional F1statistics for the two filter classes. Table 1, Column 2shows the mean estimated F1 for each of the 4 individ-ual faces, obtained from data averaged across the 24observers. Columns 3-6 show data based on estimatingF1 for each individual observer-face-filter combinationand calculating statistics across the 24 observers. TheTable-1 data indicate, in two ways, that the r=3 filter ismore stable than the r=10 filter. First, the rows marked“SD” in Columns 2-4 indicate that there is less vari-ability across faces for the r=3 filter than for the r=10filter. This is true for F1 based on mean data (Column 2)and for the median and mean of the F1 values across theindividual faces (Columns 3-4). Second, Columns 5-6show that there is similarly less variability across the 24observers for the r=3 than for the r=10 filter. Finally thedifference between the median and mean was smallerfor the r=3 than for the r=10 filter, indicating a moresymmetrical distribution for the former.

Given that stability across observers and materials,along with distributional symmetry indicates superior-ity, these data indicate that the r=3 filter is the bettercandidate for representing the MTF in this situation.Our best estimate of the human MTF for our Experi-ment-1 matching task is therefore, F0 = 14, and F1 = 42.We note that these are not the values used to create

Figure 4; the filter used for the Figure-4 demonstrationswere derived from Experiments 2-4 which used facerecognition.Discussion. The goal of Experiment 1 was to determinethe viability of the distance-as-filtering hypothesis. Bythis hypothesis, the deleterious effect of distance onface perception is entirely mediated by the loss of pro-gressively lower image frequencies, measured in cy-cles/face, as the distance between the face and the ob-server increases. The prediction of this hypothesis isthat, given the correct filter corresponding to the humanMTF in a face-perception situation, a face shrunk tocorrespond to a particular distance D is spatially fil-tered, from the visual system’s perspective in a way thatis entirely predictable. This means that if a large-imageface is filtered in exactly the same manner, it should bematched by an observer to the shrunken face; i.e., theobserver should conclude that the shrunken face and theappropriately filtered large face look alike in the senseof containing the same spatial information.

Because there are not sufficient data in the existingliterature, the correct MTF is not known, and this strongprediction could not be tested. What we did instead wasto postulate two candidate MTFs and then estimate theirparameters from the data. The general prediction is thatthe function relating the reciprocal of measured filtercutoff frequency, 1/f1 should be proportional to D, dis-tance defined by size. This prediction was confirmedfor both candidate MTFs as indicated by the two func-tions shown in Figure 7. Although the gross fits to thedata were roughly the same for the two candidate

Table 1

Filter cutoff frequencies (F1 ) statistics for two filter classes(r=10 and r=3) and the four faces(2 males, M1 and M2, and 2 females, F1 and F2).

Computed across observersr = 10Filter Face

Mean based onaveraged data Median Mean SD Range

M1 51.0 50.5 60.0 27.1 119 M2 54.7 61.9 60.7 19.5 74

F1 53.1 53.3 57.2 17.6 70F2 48.0 51.8 54.6 18.1 79

Means 51.7 54.4 58.1 20.6 85.5SD’s 2.5 4.5 2.4

r = 3Filter Face

Mean based onaveraged data Median Mean SD Range

M1 44.3 44.9 46.8 14.0 53M2 45.7 46.1 46.0 11.0 46F1 41.3 43.1 42.7 10.6 43F2 40.5 40.1 42.3 9.8 34

Means 42.9 43.6 44.5 11.3 44.0 SD’s 2.1 2.3 2.0

Note—In the rows labeled “Means” and “SD’s”, each cell contains the mean or standard deviations of the 4 numbers imme-diately above it; i.e., they refer to statistics over the 4 faces for each filter class. The columns labeled “Mean”, “Standard De-viation” and “Range” refer to statistics computed over the 24 observers


MTFs—they were both excellent—a criterion of con-sistency over observers and stimuli weighed in favor ofthe r=3 filter over the r=10 filter. We reiterate that ourestimated r=3 filter, in combination with a F1 value of42 cycles/deg, implies a MTF that passes spatial fre-quencies perfectly up to 14 cycles/deg and then falls,reaching zero at 42 cycles/deg.

How does this estimate comport with past data? TheGeorgeson & Sullivan data discussed earlier indicated afairly flat human suprathreshold MTF up to at least 25cycles/deg which is certainly higher than the 14 cy-cles/deg rolloff frequency that we estimate here.Georgeson and Sullivan used a different task from thepresent one: Their observers adjusted contrast of sine-wave gratings of specific spatial frequencies to match a5 cycles/deg standard, while the present observersmatched spatial-frequency composition of constant-contrast faces to match different-size test stimuli. Be-cause their highest comparison grating was 25 cy-cles/deg, we do not know if and how the functionwould have behaved at higher spatial frequencies.Similarly, the present measurements of MTF shape arelimited because we used only r values of 3 and 10. It ispossible that if, for instance, we had used an r=2 filter,we would have estimated a larger rolloff frequency.

Our estimated MTF shape does accord well with datadescribed earlier reported by Hayes et al. (1986). Theyreported an experiment in which faces were (1) filteredwith band-pass filters centered at difference image fre-quencies (expressed in terms of cycles/face), and (2)presented at different viewing distances which, for agiven image-frequency distribution, affected the distri-bution of absolute spatial frequencies (expressed incycles/deg). As we articulated earlier, Hayes et al.’sdata can be nicely accommodated with the assumptionsthat (1) the human MTF is low-pass for their experi-ment, and (2) it passed spatial frequencies perfectly upto somewhere between 10 and 20 cycles/deg.

In Experiments 2-4 we explore whether the MTF fil-ter estimated from the matching task used in Experi-ment 1 is also appropriate for face identification. Toanticipate, the filter that we estimate in Experiments 2-4has smaller values of F0 and F1; i.e., it is scaled towardlower spatial frequencies. In our General Discussion,we consider why that may happen. For the moment wenote that one common observer strategy in Experiment1 was to focus on small details (e.g., a lock of hair),judge how visible that detail was in the distant face, andthen adjust the comparison face so that it was equallyvisible. This focusing on small details may mean thatthe observers in Experiment 1 may have viewed theirtask as more like looking at an eye chart than a face,and that whatever processes are “special” to face proc-essing were minimized in Experiment 1. In Experi-ments 2-4 we dealt with the same general issues as inExperiment 1, but using a task that is unique to faceprocessing—recognition of known celebrities.

Experiment 2: Celebrity Recognition at a Dis-tance—Priming

Experiments 2-4 used the same logic as Experiment1, relating distance defined by low-pass spatial filteringto distance defined by size. However, the stimuli, task,and dependent variables were all very different. Oneach of a series of trials in Experiments 2-4, observersidentified a picture of a celebrity. The picture beganeither very small or very blurry—so small or blurry asto be entirely unrecognizable—and then gradually clari-fied by either increasing in size or deblurring. The ob-server’s mission was to identify the celebrity as early aspossible in this clarification process, and the claritypoint at which the celebrity was correctly identified wasrecorded on each trial. This clarity point was charac-terized as the distance implied by size, D, in the case ofincreasing size, and as filter cutoff frequency in cy-cles/face, f1, in the case of deblurring. As in Experiment1, the central prediction of the distance-as-filtering hy-pothesis is that 1/f1 is proportional to D with a propor-tionality constant of 1/(43F1). Again as in Experiment1, given confirmation of this prediction, F1 can be esti-mated by equating the observed constant of proportion-ality to 1/(43F1) and solving for F1.

Given confirmation of the prediction, it becomes ofinterest to determine how robust is the estimate of thehuman MTF. We evaluated such robustness in twoways. The first was to compare the MTF estimatesbased on recognition (Experiments 2-4) with the esti-mate based on matching (Experiment 1). The secondwas to compare MTF estimates within each of Experi-ments 2-4 under different circumstances. In particular,in each of Experiments 2-4, we implemented a di-chotomous independent variable that, it was assumedbased on past data, would affect identification perform-ance. The variable was “cognitive” or “top-down” inthat variation in it did not affect any physical aspect ofthe stimulus; rather it affected only the observer’s ex-pectations or cognitive strategies. The purpose of incor-porating these variables was to test substitutability ofthe presumed human MTF (Palmer, 1986a; 1986b; seealso Bamber, 1979). The general idea of substitutabilityis that some perceptual representation, once formed, isunaffected by variation in other factors; i.e., substitut-ability implies a kind of independence. The distance-as-filtering hypothesis is that filtering a face by somespecified amount produces a perceptual representationthat is functionally equivalent to the representation thatis obtained when the face is viewed from a distance.Addition of the stronger substitutability hypothesis isthat this equivalence is unaffected by changes in other,nonperceptual variables. Therefore the prediction ofsubstitutability is that the same MTF—i.e., the sameestimated value of F1—should describe the relationbetween distance defined by size and distance definedby filtering for both levels of the cognitive variable.

In Experiment 2 this cognitive variable was priming:


Half of the to-be-identified celebrities had been primedin that the observer had seen their names a few minutesprior to the identification part of the experiment. Theother half of the to-be-identified celebrities had notbeen primed. Numerous past studies (e.g., Reinitz &Alexander, 1996; Tulving & Schacter, 1990) have indi-cated that such priming improves eventual recognitionof the primed stimuli.

MethodObservers. Observers were 24 paid University of Wash-

ington graduates and undergraduates with normal, or cor-rected-to-normal vision. All were raised in the United States,and professed reasonable familiarity with celebrities, broadlydefined.

Apparatus. Apparatus was the same as that used in Ex-periment 1.

Materials. Pictures of 64 celebrities were obtained fromvarious sources, principally the internet and glossy maga-zines. The celebrities came from all walks of celebrity life.They included actors, musicians, politicians, business figures,and sports figures, chosen so as to be recognizable by as manypotential observers as possible. There were 43 males and 21females. They were all rendered initially as grayscale images.They were scaled to be 500 pixels high, but varied in width.Each image was luminance-scaled so as to range in grayscalelevel from 0 to 255 across pixels.

Beginning with a single original photograph of each celeb-rity, two 30-image sets were created. Images in the first setvaried in size such that, when shown on the far monitor, theysubtended visual angles corresponding to distances rangingfrom 20 to 500 ft. Images in the second set were filtered usingthe r=3 filter class described in conjunction with Experiment1. The cutoff values, f1, ranged from 129 to 5.2 cycles/face.The exact function relating degree of degradation to degrada-tion image number (1-30) was somewhat complex and repre-sented an attempt to make the transition from one degradedimage to the next less degraded image as perceptually similaras possible across all 30 degraded images for both the size-increase and the deblurring procedures, The function is shownby the circles in Figure 8. The left ordinate refers to degrada-tion defined in terms of size reduction (distance D) while theright ordinate refers to degradation defined in terms of filter-ing (cutoff frequency1/f1; note the reciprocal scale). Sizes ofthe filtered images were the same as sizes of the original im-ages (500 pixels high x variable widths).

Design and Counterbalancing. Observers were run indi-vidually. Each observer participated in 4 blocks of 16 tri-als/block. Each trial involved a single celebrity whose imageclarified by either increasing in size or by deblurring. Alltrials within a block involved just one clarification type, in-creasing in size or deblurring. For half the observers the Blur(B) and Size (S) block sequence was BSSB while for theother half, the sequence was SBBS. Within each block, halfthe celebrities had been primed in a manner to be describedshortly, whereas the other half the celebrities had not beenprimed.

Each observer had a “mirror-image” counterpart whosetrial sequence was identical except that primed-unprimed wasreversed. Therefore, 4 observers formed a complete counter-balancing module, and the 24 observers comprised 6 such

modules. The order of the 64 celebrities across trials wasconstant across the 4 observers within each counterbalancingmodule, but was randomized anew for each new module.

Procedure. The observer was told at the outset of the ex-periment that on each of a number of trials, he or she wouldsee a picture of a celebrity that, while initially degraded so asto be unrecognizable, would gradually clarify to the point thatit was entirely clear.

The priming manipulation was implemented as follows. Atthe start of each block, the observer was told, “In the nextblock, you will see 8 of the following 16 celebrities,” and thensaw 16 celebrity names, one at a time. The observer was in-structed to try to form an image of each celebrity when thecelebrity’s name appeared and then to rate on a 3-point scalewhether they thought that they would recognize the namedcelebrity if his or her picture were to appear. The sole purposeof the ratings was to get the observer to visualize the celebri-ties during the priming stage, and the ratings were not subse-quently analyzed. As promised, 8 of the 16 celebrities whosepictures the observer subsequently viewed during the blockhad been named during the initial priming phase. Observerswere assured, truthfully, that the 8 celebrity names seen dur-ing the priming stage which didn’t correspond to celebritiesviewed during that block were of celebrities who would notbe viewed at any time during the experiment.

Following instructions at the outset of the experiment, theobserver was provided 4 blocks of 2 practice trials per blockin the same block order, BSSB or SBBS that he or she wouldencounter in the experiment proper. Each of the 4 practiceblocks was the same as an experiment-proper block exceptthat there were only two trials, preceded by 2 primed names,in each practice block. No celebrity named or shown at prac-tice appeared in any form during the experiment proper.

Increasing-size images were shown on the far screen, whiledeblurring images were shown on the near screen. On eachtrial, the images clarified at the rate of 500 ms/image. Observ-ers were told that they were to watch the clarifying celebrity

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Figure 8. Experiments 2-4: Degree of degradationplotted against image number. Higher image num-bers represent more degraded pictures, i.e., picturesthat are shrunk to represent greater distances, or arefiltered with a lower cutoff frequency. The left ordi-nate represents virtual distance, D, while the rightordinate represents filter cutoff frequency, f1. Notethat decreasing f1 corresponds to increasing blur.


and make a guess about who it was whenever they believedthat they could recognize the person. Observers responded byfirst pressing the space bar, which stopped the clarificationprocess, and then typing in their guess. They were allowed touse any kind of information they wished about a celebrity toindicate that they recognized him or her. For instance, if thecelebrity were Jennifer Lopez, a valid response would be“Jennifer Lopez” or “J-Lo” or “that actress who was in ‘Maidin Manhattan’” or “affianced to Ben Affleck” or anything elsethat identified Ms. Lopez as the depicted celebrity. Once aguess had been made, the clarifying process resumed. Ob-servers were allowed to change their minds and make addi-tional guesses if and when they chose. When the imagereached the point of complete clarification, one of two ques-tions appeared on the screen. If the observer had made at leastone guess, as usually happened, the question was, “Do youstill think that this is XYZ” where XYX was the most recentguess. If the observer answered “y” the trial ended. If theobserver answered anything else, the computer asked, “OK,who do you think it is”, and the observer typed in his or herfinal guess. If, as occasionally happened, the observer hadmade no guess during the clarifying process, the computerasked, “OK, who do you think it is” and the observer wasrequired to guess.

When the observer had completed the 64 trials, an initialanalysis program was run. This program sequenced throughall 64 trials. For each trial, it displayed the true name of thecelebrity for that trial and then proceeded through all re-sponses that the observer had made on that trial (typicallyonly one response per trial, but occasionally more than one).The Experimenter indicated whether each response was cor-rect or incorrect by typing “y” or “n”. This procedure wascarried out with the observer still present, so the observercould provide occasional assistance in cases of ambiguousanswers, bizarre spelling, idiosyncratic shorthand, and thelike. Thus for each trial was recorded the distance, D (in thecase of increasing size), or the cutoff spatial frequency, f1 (inthe case of decreasing blur) at which the celebrity was firstidentified.

Results. For each observer, the geometric mean pointof initial identification was calculated for both primedand unprimed conditions. For the increasing size condi-tions, this point was measured in distance, D, while forthe deblurring conditions, it was measured in filter cut-off point, f1. Note that for distance, larger indicatesbetter performance: A longer distance, D, means thatthe observer was able to identify the celebrity at a moredegraded point. For blurring, smaller is better: Asmaller cutoff frequency, f1, means that the observerwas able to identify the celebrity at a more degradedpoint.

The priming manipulation had the expected effect:Primed celebrities could be recognized at a point thatwas 24.5%±6.4% smaller and 22.8%±11.8% moreblurred than unprimed celebrities3.

For increasing-size trials, the proportion of correctlyrecognized celebrities was calculated for each of the 30

3 Throughout this manuscript, x±y refers to a mean, x, plus or minus a

95% confidence interval.

distances, D, defined by size. Likewise, for deblurringtrials, proportion correct celebrities recognized wascalculated for each of the 30 cutoff frequencies, f1 incycles/face. The results, depicted as psychophysicalfunctions, are shown in Figure 9. Note that in Figure 9,there are 3 separate abscissas, all scaled logarithmi-cally. The bottom abscissa shows D and is relevant tothe increasing-size trials. The two top abscissas arerelevant to the decreasing-blur trials. They show f1 (forintuitive clarity) along with 1/f1 (for ease of the mathe-matical manipulation to be carried out below). The twoleft curves (circle curve symbols) correspond to in-creasing size while the two right curves (square curvesymbols) correspond to decreasing blur. The open-symbol curves correspond to unprimed curves, whilethe closed-symbol curves correspond to primed curves.

The four curves are smooth and regular with one ex-ception: There is a slight jump in performance at theleast degraded (largest or least blurry) image for all 4blur/size x priming conditions. This is almost certainlyan artifact that stems from the observers’ being forcedto guess following presentation of the least degradedimage if they had not already made a response. These 4artifactual points are not included in the analysis to bedescribed next.

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Figure 9. Experiment-2 data: Proportion celebri-ties recognized as a function of degradation level.The two left curves show data for degradation by vir-tual distance (size reduction) and are plotted as afunction of distance, D, on the bottom abscissa. Thetwo right curves show data for degradation by fil-tering and are plotted as a function of cutoff fre-quency, f1. The prediction of the distance-as-filteringhypothesis is that the two primed curves (closedsymbols) and the two unprimed curves (open sym-bols) are both horizontally parallel; MTF substitut-ability further implies that primed and unprimedcurves be separated by the same amount. Each datapoint is based on 384 observations.


To assess the prediction of the distance-as-filteringhypothesis, we begin with Equation 5 which relatesdistance defined by size (D) to distance defined by fil-tering (f1). Performance in the increasing-size conditionis predicted to equal performance in the deblurring con-dition when,

†

p 43F1

f1

Ê

Ë Á

ˆ

¯ ˜ = p(D) (7)

where p(x) refers to proportion celebrities recognized atdegradation level x. Changing to logarithms and rear-ranging terms,

†

p log(43F1) + log 1f1

Ê

Ë Á

ˆ

¯ ˜

È

Î Í

˘

˚ ˙ = p[log(D)] (8)

Thus, by Equation 8, the prediction of the distance-as-filtering hypothesis is that the curves corresponding todeblurring (measured in units of log(1/f1), and increas-ing-size (measured in units of log(D)) will be horizon-tally parallel, separated by a constant equal tolog(43F1).

Given this foundation, we can identify four possibleoutcomes that would imply four corresponding conclu-sions. They are, in increasing degree of conclusionstrength, as follows.1. Failure of Equation 8. The deblurring and distancecurves are not described by Equation 8 (i.e., they arenot log horizontally parallel). This would imply discon-firmation of the distance-as-filtering hypothesis.2. Confirmation of Equation 8 but with different shiftvalues for the two priming conditions. Both priminglevels are adequately described by Equation 8, but withdifferent shift magnitudes for the two levels. Thiswould imply confirmation of the distance-as-filteringhypothesis, but would also imply different MTFs forthe two priming levels, i.e., failure of substitutability.3. Confirmation of Equation 8 with the same shift valuefor the two priming conditions. Both priming levels areadequately described by Equation 8, with the same shiftmagnitude for the two levels. This would imply confir-mation of the distance-as-filtering hypothesis, andwould imply that a single MTF is adequate to describethe two priming levels.4. Confirmation of Equation 8 with the same shift valuefor the two priming conditions whose magnitude im-plies an F1 value of 42 cycles/deg. The outcome im-plying the strongest conclusion would be that just de-scribed but with the additional constraint that the ob-served common shift magnitude implied the same F1value of 42 cycles/deg that was estimated in Experi-ment 1. This would imply a single filter upon which (atleast) two quite different visual perception

tasks—matching and recognition—are based.Our results imply Conclusion 3. Figure 10 shows the

result of simultaneously shifting primed and unprimedsize curves by 3.13 log units. For visual clarity, the twoprimed curves have been shifted to the right by an ad-ditional 0.5 log unit. The alignment of the size curveswith their blur counterparts is almost perfect. The esti-mate of F1 corresponding to the observed 3.13 log-unitshift is 31.5±2.7 cycles/deg.

Discussion. The Experiment-2 data provide clear sup-port for the distance-as-filtering hypothesis. The psy-chophysical functions for the size and filtering degra-dation techniques are log-parallel, i.e., are proportionalto one another.

Priming, while substantially affecting performance,did not affect the relation between distance defined bysize and distance defined by blur. Thus the nature of theassumed MTF is inferred to be unaffected by priming.This constitutes confirmation of the substitutabilityhypothesis that we described earlier. To foreshadow,we observed the same kind of confirmation in Experi-ments 3 and 4.

The estimated MTF had a cutoff frequency, F1, of31.5±2.7 cycles/deg. This is somewhat different fromthe corresponding MTF estimated from Experiment 1whose F1 was approximately 42 cycles/deg. This meansthat, within the context of the distance-as-filtering hy-pothesis, there is not a single MTF for all tasks involv-ing face processing. We return to these issues in ourGeneral Discussion.

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Figure 10. Experiment-2 data: Both the primedand unprimed filtered curves from Figure 9 havebeen shifted by 3.13 log units. For visual clarity, theprimed curves are arbitrarily shifted 0.5 log units tothe right. For both the primed and unprimed curves,circles represent increasing-size trials, while squaresrepresent decreasing-blur trials.


Experiment 3: Celebrity Recognition at a Dis-tance—Perceptual Interference

Experiment 3 was largely identical to Experiment 2except that instead of priming, degradation startingpoint was varied. On half the trials, the celebrity’s pic-ture began its degradation process at a starting pointtermed far (think “celebrity far away”), which wasidentical to the starting point in Experiment 1. On theother half of the trials, the starting point termed near,was half as degraded as the far starting point. Beginningwith a well-known report by Bruner and Potter (1964)numerous investigators have demonstrated that in thiskind of experiment, beginning the degradation processat a more degraded point decreases the observer’seventual ability to recognize what the picture depictscompared to beginning at a less degraded point. Thisfinding is called the perceptual-interference effect.Based on these past data, we anticipated (correctly) thatperformance would be better with a near than with a farstarting point. The substitutability prediction is that theestimated correspondence between distance defined byfiltering and distance defined by size should not differfor the two starting points.Method

Observers. Observers were 24 paid University of Wash-ington graduates and undergraduates. All were raised in theUnited States, and professed reasonable familiarity with ce-lebrities, broadly defined.

Apparatus. Apparatus was the same as that used in Ex-periments 1-2.

Materials. The same celebrity pictures used in Experiment2 were used in Experiment 3. There were still 30 sized imagesand 30 corresponding filtered images for the varying degreesof degradation, with the same most degraded and least de-graded points. However, the particular degradation levels thatwere used varied from least to most degraded in equal dis-tance intervals for distance defined by size and, correspond-ingly, equal 1/f1 intervals for distance defined by filtering asshown by the diamonds in Figure 8. The two starting points,“far” and “near” were images whose sizes corresponded to500 and 250 ft for the distance-as-size images, and imagesfiltered with cutoff frequencies of 5.2 and 10.3 cycles/face fordistance-as-filtering images.

Design, Procedure, and Counterbalancing. Design, proce-dure, and counterbalancing were as in Experiment 2 exceptfor the following. First, of course, there was no priming pro-cedure beginning each block. Second, the primed/unprimedmanipulation of Experiment 1 was replaced by the near/far-start manipulation just described. Third, on each trial, theimages clarified at the rate of 500 ms/image in the far-startcondition and 1000 ms/image in the near-start condition. Be-cause there were only half as many images to go through inthe near compared to the far-start condition, this meant thattotal time from start to finish would, if uninterrupted, be thesame in the near and far-start conditions.

Results and Discussion. The starting-point manipula-tion had the expected effect: Celebrities could be rec-ognized at a point that was 20.7%±10.2% smaller and27.3%±15.5% more blurred in the near compared to the

far-start condition.Figure 11 shows the Experiment-3 results. The top

panel, like Figure 9, shows the raw data, The “clearestposition” artifact described in conjunction with Ex-periment 2 is again apparent. Moreover, there is a newartifact in Experiment 3 that is uninteresting but com-plicated. It is this. In all conditions, the most degradedpoint at which a celebrity could possibly be identifiedwas, of course, the starting point. The normal startingpoint, i.e., the “far” starting point in Experiment 3, issufficiently degraded that no celebrity was ever recog-nized at that point by any observer. The Experiment-3

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Figure 11. Experiment-3 data: The two panels corre-spond to Figures 9 and 10. Upper panel shows raw dataand lower panel shows shifted data. Both starting-pointcurves have been shifted by the same amount. For vis-ual clarity, the near starting-point curves are shifted0.5 log units to the right in the lower panel. Each datapoint is based on 448 observations. In both panels, forboth starting-point curve pairs, circles represent in-creasing-size trials, while squares represent decreasing-blur trials.


near starting point though, is one at which celebritieswere occasionally identified. Obviously, in the nearstarting-point condition, no celebrity can be identifiedat any point that is more degraded than the near startingpoint. This limitation affected the most degraded twopoints of the 250 starting point blur condition which, asis apparent in the top panel of Figure 11, are artificiallylow.

Figure 11, bottom panel, like Figure 10, shows theresult of shifting the near and far starting-point curvesby the same amount, in this case, 3.05 log units. Again,the artifactual points described above are excluded fromthese shifted data. The conclusions implied by the Ex-periment-3 results are analogous to those of Experiment2. First, the distance-as-filtering hypothesis is con-firmed by the log-parallel distance and filtered curves.Second, a new top-down variable, starting distance, hasno effect on the estimated filter. Finally, the MTF inExperiment 3, calculated as in Experiment 2 from theobserved best shift has a cutoff value, F1, of 25.0±2.2cycles/deg.Experiment 4: Celebrity Recognition at a Dis-tance—Hindsight Bias

Experiment 4 was largely identical to Experiments 2and 3. Here, we varied what we term normal/hindsight.On half the blocks—the normal blocks—the celebrity’spicture was shown in a normal fashion; i.e., unprimed,with a long starting point. On the other half of theblocks—the hindsight blocks—the observer was showna large, clear picture of the celebrity at the start of thetrial. He or she then proceeded through the clarificationprocess—increasing size, or deblurring, as usual—butwas asked to indicate at what point he or she wouldhave recognized the celebrity, if they did not alreadyknow who it was. Based on past data (e.g., Bernstein,Atance, Loftus, & Meltzoff, in press; Harley, Bernstein,& Loftus, 2002; Harley, Carlsen, & Loftus, in press) weanticipated that the observer would claim the celebrityto be recognizable at a more degraded point in the hind-sight compared to the normal procedure. The substitut-ability prediction is that the estimated MTF should notdiffer for normal/hindsight manipulation.Method

Observers. Observers were 32 paid University of Wash-ington graduates and undergraduates. All were raised in theUnited States, and professed reasonable familiarity with ce-lebrities, broadly defined.

Apparatus. Apparatus was the same as that used in Ex-periments 1-3.

Materials. A new set of 64 grayscale images of celebrityfaces were used in Experiment 4 (33 were taken from Ex-periments 2 and 3, while 31 were new4). As in Experiment 2,there were 30 sized images and 30 corresponding filtered images 4 Based on data from Experiments 2 and 3, and a celebrity familiarity

survey completed by lab members, less familiar celebrities from theprior experiments were replaced with new, more familiar celebrities.

created for each celebrity face. The same set of degradation lev-els used for Experiment 2 was used in Experiment 4.

Design, Procedure, and Counterbalancing. In general, de-sign, procedure, and counterbalancing were as in Experiments2-3. Again there were 4 16-trial blocks, shown in a BSSBorder for 16 observers and SBBS for the other 16 observers.Within each 16-trial block a random 8 of the trials were nor-mal (i.e., like the unprimed Experiment-2 trials) while theremaining 8 were hindsight trials. On each hindsight trial, theobserver was, as indicated, shown a completely clear pictureof the celebrity for that trial at the start of the trial, but wasinstructed to ignore this knowledge in selecting the eventualidentification point. Following presentation of the clear pic-ture, the remainder of a hindsight trial was identical to a nor-mal trial. Each observer had a mirror-image observer whosetrial sequence was identical except that normal-hindsighttrials were reversed.

Results and Discussion. The normal/hindsight ma-nipulation had the expected effect, but it was small:Celebrities could be recognized at a point that was11.2%±10.4% smaller and 6.0±10.6% more blurred inthe hindsight compared to the normal condition.

Figure 12, like Figure 11, shows the Experiment-3results: The top panel shows the main results, while thebottom panel shows the shifted curves. Again, the left-most top-panel artifactual points are excluded from theshifted data. The conclusions implied by the Experi-ment-4 results are analogous to those of Experiments 2and 3. First, the distance-as-filtering hypothesis is con-firmed by the log-parallel distance and filtered curves.Second, a third top-down variable, normal/hindsight,has no effect on the estimated filter (although, as theeffect of normal/hindsight was quite small, this result isnot as meaningful as it was in Experiments 2 or 3). Fi-nally, the MTF in Experiment 4, calculated as in Ex-periments 2 and 3 from the observed best shift has acutoff value, F1, of 31.1±2.9 cycles/deg.

GENERAL DISCUSSIONExperiments 1-4 report two different tasks: matching

face blurriness to face size, and identifying celebrities.In each task, the question was: What is the relationbetween the filter (characterized by f1), and distance(defined by D) that give rise to equal performance? Forboth tasks, to a high degree of precision, the answerwas: D and f1 are inversely proportional to one another;i.e., Equation 5 was confirmed.

Within the context of the distance-as-filtering hy-pothesis, this finding allows estimation of the parame-ters of the hypothesized filter corresponding to the hu-man MTF. Between tasks, the MTF parameters weresomewhat different: The estimates of F1, were 42 cy-cles/deg for the matching task and 25-31 cycles/deg forthe celebrity-recognition task. For all three celebrity-recognition experiments, however, the substitutabilityprediction was confirmed: The estimated MTF was the


same—that is, the F1 estimate was the same—for eachof two priming levels in Experiment 2, for each of twostarting-point levels of in Experiment 3, and for bothnormal and hindsight conditions in Experiment 3. Thisimplies a certain degree of robustness in the MTF esti-mates.

Face Degradation and Face RepresentationSeeing a face, or a picture of a face, produces a repre-

sentation of the face that can be used to carry out vari-ous tasks. The greater the distance at which the face isviewed, the poorer is the face’s representation. Thedistance-as-filtering hypothesis asserts that the repre-sentation of the face at a particular distance, d, can beobtained by either shrinking the face or low-pass filter-

ing it to simulate the effect of distance on the imagefrequency spectrum.

Figure 13 depicts the hypothesis and its application tothe experiments that we have reported. The logic ofFigure 13 is this. The left boxes represent Distance, D,and filtering, f1. Note that having specified the form ofthe MTF (Equation 4) and the parameter r (which weassume to equal 3 for this discussion) a particular fil-tered face is completely specified by f1, the filter’s cut-off frequency in cycles/face. The expression f1 =(43xF1)/D in the lower left box, along with the middle“Internal Representation” box signifies that when f1 isproportional to 1/D with a proportionality constant of(43F1), the representations of the face are functionallyequivalent.

This foundation is sufficient to account for the Ex-periment-1 data: If one face, shrunk to correspond todistance, D and another face filtered by f1 = (43xF1)/Dproduce equivalent representations, they will match.

To account for the Experiments 2-4 data, we mustspecify how celebrity identification performance is re-lated to the representation. We will not attempt to dothis in detail here, but rather we sketch two theoreticalstrategies. The first is to assume that the representation,R can be formulated as a single number on a unidimen-sional scale (see Loftus & Busey, 1992 for discussionsof how this might be done) with better representationscorresponding to higher values of R. Performancewould then be a simple monotonic function, m, of R.The second strategy is to assume that R is multidimen-sional (e.g O’Toole, Wenger, & Townsend, 2001;Townsend, Soloman, & Smith, 2001) with each dimen-sion being monotonically related to the representation’squality. Performance would again be a function, m, ofR that is monotonic in all arguments.

In either case, there would be two such monotonicfunctions corresponding to the two levels of each of thecognitive independent variables in Experiments 2-4 (wearbitrarily use primed/unprimed as our example in Fig-ure 13). Thus if m1 were defined to be the function forthe “difficult” condition, it would correspond to un-primed (Experiment 2), far starting point (Experiment3). or normal (Experiment 4) while m2 would corre-

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Figure 12. Experiment-4 data: The two panels are setup like those of Figure 11. In both panels, for both thenormal and hindsight curve pairs, circles represent in-creasing-size trials, while squares represent decreasing-blur trials. Each data point is based on 512 observa-tions.

Face filteredwith

f1=(43xF1)/Di

Face atDistance Di

UnprimedPerformance:P2 = m2(Ri)

PrimedPerformance:P1 = m1(Ri)

IndependentVariables

InternalRepresentation

DependentVariables

Equivalent FaceRepresentations: Ri

Figure 13. Depiction of distance-as-filtering hy-pothesis as applied to Experiments 1-4.


spond to the primed, near starting point, or hindsightconditions. Thus, with a given representation R, m2would produce higher performance than m1. An impor-tant property of the data captured by the Figure-13 rep-resentation however, is that in all cases the “cognitive”independent variable—priming, starting point, andnormal/hindsight—does not affect the nature of theMTF as defined by F1. This is Figure 13’s reflection ofthe substitutability hypothesis.

Different MTFs for Different TasksThe simplest incarnation of the distance-as-filtering

hypothesis would be that, under comparable physicalcircumstances, the human visual system acts as a fixedspatial filter. A comparison of Experiment 1 on the onehand and Experiments 2-4 on the other weighs againstthis possibility. For two tasks—matching and identifi-cation—the estimated MTFs, differed: For Experiment1, the estimated MTF had a cutoff of F1 = 42 cy-cles/deg, while for Experiments 2-4, the estimates of F1were approximately 31, 25, and 31 cycles/deg.

It is possible that the difference in estimated MTFsresults from the different stimuli used for the twotasks—the four computer-generated faces shown inFigure 6 were used in the matching task while celebrityphotos were used for the identification task. However,the two kinds of faces are not very different physicallyand there is no a priori reason to anticipate that onecompared to the other would produce a different MTFestimate. So it seems unlikely that the difference in theestimated MTF that emerged resulted entirely from thestimulus-set difference.

It does seem plausible however, that the differenttasks might produce the different MTF estimates.Schyns and his colleagues have, in recent years, made acase for what they refer to as “flexible scale usage”which refers to the proposition that people use spatialscales (e.g., as instantiated in different image-frequencybands) to varying degrees and in different orders de-pending on the task at hand (Gosselin & Schyns, 2001;Oliva & Schyns, 1997; Schyns & Oliva, 1999; see Mor-rison & Schyns, 2001 for a review). Thus, for example,Schyns and Oliva (1999) showed observers hybridfaces. A hybrid face is a “double exposure” of two su-perimposed faces, one composed of only low spatialfrequencies (below 8 cycles/face) and the other com-posed only of high spatial frequencies (above 24 cy-cles/face). The two faces differed on three dimensions:male/female, expressive/nonexpressive, and an-gry/happy. Observers were asked to categorize the facesalong one of these dimensions after the face was brieflypresented, and the selected member of the hybrid—thelow spatial-frequency member or the high spatial-frequency member—was noted on each trial. The in-vestigators found that different categorization tasksinfluenced which member of the pair was chosen: Intheir Experiment 1, for instance, an observer perform-

ing an expression/no expression categorization chosethe low spatial-frequency member of the hybrid 38% ofthe time, while an observer performing the happy-angrycategorization chose the low spatial-frequency memberof the exact same hybrid 66% of the time. The implica-tion, therefore was that the observers’ perception ofwhat they were seeing—and in particular which imagespatial-frequency band dominated their percep-tion—was strongly influenced by the task that theywere carrying out.

The differences between the tasks of Experiment 1 onthe one hand, and of Experiment 2-4 on the other, likelybiased the observers to attend to different spatial scales.As we have already noted, observers performing thematching task of Experiment 1, spontaneously reporteda common strategy of focusing on small details of the(shrunken) test picture—for example, on a loose lock ofhair—and then adjust the blur of the comparison pictureso as to mimic how well they could see it. This is astrategy that emphasizes high spatial-frequency infor-mation and indeed does not even require that the ob-servers be looking at a face: It seems likely that muchthe same results would have been obtained had the ob-servers been looking at any complex visual stimulus. Incontrast, the identification task in Experiments 2-4 re-quired that the stimuli be treated as faces.

Despite these observations however, our finding ofdifferent MTFs for different tasks, while analogous toSchyns’s findings, goes beyond the observation thatobservers are attending to different image frequenciesfor different tasks. While the data reported by Schynsand his colleagues imply attention to different imagescales expressed in terms of cycles/face, our findingsindicate a difference in something more fundamental,viz., a different absolute MTF for different tasks ex-pressed in terms of cycles/deg. We do not have a readyexplanation for why this happens; we can only specu-late that it may be related to the alleged “specialness” offace processing (e.g., Farah, Wilson, Drain, & Tanaka,1998) which, while clearly needed in Experiments 2-4,was not needed for Experiment 1.

Recognizing Faces at a DistanceOne of the goals of this research was to provide some

quantitative information about the distance at whichpeople can be recognized. What can we infer from ourdata?Celebrity Identification. Celebrity identification pro-vides a good paradigm for investigating the ability toidentify people who are known to the observer. Ourdata provide some estimates of the degree of clarityrequired for such identification. In particular, we esti-mated the degree of clarity required to identify the ce-lebrities at 25% and 75% rates for three comparableconditions in the three identification experiments: un-primed in Experiment 2, far start in Experiment 3, and“normal” in Experiment 4. Averaged across the three


experiments the 25% and 75% identification-level dis-tances, D, were 77 and 34 feet, and the filters, ex-pressed as cutoff, f1, were 14 and 39 cycles/face. Toprovide a sense of the degree of degradation that thesenumbers represent, Figure 14 shows Julia Roberts, fil-tered so as to represent her presumed appearance atthese two degradation levels.

A number of studies have reported data concerningspatial frequency bands that are optimal for face identi-fication. Morrison and Schyns (2001) summarize these

studies. The common finding is that there is an optimalspatial-frequency band centered around 11-20 cy-cles/face height. It is not entirely clear, however, howthese findings should be compared to ours, as there area number of important differences in the experimentalprocedures.

First, these experiments did not involve identificationof previously familiar individuals. Instead, one of twoprocedures was used: Observers were initially taught“names” corresponding to a small set of faces and thenattempted to match the filtered faces to the names (e.g.,Costen, Parker, & Craw, 1996; Fiorentini, Maffei, &Sandini, 1983), or observers were asked to match thefiltered faces to nonfiltered versions of a small set offaces that was perpetually visible (e.g., Hayes, Mor-rone, & Burr, 1986). Second, the faces were typicallyshown for only brief durations (on the order of 100 ms)to avoid ceiling effects. Third, the studies used band-pass rather than low-pass filtered faces as in the currentexperiments.

So it is not entirely clear how the results of thesestudies should be compared to the present results. Thesestudies do, however, in conjunction with the presentdata, suggest at least a rough way of demonstrating theeffect of distance on face identification, based on fun-damental image data. In particular, we calculated thecontrast energy spectrum of each of our celebrities,filtered them with our F1=31 cycles/deg MTF, and thendetermined the total contrast energy remaining in the11-20 cycles/face range at varying distances. Figure 15shows the function relating this alleged “face-identification energy” to distance. If the result is to betaken seriously, face identification should remain at 1.0up to a distance of approximately 25 feet and then de-

75%: f1 = 39 c/face, D = 34 ft

25%: f1 = 14 c/face, D = 77 ft

Figure 14. Low-pass filtered stimuli corre-sponding to 75% correct (top) and 25% correct(bottom).

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250Rela

tive

Face

-Iden

tifica

tion

Ener

gy

Distance (ft)Figure 15. Total “face identification energy” (en-

ergy in 11-20 c/face region) as a function of face dis-tance from the observer. Data are averaged over 64celebrities.


scend, reaching zero at a around 110 feet. This is closeto what we observed in our Experiments 2-4. Althoughthis correspondence occurs in part because we used theExperiment-2-4 MTF estimate to generate the Figure-15 function, the Figure-15 function is not based entirelyon our data, and the correspondence may be useful as afoundation for further study of “face-identification en-ergy”.

Memorizing Unfamiliar Faces. We introduced thisresearch by reference to a hideous crime in which aneyewitness, Arlo Olson, claimed to be able to recognizeindividuals whom he had previously watched commit-ting the crime. Mr. Olson did not claim to know theculprits; thus the identification procedure consisted ofselecting suspects from a photographic lineup. Thiskind of recognition is different from the identificationprocess studied here in Experiments 2-4 wherein ob-servers attempted to identify people who were alreadyfamiliar to them. Given that we have determined thatthe MTF for one task (e.g., matching as in Experiment1) is not necessarily the same as the MTF for anothertask (identification as in Experiments 2-4) we cannotmake an unqualified claim as to the degree of high spa-tial-frequency information lost to Mr. Olson.

However, even taking a conservative view—that theMTF relevant to Mr. Olson’s recognition task is the lesslow-passed, F1=42 cycles/deg MTF from Experiment1—the degree of degradation for an individual seenfrom a distance of 450 ft. is considerable. Can youidentify the well-known celebrity pictured in Figure 16?You can’t? If you can’t even identify him, it is unlikelythat you would have been able to recognize him in alineup had he been just a random, unfamiliar individualwhom you had briefly watched commit a crime.

EPILOGUEOn August 19, 1999, after an eleven-day trial, and

two days of deliberations, a jury convicted the Fair-banks defendants of assault and murder. The defenseattorney, the expert witness, and even the prosecutorwere astonished, because implicit in the jurors’ verdictwas their belief that Arlo Olson must have accuratelyperceived and memorized the assailants from 450 feetaway. So much for persuasive effects of the YankeeStadium analogy!

On February 24, 2003, the expert witness was sittingat his desk, writing a manuscript describing researchthat had been motivated by this case. Suddenly, out ofthe blue, an e-mail message appeared on his computer.It was from the defense attorney in the case! She wrote,

Greetings from Alaska!We may have figured out why the jurors believed thatArlo Olson could identify [the defendants] at such adistance. A newspaper reporter turned journalism pro-fessor taught a class on our case last year. He had all his

students interview witnesses, family members, jurors,etc. Four jurors have confirmed that they did their ownexperiment in broad daylight during a break. They hadone or more jurors pace off a given distance and thenthey all stood and decided if they could recognize them!One lady said that because they could, it defeated eve-rything that the defense attorneys said. Another saidthat he had bad eyesight and so even though he couldnot see, because the others could, he believed them.They all said it gave credibility to what Olson said.They were under the impression that they had permis-sion to do this. The judge confirmed in an interviewthat he knew nothing about it.That sure explains things! The article is coming outlater this week. It was supposed to come out in thespring, but he moved it up so we could get the names ofthe jurors to file a motion for a new trial. I will sendyou a copy of the article when it is published.Thought you might be interested.

REFERENCESBamber, D. (l979). State trace analysis: A method of testing

simple theories of causation. Journal of MathematicalPsychology, 19, 137-181.

Bernstein, D.M., Atance, C., Loftus, G.R, & Meltzoff, A.N.(2004). We saw it all along: Visual hindsight bias in chil-dren and adults. Psychological Science, in press.

Figure 16. Mystery celebrity filtered assuming adistance of 450 ft. The MTF has a cutoff parameterF1 of 42 cycles/deg.


Blakemore, C., & Campbell, F.W. (1969). On the existence ofneurons in the human visual system selectively sensitiveto the orientation and size of retinal images. Journal ofPhysiology, 203, 237-260.

Bracewell, R.N. (1986). The Fourier Transform and its Appli-cations (Second Edition), New York: McGraw Hill.

Brainard, D. H. (1997). The psychophysics toolbox. SpatialVision, 10, 433-436.

Bruner, J.S., & Potter, M.C., (1964). Interference in visualsearch. Science, 144, 424-425.

Campbell, F. & Robson, J. (1968) Application of Fourieranalysis to the visibility of gratings. Journal of Physiol-ogy, 197, 551-566.

Costen, N.P., Parker, D.M., & Craw, I. (1996). Effects ofhigh-pass and low-pass spatial filtering on face identifica-tion. Perception & Psychophysics, 58, 602-612.

De Valois, R.L., & De Valois, K.K. (1980). Spatial vision.Annual Review of Psychology, 31, 309-341.

De Valois, R.L., & De Valois, K.K. (1988). Spatial Vision.New York: Oxford University Press, 1988.

Farah, M.J., Wilson, K.D., Drain, M., & Tanaka, J.N. (1998).What is “special” about face perception? PsychologicalReview, 105, 482-498.

Fiorentini, A., Maffei, L., & Sandini, G. (1983). The role ofhigh spatial frequencies in face perception, Perception,12, 195-201.

Georgeson, M.A. & Sullivan, G.D. (1975). Contrast con-stancy: Deblurring in human vision by spatial frequencychannels. Journal of Physiology, 252, 627-656.

Gosselin, F., & Schyns,, P. (2001). Bubbles: A technique toreveal the use of information in recognition tasks. VisionResearch, 41, 2261-2271.

Graham, N. (1989). Visual pattern analyzers. New York:Oxford.

Harley, E.M., Carlsen, K., & Loftus, G.R. (in press). The “Isaw it all along” effect: Demonstrations of visual hind-sight bias. Journal of Experimental Psychology: Learning,Memory, & Cognition.

Harley, E.M., Dillon, A., & Loftus, G.R. (in press). Why is itdifficult to see in the fog: How contrast affects visual per-ception and visual memory. Psychonomic Bulletin & Re-view.

Harmon, L.D., & Julesz, B. (1973). Masking in visual recog-nition: Effects of two dimensional filtered noise. Science,180, 1194-1197.

Hayes, T., Morrone, M.C., & Burr, D.C. (1986). Recognitionof positive and negative bandpass-filtered images. Per-ception, 15, 595-602.

Loftus, G.R. & Busey, T.A. (1992). Multidimensional modelsand Iconic Decay. Journal of Experimental Psychology:Human Perception and Performance, 18, 356-361.

Morrison, D.J. & Schyns, P.G. (2001). Usage of spatial scalesfor the categorization of faces, objects, and scenes. Psy-chonomic Bulletin & Review, 8, 434-469.

O’Toole, A.J., Wener, M.J., & Townsend, J.T. (2001). Quan-titative models of perceiving and remembering faces:Precedents and possibilities. In Wenger, M.J. & Town-send, J.T. (eds). Computational, Geometric, and ProcessPerspectives on Facial Cognition. Mahwah NJ: ErlbaumAssociates.

Oliva, A., & Schyns, P.G. (1997). Coarse blobs or fine edges:Evidence that information diagnosticity changes the per-ception of complex visual stimuli. Cognitive Psychology,34, 72-107.

Olzak, L.A. & Thomas, J.P. (1986). Seeing spatial patterns. InK.R. Boff, L. Kaufman, and J.P. Thomas (Eds.), Hand-book of Perception and Human Performance (Vol I). NewYork: Wiley.

Palmer, J.C. (1986). Mechanisms of displacement discrimina-tion with and without perceived movement. Journal ofExperimental Psychology: Human Perception and Per-formance, 12, 411-421. (a)

Palmer, J.C. (1986). Mechanisms of displacement discrimina-tion with a visual reference. Vision Research, 26, 1939-1947. (b)

Parish, D. H. & Sperling, G. (1991). Object spatial frequen-cies, retinal spatial frequencies, noise, and the efficiencyof letter discrimination. Vision Research, 31, 1399-1415.

Pelli, D. G. (1997). The videotoolbox software for visualpsychophysics: transforming numbers into movies. Spa-tial Vision, 10, 437-442.

Reinitz, M.T. & Alexander, R. (1996). Mechanisms of facili-tation in primed perceptual identification. Memory &Cognition, 24, 129-135.

Robson, J.G. (1966). Spatial and temporal contrast sensitivityfunctions of the visual system. Journal of the Optical So-ciety of America, 56, 1141-1142.

Shlaer, S. (1937) The relation between visual acuity and illu-mination. Journal of General Psychology, 21, 165-188.

Schyns, P.G. & Oliva, A. (1999). Dr. Angry and Mr. Smile:When categorization flexibly modifies the perception offaces in rapid visual presentation. Cognition, 69, 243-265.

Townsend, J.T., Soloman, B., & Smith, J.S. (2001). The per-fect gestalt: Infinite dimensional Riemannian face spacesand other aspects of face perception. In Wenger, M.J. &Townsend, J.T. (eds). Computational, Geometric, andProcess Perspectives on Facial Cognition. Mahwah NJ:Erlbaum Associates.

Tulving, E, & Schacter, D.L. (1990) Priming and humanmemory systems. Science 247, 301-306.

van Nes, R.L. & Bouman, M.A. (1967). Spatyial modulationtransfer in the human eye. Journal of the Optical Societyof America, 57, 401-406.

(Manuscript received July 22, 2003revision accepted for publication March 31, 2004)

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