Retinal blur and the perception of egocentric distanceSchool of Psychology, University of St. Andrews,

St. Andrews, Fife, UKDhanraj Vishwanath

Department of Psychology, University of Massachusetts,Boston, MA, USAErik Blaser

A central function of vision is determining the layout and size of objects in the visual field, both of which require knowledgeof egocentric distance (the distance of an object from the observer). A wide range of visual cues can reliably signal relativedepth relations among objects, but retinal signals directly specifying distance to an object are limited. A potential source ofdistance information is the pattern of blurring on the retina, since nearer fixation generally produces larger gradients of bluron the extra-foveal retina. While prior studies implicated blur as only a qualitative cue for relative depth ordering, we find thatretinal blur gradients can act as a quantitative cue to distance. Surfaces depicted with blur gradients were judged assignificantly closer than those without, with the size of the effect modulated by the degree of blur, as well as the availabilityof other extra-retinal cues to distance. Blur gradients produced substantial changes in perceived distance regardless ofrelative depth relations of the surfaces indicated by other cues, suggesting that it operates as a robust cue to distance,consistent with the empirical relationship between blur and fixation distance.

Keywords: perception, retinal blur, egocentric distance, depth, slant, familiar size cues, tilt-shift miniaturizationCitation: Vishwanath, D., & Blaser, E. (2010). Retinal blur and the perception of egocentric distance. Journal of Vision,10(10):26, 1–16, http://www.journalofvision.org/content/10/10/26, doi:10.1167/10.10.26.

Introduction

A critical component of visual function is deriving metricestimates of the distance, depth relations, and size of objects,scaled in some meaningful way with respect to the observer.The majority of depth cues available to the visual system(e.g., binocular disparity, motion parallax, perspective, inter-position, etc.) only provide estimates of unscaled relativedepth relations. To obtain estimates of egocentric (abso-lute) depth and size, these cues must be scaled usingegocentric distance information. Cues directly specifyingegocentric distance to an object are limited (Gogel, 1963;Loomis & Knapp, 2003). The extra-retinal cues of vergenceand accommodation have been shown to provide distanceinformation only within near space, about half a meter foraccommodation (Fisher & Ciuffreda, 1988) and about 1 mor less for vergence (Foley & Held, 1972; Komoda & Ono,1974; Mon-Williams & Tresilian, 1999a; Viguier, Clement,& Trotter, 2001). For farther distances, when judgments arerestricted to a visible ground plane, angular declinationfrom sensed horizontal eye level has been shown to affectperceived distance (Ooi, Wu, & He, 2001; Philbeck &Loomis, 1997) consistent with proposals on the use of“horizon” information (Gibson, 1950; Sedgwick, 1986).Though high-level cognitive cues such as familiar size canalso be used to judge size and distance (Gogel, 1969;O’Leary & Wallach, 1980), it is unclear if they operate asnormal quantitative visual cues, or only afford cognitiveinferences of distance (Gogel, 1963, 1969; Predebon, 1992,1993). The only retinal visual information so far implicated

in signaling distance is the binocular cue of the horizontalgradient of vertical disparity (Gillam & Lawergren, 1983;Mayhew & Longuet-Higgins, 1982; Rogers & Bradshaw,1993), which has been shown to affect absolute distanceand size judgments (Rogers & Bradshaw, 1995).A potential source of monocular information for per-

ceiving distance is retinal blur. When an object at aparticular distance is fixated, it is imaged onto the foveaand it is brought into focus by the accommodative actionof the lens. However, parts of the visual field that lie atsome distance away from the fixated object will notalways be in focus, creating a pattern of blur on the extra-foveal retina (Mather, 1996; Wang, Ciuffreda, & Irish,2006). Figure 1a is a graphical representation of phenom-enon, while Figure 1b shows the degree of retinal blurringfor a point in the scene as a function of distance for fourdifferent fixation distances. Points at fixation are sharplyfocused, but points away from fixation increasinglyblurred, with greater degrees of blurring for nearer fix-ations. The depth of field for the human eye (regions aroundthe point of fixation that appear sharp) therefore reduceswith closer viewing. While we seldom notice the blur, it isoften recognized in photographic close-ups (macro pho-tography) where regions around the central object ofinterest are significantly blurred. It is plausible that thevisual system may exploit this relationship between fixa-tion distances and blur to determine perceived egocentricdistance of the fixated object(s).The first evidence that blur may play a role in distance

perception comes from art photography in (so-called) tilt-shift miniaturization. Here, photographs of life size

Journal of Vision (2010) 10(10):26, 1–16 http://www.journalofvision.org/content/10/10/26 1

doi: 10 .1167 /10 .10 .26 Received December 3, 2009; published August 25, 2010 ISSN 1534-7362 * ARVO

objects are taken from a specific vantage point (usuallydistant aerial views) in which the image size of objects issmall relative to the depicted scene. The addition of astrong vertical blur gradient to the image (either by tiltingthe camera lens relative to the film plane, or by artificialblurring) causes the objects to appear miniature or toy-like(Figure 2).Since perceived object size is determined by retinal image

size scaled by perceived distance (Holway & Boring, 1941),this effect suggests that blur gradients may be changingperceived distance in pictorial space. Vice versa, inferredsize of familiar objects is the primary cue to perceiveddistance in pictures. The salience of the miniaturization effectappears to depend on choice of subject matter (familiar

objects) and proper vantage points (views that already makeobjects look small). It is unclear without empirical testingif miniaturization is therefore a consequence of perceivedchange in distance, or whether perceived change in distanceis itself a secondary effect of miniaturization; one result-ing from cognitive interactions in pictorial space offamiliar size information, relative retinal sizes of objectsconsistent with a “toy” scene, and/or familiarity with photoblur under macro photography, e.g., for scale models.An alternative demonstration that more readily suggests

a primary role of blur in distance perception is shown inFigure 3. Here, a generic rock face with no familiar cues tosize is shown with and without a strong vertical blurgradient. A robust effect in perceived distance is seen bymost observers, with the blurred version appearing signifi-cantly closer than the no-blur version.How could such blur gradients effect perceived dis-

tance? Figure 4b shows the rate of blurring on the retina asa function of visual angle from the fovea when viewing aplanar horizontally slanted surface (Figure 4a) for fourdifferent fixation distances. The closer the distance offixation, the larger the gradient of blur increasing fromnear to far retinal periphery as indicated by the increase inslope (Figure 4). Figure 4c shows two textured, slantedsurfaces with different gradients of blur, consistent withdifferent viewing distances. If the visual system is able tomeasure the gradient of blurring for some region aroundthe fovea, it could in principle derive an estimate of distancefrom this.The pattern of the blurring, however, depends not only

on fixation distance but also the pupil diameter and therelative depth relations of points in the visual scene. Thiscomplicates the derivation of fixation distance from blurpatterns for even a simple stimulus such as a planarslanted surface. For example, any specific blur curve inFigure 4 can be nearly replicated by assuming a different

Figure 1. Retinal blur and distance. (a) The fixation point is atdistance Z0 and is imaged sharply on the retina at b0. Points atother distances from the eye will appear blurred, the degree ofblur determined by the distance of fixation Z0. (b) Rate of retinalblurring for a point in the scene plotted as a function of the distanceof that point for four different fixation distances (0.28, 0.57, 1.14,and 10 m). The point at fixation (where the curve touches theordinate) has no blur. The rate of blurring away from this point islarger for nearer fixation. See Methods section for the equationused to derive these curves.

Figure 2. An example of tilt-shift miniaturization. A photograph of areal scene with a simulated vertical gradient of blur.

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combination of fixation distance, slant, and pupil size.Computing an estimate of the actual quantitative distancebased on the slope of the blur gradient would requireinformation on slant and the pupil diameter. In naturalscenes, depth structure is much more variable than aplanar slanted surface and ambient light levels affectingpupil diameter can vary dramatically, further confoundingan independent estimate of distance based on blur patterns.However, under comparable conditions (pupil size, scenelayout), the blur gradient does increase in a monotonicfashion from far to near fixation (Figure 1a), hence statis-tically, higher blur gradients should be associated withnearer viewing.Another consideration is that blur discrimination thresh-

olds in humans are quite high, with Weber fractions exceed-ing 0.5 even at the fovea (Mather & Smith, 2002; Wang &Ciuffreda, 2004). For example, according to previouslyreported thresholds for blur detection and discrimination(Wang&Ciuffreda, 2004; Wang et al., 2006), blur gradientswould only be perceptible for a 70- slanted surfaceviewed through a 5-mm pupil when such a surface is less

than 50 cm away (see Figure 4b). For smaller pupil sizes,and/or less slant, the surface would need to be even closer.Therefore, independent of surface layout, detectable blurgradients would typically arise only when the viewedsurface(s) is relatively near. Blur gradients would there-fore be most effective as a quantitative near-distance cue,based on the statistical regularity of higher detectable blurgradients with closer viewing (less than a meter).

Prior evidence for blur and distanceperception

Variation of the human depth of field with fixationdistance had been tabulated as early as Helmholtz’streatise on optics (Helmholtz, 1924). However, psycho-physical studies in blur-mediated depth perception have todate focused on the role of discrete foveal blur differencesbetween two surfaces (e.g., at occlusion edges) in dis-ambiguating relative depth relations. These studies haveimplicated blur as a qualitative or ordinal cue to relative

Figure 3. Effect of blur gradients on perceived distance in natural textures. (a) Generic rock face that appears to have a slight vertical slant(top away). (b) The same image with the addition of a blur gradient. The rock face now appears substantially closer and appears moreslanted. The effect also works if the images are rotated by 90-. The effect is best seen when the figure is viewed on a full screen.

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depth (Lewis & Maler, 2002; Marshall, Burbeck, Ariely,Rolland, & Martin, 1996; Mather, 1996; Mather & Smith,2002; O’Shea, Govan, & Sekuler, 1997).1 Relative blur isambiguous in terms of quantitative depth difference anddepth order, compromising such blur change as an inde-pendent depth cue (Mather & Smith, 2002; though seeNguyen, Howard, and Allison, 2005). Other studies haveimplicated the role of accommodation and blur on slantperception and the scaling of binocular disparities (Watt,Akeley, Ernst, & Banks, 2005).2

Aims

In order to determine the effects of blur gradients ondistance perception, we tested observer’s perceived dis-tance judgments varying the degree of blur, the directionof blur, the consistency of blur with underlying relative

depth structure, and availability of other extra-retinal dis-tance cues.

Perceptual judgments of egocentric distance

Obtaining reliable judgments of absolute distance posesseveral methodological and interpretive challenges (Loomis& Knapp, 2003). Observer’s direct numerical judgments,or comparisons to frontoparallel intervals, are subject toobserver’s biases and capacity to match distances to lateralextents or numerical values (Foley, 1977; Loomis & Knapp,2003; Philbeck & Loomis, 1997). Moreover, reliable per-ceptual estimation can only be made to about 50 m (Loomis&Knapp, 2003). Open loopmotor response, where observersset a marker moved by their unseen hand near the mid-saggital plane, is restricted by hand reach to 60–80 cm (Fisher&Ciuffreda, 1988; Foley, 1977; Mon-Williams & Tresilian,1999a, 1999b). Blind-walking paradigms (e.g., Loomis,Da Silva, Philbeck, & Fukusima, 1996) are ineffective fortesting near space perception, which is of interest in thecurrent study.A further complication is that stimuli with simulated

blur need to be presented as spatially extended pictorialimages (of textured surfaces or objects) on a 2D display.This requires distinguishing between whether distancejudgments are to be made in pictorial space or in displayspace (Loomis & Knapp, 2003). Moreover, under pictorialviewing, distance information from vergence and accom-modation remains relatively constant, while in real scenes,vergence and accommodation will co-vary significantlywith fixation distance, and therefore in concert with thepattern of retinal blur.

Figure 4. (a) Viewing a planar horizontally slanted surface. (b) Blurgradients when viewing a surface slanted at 70- viewed from4 different distances assuming a 5-mm pupil (see Methods section).For each distance, blur increases as a function of angular distanceof a point on the surface (E) from the point of fixation (which isimaged on the fovea; indicated by 0 on the ordinate). The rate ofblurring (indicated by the slope of the curve) is much higher for asurface viewed at 28 cm than for surface viewed at over a meter.For a less slanted surface, or for a smaller pupil size, the slopes ofall the lines will be systematically less. The thin and thick gray dottedlines indicated human blur detection and discrimination thresholds,respectively (Wang et al., 2006). Blur for a point on the surface isdetectable or discriminable if the blur levels, or blur differences, aregreater than those specified by the dotted curves. Note that the plotof these curves on this graph is independent of the slant of thesurface. They merely indicate the level of blur that has to beachieved at points around the fovea for them to be detected ordiscriminated. For the 70- slanted surfaces (5-mm pupil), we cansee that near-peripheral blur will be perceived only for distancesunder a meter. For smaller slants or smaller pupil sizes, peripheralblur will only be perceived for even nearer distances. (c) A slantedtextured surface with two levels of simulated blur consistent with twodifferent viewing distances.

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Taking into consideration these factors, we ran twoexperiments testing observer’s perceived distance judg-ments in the presence or absence of blur. In the firstexperiment, we tested judgments in pictorial space with afixed display using a variant of a magnitude estimationtask that did not require numerical responses. This methodallowed us to effectively test a large distance-judgmentrange independent of changes in vergence and accommo-dation. In the second experiment, we tested judgments inreal (display) space with a movable display using adistance matching task, where we were able to examinethe effect of blur in the presence of changes in accom-modation and vergence in near space.

Experiment 1

Selection of stimuli

We tested judgments of apparent distance to depictionsof natural textured surfaces. Unlike judgments of slant orrelative depth, judging the apparent distance of a synthetictextured surface in pictorial space is highly ambiguous(Loomis & Knapp, 2003; see for example Figure 6). Onthe other hand, scenes with familiar objects could causeobservers to make cognitive or categorical judgmentsrather than relying on perceived distance (Gogel, 1969;Predebon, 1992). For example, in pictorial images thathave familiar objects taken from a very far distance (e.g.,standard tilt-shift photography), observers will likely onlyhave categorical knowledge of distanceVe.g., “it wastaken from a helicopter, so must be half a kilometer away.”Observers may consciously compute distances based onthe size of the object relative to the image, complicatinginterpretations of the effect of blur.Natural textures such as rock faces present a viable

alternative stimulus as observers find egocentric distancejudgments of random rock faces a straightforward taskdespite the lack of any familiar size cue and the high levelof self-similarity of spatial structures; observer’s reportsof perceived distance to cropped images of random rockfaces show significant degree of correlation with actualphotographed distances ranging from 25 cm to 50 m(Blaser, 2006). These stimuli therefore provide a way tovary apparent distance information in pictorial imagesindependent of blur manipulations for a large range ofdistances and without resorting to familiar size cues.

Binocular vs. monocular viewing

We chose to test distance judgments to these imagesunder binocular viewing through apertures. Under binoc-ular viewing of pictorial images, disparity cues specify thelocation of the pictorial surface. For monocular viewingthrough an aperture, where the information for the picture

surface is effectively eliminated, there is the potential thatremaining accommodation-based distance informationmay be assigned to pictorial contents, confounding theeffect of blur. We have observed changes in perceiveddistance and scale under monocular-aperture viewing con-sistent with an accommodation-related micropsia in pictorialspace (Alexander, 1975; McCready, 1965; see Figure 11and Discussion section). This has been confirmed in reportsof naive observers in a separate study (Vishwanath &Hibbard, 2009). Moreover, vergence responses to per-ceived pictorial depth have been demonstrated undermonocular viewing (Enright, 1987) but not binocularviewing (Takeda, Hashimoto, Hiruma, & Fukui, 1999).By promoting the visibility and awareness of the picturesurface, binocular viewing should inhibit changes invergence or accommodation due to pictorial contents, ortheir use as distance cues in pictorial space. Thus, distancecues in pictorial space will be limited to those inherent to theimage contents, including any simulated blur.

MethodsImage creation

Rock face images were taken with a Canon EOS 400DSLR (10 megapixels) with a fixed 60-mm lens operatedunder automatic exposure mode in bright daylight. Inorder to minimize intrinsic focal blur in the images, noimages were taken at closer than 2 m. For closer distances,images were taken at 2 m and then cropped to theappropriate size. Images were recorded in JPEG format,which were batch-processed (Irfanview) with a single passof a sharpening filter and converted to grayscale BMPs.Images were manually inspected to eliminate ones thatdid not appear to have uniform sharpness. Implied distanceof the image set ranged from 50 cm to over 12 m. Thedepicted rock surfaces had a global depth structure that waseither near-frontoparallel (typically with small slantVtoprecedingVdue to the position from which photos weretaken) or a significant slant about the vertical axis (mostimages were right receding).Blur was simulated on the natural images by convolving

them with circular averaging filters whose diameters weredetermined by using the following equations adapted fromequations for a simplified eye (Le Grand & El Hage, 1980,p. 76):

f ! 1="1=b0 # 1=z0$b ! 1="1=f j1=z$d ! Dkb0jbk="b# "Pj1$ f $

; "1$

where f is the accommodated focal length of the eye, b0 isthe distance to the retina, z0 is the distance to the fixationpoint, b is the distance of the image of a point at viewingdistance z, d is the blur circle diameter, D is the pupil size(assumed to be 5 mm), and P is the pupil factor (assumedto be 0.9; Le Grand & El Hage, 1980). The distance of a

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point on the slanted surface to be input into the equationto determine the blur circle was calculated using simpletrigonometry. Selected parameter values (pupil size, slant)were based solely on achieving blur gradient levels thatwere near or above threshold for the different blur levelssimulated (based on Wang et al.’s (2006) data). Blurlevels (methods and results) are indicated by the simulatedfixation distance; these values had no relation to structurein the photographic images or actual observer pupil sizes,which was not measured.

Stimulus presentation

Stimuli were presented on a 24W WUXGA LCD display(portrait mode) set at a resolution of 1200 % 1920 andabout 3.8 pixels/mm (BMP images) at a fixed distance of75 cm. The luminance of images on average was about18 cd/m2, with values ranging from 0.2 to over 40 cd/m2.Observers viewed the display with both eyes (see above) ona chin and head rest through oval apertures whose lateraland vertical positions were adjusted individually such thatthe frame of the display or edges of the image were notvisible. The visual angle of the display visible through theaperture(s) was approximately 18.5- (horizontal) % 28-(vertical). A rigid black screen separated the chin restassembly and the display such that observers had no visualaccess to any part of the display apparatus while seated onthe chin rest.

Task

Observers reported perceived distance using a responseimage set that contained familiar size information todistance (Blaser, 2006; Gogel, 1976). The response imageset was of a stone wall with a human model present(Figure 5). Response images ranged in implied distancefrom 20 cm and 30 cm to 9.6 m and 12.8 m in alternatinglog units (as follows: 20, 30, 40, 60I1.9 m, 12.8 m).

ProcedureObservers were first shown sample natural rock images

to explain the task and were required to individually step

through the full response set in both directions (zoomingin, zooming out) during the practice trials so that they gota sense of the full response range available. Observersinitiated a trail via a key press, at which time the targetstimulus was displayed for 1.25 s. Observers wereinstructed to maintain fixation on the center of the targetstimulus for the duration of the display. Eye movementswere not measured as the instruction was only intended tomaintain relatively consistent viewing conditions acrosstrial and observers. Since the simulated peripheral blurwas deliberately selected to be above threshold, weexpected that observers would perceive the presence ofblur even when fixating the center. Observers found thefixation requirement easy to follow, presumably becausethe trial duration was too short to simultaneously try tojudge distance and inspect the image.The first image of the comparison set (most distal)

automatically appeared 2 s after stimulus offset, at whichtime the observer selected the response image (method ofadjustment) that best matched the distance perceived inthe target surface via a keyboard input. They were allowedas much time as necessary to select a response but wereinstructed not to dwell on a single trial excessively.Observers were typically able to do a single trial in about 5 s.

Observers

All observers were stereo normal as measured using theTNO butterfly test and had normal or corrected visualacuity of 20/30 or better. Five naive observers were testedon the first part of this experiment that compared twolevels of vertical blur. In the second part that compareddifferent directions of blur and slant, 7 naive observers, 3from the first test and 4 new ones, were tested. In the thirdpart in which we further manipulated the blur magnitudeand direction, 5 naive observers, 1 from the previous testand 4 new ones, were tested.

Stimuli tested

In the first test, we compared distance judgments for threelevels of vertical blur: no blur, low blur, and high blur. Thetwo blur conditions simulated 60 cm (Low) or 30 cm (High)

Figure 5. Examples of distance response images used in Experiment 1.

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viewing (based on selected simulation parameters). Tentest stimuli for each of the blur conditions (no blur, highblur, and low blur) per observer were tested, which includedrock faces that were near-frontoparallel and depth reced-ing toward the right side (overall slant about vertical axis).Therefore, there were a total of 50 possible comparisonsfrom the 5 observers. Results are based on 49 comparisonsbecause one observer inadvertently ended a trial beforemaking a selection. The images were embedded in alarger set of similar filler no-blur images. Test imagesrepresented distances of 2, 4, 8, or 12 m. Filler no-blurimages included samples from the full range of 0.5 m toover 12 m. Each observer was tested on 2 sessionscontaining 48 target and filler images each.

ResultsEffect of blur magnitude on perceived distance

For control no-blur images of natural rock faces, observersreported a range of perceived distances generally consis-tent with underlying distances depicted (mean: 5.26 m;median: 4.8 m; range: 1.6 m–12.8 m; standard deviation:2.9 m; Figure 6, top panels). In the presence of blur,observers reported significantly nearer perceived distances,and the range was smaller (see Figure 6, top right; note thatthe ordinate is log distance). For example, in the high-blurcondition, mean perceived distance was 1.58 m; medianwas 1.2 m; and the values ranged from 40 cm to 4.8 m,only a single observation was greater than 4.8 m).Since this is an indirect magnitude estimation task, the

selected comparison image does not necessarily provide anindication of the actual perceived distance. We therefore

calculated the ratio of perceived distances for the blur andno-blur versions of the same image in order to compareeffect sizes. A clear effect of blur on perceived distance isevident for both blur levels, with the mean ratio of over 5.3for the high-blur level (Figure 6, lower left panel). Therewas a significant main effect of blur level (F(1, 83) = 5.04;p = 0.027; with subject and image as random factors).

The role of blur direction and its consistencywith depth structureThe direction of a blur gradient when viewing a slanted

planar surface is aligned with the direction of slant (tiltdirection in frontoparallel space). However, the distribu-tions of blur under natural viewing will not necessaryfollow a clear direction, since the depth distribution ofpoints in natural scenes is usually far more complex than aplanar surface. However, under natural viewing, the lowerhemi-field typically contains points closer than fixation,while the upper hemi-field contains points further away,mimicking roughly the distance distributions on a hori-zontally slanted surface that produce a vertical gradient ofblur on the retina (Figure 4, lower panels). Does the roleof the blur cue to distance depend on the direction of theoverall blur gradient, or, on the correlation of the blurgradient with the underlying depth structure of the scenespecified by other cues?We examined this by the varying the direction of blur

(vertical or horizontal gradient) and the consistency of blurdirection with underlying slant direction of the rock face.There are four types of images: (a) frontoparallel/verticalblur, (b) horizontal slant/vertical blur, (c) frontoparallel/horizontal blur, and (d) vertical slant/horizontal blur. In(b) and (d), the overall slant of the rock surface is orthogonal

Figure 6. Effects of varying the amount of blur on judgments of egocentric distance of natural textured surfaces (5 observers).(a) Distributions of matched distance judgments for the base (no-blur) images plotted against image distance. Size of the dots representsnumber of observations (ranging from 1 to 6). Dotted line plots mean matched distance. (b) Distribution of matched distances for no-blur,low-blur (60 cm), and high-blur (30 cm) images of natural rock faces. (c) Gray bars are the average ratio of judged distance of no-blurimages to the corresponding blurred images for two different levels of blur shown in (a). Error bars are standard errors. The dashed barrepresents ratios obtained in a subsequent test for 45-cm simulated blur (see Figure 8).

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to simulated blur gradient and therefore highly incon-sistent with it (IS condition); in (a) and (c), the underlyingslant is neutral to the direction of blur (NS condition),since a frontoparallel surface viewed close will have anisotropic distribution of blur. Note that some of the“frontoparallel” images had a small slant (see Methods),and in these cases the small slant was consistent with thedirection of the blur. The four possible conditions wereconstructed from the same base image, such that, forexample, the difference between the horizontal andvertical versions was just a 90 deg image rotation (seeFigure 7). In both original and rotated versions, perceivedlocal 3D structure was maintained across rotations and noinversions from perceived convexity to concavity occurred

(which can occur for some images and rotations due tothe perceptual assumption of the light source above theobserver). Thus, rotation only changed the perceivedorientation or overall slant direction of the rock face. Targetimages were constructed from 10 base images (4 fronto-parallel and 6 orthogonal-slant images) for a total of40 target images. Images were square and viewed throughcircular apertures (18.5- % 18.5-). Target images wereagain embedded in random order in a larger set of no-blurfiller images. Each observer was tested on 4 sessions of32 images each.All four conditions showed similar mean ratios for the

seven observers tested (Figure 8, left) and were consistentwith ratios seen in the preceding test for similar simulated

Figure 7. Examples of rock face stimuli showing frontoparallel slant (top row) and slanted surfaces (middle and bottom rows). The firstcolumn is the no-blur base image for each set. The second and fourth columns show stimuli with vertical blur gradients (60-cm and 45-cmsimulations, respectively), and the third column shows a horizontal blur gradient (60-cm simulation). The blur in the fourth column (vertical,45 cm) was perceptually judged as having the same degree of blurring as the one in the third column (horizontal, 60 cm). The first rowblurred images represent the Neutral Slant (NS) condition, while the blurred images in the second and third rows represent theInconsistent Slant (IS) condition.

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blur levels (low blur: 60-cm distance simulation). Whileratios for inconsistent slant (IS) conditions were slightlysmaller, the differences were not statistically significant.No systematic differences between vertical and horizontalblur gradients were found.

Differences in perception of vertical and horizontalblur

When we constructed the stimuli for the previous test,our informal observation indicated that identical levels ofphysical blur appeared blurrier in the horizontal directionthan in the vertical direction, an observation that to ourknowledge has not been previously reported. This phenom-enon is interesting because vertical blur gradients should beencountered statistically more frequently than horizontalblur gradients due to the dominance of the horizontalground plane. Previous studies have demonstrated thatperceived blur is adaptable (e.g., Battaglia, Jacobs, & Aslin,2004; Webster, Georgeson, & Webster, 2002), and thatsuch a mechanism may serve a role to reduce perceivedblur when it occurs regularly, e.g., due to optical defects.If the blur-distance cue operates on perceived rather

than physical blur, perceived distance due to blur shouldbe different for the same physical magnitude of verticaland horizontal blur. The results of the previous testsuggested that this was not the case, since the change inperceived distances for both directions were similar. Tofurther confirm this, we tested another group of subjectswhere we used stimuli in which vertical and horizontalblurs were perceptually rather than physically matched(see Appendix A).

The vertical gradients now showed larger mean effectsthan horizontal gradients as predicted by their greaterphysical magnitude (Figure 8, right panel). Again, nosignificant differences between the IS and NS conditionswere found. The overall effect sizes for the vertical blurgradients for the two blur levels were consistent with thosein the previous tests (the value for the 45-cm simulationwas in between those observed for the 30-cm and 60-cmblur in the first test; Figure 6, lower panel, dashed bar).While there was a weak trend in the data, we found no

significant effect of the orientation of the blur relative tounderlying depth structure; perceived distance was primar-ily modulated by the physical magnitude of the blurring.

Slant cues in the image

One potential reason for the insignificant differencebetween the inconsistent (IS) and neutral slant (NS)conditions in the second and third tests is that theunderlying relative depth cues (shading, texture, perspec-tive) were insufficient for recovering slant, particularly inthe short stimulus presentation duration. We examinedthis (see Appendix B) and found that observers can readilyperceive slant consistent with the underlying texture forthe presentation duration tested.

Experiment 2

In order to independently vary distance informationavailable from blur and accommodation/vergence, stimuliwere presented on a movable display platform, withimages scaled to viewing distance. Since obtaining motorresponses (pointing) of perceived egocentric distance wasprecluded by the stimulus and apparatus size, observersadjusted a comparison distance to match a previouslyviewed standard distance; a task that provides a directmeasure of the reliability of available distance cues (e.g.,Brenner & van Damme, 1998), and where any bias insettings provides evidence of the role of blur.We first tested if observers had reliable distance infor-

mation for no-blur images in the presence of (i) vergenceand accommodation (binocular viewing) or (ii) accom-modation alone (monocular viewing). Prior studies haveshown that vergence provides an effective cue to distanceto at least 80 cm (Foley, 1977; Mon-Williams & Tresilian,1999a, 1999b; Viguier et al., 2001). However, reliable dis-tance judgment based on accommodation has only beendemonstrated (in some observers) up to 50 cm, beyondwhich the accommodative response itself is non-linear anderror prone (Fisher & Ciuffreda, 1988). Even within thelinear range, accommodation is not as effective a cue asvergence, showing significant compression of perceiveddistance range and considerable variation in subject’scapacity to use accommodation as a distance cue (Fisher& Ciuffreda, 1988).

Figure 8. (a) Ratio of judged distances for identical vertical andhorizontal blur gradients (simulating 60 cm viewing) where theunderlying slant of the rock surface was either neutral (NS) orinconsistent (IS) with the underlying slant of the rock face(7 subjects, see text). (b) Ratio of judged distances for percep-tually matched vertical and horizontal blur gradients (NS and ISconditions; 5 subjects). Mean combined ratio (IS and NS) forvertical blur is plotted in (b), dashed bar.

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In initial pilots, we found that while some observerswere able to successfully do the task with differing degrees ofprecision, some were unable to do the task (no staircasereversals) even with feedback. They appeared to be report-ing exactly the opposite distance relationship, consistentwith the size–distance paradox (Epstein, Park, & Casey,1961; Komoda & Ono, 1974). Similar effects have beenimplicated in between-observer differences reported pre-viously for distance judgments using accommodation(Fisher & Ciuffreda, 1988), and studies have suggestedthat this is a cognitive phenomenon in distance reporting(Mon-Williams & Tresilian, 1999b).When we converted the instruction to one of judging the

apparent size of the 2D image, these observers weresuccessfully able to do the task. In the actual experiment,we therefore first did an initial test with the observersusing the distance task; if they failed in the predictableway, we then tested them on the size task. Successfulperformance in both tasks is given by the point of subjectiveequality (PSE) of the comparison setting being at, or closeto, the standard. A matched PSE does not necessarilyimply that perceived distance is veridical, but rather thatobservers had a reliable estimate of apparent distance;prior studies have shown that both accommodation- andvergence-specified distance judgments show biases(Fisher & Ciuffreda, 1988; Foley, 1977; Mon-Williams &Tresilian, 1999a; Viguier et al., 2001).We then tested the observers on a condition where

comparison images with a blur gradient simulating a viewingdistance of 25 cm were matched to a no-blur standardat 40 cm. Thus, blur specified a distance closer than thestandard. If blur was an effective cue to distance, acomparison display should appear closerVand the imagesmallerVand would need to be set at some distance furtherthan the standard to be matched to it.

MethodsStimuli

Stimuli were 2D images of slanted planar surfaces(70- slant) with a random pattern of circular disks generatedon POV-Ray rendering software (Figure 1c). The size andlocation of individual disks (except the central one) in 3Dmodel space was randomly varied from trial to trial (sizesvaried by T10%). The individual disks had a high-contrasttextured pattern to disrupt visibility of the display pixels atthe nearest viewing distance. Blur was simulated on therendered image in the same way as described previously,but assuming a fixation distance of 25 cm, surface slant of70- (matching the textured surface), and a pupil diameterof 5 mm.

Stimulus presentation

Stimuli were presented on an LCD display (same as theprevious experiment) on a platform that could be movedmanually between 25 and 80 cm in steps of 5 cm. We

limited near viewing to 25 cm because screen pixelizationwas visible at nearer distances. Far distance was selectedbased on distances used in previous studies (Mon-Williams& Tresilian, 1999a; Viguier et al., 2001). The luminance ofthe dark background was 0.2 cd/m2 while the luminance oftexture elements varied from about 6.2 to 10.5 cd/m2. Wechose these relatively low luminance levels because in pilottesting observers reported discomfort and difficulty due tothe high visual transients and afterimages, which likelyoccurred because observers had their eyes closed duringthe significant portion of the session. At the testedluminance, observers reported that overall visibility wassufficient for clearly seeing the textured objects. Priorstudies that have found effects of accommodation and blurin depth perception have used maximum luminance levelsas low as 0.9 cd/m2 (Watt et al., 2005).Viewing conditions were the same as the previous exper-

iment. The lateral and vertical positions of the apertures(approximately 16.5- % 26-) were first adjusted individuallyso that the frame of the display was not visible at anyviewing distance. Observer wore earmuffs to prevent hearingthe movement of the display between presentations.

Procedure

Each trial consisted of a sequential presentation (inrandom order) of a standard image at a fixed distance fromthe observer and a comparison at some other distance. Toprevent observers from viewing the movement of thedisplays between presentations, observers had eyes closedat all times except on voice signal to initiate the image viaa keyboard entry. The image was extinguished after 1.5 sat which time observers closed their eyes again. Inter-stimulus intervals averaged about 2–3 s. Observers wereinstructed to maintain fixation on the central disk duringstimulus presentation, so as to maintain uniformity ofviewing across observer. Observers matched the distanceof the comparison and the standard with an adaptive one-up one-down staircase procedure (5 reversals). For thedistance task, they were required to report which of twoconsecutively presented displays appeared closer to them.They were instructed to make judgments regarding theactual physical display surface and not the pictorial scene.Similarly, for those who did the size task, they wereinstructed to report which image appeared smaller;reporting on the size of the displayed 2D image and notthe perceived size of objects in the pictorial scene.Observers were first shown the entire apparatus includingthe movable display and images in order to explain thetask and make clear they were making judgmentsregarding the display surface or image. Observers weretested under both monocular and binocular conditions.Observers were initially tested on a control task where

both standard and comparison had no blur. We first testedwithout feedback, and then with feedback (a short beep ifthe reported display was not the closer one). Performanceon control feedback and no-feedback trials was similar,

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which is expected because the nature of feedback andstimulus presentation precluded any trial-to-trial learning(order of the standard and comparison was random, andeach session had multiple staircases, so information ofwhether or not one correctly reported the closer displayon any particular trial cannot be used to adjust responseon a future trial). The feedback only served as a diagnostic tothe observer if they were generally doing the task success-fully, or if there was a drop in concentration or effort.In the experimental trials, the comparison was an image

with a blur gradient simulating a viewing distance of 25 cm,and the standard no-blur display was set at a distance of40 cm. Control no-blur trials were interleaved with theexperimental blur trials. Feedback was provided for thecontrol no-blur trials only. This was done as a precautionto maintain overall response effort and criteria. No-blurcontrol trial data in Figure 9 is from concurrent inter-leaved trials.

Observers

Seven observers were initially tested on control no-blurtrials. All except one were stereo normal as measuredusing the TNO butterfly test and had normal or correctedvisual acuity of 20/30 or better. The observer who was notstereo normal reported uncorrected strabismus and hadnormal acuity in his dominant eye. We tested this observerwondering if he might still be effective at the distance/sizetask under monocular viewing with his dominant eye.Observers were first tested without feedback to confirmthat the task could be done on the basis of instructionsalone. Those who could not do the distance task were thentested on the size task. The strabismic observer could notdo either task under binocular or monocular viewing; andanother observer, despite being stereo normal, was alsounable to do either task even with feedback. These twoobservers were not tested any further. Of five remainingnaive observers, two of the observers did the distance taskand three the size task under binocular viewing.

Results

Figures 9a and 9b show data for one observer in theno-blur size judgment task. CH was able to do the taskunder binocular viewing for both tested distances (PSE forthe comparison stimuli is the same as the standard). CHwas only able to attain a perceptual match under monocularviewing for the nearer 40-cm distance (Figure 6, lower leftpanel), and in the binocular condition variability ofjudgments for the farther viewing distance (65 cm) washigher (Figure 6, upper left panel).Two of the five observers could not do the task under

monocular viewing, even for the near 40 cm standard.Prior studies have found that a significant proportion ofobservers is unable to use accommodation as a cue for

distance estimation (Fisher & Ciuffreda, 1988). Only oneout of three successful monocular observers was able toattain a perceptual match for the farther 65 cm standardunder monocular viewing. During testing, we observedthat when the display was at the 75- or 80-cm setting,some monocular observers often repeatedly reported itcloser than standard, preventing convergence of theadaptive staircase. These results appear consistent withthe fact that accommodative response is linear only toabout 50 cm (2 diopters) and that it likely does notprovide a reliable distance signal much beyond that point

Figure 9. (a, b) Psychometric functions for one observer (sizetask) in the control no-blur condition under binocular viewing andmonocular viewing, with standard display set at 40 cm or 65 cmand a no-blur movable comparison. Data fitted by cumulativeGaussians (MLE fit; Wichmann & Hill, 2001). Number of trials perdata point varies, with larger sampling near the PSE (staircaseprocedure). Large error bars are SD’s; small error bars are SEM ’s.Black dashed line indicates location of the standard display(40 cm) and red arrow indicates matched PSE for comparisondisplay. Observer CH was not able to do the task at the 65-cmsetting under monocular viewing (see text). (c, d) Data for the sameobserver in trials where the standard no-blur display was set at40 cm and the movable comparison had a blur gradient specifyinga viewing distance of 25 cm. Black arrow indicates the distanceused to simulate blur (25 cm). Light gray curves are psychometriccurves for the no-blur control shown in the left panels forcomparison. As predicted, the PSE in the blur condition is shiftedto the right (the display with the blurred image was set further way,to be matched with a standard no-blur display at 40 cm).

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(Fisher & Ciuffreda, 1988). As expected, judgment in thebinocular condition where vergence information wasavailable was more reliable than the monocular conditionfor all observers. Figures 9c and 9d show data from “blur”trials (red curves) for observer CH. Control “no-blur”trials are replotted as gray curves. As predicted, displaysin the “blur” trials were set further away from the observer(compare gray and red curves). Figure 10 shows data forthe other four observers.Within observers, the effect was consistently larger

under monocular (accommodation only) than binocularviewing. There was a significant correlation between thechange in perceived distance due to blur and the under-lying variance of responses in the control no-blurcondition (Figure 10, lower right panel). For four out offive observers, the overall variances were comparable withor without blur (red vs. gray curves in the psychometricfunctions), and one of these observers (AN) showed areduction in variability in the blur condition. Only oneobserver (KR) showed a large increase in variability in theblur condition. Moreover, there was no correlationbetween the effect sizes and changes in variance fromno-blur to blur conditions (r2 = 0.03; p = 0.67).

Discussion

Based on two experiments, the present study providespsychophysical evidence of the role of blur gradients indistance perception. The effect of blur on distanceperception we found in the first experiments was robust,and its size depended on the degree of extra-fovealblurring, but not on the consistency of the direction ofblur relative to implied depth structure. In the secondexperiment, we found that the effect of blur on perceiveddistance was significantly correlated with the variance ofdistance information available from other cues, but not onthe change in variance from no-blur to blur conditions.Overall, the pattern of results suggests that the blur gradientlikely operates as a quantitative cue to egocentric distanceconsistent with the empirical relationship between retinalblur and viewing distance, and not a precise computationthat compare patterns of blurring, pupil size, and relativedepth structure. This is consistent with the fact that blurdetection and discrimination thresholds are themselvesquite large (Mather & Smith, 2002; Wang & Ciuffreda,2004), and that the cue would therefore only be effectiveunder near viewing where extra-foveal blur would bedetected.

Blur gradients and the underlying depthstructure of the scene

The effect of blur on distance perception appeared to belargely independent of the depth structure implied by

Figure 10. Data for the four other observers (distance task: LS,AN; size task: KR, GM). See Figure 9 and text for details. Graycurves are the settings for the control no-blur condition where boththe standard (40 cm) and the movable comparison were notblurred. Red curves are for trials in which the comparison wasblurred and the standard no-blur stimulus was set at 40 cm. Leftcolumns are for binocular viewing and control no-blur condition(standard deviation of the gray curves). In all cases the blurredcomparison display had to be set farther than the no-blur standardto be matched to it. Observers AN and KR were unable to do themonocular control task. The scatter plot summarizes the effectsize of blur on distance judgments (shift of red curve relative tothe gray curve) for all five observers plotted as a function of theunderlying variability in the control no-blur condition (standarddeviation of the gray curves). Larger values on the abscissaindicate greater variability of distance judgments based onaccommodation/vergence alone.

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relative depth cues, with comparable effect sizes obtainedregardless of the consistency of the blur gradient directionwith slant direction. The general insensitivity to depthstructure may explain why tilt-shift miniaturization occursusing a generic vertical blur gradient regardless of therelative depth structure of the scene.We did not find any significant differences in the role of

vertical and horizontal blur gradients even though the formerare statistically more likely under typical near-viewing innatural scenes (where a horizontal ground plane predom-inates). However, we found that the appearance of blurdiffers between physically identical horizontal and verticalgradients, suggesting that the perception of vertical blurgradients may be adapted by its statistically morecommon occurrence under near viewing. Prior studieshave suggested that blur adaptation mechanisms may playa role in increasing perceived sharpness under conditionsof a regular occurrence of blurring, for example, due tooptical defects. Such a mechanism could also serve togive the impression of sharpness for a larger regionaround the fovea under near viewing, and thus creating agreater apparent depth of field. Whether the perceived blurdifference we found is due to such long-term adaptation orother factors remains to be examined. However, the effectof blur on distance appeared to depend on the physicalrather than the perceived level of blur.A future more detailed examination will be needed to

shed more light on specific properties of the blur cue, inrelation to both statistical distributions of blur gradientsempirically encountered and other relative depth cues.

Blur, accommodation, and vergence

The second experiment confirmed the role of blur indistance perception within near space, using a differentparadigm where it was pitted against vergence andaccommodation. Specifically, we found that the effect ofthe blur gradient cue on apparent distance depended onthe reliability of other available cues as indicated by thevariance in distance judgments in control no-blur trials.This suggests that blur might combine with extra-retinaldistance cues in a manner consistent with cue-combinationmodels, where the influence of a depth/distance cue isinversely related to its reliability relative to other availablecues (e.g., Hillis, Watt, Landy, & Banks, 2004). A moredetailed study will be needed to determine if blur combineswith other distance cues in the statistically optimal mannersuggested by such models. Generally, the effect of blur wasmoderate to weak in the presence of vergence (in 4 out of5 observers), which is consistent with the fact that vergenceis a relatively reliable cue to distance at less than 60 cm(Foley, 1980; Mon-Williams & Tresilian, 1999a; Viguieret al., 2001). Effects were larger in observers who could dothe monocular task. However, the fact that the role ofaccommodation in distance perception remains controversial(Mon-Williams&Tresilian, 1999a), and given the significant

inter-subject variability in this and other studies (Fisher &Ciuffreda, 1988), future studies that more closely examinehow the blur gradient cue combines with other distancecues will likely be best done by pitting vergence and blurand testing distances beyond 1 m where the vergence signalbecomes increasingly less reliable.

Blur, familiar size, and tilt-shift miniaturization

The effect of blur gradients on distance perceptionsuggests that blur-based miniaturization in photography isthe result of a visual phenomenon, rather than just acognitive outcome dependent on relative object size,object familiarity, or familiarity with macro photography.Under normal binocular viewing of a picture, extra-retinaldistance information (accommodation, vergence) as wellas egocentrically scaled relative depth cues (parallax anddisparity) together specify the structure and distance of thepicture surface (Vishwanath, Girshick, & Banks, 2005;Watt et al., 2005). The only source of distance informationin pictorial space is familiar size. The presence of a blurgradient introduces a quantitative distance cue intopictorial space, which appears to change perceiveddistance by overriding familiar size cues. “Familiarity” isturned on its head, and objects appear toy-like. The effectis so powerful that it appears to alter even perceivedmaterial qualities (objects often look like they are madeout of plastic or cardboard).We have observed informally that monocular viewing

of images through an aperture produce similar effects ofscaling and distance (Figure 11). How might this berelated to blur-based scaling effects? During monocularviewing through an aperture, the visibility of the picture

Figure 11. Original photograph used to demonstrate the tilt-shiftminiaturization effect in Figure 2. When viewing an enlargedversion of this image through an oval aperture (1.5–2 cm wide),the apparent scale of the image changes, and the scene appearsto most observers to be closer or smaller.

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surface is removed and disparity-driven vergence iseliminated. The only putative distance cue remaining (attypical picture viewing distances) is accommodation,which, in the absence of a perceived picture surface, appearsto be assigned to pictorial surfaces, scaling pictorial depth,and size in a micropsia-like effect (Alexander, 1975;McCready, 1965). Thus, accommodation (or accommoda-tive vergence), under appropriate conditions, could lead toa similar miniaturization in pictures.Interestingly, the reverse phenomenon is also observed.

Photographs of scale models appear life size when normalblur gradients are eliminated by using small cameraapertures. This is vividly demonstrated in the work ofartist James Casebere (Figure 12). Photographs of tabletoparchitectural models taken such that no blur gradientsare visible make the spaces appear uncannily realdespite the visibility of construction marks and material(e.g., cardboard) which clearly give away the small scaleof the objects (In gallery presentations, the originalphotographs are several feet in dimension). However, itis possible that the lack of blur, rather than signaling a farviewing distance, only makes a blur-based judgment ofdistance in pictures highly ambiguous because the lack ofdetected extra-foveal blur is consistent with a large rangeof distances anywhere from a meter to infinity; allowingcognitive familiar size information to disambiguate per-ceived distance and size.The various scaling effects in pictures supports a view

that cognitive sources of information like familiar sizelikely do not operate as normal visual cues, in the sensethat they do not combine with or scale other distance cues(Gogel, 1969; Predebon, 1993). Rather, they might onlyoperate to disambiguate perceptual judgments in a catego-rical manner under high levels of sensory uncertainty, as ispresent in pictures, and be overridden to conform to evenrelatively high threshold optical signals such as blur oraccommodation.

Appendix A

Perceptually matching horizontal and verticalblur

Five experienced naive psychophysical observers sub-jectively matched perceived blur (Battaglia et al., 2004;Webster et al., 2002) for horizontal and vertical blurgradients while fixating the center of the image (methodof limits; increasing and decreasing blur levels). Theyreported which of two images appeared to be more blurred(Battaglia et al., 2004). Simulated blur varied in incre-ments of 5 cm of viewing distance for a 70- slantedsurface. A representative sample of 5 rock face imageswas tested. All five observers found the blur comparisontask straightforward. Vertical blur gradients simulating45 cm viewing were on average selected as perceptuallymatching horizontal blur gradients simulating 60 cmviewing. Judgment noise was negligible, with all observersindividually selecting the 45 cm match, and 3 out of5 observers selecting the exact 45 cm match for everysample image tested.

Appendix B

Effectiveness of depth cues in test images

To examine this, we had 7 naive observers (who had notbeen previously tested on the images) judge perceivedslant in the rock faces images used, reporting the slantdirection (frontoparallel, left, right, top, or bottom) andslant magnitude (slight, moderate, or large) under identi-cal viewing and timing conditions to the original experi-ment. The results of the test are shown in Figure B1, plotted

Figure 12. James Casebere, Pink Hallway, #2, 2000.

Figure B1. Reported slants plotted as vectors whose orientationindicates perceived tilt (direction of slant). Left panel is for imagesdepicting slanted rock faces (IS condition) and right panel fornear-frontoparallel (NS) condition.

Journal of Vision (2010) 10(10):26, 1–16 Vishwanath & Blaser 14

as vectors (direction = tilt; length = slant magnitude; 1, 2,and 3 coded slight, moderate, large slants). In the no-blurimages, observers clearly perceived moderate-to-largeslants in the predicted direction in the IS images (verticalor horizontal slant), while the NS condition (fronto-parallel) showed only slight to negligible slant magnitudes,consistent with the images. The reported slants in thevertical tilt direction were smaller than for the horizontaltilt direction (vertical-slant images can look like fronto-parallel rock faces viewed from below, which could havebiased observer’s to under-report magnitude of slant). Forthe blurred images, observers still perceived significantslants in the predicted directions (IS condition), thoughreduced somewhat compared to the no-blur images. In theNS condition, the perceived slant with blur was larger thanin the comparable no-blur condition and biased in the direc-tion of blur. This is consistent with the informal observationthat blur gradients make near-frontoparallel surfaces appearmore slanted in the blur direction (see Figure 3).

Acknowledgments

This research was supported by a Research Council UKfellowship to DV. We thank Harold Nefs for technicaladvice on image processing and Paul Hibbard and JulieHarris for comments on an earlier version of the manuscript.

Commercial relationships: none.Corresponding author: Dhanraj Vishwanath.Email: dv10@st-andrews.ac.uk.Address: School of Psychology, University of St.Andrews, Fife KY16 9JP, UK.

Footnotes

1Egocentric or absolute distance is the distance from theobserver to a point in the scene. Relative distance(absolute depth) is the depth separation between twopoints in egocentrically scaled units. Relative depth is thenon-metric depth ordering of two or more points, or theratios of depth separations between more than two points(e.g., slant).

2The use of the term “distance” in Lewis and Maler’s(2002) study is technically incorrect. Their data showedthe tradeoff between blur and contrast as relative depthordering cues in human observers.

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