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Research Article  |   August 2010
Retinal blur and the perception of egocentric distance
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Journal of Vision August 2010, Vol.10, 26. doi:10.1167/10.10.26
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      Dhanraj Vishwanath, Erik Blaser; Retinal blur and the perception of egocentric distance. Journal of Vision 2010;10(10):26. doi: 10.1167/10.10.26.

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

Introduction
A critical component of visual function is deriving metric estimates 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, interposition, etc.) only provide estimates of unscaled relative depth relations. To obtain estimates of egocentric (absolute) depth and size, these cues must be scaled using egocentric distance information. Cues directly specifying egocentric distance to an object are limited (Gogel, 1963; Loomis & Knapp, 2003). The extra-retinal cues of vergence and accommodation have been shown to provide distance information only within near space, about half a meter for accommodation (Fisher & Ciuffreda, 1988) and about 1 m or less for vergence (Foley & Held, 1972; Komoda & Ono, 1974; Mon-Williams & Tresilian, 1999a; Viguier, Clément, & Trotter, 2001). For farther distances, when judgments are restricted to a visible ground plane, angular declination from sensed horizontal eye level has been shown to affect perceived 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 can also be used to judge size and distance (Gogel, 1969; O'Leary & Wallach, 1980), it is unclear if they operate as normal quantitative visual cues, or only afford cognitive inferences 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 horizontal gradient of vertical disparity (Gillam & Lawergren, 1983; Mayhew & Longuet-Higgins, 1982; Rogers & Bradshaw, 1993), which has been shown to affect absolute distance and size judgments (Rogers & Bradshaw, 1995). 
A potential source of monocular information for perceiving distance is retinal blur. When an object at a particular distance is fixated, it is imaged onto the fovea and it is brought into focus by the accommodative action of the lens. However, parts of the visual field that lie at some distance away from the fixated object will not always 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 phenomenon, while Figure 1b shows the degree of retinal blurring for a point in the scene as a function of distance for four different fixation distances. Points at fixation are sharply focused, but points away from fixation increasingly blurred, with greater degrees of blurring for nearer fixations. The depth of field for the human eye (regions around the point of fixation that appear sharp) therefore reduces with closer viewing. While we seldom notice the blur, it is often recognized in photographic close-ups (macro photography) where regions around the central object of interest are significantly blurred. It is plausible that the visual system may exploit this relationship between fixation distances and blur to determine perceived egocentric distance of the fixated object(s).
Figure 1
 
Retinal blur and distance. (a) The fixation point is at distance Z 0 and is imaged sharply on the retina at b 0. Points at other distances from the eye will appear blurred, the degree of blur determined by the distance of fixation Z 0. (b) Rate of retinal blurring for a point in the scene plotted as a function of the distance of that point for four different fixation distances (0.28, 0.57, 1.14, and 10 m). The point at fixation (where the curve touches the ordinate) has no blur. The rate of blurring away from this point is larger for nearer fixation. See Methods section for the equation used to derive these curves.
Figure 1
 
Retinal blur and distance. (a) The fixation point is at distance Z 0 and is imaged sharply on the retina at b 0. Points at other distances from the eye will appear blurred, the degree of blur determined by the distance of fixation Z 0. (b) Rate of retinal blurring for a point in the scene plotted as a function of the distance of that point for four different fixation distances (0.28, 0.57, 1.14, and 10 m). The point at fixation (where the curve touches the ordinate) has no blur. The rate of blurring away from this point is larger for nearer fixation. See Methods section for the equation used to derive these curves.
 
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 objects are taken from a specific vantage point (usually distant aerial views) in which the image size of objects is small relative to the depicted scene. The addition of a strong vertical blur gradient to the image (either by tilting the camera lens relative to the film plane, or by artificial blurring) causes the objects to appear miniature or toy-like (Figure 2).
Figure 2
 
An example of tilt-shift miniaturization. A photograph of a real scene with a simulated vertical gradient of blur.
Figure 2
 
An example of tilt-shift miniaturization. A photograph of a real scene with a simulated vertical gradient of blur.
 
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 changing perceived distance in pictorial space. Vice versa, inferred size of familiar objects is the primary cue to perceived distance in pictures. The salience of the miniaturization effect appears to depend on choice of subject matter (familiar objects) and proper vantage points (views that already make objects look small). It is unclear without empirical testing if miniaturization is therefore a consequence of perceived change in distance, or whether perceived change in distance is itself a secondary effect of miniaturization; one resulting from cognitive interactions in pictorial space of familiar size information, relative retinal sizes of objects consistent with a “toy” scene, and/or familiarity with photo blur 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 in Figure 3. Here, a generic rock face with no familiar cues to size is shown with and without a strong vertical blur gradient. A robust effect in perceived distance is seen by most observers, with the blurred version appearing significantly closer than the no-blur version.
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 more slanted. 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.
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 more slanted. 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.
 
How could such blur gradients effect perceived distance? Figure 4b shows the rate of blurring on the retina as a function of visual angle from the fovea when viewing a planar horizontally slanted surface (Figure 4a) for four different fixation distances. The closer the distance of fixation, the larger the gradient of blur increasing from near to far retinal periphery as indicated by the increase in slope (Figure 4). Figure 4c shows two textured, slanted surfaces with different gradients of blur, consistent with different viewing distances. If the visual system is able to measure the gradient of blurring for some region around the fovea, it could in principle derive an estimate of distance from this.
Figure 4
 
(a) Viewing a planar horizontally slanted surface. (b) Blur gradients when viewing a surface slanted at 70° viewed from 4 different distances assuming a 5-mm pupil (see Methods section). For each distance, blur increases as a function of angular distance of a point on the surface (θ) from the point of fixation (which is imaged on the fovea; indicated by 0 on the ordinate). The rate of blurring (indicated by the slope of the curve) is much higher for a surface 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 of all the lines will be systematically less. The thin and thick gray dotted lines indicated human blur detection and discrimination thresholds, respectively (Wang et al., 2006). Blur for a point on the surface is detectable or discriminable if the blur levels, or blur differences, are greater than those specified by the dotted curves. Note that the plot of these curves on this graph is independent of the slant of the surface. They merely indicate the level of blur that has to be achieved at points around the fovea for them to be detected or discriminated. For the 70° slanted surfaces (5-mm pupil), we can see that near-peripheral blur will be perceived only for distances under a meter. For smaller slants or smaller pupil sizes, peripheral blur will only be perceived for even nearer distances. (c) A slanted textured surface with two levels of simulated blur consistent with two different viewing distances.
Figure 4
 
(a) Viewing a planar horizontally slanted surface. (b) Blur gradients when viewing a surface slanted at 70° viewed from 4 different distances assuming a 5-mm pupil (see Methods section). For each distance, blur increases as a function of angular distance of a point on the surface (θ) from the point of fixation (which is imaged on the fovea; indicated by 0 on the ordinate). The rate of blurring (indicated by the slope of the curve) is much higher for a surface 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 of all the lines will be systematically less. The thin and thick gray dotted lines indicated human blur detection and discrimination thresholds, respectively (Wang et al., 2006). Blur for a point on the surface is detectable or discriminable if the blur levels, or blur differences, are greater than those specified by the dotted curves. Note that the plot of these curves on this graph is independent of the slant of the surface. They merely indicate the level of blur that has to be achieved at points around the fovea for them to be detected or discriminated. For the 70° slanted surfaces (5-mm pupil), we can see that near-peripheral blur will be perceived only for distances under a meter. For smaller slants or smaller pupil sizes, peripheral blur will only be perceived for even nearer distances. (c) A slanted textured surface with two levels of simulated blur consistent with two different viewing distances.
 
The pattern of the blurring, however, depends not only on fixation distance but also the pupil diameter and the relative depth relations of points in the visual scene. This complicates the derivation of fixation distance from blur patterns for even a simple stimulus such as a planar slanted surface. For example, any specific blur curve in Figure 4 can be nearly replicated by assuming a different combination of fixation distance, slant, and pupil size. Computing an estimate of the actual quantitative distance based on the slope of the blur gradient would require information on slant and the pupil diameter. In natural scenes, depth structure is much more variable than a planar slanted surface and ambient light levels affecting pupil diameter can vary dramatically, further confounding an independent estimate of distance based on blur patterns. However, under comparable conditions (pupil size, scene layout), the blur gradient does increase in a monotonic fashion from far to near fixation (Figure 1a), hence statistically, higher blur gradients should be associated with nearer viewing. 
Another consideration is that blur discrimination thresholds in humans are quite high, with Weber fractions exceeding 0.5 even at the fovea (Mather & Smith, 2002; Wang & Ciuffreda, 2004). For example, according to previously reported thresholds for blur detection and discrimination (Wang & Ciuffreda, 2004; Wang et al., 2006), blur gradients would only be perceptible for a 70° slanted surface viewed 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 blur gradients would typically arise only when the viewed surface(s) is relatively near. Blur gradients would therefore be most effective as a quantitative near-distance cue, based on the statistical regularity of higher detectable blur gradients with closer viewing (less than a meter). 
Prior evidence for blur and distance perception
Variation of the human depth of field with fixation distance had been tabulated as early as Helmholtz's treatise on optics (Helmholtz, 1924). However, psychophysical studies in blur-mediated depth perception have to date focused on the role of discrete foveal blur differences between two surfaces (e.g., at occlusion edges) in disambiguating relative depth relations. These studies have implicated blur as a qualitative or ordinal cue to relative depth (Lewis & Maler, 2002; Marshall, Burbeck, Ariely, Rolland, & Martin, 1996; Mather, 1996; Mather & Smith, 2002; O'Shea, Govan, & Sekuler, 1997). 1 Relative blur is ambiguous in terms of quantitative depth difference and depth order, compromising such blur change as an independent depth cue (Mather & Smith, 2002; though see Nguyen, Howard, and Allison, 2005). Other studies have implicated the role of accommodation and blur on slant perception and the scaling of binocular disparities (Watt, Akeley, Ernst, & Banks, 2005). 2  
Aims
In order to determine the effects of blur gradients on distance perception, we tested observer's perceived distance judgments varying the degree of blur, the direction of blur, the consistency of blur with underlying relative depth structure, and availability of other extra-retinal distance cues. 
Perceptual judgments of egocentric distance
Obtaining reliable judgments of absolute distance poses several methodological and interpretive challenges (Loomis & Knapp, 2003). Observer's direct numerical judgments, or comparisons to frontoparallel intervals, are subject to observer's biases and capacity to match distances to lateral extents or numerical values (Foley, 1977; Loomis & Knapp, 2003; Philbeck & Loomis, 1997). Moreover, reliable perceptual estimation can only be made to about 50 m (Loomis & Knapp, 2003). Open loop motor response, where observers set 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 for testing near space perception, which is of interest in the current study. 
A further complication is that stimuli with simulated blur need to be presented as spatially extended pictorial images (of textured surfaces or objects) on a 2D display. This requires distinguishing between whether distance judgments are to be made in pictorial space or in display space (Loomis & Knapp, 2003). Moreover, under pictorial viewing, distance information from vergence and accommodation remains relatively constant, while in real scenes, vergence and accommodation will co-vary significantly with fixation distance, and therefore in concert with the pattern of retinal blur. 
Taking into consideration these factors, we ran two experiments testing observer's perceived distance judgments in the presence or absence of blur. In the first experiment, we tested judgments in pictorial space with a fixed display using a variant of a magnitude estimation task that did not require numerical responses. This method allowed us to effectively test a large distance-judgment range independent of changes in vergence and accommodation. In the second experiment, we tested judgments in real (display) space with a movable display using a distance matching task, where we were able to examine the effect of blur in the presence of changes in accommodation and vergence in near space. 
Experiment 1
Selection of stimuli
We tested judgments of apparent distance to depictions of natural textured surfaces. Unlike judgments of slant or relative depth, judging the apparent distance of a synthetic textured surface in pictorial space is highly ambiguous (Loomis & Knapp, 2003; see for example Figure 6). On the other hand, scenes with familiar objects could cause observers to make cognitive or categorical judgments rather than relying on perceived distance (Gogel, 1969; Predebon, 1992). For example, in pictorial images that have familiar objects taken from a very far distance (e.g., standard tilt-shift photography), observers will likely only have categorical knowledge of distance—e.g., “it was taken from a helicopter, so must be half a kilometer away.” Observers may consciously compute distances based on the size of the object relative to the image, complicating interpretations of the effect of blur. 
Natural textures such as rock faces present a viable alternative stimulus as observers find egocentric distance judgments of random rock faces a straightforward task despite the lack of any familiar size cue and the high level of self-similarity of spatial structures; observer's reports of perceived distance to cropped images of random rock faces show significant degree of correlation with actual photographed distances ranging from 25 cm to 50 m (Blaser, 2006). These stimuli therefore provide a way to vary apparent distance information in pictorial images independent of blur manipulations for a large range of distances and without resorting to familiar size cues. 
Binocular vs. monocular viewing
We chose to test distance judgments to these images under binocular viewing through apertures. Under binocular viewing of pictorial images, disparity cues specify the location of the pictorial surface. For monocular viewing through an aperture, where the information for the picture surface is effectively eliminated, there is the potential that remaining accommodation-based distance information may be assigned to pictorial contents, confounding the effect of blur. We have observed changes in perceived distance and scale under monocular-aperture viewing consistent with an accommodation-related micropsia in pictorial space (Alexander, 1975; McCready, 1965; see Figure 11 and Discussion section). This has been confirmed in reports of naive observers in a separate study (Vishwanath & Hibbard, 2009). Moreover, vergence responses to perceived pictorial depth have been demonstrated under monocular viewing (Enright, 1987) but not binocular viewing (Takeda, Hashimoto, Hiruma, & Fukui, 1999). By promoting the visibility and awareness of the picture surface, binocular viewing should inhibit changes in vergence or accommodation due to pictorial contents, or their use as distance cues in pictorial space. Thus, distance cues in pictorial space will be limited to those inherent to the image contents, including any simulated blur. 
Methods
Image creation
Rock face images were taken with a Canon EOS 400D SLR (10 megapixels) with a fixed 60-mm lens operated under automatic exposure mode in bright daylight. In order to minimize intrinsic focal blur in the images, no images were taken at closer than 2 m. For closer distances, images were taken at 2 m and then cropped to the appropriate size. Images were recorded in JPEG format, which were batch-processed (Irfanview) with a single pass of a sharpening filter and converted to grayscale BMPs. Images were manually inspected to eliminate ones that did not appear to have uniform sharpness. Implied distance of the image set ranged from 50 cm to over 12 m. The depicted rock surfaces had a global depth structure that was either near-frontoparallel (typically with small slant—top receding—due to the position from which photos were taken) or a significant slant about the vertical axis (most images were right receding). 
Blur was simulated on the natural images by convolving them with circular averaging filters whose diameters were determined by using the following equations adapted from equations for a simplified eye (Le Grand & El Hage, 1980, p. 76): 
f = 1 / ( 1 / b 0 + 1 / z 0 ) b = 1 / ( 1 / f 1 / z ) d = D | b 0 b | / ( b + ( P 1 ) f ) ,
(1)
where f is the accommodated focal length of the eye, b 0 is the distance to the retina, z 0 is the distance to the fixation point, b is the distance of the image of a point at viewing distance z, d is the blur circle diameter, D is the pupil size (assumed to be 5 mm), and P is the pupil factor (assumed to be 0.9; Le Grand & El Hage, 1980). The distance of a point on the slanted surface to be input into the equation to determine the blur circle was calculated using simple trigonometry. Selected parameter values (pupil size, slant) were based solely on achieving blur gradient levels that were near or above threshold for the different blur levels simulated (based on Wang et al.'s (2006) data). Blur levels (methods and results) are indicated by the simulated fixation distance; these values had no relation to structure in the photographic images or actual observer pupil sizes, which was not measured. 
Stimulus presentation
Stimuli were presented on a 24″ WUXGA LCD display (portrait mode) set at a resolution of 1200 × 1920 and about 3.8 pixels/mm (BMP images) at a fixed distance of 75 cm. The luminance of images on average was about 18 cd/m2, with values ranging from 0.2 to over 40 cd/m2. Observers viewed the display with both eyes (see above) on a chin and head rest through oval apertures whose lateral and vertical positions were adjusted individually such that the frame of the display or edges of the image were not visible. The visual angle of the display visible through the aperture(s) was approximately 18.5° (horizontal) × 28° (vertical). A rigid black screen separated the chin rest assembly and the display such that observers had no visual access to any part of the display apparatus while seated on the chin rest. 
Task
Observers reported perceived distance using a response image set that contained familiar size information to distance (Blaser, 2006; Gogel, 1976). The response image set was of a stone wall with a human model present (Figure 5). Response images ranged in implied distance from 20 cm and 30 cm to 9.6 m and 12.8 m in alternating log units (as follows: 20, 30, 40, 60…1.9 m, 12.8 m).
Figure 5
 
Examples of distance response images used in Experiment 1.
Figure 5
 
Examples of distance response images used in Experiment 1.
 
Procedure
Observers 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 (zooming in, zooming out) during the practice trials so that they got a sense of the full response range available. Observers initiated a trail via a key press, at which time the target stimulus was displayed for 1.25 s. Observers were instructed to maintain fixation on the center of the target stimulus for the duration of the display. Eye movements were not measured as the instruction was only intended to maintain relatively consistent viewing conditions across trial and observers. Since the simulated peripheral blur was deliberately selected to be above threshold, we expected that observers would perceive the presence of blur even when fixating the center. Observers found the fixation requirement easy to follow, presumably because the trial duration was too short to simultaneously try to judge distance and inspect the image. 
The first image of the comparison set (most distal) automatically appeared 2 s after stimulus offset, at which time the observer selected the response image (method of adjustment) that best matched the distance perceived in the target surface via a keyboard input. They were allowed as much time as necessary to select a response but were instructed 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 the TNO butterfly test and had normal or corrected visual acuity of 20/30 or better. Five naive observers were tested on the first part of this experiment that compared two levels of vertical blur. In the second part that compared different directions of blur and slant, 7 naive observers, 3 from the first test and 4 new ones, were tested. In the third part in which we further manipulated the blur magnitude and direction, 5 naive observers, 1 from the previous test and 4 new ones, were tested. 
Stimuli tested
In the first test, we compared distance judgments for three levels of vertical blur: no blur, low blur, and high blur. The two blur conditions simulated 60 cm (Low) or 30 cm (High) viewing (based on selected simulation parameters). Ten test stimuli for each of the blur conditions (no blur, high blur, and low blur) per observer were tested, which included rock faces that were near-frontoparallel and depth receding toward the right side (overall slant about vertical axis). Therefore, there were a total of 50 possible comparisons from the 5 observers. Results are based on 49 comparisons because one observer inadvertently ended a trial before making a selection. The images were embedded in a larger set of similar filler no-blur images. Test images represented distances of 2, 4, 8, or 12 m. Filler no-blur images included samples from the full range of 0.5 m to over 12 m. Each observer was tested on 2 sessions containing 48 target and filler images each. 
Results
Effect of blur magnitude on perceived distance
For control no-blur images of natural rock faces, observers reported a range of perceived distances generally consistent 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 that the ordinate is log distance). For example, in the high-blur condition, mean perceived distance was 1.58 m; median was 1.2 m; and the values ranged from 40 cm to 4.8 m, only a single observation was greater than 4.8 m).
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 represents number 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-blur images to the corresponding blurred images for two different levels of blur shown in (a). Error bars are standard errors. The dashed bar represents ratios obtained in a subsequent test for 45-cm simulated blur (see Figure 8).
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 represents number 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-blur images to the corresponding blurred images for two different levels of blur shown in (a). Error bars are standard errors. The dashed bar represents ratios obtained in a subsequent test for 45-cm simulated blur (see Figure 8).
 
Since this is an indirect magnitude estimation task, the selected comparison image does not necessarily provide an indication of the actual perceived distance. We therefore calculated the ratio of perceived distances for the blur and no-blur versions of the same image in order to compare effect sizes. A clear effect of blur on perceived distance is evident for both blur levels, with the mean ratio of over 5.3 for the high-blur level (Figure 6, lower left panel). There was 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 consistency with depth structure
The direction of a blur gradient when viewing a slanted planar surface is aligned with the direction of slant (tilt direction in frontoparallel space). However, the distributions of blur under natural viewing will not necessary follow a clear direction, since the depth distribution of points in natural scenes is usually far more complex than a planar surface. However, under natural viewing, the lower hemi-field typically contains points closer than fixation, while the upper hemi-field contains points further away, mimicking roughly the distance distributions on a horizontally slanted surface that produce a vertical gradient of blur on the retina (Figure 4, lower panels). Does the role of the blur cue to distance depend on the direction of the overall blur gradient, or, on the correlation of the blur gradient with the underlying depth structure of the scene specified by other cues? 
We examined this by the varying the direction of blur (vertical or horizontal gradient) and the consistency of blur direction with underlying slant direction of the rock face. There are four types of images: (a) frontoparallel/vertical blur, (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 to simulated blur gradient and therefore highly inconsistent with it (IS condition); in (a) and (c), the underlying slant is neutral to the direction of blur (NS condition), since a frontoparallel surface viewed close will have an isotropic 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 the direction of the blur. The four possible conditions were constructed from the same base image, such that, for example, the difference between the horizontal and vertical versions was just a 90 deg image rotation (see Figure 7). In both original and rotated versions, perceived local 3D structure was maintained across rotations and no inversions from perceived convexity to concavity occurred (which can occur for some images and rotations due to the perceptual assumption of the light source above the observer). Thus, rotation only changed the perceived orientation or overall slant direction of the rock face. Target images were constructed from 10 base images (4 frontoparallel and 6 orthogonal-slant images) for a total of 40 target images. Images were square and viewed through circular apertures (18.5° × 18.5°). Target images were again embedded in random order in a larger set of no-blur filler images. Each observer was tested on 4 sessions of 32 images each.
Figure 7
 
Examples of rock face stimuli showing frontoparallel slant (top row) and slanted surfaces (middle and bottom rows). The first column is the no-blur base image for each set. The second and fourth columns show stimuli with vertical blur gradients (60-cm and 45-cm simulations, 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 row blurred images represent the Neutral Slant (NS) condition, while the blurred images in the second and third rows represent the Inconsistent Slant (IS) condition.
Figure 7
 
Examples of rock face stimuli showing frontoparallel slant (top row) and slanted surfaces (middle and bottom rows). The first column is the no-blur base image for each set. The second and fourth columns show stimuli with vertical blur gradients (60-cm and 45-cm simulations, 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 row blurred images represent the Neutral Slant (NS) condition, while the blurred images in the second and third rows represent the Inconsistent Slant (IS) condition.
 
All four conditions showed similar mean ratios for the seven observers tested (Figure 8, left) and were consistent with ratios seen in the preceding test for similar simulated blur levels (low blur: 60-cm distance simulation). While ratios for inconsistent slant (IS) conditions were slightly smaller, the differences were not statistically significant. No systematic differences between vertical and horizontal blur gradients were found.
Figure 8
 
(a) Ratio of judged distances for identical vertical and horizontal blur gradients (simulating 60 cm viewing) where the underlying slant of the rock surface was either neutral (NS) or inconsistent (IS) with the underlying slant of the rock face (7 subjects, see text). (b) Ratio of judged distances for perceptually matched vertical and horizontal blur gradients (NS and IS conditions; 5 subjects). Mean combined ratio (IS and NS) for vertical blur is plotted in (b), dashed bar.
Figure 8
 
(a) Ratio of judged distances for identical vertical and horizontal blur gradients (simulating 60 cm viewing) where the underlying slant of the rock surface was either neutral (NS) or inconsistent (IS) with the underlying slant of the rock face (7 subjects, see text). (b) Ratio of judged distances for perceptually matched vertical and horizontal blur gradients (NS and IS conditions; 5 subjects). Mean combined ratio (IS and NS) for vertical blur is plotted in (b), dashed bar.
 
Differences in perception of vertical and horizontal blur
When we constructed the stimuli for the previous test, our informal observation indicated that identical levels of physical blur appeared blurrier in the horizontal direction than in the vertical direction, an observation that to our knowledge has not been previously reported. This phenomenon is interesting because vertical blur gradients should be encountered statistically more frequently than horizontal blur gradients due to the dominance of the horizontal ground plane. Previous studies have demonstrated that perceived blur is adaptable (e.g., Battaglia, Jacobs, & Aslin, 2004; Webster, Georgeson, & Webster, 2002), and that such a mechanism may serve a role to reduce perceived blur 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 should be different for the same physical magnitude of vertical and horizontal blur. The results of the previous test suggested that this was not the case, since the change in perceived distances for both directions were similar. To further confirm this, we tested another group of subjects where we used stimuli in which vertical and horizontal blurs were perceptually rather than physically matched (see 1). 
The vertical gradients now showed larger mean effects than horizontal gradients as predicted by their greater physical magnitude (Figure 8, right panel). Again, no significant differences between the IS and NS conditions were found. The overall effect sizes for the vertical blur gradients for the two blur levels were consistent with those in the previous tests (the value for the 45-cm simulation was in between those observed for the 30-cm and 60-cm blur 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 to underlying depth structure; perceived distance was primarily modulated by the physical magnitude of the blurring. 
Slant cues in the image
One potential reason for the insignificant difference between the inconsistent (IS) and neutral slant (NS) conditions in the second and third tests is that the underlying relative depth cues (shading, texture, perspective) were insufficient for recovering slant, particularly in the short stimulus presentation duration. We examined this (see 2) and found that observers can readily perceive slant consistent with the underlying texture for the presentation duration tested. 
Experiment 2
In order to independently vary distance information available from blur and accommodation/vergence, stimuli were presented on a movable display platform, with images scaled to viewing distance. Since obtaining motor responses (pointing) of perceived egocentric distance was precluded by the stimulus and apparatus size, observers adjusted a comparison distance to match a previously viewed standard distance; a task that provides a direct measure of the reliability of available distance cues (e.g., Brenner & van Damme, 1998), and where any bias in settings provides evidence of the role of blur. 
We first tested if observers had reliable distance information for no-blur images in the presence of (i) vergence and accommodation (binocular viewing) or (ii) accommodation alone (monocular viewing). Prior studies have shown that vergence provides an effective cue to distance to at least 80 cm (Foley, 1977; Mon-Williams & Tresilian, 1999a, 1999b; Viguier et al., 2001). However, reliable distance judgment based on accommodation has only been demonstrated (in some observers) up to 50 cm, beyond which the accommodative response itself is non-linear and error prone (Fisher & Ciuffreda, 1988). Even within the linear range, accommodation is not as effective a cue as vergence, showing significant compression of perceived distance range and considerable variation in subject's capacity to use accommodation as a distance cue (Fisher & Ciuffreda, 1988). 
In initial pilots, we found that while some observers were able to successfully do the task with differing degrees of precision, some were unable to do the task (no staircase reversals) even with feedback. They appeared to be reporting exactly the opposite distance relationship, consistent with the size–distance paradox (Epstein, Park, & Casey, 1961; Komoda & Ono, 1974). Similar effects have been implicated in between-observer differences reported previously for distance judgments using accommodation (Fisher & Ciuffreda, 1988), and studies have suggested that 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 were successfully able to do the task. In the actual experiment, we therefore first did an initial test with the observers using the distance task; if they failed in the predictable way, we then tested them on the size task. Successful performance in both tasks is given by the point of subjective equality (PSE) of the comparison setting being at, or close to, the standard. A matched PSE does not necessarily imply that perceived distance is veridical, but rather that observers had a reliable estimate of apparent distance; prior studies have shown that both accommodation- and vergence-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 viewing distance of 25 cm were matched to a no-blur standard at 40 cm. Thus, blur specified a distance closer than the standard. If blur was an effective cue to distance, a comparison display should appear closer—and the image smaller—and would need to be set at some distance further than the standard to be matched to it. 
Methods
Stimuli
Stimuli were 2D images of slanted planar surfaces (70° slant) with a random pattern of circular disks generated on POV-Ray rendering software (Figure 1c). The size and location of individual disks (except the central one) in 3D model space was randomly varied from trial to trial (sizes varied by ±10%). The individual disks had a high-contrast textured pattern to disrupt visibility of the display pixels at the nearest viewing distance. Blur was simulated on the rendered image in the same way as described previously, but assuming a fixation distance of 25 cm, surface slant of 70° (matching the textured surface), and a pupil diameter of 5 mm. 
Stimulus presentation
Stimuli were presented on an LCD display (same as the previous experiment) on a platform that could be moved manually between 25 and 80 cm in steps of 5 cm. We limited near viewing to 25 cm because screen pixelization was visible at nearer distances. Far distance was selected based on distances used in previous studies (Mon-Williams & Tresilian, 1999a; Viguier et al., 2001). The luminance of the dark background was 0.2 cd/m2 while the luminance of texture elements varied from about 6.2 to 10.5 cd/m2. We chose these relatively low luminance levels because in pilot testing observers reported discomfort and difficulty due to the high visual transients and afterimages, which likely occurred because observers had their eyes closed during the significant portion of the session. At the tested luminance, observers reported that overall visibility was sufficient for clearly seeing the textured objects. Prior studies that have found effects of accommodation and blur in depth perception have used maximum luminance levels as low as 0.9 cd/m2 (Watt et al., 2005). 
Viewing conditions were the same as the previous experiment. The lateral and vertical positions of the apertures (approximately 16.5° × 26°) were first adjusted individually so that the frame of the display was not visible at any viewing distance. Observer wore earmuffs to prevent hearing the movement of the display between presentations. 
Procedure
Each trial consisted of a sequential presentation (in random order) of a standard image at a fixed distance from the observer and a comparison at some other distance. To prevent observers from viewing the movement of the displays between presentations, observers had eyes closed at all times except on voice signal to initiate the image via a keyboard entry. The image was extinguished after 1.5 s at which time observers closed their eyes again. Inter-stimulus intervals averaged about 2–3 s. Observers were instructed to maintain fixation on the central disk during stimulus presentation, so as to maintain uniformity of viewing across observer. Observers matched the distance of the comparison and the standard with an adaptive one-up one-down staircase procedure (5 reversals). For the distance task, they were required to report which of two consecutively presented displays appeared closer to them. They were instructed to make judgments regarding the actual physical display surface and not the pictorial scene. Similarly, for those who did the size task, they were instructed to report which image appeared smaller; reporting on the size of the displayed 2D image and not the perceived size of objects in the pictorial scene. Observers were first shown the entire apparatus including the movable display and images in order to explain the task and make clear they were making judgments regarding the display surface or image. Observers were tested under both monocular and binocular conditions. 
Observers were initially tested on a control task where both standard and comparison had no blur. We first tested without feedback, and then with feedback (a short beep if the reported display was not the closer one). Performance on control feedback and no-feedback trials was similar, which is expected because the nature of feedback and stimulus presentation precluded any trial-to-trial learning (order of the standard and comparison was random, and each session had multiple staircases, so information of whether or not one correctly reported the closer display on any particular trial cannot be used to adjust response on a future trial). The feedback only served as a diagnostic to the observer if they were generally doing the task successfully, 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 of 40 cm. Control no-blur trials were interleaved with the experimental blur trials. Feedback was provided for the control no-blur trials only. This was done as a precaution to maintain overall response effort and criteria. No-blur control trial data in Figure 9 is from concurrent interleaved trials.
Figure 9
 
(a, b) Psychometric functions for one observer (size task) in the control no-blur condition under binocular viewing and monocular viewing, with standard display set at 40 cm or 65 cm and a no-blur movable comparison. Data fitted by cumulative Gaussians (MLE fit; Wichmann & Hill, 2001). Number of trials per data point varies, with larger sampling near the PSE (staircase procedure). 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 comparison display. Observer CH was not able to do the task at the 65-cm setting under monocular viewing (see text). (c, d) Data for the same observer in trials where the standard no-blur display was set at 40 cm and the movable comparison had a blur gradient specifying a viewing distance of 25 cm. Black arrow indicates the distance used to simulate blur (25 cm). Light gray curves are psychometric curves for the no-blur control shown in the left panels for comparison. As predicted, the PSE in the blur condition is shifted to the right (the display with the blurred image was set further way, to be matched with a standard no-blur display at 40 cm).
Figure 9
 
(a, b) Psychometric functions for one observer (size task) in the control no-blur condition under binocular viewing and monocular viewing, with standard display set at 40 cm or 65 cm and a no-blur movable comparison. Data fitted by cumulative Gaussians (MLE fit; Wichmann & Hill, 2001). Number of trials per data point varies, with larger sampling near the PSE (staircase procedure). 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 comparison display. Observer CH was not able to do the task at the 65-cm setting under monocular viewing (see text). (c, d) Data for the same observer in trials where the standard no-blur display was set at 40 cm and the movable comparison had a blur gradient specifying a viewing distance of 25 cm. Black arrow indicates the distance used to simulate blur (25 cm). Light gray curves are psychometric curves for the no-blur control shown in the left panels for comparison. As predicted, the PSE in the blur condition is shifted to the right (the display with the blurred image was set further way, to be matched with a standard no-blur display at 40 cm).
 
Observers
Seven observers were initially tested on control no-blur trials. All except one were stereo normal as measured using the TNO butterfly test and had normal or corrected visual acuity of 20/30 or better. The observer who was not stereo normal reported uncorrected strabismus and had normal acuity in his dominant eye. We tested this observer wondering if he might still be effective at the distance/size task under monocular viewing with his dominant eye. Observers were first tested without feedback to confirm that the task could be done on the basis of instructions alone. Those who could not do the distance task were then tested on the size task. The strabismic observer could not do either task under binocular or monocular viewing; and another observer, despite being stereo normal, was also unable to do either task even with feedback. These two observers were not tested any further. Of five remaining naive observers, two of the observers did the distance task and three the size task under binocular viewing. 
Results
Figures 9a and 9b show data for one observer in the no-blur size judgment task. CH was able to do the task under binocular viewing for both tested distances (PSE for the comparison stimuli is the same as the standard). CH was only able to attain a perceptual match under monocular viewing for the nearer 40-cm distance (Figure 6, lower left panel), and in the binocular condition variability of judgments for the farther viewing distance (65 cm) was higher (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 of observers is unable to use accommodation as a cue for distance estimation (Fisher & Ciuffreda, 1988). Only one out of three successful monocular observers was able to attain a perceptual match for the farther 65 cm standard under monocular viewing. During testing, we observed that when the display was at the 75- or 80-cm setting, some monocular observers often repeatedly reported it closer than standard, preventing convergence of the adaptive staircase. These results appear consistent with the fact that accommodative response is linear only to about 50 cm (2 diopters) and that it likely does not provide a reliable distance signal much beyond that point (Fisher & Ciuffreda, 1988). As expected, judgment in the binocular condition where vergence information was available was more reliable than the monocular condition for 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, displays in the “blur” trials were set further away from the observer (compare gray and red curves). Figure 10 shows data for the other four observers.
Figure 10
 
Data for the four other observers (distance task: LS, AN; size task: KR, GM). See Figure 9 and text for details. Gray curves are the settings for the control no-blur condition where both the standard (40 cm) and the movable comparison were not blurred. Red curves are for trials in which the comparison was blurred and the standard no-blur stimulus was set at 40 cm. Left columns are for binocular viewing and control no-blur condition (standard deviation of the gray curves). In all cases the blurred comparison display had to be set farther than the no-blur standard to be matched to it. Observers AN and KR were unable to do the monocular control task. The scatter plot summarizes the effect size of blur on distance judgments (shift of red curve relative to the gray curve) for all five observers plotted as a function of the underlying variability in the control no-blur condition (standard deviation of the gray curves). Larger values on the abscissa indicate greater variability of distance judgments based on accommodation/vergence alone.
Figure 10
 
Data for the four other observers (distance task: LS, AN; size task: KR, GM). See Figure 9 and text for details. Gray curves are the settings for the control no-blur condition where both the standard (40 cm) and the movable comparison were not blurred. Red curves are for trials in which the comparison was blurred and the standard no-blur stimulus was set at 40 cm. Left columns are for binocular viewing and control no-blur condition (standard deviation of the gray curves). In all cases the blurred comparison display had to be set farther than the no-blur standard to be matched to it. Observers AN and KR were unable to do the monocular control task. The scatter plot summarizes the effect size of blur on distance judgments (shift of red curve relative to the gray curve) for all five observers plotted as a function of the underlying variability in the control no-blur condition (standard deviation of the gray curves). Larger values on the abscissa indicate greater variability of distance judgments based on accommodation/vergence alone.
 
Within observers, the effect was consistently larger under monocular (accommodation only) than binocular viewing. There was a significant correlation between the change in perceived distance due to blur and the underlying variance of responses in the control no-blur condition (Figure 10, lower right panel). For four out of five observers, the overall variances were comparable with or without blur (red vs. gray curves in the psychometric functions), and one of these observers (AN) showed a reduction in variability in the blur condition. Only one observer (KR) showed a large increase in variability in the blur condition. Moreover, there was no correlation between the effect sizes and changes in variance from no-blur to blur conditions (r 2 = 0.03; p = 0.67). 
Discussion
Based on two experiments, the present study provides psychophysical evidence of the role of blur gradients in distance perception. The effect of blur on distance perception we found in the first experiments was robust, and its size depended on the degree of extra-foveal blurring, but not on the consistency of the direction of blur relative to implied depth structure. In the second experiment, we found that the effect of blur on perceived distance was significantly correlated with the variance of distance information available from other cues, but not on the change in variance from no-blur to blur conditions. Overall, the pattern of results suggests that the blur gradient likely operates as a quantitative cue to egocentric distance consistent with the empirical relationship between retinal blur and viewing distance, and not a precise computation that compare patterns of blurring, pupil size, and relative depth structure. This is consistent with the fact that blur detection and discrimination thresholds are themselves quite large (Mather & Smith, 2002; Wang & Ciuffreda, 2004), and that the cue would therefore only be effective under near viewing where extra-foveal blur would be detected. 
Blur gradients and the underlying depth structure of the scene
The effect of blur on distance perception appeared to be largely independent of the depth structure implied by relative depth cues, with comparable effect sizes obtained regardless of the consistency of the blur gradient direction with slant direction. The general insensitivity to depth structure may explain why tilt-shift miniaturization occurs using a generic vertical blur gradient regardless of the relative depth structure of the scene. 
We did not find any significant differences in the role of vertical and horizontal blur gradients even though the former are statistically more likely under typical near-viewing in natural scenes (where a horizontal ground plane predominates). However, we found that the appearance of blur differs between physically identical horizontal and vertical gradients, suggesting that the perception of vertical blur gradients may be adapted by its statistically more common occurrence under near viewing. Prior studies have suggested that blur adaptation mechanisms may play a role in increasing perceived sharpness under conditions of a regular occurrence of blurring, for example, due to optical defects. Such a mechanism could also serve to give the impression of sharpness for a larger region around the fovea under near viewing, and thus creating a greater apparent depth of field. Whether the perceived blur difference we found is due to such long-term adaptation or other factors remains to be examined. However, the effect of blur on distance appeared to depend on the physical rather 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, in relation to both statistical distributions of blur gradients empirically encountered and other relative depth cues. 
Blur, accommodation, and vergence
The second experiment confirmed the role of blur in distance perception within near space, using a different paradigm where it was pitted against vergence and accommodation. Specifically, we found that the effect of the blur gradient cue on apparent distance depended on the reliability of other available cues as indicated by the variance in distance judgments in control no-blur trials. This suggests that blur might combine with extra-retinal distance cues in a manner consistent with cue-combination models, where the influence of a depth/distance cue is inversely related to its reliability relative to other available cues (e.g., Hillis, Watt, Landy, & Banks, 2004). A more detailed study will be needed to determine if blur combines with other distance cues in the statistically optimal manner suggested by such models. Generally, the effect of blur was moderate to weak in the presence of vergence (in 4 out of 5 observers), which is consistent with the fact that vergence is a relatively reliable cue to distance at less than 60 cm (Foley, 1980; Mon-Williams & Tresilian, 1999a; Viguier et al., 2001). Effects were larger in observers who could do the monocular task. However, the fact that the role of accommodation 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 examine how the blur gradient cue combines with other distance cues will likely be best done by pitting vergence and blur and testing distances beyond 1 m where the vergence signal becomes increasingly less reliable. 
Blur, familiar size, and tilt-shift miniaturization
The effect of blur gradients on distance perception suggests that blur-based miniaturization in photography is the result of a visual phenomenon, rather than just a cognitive outcome dependent on relative object size, object familiarity, or familiarity with macro photography. Under normal binocular viewing of a picture, extra-retinal distance information (accommodation, vergence) as well as egocentrically scaled relative depth cues (parallax and disparity) together specify the structure and distance of the picture surface (Vishwanath, Girshick, & Banks, 2005; Watt et al., 2005). The only source of distance information in pictorial space is familiar size. The presence of a blur gradient introduces a quantitative distance cue into pictorial space, which appears to change perceived distance by overriding familiar size cues. “Familiarity” is turned on its head, and objects appear toy-like. The effect is so powerful that it appears to alter even perceived material qualities (objects often look like they are made out of plastic or cardboard). 
We have observed informally that monocular viewing of images through an aperture produce similar effects of scaling and distance (Figure 11). How might this be related to blur-based scaling effects? During monocular viewing through an aperture, the visibility of the picture surface is removed and disparity-driven vergence is eliminated. The only putative distance cue remaining (at typical picture viewing distances) is accommodation, which, in the absence of a perceived picture surface, appears to be assigned to pictorial surfaces, scaling pictorial depth, and size in a micropsia-like effect (Alexander, 1975; McCready, 1965). Thus, accommodation (or accommodative vergence), under appropriate conditions, could lead to a similar miniaturization in pictures.
Figure 11
 
Original photograph used to demonstrate the tilt-shift miniaturization effect in Figure 2. When viewing an enlarged version of this image through an oval aperture (1.5–2 cm wide), the apparent scale of the image changes, and the scene appears to most observers to be closer or smaller.
Figure 11
 
Original photograph used to demonstrate the tilt-shift miniaturization effect in Figure 2. When viewing an enlarged version of this image through an oval aperture (1.5–2 cm wide), the apparent scale of the image changes, and the scene appears to most observers to be closer or smaller.
 
Interestingly, the reverse phenomenon is also observed. Photographs of scale models appear life size when normal blur gradients are eliminated by using small camera apertures. This is vividly demonstrated in the work of artist James Casebere (Figure 12). Photographs of tabletop architectural models taken such that no blur gradients are visible make the spaces appear uncannily real despite the visibility of construction marks and material (e.g., cardboard) which clearly give away the small scale of the objects (In gallery presentations, the original photographs are several feet in dimension). However, it is possible that the lack of blur, rather than signaling a far viewing distance, only makes a blur-based judgment of distance in pictures highly ambiguous because the lack of detected extra-foveal blur is consistent with a large range of distances anywhere from a meter to infinity; allowing cognitive familiar size information to disambiguate perceived distance and size.
Figure 12
 
James Casebere, Pink Hallway, #2, 2000.
Figure 12
 
James Casebere, Pink Hallway, #2, 2000.
 
The various scaling effects in pictures supports a view that cognitive sources of information like familiar size likely do not operate as normal visual cues, in the sense that they do not combine with or scale other distance cues (Gogel, 1969; Predebon, 1993). Rather, they might only operate to disambiguate perceptual judgments in a categorical manner under high levels of sensory uncertainty, as is present in pictures, and be overridden to conform to even relatively high threshold optical signals such as blur or accommodation. 
Supplementary Materials
Movie - Movie File 
Appendix A
Perceptually matching horizontal and vertical blur
Five experienced naive psychophysical observers subjectively matched perceived blur (Battaglia et al., 2004; Webster et al., 2002) for horizontal and vertical blur gradients while fixating the center of the image (method of limits; increasing and decreasing blur levels). They reported which of two images appeared to be more blurred (Battaglia et al., 2004). Simulated blur varied in increments of 5 cm of viewing distance for a 70° slanted surface. A representative sample of 5 rock face images was tested. All five observers found the blur comparison task straightforward. Vertical blur gradients simulating 45 cm viewing were on average selected as perceptually matching horizontal blur gradients simulating 60 cm viewing. Judgment noise was negligible, with all observers individually selecting the 45 cm match, and 3 out of 5 observers selecting the exact 45 cm match for every sample image tested. 
Appendix B
Effectiveness of depth cues in test images
To examine this, we had 7 naive observers (who had not been previously tested on the images) judge perceived slant in the rock faces images used, reporting the slant direction (frontoparallel, left, right, top, or bottom) and slant magnitude (slight, moderate, or large) under identical viewing and timing conditions to the original experiment. The results of the test are shown in Figure B1, plotted as vectors (direction = tilt; length = slant magnitude; 1, 2, and 3 coded slight, moderate, large slants). In the no-blur images, observers clearly perceived moderate-to-large slants in the predicted direction in the IS images (vertical or horizontal slant), while the NS condition (frontoparallel) showed only slight to negligible slant magnitudes, consistent with the images. The reported slants in the vertical tilt direction were smaller than for the horizontal tilt direction (vertical-slant images can look like frontoparallel rock faces viewed from below, which could have biased observer's to under-report magnitude of slant). For the blurred images, observers still perceived significant slants in the predicted directions (IS condition), though reduced somewhat compared to the no-blur images. In the NS condition, the perceived slant with blur was larger than in the comparable no-blur condition and biased in the direction of blur. This is consistent with the informal observation that blur gradients make near-frontoparallel surfaces appear more slanted in the blur direction (see Figure 3).
Figure B1
 
Reported slants plotted as vectors whose orientation indicates perceived tilt (direction of slant). Left panel is for images depicting slanted rock faces (IS condition) and right panel for near-frontoparallel (NS) condition.
Figure B1
 
Reported slants plotted as vectors whose orientation indicates perceived tilt (direction of slant). Left panel is for images depicting slanted rock faces (IS condition) and right panel for near-frontoparallel (NS) condition.
 
Acknowledgments
This research was supported by a Research Council UK fellowship to DV. We thank Harold Nefs for technical advice on image processing and Paul Hibbard and Julie Harris 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. 
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