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From the Department of Optometry and Vision Sciences, Cardiff University, United Kingdom.
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Abstract |
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 Top Abstract IntroductionMethodsResultsDiscussionReferences |
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METHODS. Contrast sensitivities were measured for detection (N = 1) and identification (N = 2–8) of a target face as a function of size (0.4o–10o) across eccentricities (E = 0o–10o).
RESULTS. In all conditions contrast sensitivity first increased and then
saturated, as a function of stimulus size. Maximum sensitivity
(Smax) decreased, whereas critical
size (where S =
Smax/
) increased with eccentricity
and set size (N). At each set size, sensitivities from all
eccentricities could be equated by double scaling—i.e., translation in
horizontal (size) and vertical (contrast) dimensions on log–log axes.
Similarly, at each eccentricity, data from all set sizes could be
superimposed using double scaling. Furthermore, all data could be
superimposed onto the foveal detection curve when double scaled
according to the equation F = 1 +
E/E2i +
logN/logN2i +
E(logN)/K, where i is
horizontal or vertical. This equation incorporates the eccentricity
(E2) and set size
(N2), where contrast and size double,
as well as the interaction term (K).
CONCLUSIONS. Double scaling superimposes data. Not only is this possible across set sizes or eccentricities separately, but by combining their effects, a function is provided that collapses all data to a single curve, explaining all performance variation across eccentricity and set size. Our results support the proposition based on numeral recognition that failures of spatial scaling across eccentricities may simply reflect the need for scaling both size and contrast.
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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A common measure for eccentricity-dependent performance is E2—the eccentricity at which stimulus size must double to maintain foveal performance level.8 More demanding extrafoveal tasks have smaller E2 values, indicating that stimulus size must double at a smaller eccentricity. E2 values show a 100-fold intertask variation.9
Extrafoveal performance in some tasks is consistently poorer, irrespective of stimulus magnification.10 11 12 13 14 15 Spatial scaling cannot normalize low-contrast alphanumeric character recognition or high-contrast reading15 across eccentricities,10 11 12 but can equalize high-contrast character recognition16 and reading of nonmeaningful word strings.6 Therefore, scaling of both size and contrast is needed to superimpose data curves at all contrasts.10 11 12 14
Face recognition involving four front-posed faces is not spatially scalable.14 However, shifting the data in two dimensions (i.e., scaling both size and contrast) allows superimposition of all data.14 This double scaling is possible, because curves at all eccentricities have the same shape and also maximum sensitivity and size for performance saturation change. However, little is known of how eccentricity interacts with task demands in face perception. We therefore investigated the effect of the number of faces on the scalability of face recognition and E2 values required, by measuring foveal and extrafoveal contrast sensitivities as a function of image size.
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Stimuli
Photographs of eight male faces with three poses (front-on and
45o both left and right) were digitized and
standardized by removing nonfacial features (hair, ears). Faces were
stretched to a standard 100 x 130 pixels (4.7 x 6.1 cm on
the screen). Individual faces did not appear distorted: A naturally
narrow face does not appear unusual when slightly widened. To ensure
that subjects were recognizing the individual in the two-to-eight faces
conditions rather than simply detecting unique local features, three
poses of each face were interchanged randomly (Fig. 1B
). Image root mean square (RMS) contrast values were equalized, and
subjective brightness was matched by shifting average image luminance.
All faces were equally detectable, and the contrast thresholds of all
face pairs were equally discriminable.
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Trials started at suprathreshold contrast, and if subjects responded
correctly, contrast was reduced by a factor of 1.26. The second
incorrect response initiated a staircase procedure with a
four-correct-down/one-incorrect-up algorithm. Contrast thresholds
obtained represented the probability level of 84%, 84%, 71%, and
59% correct for N = 1, 2, 4, and 8,
respectively.19
Corresponding chance performance levels
were 50%, 50%, 25%, and 12.5%. Threshold was calculated as the
arithmetic mean of eight contrast reversals. RMS contrast sensitivity
is the inverse of RMS contrast at threshold, defined as
where 
is contrast energy at
threshold and A is stimulus area in degrees squared.
Stimulus energy is given as = 
c2(x,y)p2, where
c(x, y)=[L(x, y)-L0]/L0 is local contrast
at each image pixel, and p is pixel side length in degrees.
L(x, y) refers to local luminance, and
L0 indicates average luminance.
Goodness of Fit
Goodness of fit can be described20
as
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 | (2) |
 | (3) |
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Results |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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The increase of recognition sensitivity with image height has been described14 as
 | (4) |
at h =
hc. Percentage values indicate
goodness of fit.19 Comparing curves within each frame of Figure 3 shows that critical size increased with eccentricity. In spatial scaling, peripheral data curves are traditionally shifted horizontally to superimpose onto foveal data. If the slope of increase and maximum sensitivities are the same, superimposition is successful, because the only difference is critical size.
Figure 3 shows that this is not the case, because maximum sensitivity decreases with increasing eccentricity. Thus, identification (N = 2–8) and even detection of a single face (with three poses) cannot be normalized across the visual field by spatial scaling alone. However, dependence of sensitivity on size is essentially identical in qualitative terms across eccentricities, because all curves have the same slope of increase and saturation rate. Thus, peripheral curves for each set size can be superimposed onto the corresponding foveal curve by scaling data in two dimensions: size and contrast. A deficit in contrast after size scaling has been reported by Strasburger et al.,10 11 who found a hyperbolic relationship between size and logarithmic threshold contrast. Therefore, their data were not scaled with the traditional log–log method where sizes are divided by scaling factors. Therefore, no previous attempt has been made to simultaneously scale contrast and size in the same manner as size has been scaled in numerous earlier reports, nor are there any previous estimates of E2 values for contrast.
To scale the data, we took maximum sensitivities and critical heights and divided peripherally increasing critical heights of each task by the corresponding foveal value, while foveal maximum sensitivity of each task was divided by the corresponding peripherally decreasing values. This provided the scaling factors that superimposed peripheral and foveal data. This is possible because all data curves, irrespective of eccentricity, have the same shape, and superimposing is therefore simply a matter of translation in two dimensions.
Figure 4 presents the scaling factors obtained. Irrespective of the number of faces1 2 3 4 5 6 7 8 or type of scaling (horizontal or vertical), factors increased linearly with eccentricity. The gradients of the lines indicate how quickly scaling factors must increase to maintain constant performance with increasing eccentricity. The slope’s inverse, called E2, represents the eccentricity at which stimulus size8 (horizontal scaling) or contrast (vertical scaling) must double to maintain performance at the foveal level.
Scaling factors (Fh and
Fv) necessary to maintain foveal
performance at any eccentricity (E) are
 | (5) |
We fitted equation 5 to each data set in Figure 4 and calculated the scaling factors for each eccentricity using the E2 values. On average, goodness of fit was 90% indicating that the lines describe the data of Figure 4 well. E2 values for spatial scaling (E2h) and contrast scaling (E2v) are shown separately for each task and subject.
Figure 5 shows the original data from Figure 3 double scaled according to equation 5 . The curve fitted to the foveal data using equation 4 for each set size is included in each frame. All data superimpose and are described very well by the foveal curve.
Double E2 scaling thus compensates for extrafoveal increase in critical size and decrease in maximum sensitivity by comparing performance at each set size across eccentricities and scaling them to foveal performance (i.e., scaling data within each frame of Fig. 3 ). However, comparing curves of Figure 3 across set sizes at each eccentricity shows that critical size increased and maximum sensitivity decreased with increasing number of faces. Given the uniform shape of all functions, it was thus possible to scale data across set sizes at each eccentricity separately rather than scaling data across eccentricities for each set size separately, as in Figure 5 .
Figure 6
shows scaling factors that superimpose set sizes N = 2 to 8
onto the detection curve (N = 1) at each eccentricity.
Irrespective of eccentricity or direction of scaling (horizontal or
vertical) scaling factors increased as a linear function of the
logarithmic number of faces. Analogous to
E2, we introduced an
N2 value relating to the rate of
scaling necessary to superimpose data of increasing set size. We thus
obtained vertical and horizontal scaling factors for any number of
faces using equation
 | (6) |
Figure 7 shows the original data from Figure 3 replotted so that each frame represents a different eccentricity, rather than a different set size (Fig. 5) , and scaled according to the N2v and N2h values, by using equation 6 . The smooth curve is the detection function (N = 1) for each eccentricity from Figure 3 . Again, all data superimpose well, showing that simple quantitative shifts can compensate for all changes with set size.
All eccentricities were successfully scaled to foveal data (Figs. 4 5) and all set sizes to N = 1 (Figs. 6 7) . This was possible, because all curves had the same shape, suggesting that all data could be scaled to a single function combining both eccentricity and set size. This function would superimpose all data onto the foveal detection curve (E = 0, N = 1). To reveal the function, critical size and maximum sensitivity values were divided as before, but instead of using the foveal function of each set size separately (E2 scaling) or the detection task of each eccentricity separately (N2 scaling), all functions were scaled to the foveal detection curve.
Figures 8A 8B 8C 8D show the resultant scaling factors. Each scaling surface shows a series of scaling factors as a function of eccentricity resembling those in Figure 4 but separated in depth by the number of faces on logarithmic axis. Because all data are scaled to foveal detection, only this value is set at unity.
Figures 8A 8B 8C 8D show that double scaling is required after an increase in either eccentricity or set size, reflecting the decrease in maximum sensitivity and increase in critical size seen in Figure 3 . A scaling surface equation has more validity than the tailor-made values of Figures 8A 8B 8C 8D or specific E2 and N2 values for each task and eccentricity, if that surface can explain all variation across eccentricities and set sizes. We suggested the following equation for all scaling factors (F):
 | (7) |
Figures 8E 8F 8G 8H show the values predicted by equation 7 fitted in logarithmic form to the data of Figures 8A 8B 8C 8D . Percentage values indicate the goodness of fit.
Equation 7 represents a combination of equations 5 and 6 plus a term accounting for the interaction between eccentricity and set size. When E = 0 (foveal tasks) or N = 1 and thus logN = 0 (detection tasks), equation 7 reduces to equation 6 or 5 , respectively. Thus, E2 and N2 values of Figures 8E 8F 8G 8H ) resemble the detection E2 values (Figs. 4A 4B) and foveal N2 values (Figs. 6A 6B) , respectively.
Figure 9 shows the original data from Figure 3 scaled according to the surfaces of Figures 8E 8F 8G 8H . Goodness of fit indicates the success of scaling. All data collapse to a single function, described well by the foveal detection curve, showing that equation 7 can account for all changes in performance across eccentricities and set sizes.
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Discussion |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Detection of geometric distortions of a high-contrast face is spatially scalable,21 whereas in the present study spatial scaling alone was not sufficient for any task, including detection. This is presumably due to low contrast and/or random presentation of three poses preventing the visual system using a single template.
The need for spatial scaling with increasing eccentricity indicates that the neural templates used for face perception suffer from positional uncertainty inherent in peripheral vision.22 23 24 25 Stimulus magnification also takes care of reduced sampling, poorer resolution and larger receptive fields. The need for contrast scaling suggests an additional deficit of extrafoveal viewing. A study using four faces with a single front-on pose showed that decreasing Smax with increasing eccentricity is due to reduced efficiency (Mäkelä et al., unpublished data, 1999), which can be compensated for by increasing contrast.
Although contrast sensitivity decreased with increasing set size at each eccentricity, all sensitivity curves had the same shape. Thus, an approach analogous to double E2 scaling equated sensitivities across set sizes at each eccentricity (N2 scaling), superimposing data for N = 2 to 8 onto the N = 1 curve. Face perception became more demanding with increasing set size, presumably because a greater number of face stimuli (and therefore nonorthogonal neural templates) results in the increased probability of a wrong choice. The success of double scaling implies that with an increasing number of faces the templates have two types of noise: positional inaccuracy, which can be compensated by increasing image size and reduced efficiency, possibly through decreased signal-to-noise ratio of the template,26 which can be compensated by increasing contrast.
Combining E2 and N2 scaling showed that when eccentricity, set size, and their interaction are taken into account, all data can be scaled to a single function. The close match of the scaling surfaces to the observed factors (Fig. 8) and the goodness of fit of the collapsed data (Fig. 9) to the foveal detection curve validate the accuracy of E2N2 scaling of size and contrast.
Peripheral vision is affected by the crowding effect, where adjacent contours interact making stimuli very difficult to interpret.6 27 to 32 Thus, it is surprising that for face recognition, scaling contrast in addition to size is sufficient to compensate for all extrafoveal deficits. With word recognition, letter spacing has been increased in addition to magnification to reduce the crowding effect.6 30 Scaling size produces a downward shift in stimulus spatial frequencies, eventually disrupting recognition. Furthermore, although increasing letter separation reduces the magnification requirement, the overall size of words is larger, due to greater letter spacing.6 If scaling contrast reduces the need to increase size and spacing, the crowding problem, and that of trying to produce large images on a limited display, may be overcome.
Double scaling makes task comparison harder: if one task has a lower horizontal E2 value, whereas another has a lower vertical E2 value, which is affected more in extrafoveal vision? First, a distinction must be made regarding the interpretation of E2 values. Spatial scaling reflects compensation for cortical factors, relating to the spatial grain of the visual field, whereas contrast scaling compensates for reduced efficiency and may therefore be task specific. It could be speculated that one of a few general horizontal E2 values reflecting the known processing streams33 could be applied to all tasks, with task-specific contrast scaling added as required. This may help to explain the apparent 100-fold intertask difference between spatial E2 values9 found without contrast scaling. If double scaling is actually required, the sole horizontal shift that superimposes the lower, high-contrast, portions of the curves will be greater because in double scaling, data are superimposed through the shortest Euclidean distance.
This scenario is complicated by the significant effect (up to half the total scaling requirement) of the interaction term. It may be assumed that interaction increases with task difficulty, and thus interaction (K) could serve as a relative measure of difficulty for double-scaled tasks as E2 does for spatially scaled tasks. Compensation for parameter interaction could, in fact, be compensating for the effect of crowding, which is known to increase with both eccentricity32 and, for example, the addition of flanking stimuli.30 In our study interaction increased with both eccentricity and set size. Size and contrast scaling firstly compensated for task difficulty but also eliminated the need for further manipulation to overcome crowding. It is therefore likely that the interaction observed and quantified here reflects extrafoveal crowding.
Success or failure of spatial scaling has been used as evidence of quantitative versus qualitative changes in processing across the visual field.34 35 36 37 The premise that failure of spatial scaling indicates a qualitative difference between foveal and extrafoveal processing was valid when stimulus size was the only dimension considered. However, the current results and those of Strasburger et al.10 11 12 show that this is insufficient. Regardless of the number of dimensions, if purely quantitative manipulations can normalize performance, the parsimonious conclusion is that only quantitative differences exist. Therefore, using size, contrast, and perhaps other quantitative stimulus characteristics (e.g., velocity, exposure duration, temporal frequency) it may be possible to normalize performance for more tasks, and some previous deficits in peripheral vision may be revealed as products of insufficient scaling, not qualitative differences.
Although double scaling explains extrafoveal performance for face recognition, and would presumably work for alphanumeric character recognition too, some eccentricity-dependent changes may not be compensated for in this manner. Jüttner and Rentschler13 report distortions of image representations and decreased learning speed outside the fovea. It is possible that insufficient size and contrast scaling meant that foveal and extrafoveal images were not processed and encoded similarly. For example, size scaling normalizes extrafoveal color perception, but fully saturated hues cannot be perceived at far eccentricities,38 and the color spectrum locus becomes smaller and changes shape,39 which presumably could be corrected by scaling size and saturation. It is possible that a comparable phenomenon occurred in the experiments of Jüttner and Rentschler. Additional stimulus manipulation may be required to correctly equate stimulus perception before learning can begin. Despite this, it must be acknowledged that there may be tasks that simply cannot be normalized by scaling stimulus size and/or contrast.
Strasburger et al.12 proposed a "window of visual intelligence" in which fine details and low contrasts are processed: The more demanding the task, the narrower the window. Our results do not dispute this interpretation. Because of the huge demand on cortical resources, a logical evolutionary strategy would be to have a narrow specialized field, with the rest of the retina handling simple processing. The qualitative similarity between all data shows that sufficient double scaling would allow the periphery to process demanding tasks. Thus, our interpretation of the window is that, although this dichotomy exists in everyday life, it is quantitative not qualitative (at least for face recognition) and, given artificial manipulation to compensate for reduced resolution and contrast efficiency, performance can be equated.
Peripheral visual performance is far more complicated than M scaling predicts. Strasburger and Rentschler12 observe that "spatial resolution is but one factor of the visual sense of form," whereas Chung et al.15 conclude that "size is not the only factor limiting reading speed in peripheral vision." The present study leads to a similar conclusion. Changes in resolution, crowding, and efficiency of contrast usage all play a role in extrafoveal performance. Scaling in multiple dimensions does increase the complexity of any extrafoveal model, but shows how alternative manipulations can enhance performance. This could benefit both theoretical study and practical performance-oriented application. The proposed shift from one-dimensional spatial scaling to double scaling mirrors the transition from M scaling3 to spatial scaling,1 2 36 when it became apparent that the restrictions of predetermined M scaling produced false-negative results for tasks that were actually spatially scalable.36 Again, the problem of scaling failures must be addressed by adopting a more versatile approach when comparing foveal and peripheral visual performance.
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Footnotes |
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Commercial relationships policy: N.
Corresponding author: Dean R. Melmoth, Department of Optometry and Vision Sciences, Cardiff University, P.O. Box 905, Cardiff CF1 3XF, UK. melmothd{at}cardiff.ac.uk
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References |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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