Spatial scale shifts in peripheral vernier acuity

Pergamon

00424989(93)E0067-H

Vision Rex. Vol. 34, No. 17, pp. 22x5-2238, 1994 Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0042-6989194 $7.00 + 0.00

Spatial Scale Shifts in Peripheral Vernier Acuity DENNIS M. LEVI,* SARAH J. WAUGH*t Received 29 July 1993; in revised form 13 December 1993

Abutting line vernier acuity oriole are markedly degraded in ~~pber~ vision, while line detection thresholds are elevated to a much lesser extent. To study the spatial and orientation tuning properties of the mechanisms underlying peripheral line vernier acuity, abutting vernier thresholds were measured in the presence of one-dimensional band-limited spatial noise masks varying in orientation and spatial frequency. To examine the effects of these masks on target visibility, line detection thresholds were also measured. We find that in both the fovea and the periphery, noise masking produces marked elevations of vernier thresholds, which are tuned to both spatial frequency and o~entation. (i) S~ff?~ul fvequency tuning: in the fovea, the spatial frequency tuning is handpass, with a bandwidth of x2.5 octaves, and a peak spatial frequency of about 10 c/deg. In the periphery the spatial tuning is similar in bandwidth, however the peak shifts systematically to lower spatial frequencies with increasing eccentricity, implying that thresholds are mediated by spatial m~hanisms tuned to progressively larger spatial scales with eccentricity. (ii) Orientation tuning: at all eccentricities there is a bimodai orientation tuning function for vernier acuity, consistent with the hy~thesis that the responses of at least two filters, whose orientations straddle the target lines, are combined to extract vernier offset information. In contrast, at all eccentricities, line detection is most strongly masked when the mask and line target have the same orientation. For both the line detection and tine vernier tasks, the scale of the most sensitive spatial mechanisms shifts SystematicaIly with ecce~t~~i~. The change in line detection threshold with eccentricity is approximately proportional to the variation in spatial scale; however this shift in spatial scale is not sufficient to account for the degraded peripheral vernier acuity. The extra increase in peripheral vernier tkreshol~ may be a consequence of a high degree of positional uncertainty which adds noise at a stage following the combination of filter responses. Vernier acuity Contrast sensitivity Orientation tuning

Hyperacuity

Peripheral vision

Spatial scale -~.-

Spatial masking

peripheral vernier acuity can be accounted for on the basis of the known variation of retinal mechanisms; While relative position discrimination can be accomprimarily, reduced quanta1 catch by peripheral cones, plished with high precision in the normal fovea (Westand increased spatial pooling by retinal ganglion cells. heimer, 1975), it is markedly degraded in peripheral On the other hand, several workers suggest that advision (Bourdon, 1902; Westheimer, 1982; Levi, Klein & ditional loss of spatial precision may occur at the cortex Aitsebaomo, 1985; Whitaker, MacVeigh & Makela, (Wilson, 1991; Levi et al., 1985; Levi & Klein, 1990, 1992; Yap, Levi & Klein, 1987a, 1989), even when the 1992; Waugh & Levi, 1993a). For example, Wilson stimuli are equated for visibility [Levi & Klein, 1990, (1991) had to introduce shifts in the spatial scale of the 1992; Hess & Watt, 1990; Waugh & Levi, 1993a; and see putative cortical filters, increased positional uncertainty Fig. l(A) of the present paper], Several explanations (proportional to cone jitter), and spatial undersampling, have been offered for the degraded peripheral positional into his line element model in order to model (i) the acuity. One hypothesis is that the fovea has special greater degradation of positional acuity than resolution, purpose machinery, devoted to fine spatial discrimiand (ii) the effects of flanks on vernier acuity. It is nations, which is simply not present in the peripheral interesting to note that both the Banks et al. (1991), and visual field (e.g. Westheimer, 1982). Under this hypoththe Wilson (1991) models assume that the spatial scale esis, positional acuity in central and peripheral vision are of the mechanisms underlying peripheral vernier acuity qualitatively different. Recent computational work leads vary with retinal eccentricity. to a rather different viewpoint. For example, Banks, In the present paper, we use a simultaneous spatial Sekuler and Anderson (1991) suggest that the reduced masking paradigm ~Waugh, Levi & Carney, 1993) to *University of Houston, College of Optometry, Houston, infer how the spatial properties of the mechanisms underlying line vernier acuity and line detection vary TX 77204-6052, U.S.A. with eccentricity. Specifically, we investigate the effects TPresent address: Department of Psychology, The University of Melbourne, Parkville, Victoria, Australia. of band limited spatial masking stimuli, of varying INTRODUCTlON

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DENNIS

M. LEVI and SARAH

orientation, spatial frequency content, and contrast modulation, on (i) abutting line vernier acuity, and (ii) line detection. Our previous work (Waugh et al., 1993) showed that in the fovea, band-limited noise masks elevated thresholds most strongly when the mask had a spatial period of about 556 min arc and when the mask was oriented at an angle of 5510 deg to the target lines, suggesting that the mechanisms which process vernier offsets are selective for spatial frequency and orientation. To anticipate, the present results show that the mechanisms which process vernier acuity in the periphery are qualitatively similar to those in the fovea, but are tuned to lower spatial frequencies. The shift in spatial scale however is not sufficient to fully account for the decline in vernier thresholds with increasing eccentricity.

.I. WAUGH

which time the noise mask and the line stimulus were interleaved frame by frame, i.e. every 3.7 msec (270 Hz frame rate), so that the stimulus and masks appeared to be superimposed. Stimulus

scaling

Fovea1 measurements were made at a viewing distance of 4 m. At this distance, the circular field size subtended 1.15 deg in diameter, and the approximately square diffusing surround (mean luminance of 13 cd/m2) subtended about 2.4 deg on each side. Each stimulus line was 35 min arc in length and 0.62 min arc in width. For the peripheral measurements, viewing distance (ci,) was scaled according to: d, = d,/(l + Ecc/E?)

METHODS The methods and procedures are essentially identical to those described by Waugh et al. (1993) and are briefly described below. The stimuli The stimuli were horizontal dark lines presented on a uniform background (mean luminance of 132.5 cd/m’). The vernier stimulus consisted of two abutting dark horizontal lines which were vertically offset with respect to each other. The line detection stimulus was one of these vernier lines, whose contrast was varied in order to measure the contrast threshold. Examples of the stimuli used are shown in Fig. 1 of Waugh et al. (1993). Stimuli and masks were presented on a Tektronix 608 oscilloscope screen with a P31 phosphor, by a Neuroscientific VENUS stimulus generator, and were viewed through a circular aperture affixed to the oscilloscope screen.

(1)

where dr is the fovea1 viewing distance (4 m), Ecc is the stimulus eccentricity (deg), and E2 is equal to 2.5 deg. E2 is the eccentricity (deg) at which the threshold is twice the fovea1 value, and can be used to specify the rate of change of visual function. We chose an E, of 2.5 degrees, because this is approximately the rate at which line detection thresholds and Ricco’s dimension change with eccentricity [Levi & Klein, 1990a-also see Fig. 2(B)]. This choice of scaling procedure did not critically influence our results since in separate pilot experiments, we confirmed that our line stimuli were longer than the “critical” length for optimal performance, and narrower than Ricco’s dimension (where line width and line contrast are reciprocally related). The critical parameter of our experiments was the spatial frequency composition of the masking noise, and this was varied over a wide range at each eccentricity. We made peripheral measurements at 2.5, 5 and 10 deg in the lower visual field. For these measurements, the observer fixated a thin black strip above the stimulus.

The masks One-dimensional band-limited spatial noise masks were constructed by mathematically adding, in random phase, sinusoidal wave components specified in a 1 or 2 octave bandwidth, and presenting the combined luminance profile on the oscilloscope screen. For all experiments, the stimulus was presented for 1 set, during TABLE

Eccentricity Fovea

10deg

1. Unidirectional

contrast (line detection 1.6 2.5 3.1 4.9 7.4 9.8 2.3 9.1

units)

Observers Four observers, one of the authors (DL), and three highly practiced observers who were naive as to the purpose of the experiments, participated in this study. All were carefully refracted, and wore appropriate corrections during the experiments (including additional

vs bidirectional

vernier

Identify direction bidirectional* threshold (min arc) 1.25 i 0.08 0.71 + 0.05 0.42 k 0.05 0.31 * 0.02 0.21 + 0.01 0.17 + 0.01 16.84 Ifr 0.94 2.14+0.11

thresholds Detect offset unidirectional threshold (min arc) 0.95 0.63 0.46 0.34 0.21 0.18 11.08 1.75

i 0.10 f 0.03 $- 0.03 _f-0.02 f 0.02 &-0.01 + 0.77 + 0.14

*Bidirectional thresholds were measured using five offsets (2 above, 2 below and aligned), and the observer responded by rating the direction and magnitude of offset by giving numbers from -2 to 2). Thresholds represent the offset required to correctly identify the direction of offset at d’ = 1.

SPATIAL SCALE SHIFTS IN PERIPHERAL

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Eccentricity (degrees) FIGURE 1. (A) Vernier thresholds (in min arc) for equally visible stimuli (6 times the line detection threshold) are plotted against eccentricity in linear coordinates. The line fit to the data of all four observersis: Th = k*(Ecc + E2) (see text for details). E2 is the eccentricity at which the vernier threshold doubles. Averaged across observers, E, for vernier acuity with equally visible stimuli is 0.89 & 0.09. (B) Detection thresholds are plotted against eccentricity in linear coordinates. The open symbols and lefthand ordinate shows detection thresholds specified in %minutes (i.e. the product of line contrast and line width). E, for line detection (in %minutes) is 2.15 k 0.3 deg (dotted line). The solid symbols and righthand ordinate shows the line detection threshold specified in % contrast. The solid line has slope of 0 (the best fitting slope is 0.018 f 0.12).

peripheral correction if needed). Experiments were performed under monocular viewing conditions. Experimental methods Vernier acuity. Pilot experiments (see Table 1) suggest that in degraded vision (e.g. peripheral vision or for very low target visibility levels) it may be easier to detect a vernier offset than to identify its direction. For this

reason, and for reasons discussed elsewhere (Waugh et al., 1993), we measured thresholds for detecting a vernier offset using the self-paced method of constant stimuli described by Waugh et al., 1993. The thresholds (specified at d ‘ = 1, equivalent to 84% correct) are the mean of at least four runs, weighted by the inverse variance. The error bars are +_1 SE reflecting the larger of the within and between run variance (Klein, 1992).

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DENNIS TABLE

2. E? (deg) for line vernier

Observer

Line vernier

DL CN TN JT

1.06 0.98 0.78 0.67

Entire data (Fig. 1)

set

_t 0.23 * 0.07 +0.1x kO.19

0.89 * 0.09

M. LEVI and SARAH

and line detection Line detection (‘%minutes) 2.45 jy 0.18 2.55 i 0.13 2.04 * 0.35 1.70&0.17 2.15 10.3

Line detection. Thresholds for line detection were measured using a self-paced rating-scale method of constant stimuli (Levi & Klein, 1990). The thresholds (specified at d’ = 1) are the mean of four or more runs, weighted by the inverse variance, and the error bars show f 1 SE, reflecting the larger of the within and between run variance. Line contrast discrimination. In control experiments thresholds for our supracontrast discrimination

J. WAUCiH

threshold line stimuli were measured using a self-paced. rating-scale method of constant stimuli. A pair of horizontal dark lines, like those used in the masked-vernier experiment (but always aligned), were the stimuli. On each trial, the left line served as a “reference”. It had a fixed contrast of about six times the unmasked line detection threshold, the same as that given to each vernier line in the vernier acuity experiments. The right line served as the “test” line, and had one of five closely spaced contrasts either lower. equal to or higher than the reference, chosen at random. The observer’s task was to judge whether the test contrast was lower, equal to, or higher than the reference contrast, by giving integer numbers from -2 to +2. Feedback as to the magnitude of the test contrast was given after each trial. Thresholds for contrast discrimination (specified at rf’ = 1). are the mean of at least three runs, weighted by the inverse variance. The error bars are + 1 SE, reflecting both within and between run variance. Mask parameters. As in Waugh et al. ( 1993) the mask

(A)

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Musk Spatial Fmquency (c/deg) FIGURE

2(A). Caption on facing page

SPATIAL SCALE SHIFTS IN PERIPHERAL

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Mask Spatial Frequency (c/deg) FIGURE 2. Vernier thresholds (mitt arc) of observer JT (A) and DL (B) are plotted against the mid spatial frequency (geometric mean, specified in c/deg) of the 1 octave noise mask (contrast 30%) oriented at an angle of 10 deg relative to the target. Each curve represents a different eccentricity (from 0 to 10 deg), and the horizontal lines below each curve represent the unmasked vernier threshold. The lines fit to the data at each eccentricity represent two Gaussians as described in the text.

parameters used for all experiments were chosen (based on pilot studies) to maximize the masking effect. For example, orientation tuning functions were measured with a two octave spatial frequency noise mask with the mask spatial frequencies centered near the peak of the spatial tuning function, and the mask contrast was set at 30% or tuning functions were 10%. Spatial frequency measured using one octave bandwidths, with the mask at an angle 10deg clockwise to the stimulus lines. The contrast of a one octave band noise mask at 10 deg, containing spatial frequencies near the peak of the spatial tuning function, was also varied from 2 to 30%. Any variations from the parameters just described will be specified.

EXPERIMENT 1: VERNIER ACUITY AND LINE DETECTION VS ECCENTRICITY

In this experiment, we measured the effect of varying eccentricity on vernier and detection thresholds using our line stimuli. Vernier thresholds were measured using equally visible line stimuli, such that the line contrast at each eccentricity was set to be six times the line detection threshold. As noted previously, the line lengths and widths used for both threshold measurements were scaled for eccentricity. Results Figure l(A) shows how vernier thresholds (in min arc) for equally visible stimuli vary with eccentricity from the

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M. LEVI and SARAH

fovea to IO deg in the lower visual field. The thresholds increase approximately linearly with eccentricity (Weymouth, 1958) and the line fit to the data of all four observers is: 7% = k*(Ecc

+ I%)

thresholds in units of %minutes (see Methods). Line detection thresholds (in %min) increase more or less linearly with eccentricity, although the E2 for line detection is more than double that for vernier acuity (see Table 2). Averaged across the four observers line detection thresholds double at 2.15 k 0.3 deg (dotted line), while vernier thresholds double at ~0.9 deg. Recall that we scaled the width and length of our lines with eccentricity. If our scaling procedure equalized the visibility of the lines at each eccentricity, we would expect that the contrast threshold (in %) would be independent of eccentricity thereby resulting in a slope of 0. The solid symbols and right ordinate show detection thresholds specified in percent contrast, and it is clear that detection thresholds specified in this way are essentially invariant with eccentricity (slope of

(2)

where k is a constant, Ecc is the target eccentricity, and E, is the eccentricity at which the vernier threshold doubles (Levi et af., 1985). The overall fit is quite good, and averaged across observers, E2 for equally visible stimuli is 0.89 k 0.09 (see Table 2), similar to the results of several previous studies of abutting vernier acuity (Levi et al., 1985; Levi & Klein, 1992; Waugh & Levi, 1993a; Wilson, 1991; Alexander, Derlacki, Fishman & Szlyk, 1992). Figure l(B) shows how line detection thresholds vary with eccentricity. Because the visibility of thin lines (within Ricco’s dimension) is proportional to the product of line contrast and line width, the open symbols and left-hand ordinate of Fig. l(B) specify detection

(4

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J. WAUGH

0.018 kO.12).

Below, we describe how noise masks influence central and peripheral vernier acuity and line detection thresholds.

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Mask Spatial Frequency (c/deg) FIGURE 3. Line detection thresholds (%minutes) of observer JT (A) and DL (B) are plotted against the mid spatial frequency of the 1 octave noise mask (contrast 30%) oriented at an angle of 10 deg relative to the target. Each curve represents a different eccentricity (from 0 to 10 deg), and the horizontal lines below each curve represent the unmasked line detection threshold. The lines fit to the data at each eccentricity represent two Gaussians as described in the text.

EXPERIMENT 2: THE EFFECTS OF NOISE MASKS ON VERNIER ACUITY AND LINE DETECTION

In this series of experiments, line detection thresholds and vernier thresholds were measured in the presence of noise masks which varied in (a) spatial frequency (b) orientation and (c) contrast. For the vernier experiments, the contrast of the vernier lines was maintained at 40%. For fovea1 viewing, where the line width was 0.62 min arc, this is equivalent to a line strength (widthecontrast) of 24.8%min. Units of %minutes are useful because for thin lines, the line strength or effective contrast, is determined by the product of the line’s

tOver this range, variations in the line contrast the peak spatial frequency or bandwidth which we measured.

did not influence either of the masking effects

contrast and its width. In peripheral vision, because the viewing distance was decreased, the line strength (in %min) increased; however at all eccentricities, each target line was about 4-8 times the contrast threshold for detecting a single line, when no mask is present.? Results Spatial frequency tuning Figure 2(A, B) shows the effect of varying the spatial frequency of a 1 octave noise mask oriented at an angle of 10 deg clockwise to the target, on vernier thresholds for two observers. Each curve represents a different eccentricity (from 0 to 10 deg). Mask contrast was 30%. In each figure, vernier thresholds (min arc) are plotted against the mid spatial frequency (geometric mean, specified in c/deg) of the mask and the horizontal lines

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M. LEVI and SARAH

below each curve represent the unmasked vernier threshold. As in Fig. l(A), note that the unmasked vernier thresholds increase markedly with eccentricity. For example, for these two observers. between 0 and 5 deg, thresholds rise about &IO-fold. Second, note that at each eccentricity, the effect of the mask on vernier thresholds is clearly tuned to spatial frequency. The curves fit to the data at each eccentricity represent two Gaussians as described by: for spatial

frequency

Th = baseline for spatial

+ peak amplitude*exp(

frequency

Th = baseline

< peak spatial

> peak spatial

+ peak amplitude*exp(

frequency

masking occurs in that study was found to be slightly higher than in the present study (cf. Table 2, Waugh et a/.. 1993). This is a consequence of fitting the data with single or dual Gaussian functions. When the symmetry of the data is less than perfect, a single Gaussian (as used in Waugh et al., 1993) may overestimate slightly the position of the peak. A third point that is clearly evident in Fig. 2(A, B) is that the spatial frequency tuning curves are quite similar in shape and height at each eccentricity, but they shift systematically to the left (toward lower spatial frequencies) with increasing eccentricity. From 0 to 5 deg. the peak of the spatial tuning function shifts by about a factor of 34, from about 10-l I c/deg in the fovea, to about 334 c/deg at an eccentricity of 5 deg. These characteristics can be seen more clearly by plotting the threshold elevation, i.e. the ratio of masked to unmasked vernier thresholds against the mask spatial frequency, as shown in the upper panels of Figs &7. It is clear that spatial tuning functions are similar in form at each spatial frequency, differing primarily in their position along the (log) spatial frequency axis. As can be seen in Table 3 and Fig. 8, the bandwidths of the spatial frequency tuning functions are about 2.5 octaves, and do not vary systematically with eccentricity. Thus, the main effect of eccentricity is to shift the spatial frequency tuning toward the left (i.e. to lower spatial frequencies). Figure 3(A, B) and the lower panels in Figs 4-7 show how varying the spatial frequency of a I octave noise mask oriented at an angle of 10 deg relative to the target, elevates line detection thresholds. Each curve represents a different eccentricity (from 0 to 10 deg). In Fig. 3(A, B)

(s&p)

- (J-J‘- <&)/a, )I frequency

(&)

- ($ - ~~P)/a,)2 (3)

where baseline is the baseline threshold value, peak amplitude is the elevation from the baseline to reach the peak threshold value, sfP is the spatial frequency at which the peak occurs, and g, and 6, are the standard deviations of the Gaussians below and above the peak, respectively. This function was fit to both the raw masking data for vernier acuity [Fig. 2(A, B)] and line detection [Fig. 3(A, B)], as well as the threshold elevation plots (Figs 4-7). The parameters estimated from the data in Figs &7 (using Igor’“) were used to objectively identify several characteristics of the spatial tuning function, in particular the spatial frequency at which peak masking occurs, and the approximate bandwidth at half height (see Table 3). Note that the data for observers DL and TN are the same as those described in Waugh et al. (1993), however the spatial frequency at which peak TABLE

3. Parameters

estimated

J. WAUGH

from spatial

frequency

tuning

Peak spatial frequency Eccentricity

Observer

(c/dcg)

0 0 0 0 0

DL JT TN CN DL

(30%) (30%) (30%) (10%) (10%)

10.40 8.66 10.60 10.50 10.49

2.5 2.5 2.5 2.5 2.5

DL JT TN CN DL

(30%) (30%) (30%) (10%) (10%)

5 5 5 5 5

DL JT TN CN DL

10 10 10 10

DL JT TN CN

functions Line detection

Line vernier Full bandwidth at half height (octaves)

Peak spatial frequency (cideg)

Full bandwidth at half height (octaves)

+ 0.81 + 2.07 & 0.99 * I .58 + 1.44

2.31 3.01 2.32 1.93 2.05

kO.16 + 0.39 + 0.16 + 0.28 + 0.33

7.25 11.1 9.77 6.97 7.45

+ + * + *

1.55 1.71 1.21 0.96 0.94

4.48 2.96 4.38 3.04 2.24

+ + * + f

I. 11 0.52 0.34 0.69 0.36

2.77 3.22 2.93 3.63 2.91

+ k + k +

0.18 0.3 0.25 0.48 0.27

2.67 2.84 2.91 2.23 2.11

& 0.12 + 0.23 + 0.14 + 0.25 +0.17

3.09 4.10 3.70 4.61 2.21

* * f. + *

0.30 0.20 0.40 0.23 0.46

3.34 3.02 3.20 2.59 4.06

* + k + k

0.22 0.18 0.30 0.50 0.37

(30%) (30%) (30%) (10%) (10%)

2.81 2.92 2.67 2.34 2.86

f f k + +

0.21 0.30 0.21 0.33 0.23

2.43 2.59 2.64 2.26 2.59

+0.15 _t 0.29 + 0.18 + 0.19 k 0.15

2.56 3.34 2.85 2.89 2.69

k + k + +

0.21 0.18 0.26 0.26 0.25

3.05 2.38 3.05 3.63 2.92

* 0.19 + 0.14 & 0.24 $- 1.03 f 0.22

(30%) (30%) (30%) (10%)

2.17 + 0.14 1.89+0.12 2.13 +0.18 1.40 + 0.25

2.50 2.54 2.63 2.15

2 0.14 f 0.26 + 0.21 kO.28

1.69kO.13 1.95 + 0. I5 I .49 f 0.20 2.44 + 0.12

3.62 2.53 3.74 3.72

f + k f

Mean

2.46 k 0.07

0.34 0.23 1.28 0.61

3.26 i 0.15

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Mask Spatial Frequency (c/deg) FIGURE 4. Threshold elevation (i.e. the ratio of masked to unmasked thresholds) for vernier acuity (A) and line detection (B) is plotted against the mask spatial frequency for observer JT (from Fig. 2). The mask contrast was 30%. The spatial tuning functions are similar in form at each spatial frequency, differing primarily in their position along the (log) spatial frequency axis.

the line detection thresholds (in %min) are plotted against mask spatial frequency, using the same masking parameters used for the vernier experiments shown in Fig. 2(A, B). The lower panels of Figs 4-7 show the elevation in line detection thresholds (ratio of masked to unmasked line detection thresholds) plotted against the mid spatial frequency (geometric mean, specified in c/deg) of the mask. As was the case for vernier acuity, at each eccentricity, the effect of the mask on line detection thresholds is clearly tuned to spatial frequency, although the magnitude of the effect of this slightly tilted mask is smaller on line detection thresholds than on vernier thresholds (the peaks are higher in the top panels

than in the lower panels of Figs 4-7). As with vernier acuity, there is a systematic shift in the peak of the spatial tuning function toward lower spatial frequencies as eccentricity increases, although the bandwidth of the spatial tuning function for line detection is broader, i.e. about 3.3 octaves, than that for vernier acuity, i.e. about 2.5 octaves (see Table 3 and Fig. 8 which plots the average bandwidth for vernier at each eccentricity against the average bandwidth for line detection). As noted in Fig. 1 and Table 2, unmasked line detection thresholds increase less with eccentricity than do unmasked vernier thresholds. This can also be seen clearly in Figs 2 and 3, where unmasked line detection

DENNIS M. LEVI and SARAH J. WAUGH

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FIGURE 5. Threshotd etevation for vernier (A) and line detection (B) is plotted against the mask spatiaf frequency. Observer DL from Fig. 3. Mask contrast 30%.

thresholds of JT and DL are elevated by less than a factor of 4 between 0 and 5 deg whereas their vernier thresholds are elevated by about a factor of 8-10. Vernier and detection compared

The spatial frequency tuning functions for vernier offset detection and line detection differ in several respects: (i) the magnitude of the peak masking effect is *Possibly the vernier offset results in shghtly higher off-axis frequency components than the line with no offset; however, although the Peak spatial frequency is usually higher for vernier than for detection, this is not always so. It is also worth noting that the cue for line vernier is a “dipole” (Klein et al., 1990), which contains energy at slightly higher spatial frequencies than the line.

larger for vernier than for detection, although this is largely a consequence of using a slightly tilted mask for both threshold measures [using a parallel mask has a stronger effect on detection thresholds than the tilted mask, as shown in Fig. 7 of Waugh et al. (1993)j; (ii) the spatial frequency at which peak masking occurs is not always the same for the two tasks;* and (iii) the masking bandwidths for detection are almost an octave wider than for vernier (see Table 3 and Fig. 8). Note that while the bandwidths for each task are similar at all eccentricities implying that the underlying mechanisms are similar in shape, they are consistently wider for the line detection task. To test whether this difference was a consequence of the differences in line contrast in the two tasks,

SPATIAL SCALE SHIFTS IN PERIPHERAL

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Mask Spatial Frequency (c/deg)

..

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1

Mask Spatial Frequency (c/deg) FIGURE 6. Threshold elevation for vernier (A) and line detection (B) is plotted against the mask spatial frequency. Observer TN. Mask contrast 30%.

we measured the effects of our masks on suprathreshold line contrast discrimination using the same stimulus contrasts as in the vernier task. Figure 9 replots the threshold elevation data of DL at 0 and 5 deg (from Fig. 5) for vernier offset detection (solid symbols). The open symbols show the contrast discrimination results at 0 (circles) and 5 (triangles) deg. Note that the contrast discrimination data are similar to the detection data in showing less threshold elevation, broader bandwidths, and (at least in the fovea) lower peak spatial frequencies than the vernier data, suggesting that the narrower bandwidths obtained for vernier acuity are not

simply a consequence of using suprathreshold lines.

contrast

Shifts in spatial scale with eccentricity Clearly, there are systematic shifts in the peak masking spatial frequency with eccentricity for both vernier acuity and line detection. Figure 10 summarizes the eccentricity variation by plotting the peak spatial period (l/peak spatial frequency in minutes) as a function of eccentricity for vernier [Fig. 10(A)] and line detection [Fig. 10(B)]. In these figures, each symbol represents a different observer. The lines fit to all of the data, show

7376 ___

DENNIS M. LEVI and SARAH J. WAUGH

that peak spatial period increases with eccentricity with an Ez z 2.4 + 0.4 for vernier and 3.4 k 0.7 for detection. Or~enra~ion~u~i~l~

The effect of varying the orientation of a spatial noise mask on abutting vernier thresholds, is shown in Figs I I(A) and 12(A). The orientation tuning function was measured using a 2 octave noise mask of either 10% [DL-Fig. I l(A)] or 30% contrast [TN-Fig. 12(A)] where at each eccentricity, the band of spatial frequencies was centered close to the peak of the spatial frequency tuning function (see Figs 5 and 6). Figures 11 and 12 plot the threshold elevation plotted as a function of the orientation of the mask relative to the target line.

-

e

0

-

+

2.5 deg

-A -

m

il

As shown previously for fovea1 viewing (Findlay. 1973: Waugh et uf., 1993) vernier thresholds are elevated most when the mask is oriented at a slight angle to either side of the target lines. The bimodal nature of the orientation tuning function appears more clearly defined for data obtained using the lower contrast mask, where the effect of the mask was also considerably smaller. In the fovea. vernier thresholds are increased most when the mask is at about .5--10deg to either side of the target lines. As the angle between the vernier target and the mask increases and decreases, the effect of the mask decreases, so that the angle at which the peak masking effect is halved is about IS-20 deg away. In peripheral vision, the peak masking occurred at slightly larger

deg

fjdw 10 deg

FIGURE 7. Threshold elevation for vernier (A) and line detection (B) is plotted against the mask spatial frequency. Observer CN. Mask contrast 10%.

SPATIAL SCALE SHIFTS IN PERIPHERAL

2227

VISION

0 Odeg + n

n

1

2.5 deg 5deg 10 deg

3

2

Detection

Bandwidth

5

4

(octaves)

FIGURE 8. The bandwidths of the tuning functions for vernier (ordinate) are plotted against the bandwidths for detection (abscissa). Both are specified as the full bandwidth in octaves, and the data shown are averaged across our four observers. The bandwidths were estimated from the fits to the threshold elevation data-Figs 4-7 and the individual data are given in Table 3. Note that: (i) the bandwidths for a given task are similar at all eccentricities, and (ii) the mean bandwidth for detection is considerably broader than the mean bandwidth for vernier.

angles for DL (but not for TN), and the orientation tuning broadened slightly, as might be expected to occur when thresholds are mediated by lower spatial frequency mechanisms (Carney & Klein, 1991). Figures 1l(B) and 12(B) show the effect of varying the orientation of the same spatial noise masks on line detection thresholds. Unlike the bimodal masking effect found for the vernier task [Figs 1l(A) and 12(A)], the maximum effect of the mask on line detection thresholds was unimodal, and occurred when the angle of the mask coincided with that of the line target. For a mask contrast of 10% (DL-Fig. 11) peak threshold elevation appeared to be reduced by half when the angle between the mask and the line was about 7.5 deg, and this tuning appeared to broaden slightly with increasing eccentricity. For the 30% mask (TN-Fig. 12) the tuning functions were slightly broader at all eccentricities; however, all curves showed a sharp peak when the mask and target were parallel (orientation 0). We have argued elsewhere (Waugh et al., 1993) that the clear differences in orientation tuning suggest that those spatial mechanisms contributing most to fovea1 vernier acuity and line detection thresholds are different. The present results extend the argument to the peripheral field of vision.

Mask contrast Figure 13 shows how thresholds for vernier acuity (A) and line detection (B) are elevated as the contrast of a l-octave noise mask, oriented at 10 deg clockwise to the target lines and centered near the peak of the spatial frequency tuning function at each eccentricity, increases. Note that the masks were identical for the two tasks. At each eccentricity, as the mask contrast (c) increases, both vernier and line detection thresholds become elevated. The rate of this threshold elevation approximately follows a power function such that Th = kc”

(4)

where Th is the threshold elevation, k is a multiplicative constant which identifies the position of the function on the threshold ordinate, and n is the exponent or the slope of the best fitting line on log-log axes. Table 4 provides estimates of the exponent from the best fitting power functions, for each observer and each eccentricity. The average of those exponents fit to the data for all eccentricities for the two observers, are shown for comparison with the data in Fig. 13. Despite the between subject variability, increasing the mask contrast generally has a stronger effect on elevating

777x ___

DENNIS

M. LEVI and SARAH

vernier thresholds than line detection thresholds, except perhaps at the fovea [see also Waugh et ul. (1993) who showed that at the fovea, the best fitting power functions for a slightly wider range of mask contrasts were similar for the two tasks]. In the periphery, the difference between the exponents found for the two tasks remains approximately constant. A slightly steeper exponent has previously been reported for a “contrast discrimination” task, where the orientation of the target and the mask are coincident (e. g. Legge & Kersten, 1978). than for a “pattern discrimination” task, where the orientation of the target and the mask is different (Wilson. McFarlane & Phillips, 1983; Wilson & Gelb, 1984). This may explain in part why a 10 deg noise mask has a greater effect on vernier acuity. where the mask coincides with the cue, than on line detection, where the mask is oriented with respect to cue. It is possible that the apparent difference between data obtained at the fovea and in the periphery, is due to the effects of spatial interference such as crowding, being more potent in the periphery. The effects qf noise masks on vernier acuit! visible line targets

nlith equall~~

The results presented above indicate that our spatial noise masks influence both vernier and line detection thresholds. Since abutting vernier acuity is strongly dependent on stimulus visibility (Banton & Levi, 1991; Waugh & Levi, 1993a, b; Levi & Klein, 1992; Klein, Casson & Carney, 1990; Wehrhahn & Westheimer, 1990), the question arises: are the effects of masks on vernier acuity simply a consequence of contrast masking,

lo9a-

-

l

j/Fqkj

A

VEqN . . . ...’

.__.__.

0 n

J. WAIJGH

(i.e. are vernier thresholds raised due to the lowered visibility of the target lines)‘? Since vernier thresholds depend strongly on target visibility, here we attempt to predict what effects spatial masking would have on the vernier task, for equally visible targets, i.e. once the effects of target visibility are accounted for (Waugh et al., 1993). First, all vernier and detection thresholds were expressed in units of threshold elevation relative to the unmasked threshold. Then, assuming an approximately proportional relationship between target visibility and vernier threshold. we discount the effect of the mask on target visibility. Specifically, the effect of our masks on line detection provides a direct measure of the reduced visibility of the lines. Since vernier thresholds are approximately proportional to line visibility (exponents between -0.8 and - 1 were found for the four observers in the present study), we subtract the threshold elevation for line detection (raised to the exponent found for each observer) from the threshold elevation for vernier acuity. both expressed in log units. Figure 14(A, B) shows the spatial frequency tuning functions for vernier acuity after discounting the effect of the mask on visibility for observers JT and DL. As noted for fovea1 viewing (Waugh et al., 1993), there is a small resultant effect of masking (about a factor of 2 at the peak); however. it is interesting to note that the positions of the peaks are quite similar to those shown in Figs 4 and 5. Figure 15 shows the orientation tuning of vernier acuity for the two observers shown in Figs 11 and 12

JND -0deg JND-5deg

1 DL-m-1

76: ._

5

z

4-

z w

3-

s ro ;

2-

l96-

FIGURE 9. Threshold elevation data of DL at 0 and 5 deg for vernier offset detection (solid symbols-replotted from Fig. 3). The open symbols show how the noise masks elevate the contrast discrimination thresholds at 0 (circles) and 5 (triangles) deg. Note that the contrast discrimination data show less threshold elevation and broader bandwidths than the vernier data.

SPATIAL SCALE SHIFTS IN PERIPHERAL

Line

2229

VISION

Vernler

= 20 ._ i?J Q vJ Y g II

10 !& = 2.4 C .4 0

2

4

6

Eccentricity

8

10

(degrees)

50 Line Detection

z 5 .f

40

E

3 .I

20

iG n * x g

10 4

= 3.4 f .67

0. 0

Eccentricity

(degrees)

FIGURE 10. The peak masking spatial period (l/peak spatial frequency in minutes) is plotted as a function of eccentricity for vernier (A) and line detection (B). In these figures, each symbol represents a different observer. The lines fit to all of the data, show that peak spatial period increases with eccentricity with an E, x 2.4 f 0.4 for vernier and 3.4 + 0.7 for detection.

after discounting the effect of the masks on line visibility. When the orientation tuning function for line detection is subtracted from that for vernier acuity, despite substantial individual differences, the bimodal orientation tuning is more clearly observed (in particular for TN). While the peak of the orientation tuning appears to broaden very slightly in the periphery of DL; it shows little change with eccentricity in TN. Discussion Positional acuity is markedly degraded in peripheral vision, even when stimulus visibility is accounted for (Levi & Klein, 1990, 1992; Hess & Watt, 1990; Waugh

& Levi, 1993a). In the present study, we used onedimensional spatial noise masking in an attempt to infer the spatial properties of the mechanisms which underlie line detection and line vernier acuity, particularly in peripheral vision. The present results, in agreement with previous work at the fovea (Waugh et al., 1993), suggest that there are indeed spatially tuned mechanisms which are sensitive to the offset of a vernier target. The effects of our masks on vernier and detection thresholds measured both at the fovea and in the periphery differ in two important ways: (i) orientation tuning (bimodal for vernier, unimodal for detection), and (ii) spatial frequency tuning (the bandwidths for vernier are about

230

DENNIS

M. LEVI and SARAH

faCtOr Of 2 narrower than for detection). Thus. we argue that in particular, differently oriented spatial mechanisms contribute to abutting vernier and line detection thresholds. Waugh et ul. (1993) suggested that the effects of masking on vernier offset detection might be understood in terms of a second stage. possibly opponent mechanism, which combines inputs from at least two filters with orientations which straddle the target lines to extract relative position information. This combination process may result in a narrowing of the spatial frequency tuning function measured for vernier iI

J. WAUGH

acuity compared with line detection. and thereby contribute to vernier precision. An alternative possibility is that with the introduction of a vernier offset. the energy generated at a range of orientations is detected by spatial mechanisms at other orientations to that of the one-dimensional mask, thereby contributing to a measured narrowing of the spatial frequency response. Our experimental results on suprathreshold contrast discrimination show that the narrower bandwidths evidenced in the vernier task are not simply a consequence of using suprathreshold contrast lines.

(4 4

’ DL-lD968t?l?8k]

1

-90

-60

I

“0”. 0 deg 2.5 de6 I

+-

-30

Mask Orient&m

(w O- 0 deg -+ 2.5 de6 *-A- 5 deg

El -e

7

I

-90

I

-60

I

I

I

-30

10deg

I

I

90

Mask Oden~“tilon ;&me:) FIGURE 11. The effect of varying the orientation of a spatial noise mask on abutting vernier (A) and line defection (B) thresholds for DL. The orientation tuning function was measured using a noise mask with 10% contrast. At each eccentricity, the spatial frequency of the noise mask was centered close the peak of the spatial frequency tuning function. The ordinate shows the threshold elevation plotted as a function of the orientation of the mask relative to the target line.

SPATIAL

SCALE

SHIFTS

IN PERIPHERAL

VISION

2231

-O- 0 deg

II

FIGURE thresholds

+

2.5 de9

-A-

5 deg

a-

10deg

12. The effect of varying the orientation for TN. The orientation tuning function

of a spatial noise mask on abutting vernier (A) and line detection (B) was measured using a noise mask with 30% contrast. All other details as in Fig. Il.

SpeciJicity of masking

Our results show that the specificity of masking (i.e. the spatial frequency and orientation tuning) is similar at all eccentricities. For example, the results summarised in Table 3 and Fig. 8 show that there is no significant or systematic variation in the spatial frequency bandwidth of masking with eccentricity. Thus, our study does not support the notion that the fovea has special purpose machinery devoted to fine spatial discriminations, which is simply not present in the periphery. The strong bimodal orientation tuning evident in our data suggest that the underlying mechanisms are cortical.

Do shifts in spatial scale account for the loss of peripheral vernier acuity?

A primary goal of this paper is to ask whether there are shifts in the spatial scale of the mechanisms underlying line detection and line vernier acuity as eccentricity increases, and whether these can account for the loss in positional acuity. A shift in spatial scale toward lower spatial frequencies would be expected to degrade vernier acuity on two counts: Firstly, on statistical grounds the accuracy of locating the centroid of a luminance distribution in noise is inversely proportional to the blur of the distribution (Morgan & Aiba, 1985; Morgan, 1991; Krauskopf & Farell, 1991), thus a shift in the scale of

DENNIS M. LEVI and SARAH J. WAUGH

3,1__. _

processing toward lower spatial frequencies would be expected to raise thresholds proportionally. Secondly, since the slope of the spatial tuning function will determine the precision of spatial localization, a shift toward lower spatial frequencies will necessitate a proportional increase in the spatial offset required to reach threshold. Figure 16 summarizes our key results by showing how line vernier thresholds and line detection thresholds, as well as the peak spatial periods of the most effective noise masks vary with eccentricity. SpecificalIy, plotted

in this figure are the ratio of peripheral to fovea1 thresholds (or peak spatial periods) as a function of eccentricity. The fovea1 values are normalized to 1. Jt is clear from this figure that line detection thresholds, and the peak masking spatial period (for both vernier and line detection) increase with eccentricity at close to the same rate (L = 2-3 deg). Discounting the effect of our masks on target visibility changes the positions of the peaks slightly (at all eccentricities), however, it does not significantly alter the & value ( ~3.4 + I). In contrast,

expon&t=O

I

I

2

3

4

r

5

1111

6

.56

I

7

89’

2

3

IO

lhak

Contrast (%)

expone\nt=O.34

FIGURE 13. Threshold elevation for vernier (A) and for line detection (B) plotted as a function of the contrast of a l-octave noise mask, for observers DL (open symbols) and TN (solid symbols). The mask was oriented at IOdeg, and centered near the peak of the spatial frequency tuning function at each eccentricity. The masks were identical for the two tasks. Each symbol represents a different eccentricity. For each eccentricity, as the mask contrast increases both vernier and line detection thresholds are elevated. The dotted lines show the slopes of the power functions (shifted for clarity) fit to the entire data sets which are of the form: Th = kc n. See text for details.

SPATIAL SCALE SHIFTS IN PERIPHERAL TABLE 4. Effects of increasing noise mask contrast--+Xponents obtained from best fitting power functions Observer TN

DL

Eccentricity

Vernier exponent

Line detection exponent

0 2.5 5 10 Combined 0 2.5 5 10 Combined

0.33 + 0.04 0.60 f 0.06 0.62 + 0.06 0.62 & 0.06 0.52 k 0.03 0.39 5 0.04 0.71 & 0.06 0.69 f 0.04 0.97 f 0.08 0.60 4 0.03

0.33 f 0.04 0.28 + 0.04 0.37 + 0.04 0.31 * 0.04 0.32 4 0.02 0.26 + 0.03 0.36 -i_0.03 0.39 + 0.02 0.58 + 0.04 0.35 + 0.02

thresholds (for equally visible stimuli) increase much more rapidly (& = 0.9 deg). One might contend that because the visibility of the vernier target was primarily determined by that of the lines themselves (and only a little by the local region of offset), that the change in spatial scale we measured by masking may reflect the change in detectability of the line, rather than the vernier cue itself. However the bimodal orientation tuning function (which is characteristic of vernier acuity), especially that obtained once the effects of the mask on line detectability are accounted for (see Fig. 15), is equally distinctive at all eccentricities and for both mask contrasts. In addition, vernier thresholds for abutting line targets have been proposed to be calculated from relative orientation information obtained across some portion (approx. IOminarc in the fovea) of the constituent lines (Watt, Morgan & Ward, 1983), so that masking of the lines themselves is important if one wishes to mask the vernier cue.

vernier

RELATIONSHIP

TO PREVIOUS

STUDIES

The full-off of vernier acuity with eccentricity for abutting line targets The rapid decline in abutting vernier acuity with eccentricity found in this study using equally visible targets, i.e. E, x; 1, is similar to that described by several other investigators (see Table 5). These values vary somewhat across individuals within a given study, whether the task is to detect a vernier offset or to identify its direction (see Table I), and also across experimental conditions such as stimulus orientation (Wilson, 1991; Yap, Levi & Klein, 1987b; Fable, 1986; Rovamo, Virsu, Laurinen & Hyvarinen, 1982; Heeley & Timney, 1988), stimulus contrast (Levi & Klein, 1992) and the region of the visual field tested (Fahle, 1986). A similar rate of decline also occurs for other relative position tasks, such as two dot spatial interval discrimination (Yap et al., 1989) (E2 z O.?), three-dot bisection, (Yap et aI., 1987a) (E, z 0.6) and two-dot vernier acuity (Westheimer, 1982) (,!$ z 1). The very steep decline in threshold with eccentricity, or very small E,, found for the abutting vernier acuity data of Bourdon (1902) (see Table 5) does not fairly

VISION

2233

reflect the effects of eccentricity on vernier acuity per se, because the peripheral stimuli used in that study were not optimized in size or visibility. Thus, the effects of eccentricity on target visibility, target size, and vernier acuity were confounded. The largest E2 value for abutting line vernier acuity (Whitaker et al., 1992), was obtained in the horizontal meridian. The “spatial scaling” procedure employed in this and other studies (Watson, 1987; Drasdo, 1991) involves producing a series of stimuli at each eccentricity which are magnified versions of each other. Thus line length and line width covaried, and the effect of changes in both of these parameters can alter line visibility. In addition, their scaling procedure is based on the implicit assumption that a single scaling factor is appropriate for both line length and for vernier threshold. This assumption is questionable in light of previous studies, where the optimal position threshold and the optimal separation for both two-dot vernier and two-dot separation discrimination, vary at different rates with eccentricity ~Westheimer, 1982; Yap et al., 1989). Moreover, our pilot experiments suggest that the “critical” line length varies more slowly with eccentricity than do vernier thresholds for equally visible stimuli. The present study shows that the decline in vernier acuity is steeper than the shift in the peak spatial frequency at which masking occurs. This result agrees with the findings of Levi and Klein (1992) and Waugh and Levi (1993a) that abutting line vernier acuity in peripheral vision cannot be simply accounted for on the basis of reduced visibility (or quanta1 catch), and increased spatial pooling, as suggested by Banks et al. (1991). We believe that the present masking results provide a more direct test of whether spatial scale shifts contribute to the reduced peripheral vernier acuity. Masking results show that there are indeed marked shifts in the spatial scale of those mechanisms that mediate vernier offsets, however it appears that these shifts do not fully account for the poor positional acuity of the peripheral retina. Vernier acuity and spatial interference When flanking lines or dots are placed on either side of a vernier target, and within a critical distance, vernier thresholds are markedly elevated (Westheimer & Hauske, 1975; Levi et al., 1985). Waugh et al. (1993) showed a very close similarity between the spatial tuning functions produced by one-dimensional noise masks, and those produced by localized flanking stimuli in the fovea, raising the question of whether masking and spatial interference represent the same phenomena. In the present study we show that vernier thresholds and the spatial frequency at which peak masking occurs vary at different rates with increasing eccentricity. However, vernier thresholds and the peak of the spatial interference function appear to covary [the zone of spatial interference has a mean E2 value of 0.77 + 0.14 deg for the two observers (Levi et al., 1985)]. Thus, spatial interference may represent a different phenomenon to masking in the periphery. One

2234

DENNIS

M. LEVI and SARAH

possibility is that our superimposed one-dimensional noise masks uncover the filter(s) most sensitive to the vernier offset, while the flanking dots reveal the spacing between filters (as suggested by Wilson 199 I ). If this view is correct then the filter size grows more slowly with eccentricity than does the separation between filters, as is the case in primate striate cortex (Dow, Snyder, Vautin & Bauer, 1981).

J. WAlJGH

Relutionship

to the contrust

.sensitivit!* junction

It is of some interest to examine the relationship of our spatial frequency tuning functions obtained by masking. to the contrast sensitivity function. Figure 17(A) shows contrast thresholds for a patch of cosine grating. measured as a function of spatial frequency _ _ for two observers (JT and DL) using the same display and

-

0

...........

@

2.5 deQ

-----

0

5 deQ

0 deg

1

0.1

Mask Spatial Frequency w 3-

-0

El ...........

l

...... 0

*__.

5 ._

2-

;ji

Odeg 2.5 deQ

5 deg

n

lo’%

5

W 0 E ua S! if

l-

a 97 1 I 0.1

I

2

3

I

4

III”,

537

I

I

I

2

3

4

mm”‘,

14. Spatial

frequency

2

587

1

Mask Spatial Frequency FIGURE

(C’SF)

34s

10

(c/deg)

tuning functions for vernier acuity after discounting the effect of the mask on visibility observer JT (A) and DL (B). See text for details.

for

SPATIAL SCALE SHIFTS IN PERIPHERAL

2235

VISION

(4 1m

vWfMy olscount6d

- 10% mati

‘I #

43I

I

-90

-60

I

I

I

-30Orienthm

(&ree~

I

I

90

Mask

1 TN

-90

-60

- 30%

mask

- ViNbii#y

-30

Discounted

90

Mask Orlent~tlon (Ggreei; FIGURE

15. Orientation tuning of vernier acuity for DL (A) and TN (B) after discounting the effect of the masks on line visibility. For clarity, data are only shown for 0, 2.5 and IOdeg.

psychophysical methods (see Waugh & Levi, 1993b for detailed methods). Open symbols represent data obtained for fovea1 viewing, solid symbols are those measured with the patch centered at 5 deg in the lower visual field, and the thin lines are Cauchy functions (Klein & Levi, 1985) fit to the data. It is clear that at 5 deg, the high spatial frequency limb of the contrast sensitivity function is, more or less, a scaled version of the fovea1 CSF shifted to lower spatial frequencies. The thick lines represent the fovea1 fit shifted toward lower spatial frequencies, by a factor equivalent to the shift in the spatial frequency at which line detection was most strongly masked at the fovea and at 5 deg for each

observer (from Table 3). Clearly, the “scale shift” estimated from our line detection masking experiment corresponds closely to the measured shift in contrast sensitivity with eccentricity (see also Rovamo et al., 1978). Interestingly, the horizontal “scale shift” estimated from our line vernier masking does not account well for peripheral vernier acuity measured with cosine gratings (Levi, Klein & Wang, 1994b) for the same observers. For example, for DL, optimal vernier thresholds for equally visible gratings at 5 deg in the periphery are elevated by more than a factor of 10 compared to the fovea. Applying the same scaling factor to the vertical axis still leaves a loss of close to a factor

“36 _-_

DENNIS M. LEVI and SARAH J. WAUGH

2

4

6

Eccentricity

8

10

(degrees)

FIGURE 16. The lines show how line vernier and line detection thresholds, as well as the peak spatial periods of the most effective noise masks vary with eccentricity. The ratio of peripheral to fovea1 thresholds or peak spatial periods are plotted as a function of eccentricity. The fovea) values are normalized to 1. Line detection thresholds, and the peak masking spatial period (for both vernier and line detection) increase with eccentricity at similar rates f& z 2-3 deg). Vernier thresholds (for equally visible stimuli) increase much more rapidly (Er z 0.9 deg).

of 3 in the optimal vernier acuity to be accounted for. These results, in agreement with our masking results, suggest that the poor positional acuity of the periphery cannot be fully accounted for on the basis of a shift in the effective spatial scale of processing. Relationship to anatomy and physiology Of long standing interest to vision scientists is the relationship between the decline in visual function in peripheral vision, and the eccentricity dependent changes which occur in anatomical structures and physiological functions (Weymouth, 1958; Rovamo, Virsu & Nasanen, 1978; Levi et al., 1985; Drasdo, 1991). In many respects this is a rather difIlcult enterprise, particularly given the

many uncertainties in what is known about the anatomy and physiology. For example, recent work in monkeys and humans make it clear that in the fovea there are several (perhaps 3-4) retinal ganglions for each central cone (Curcio & Allen, 1990; Wassle, Grunert, Rohrenbeck & Boycott, 1989, 1990) however the precise ratio is difficult to determine within the very central visual field. Wassle et al. (1989; 1990) have suggested that fovea1 magnification of the cortical representation of the visual field may be fully accounted for by fovea1 magnification in the retina. On the other hand, recent evidence, based on retrograde degeneration supports the idea that there is additional magnification in the visual cortex (Azzopardi & Cowey, 1993). Thus, there remains

TABLE 5. EZ values for abutting vernier acuity (from previous studies Study

Task

Range (deg)

mean .IZ> (deg)

O-20 O-10

0.07 & 0.3 0.70

O-.-IO

0.77 * 0.14

Levi and Klein (I9901

Abutting tine vernier (no scaling) Abutting line vernier (very high contrast bright lines, scaled in size) Spatial interference zone for vernier (Fig. 23) Abutting edge vernier

O-5

0.82 + 0.06 (hi c)

Wilson (1991)

Abutting line vernier

O-30

Whitaker CEal. (1992)

Abutting line vernier (size scaled bright lines) Abutting line vernier (size scaled and visibility matched) Abutting vernier (chevron line)

O-15

0.78 & 0.1 (vertical) I.38 f 0.2 (horiz) I.55

o-2.5

0.98

o-4

I .05

Bourdon (1902) Levi e? ai. (I 985) Levi et al. (1985) .

1.oo+ 0.I (low c)

Waugh and Levi (1993a, b) Alexander et al. (1992)

SPATIAL

SCALE

SHIFTS

(4 5.

0

4-

0

DLFovea DL5deg

32-

1 0: 6. 5. 43. 2-

1: 6., 5 6

6’

2

4

6

W

0 l

4

6’

2

4

10

1

JT Fovea JT5deg

IN PERIPHERAL

VISION

2237

field (at least within the central 10 deg), as suggested by Hubel and Wiesel (1974). Second, vernier acuity for equally visible targets, falls off with eccentricity more rapidly than detection, and at a faster rate than predicted by the rate of change of the spatial tuning functions derived from our masking studies. Thus it is unlikely that with increasing eccentricity, changes in cone size and spacing, which reduce light capturing capabilities (see Banks et al., 1991), or changes in the size and spacing of retinal ganglion cells and cortical receptive fields as estimated by increases in spatial pooling (Banks et al., 1991; Levi & Klein, 1992; Waugh & Levi, 1993a), limit vernier acuity. It may be relevant, that the computational work of Wilson (1991) requires the following manipulations in order to mimic peripheral vernier acuity, (i) a shift in spatial scale of the putative cortical spatial filters (a strategy supported by our masking data), (ii) spatial undersampling as predicted from the measured effects of flanking targets in the periphery [the effects of undersampling are discussed by Snyder (1982) and Levi et al., 1994a, b)], and (iii) increased positional uncertainty. Positional uncertainty of cortical filters was attributed to increased jitter in cone positions in the periphery (Hess & Watt, 1990; Wilson, 1991). That is, if the brain does not “know” the precise positions of the peripheral cones (Maloney, 1989), this would produce positional uncertainty which has a marked effect on positional tasks with much less effect on detection or resolution. The site of positional uncertainty

iI, 6

SPAThU

,“,6

2

4

FREQU&Y

66’

2

4

(c/deg)

FIGURE 17. Contrast thresholds for a patch of cosine grating, are plotted as a function of spatial frequency for two observers (DL and JT). Open symbols represent data obtained for fovea1 viewing,solid symbols are those measured with the patch centered at 5 deg in the lower visual field. The thin lines are Cauchy functions fit to the data. The thick lines represent the fovea1 fit shifted toward lower spatial frequencies, by a factor equivalent to the shift in the spatial frequency at which line detection was most strongly masked at the fovea and at 5 deg for each observer (from Table 3) and corresponds closely to the measured shift in contrast sensitivity with eccentricity.

a good deal of uncertainty regarding the precise fovea1 cortical magnification factor and its rate of variation with eccentricity (a recent review is provided by Drasdo, 1991). The present study does allow us to draw two conclusions: first the similarity of the masking data in central and peripheral vision suggests that the mechanisms which detect a line, or a vernier offset are qualitatively similar at each eccentricity. Thus, it appears that the cortical machinery involved in snatial vision is similar across the visual _.

A simple topographic jitter model, where jitter might be a consequence of irregularity in the peripheral cone mosaic (Hess & Watt, 1990) would produce an additive error (or a floor in performance) such that fovea1 and peripheral thresholds would be predicted to converge at low contrast levels. The loss of vernier acuity in peripheral vision however, appears to be multiplicative, in that thresholds are more or less uniformly elevated (on a log scale), over a wide range of contrast levels [see e.g. Fig. l(d) of Levi and Klein (1992) and Fig. 4 of Waugh and Levi (1993a)]. Waugh et al. (1993) argued that in fovea1 vision, vernier acuity might be determined by an opponent mechanism which combines the responses of filters at different orientations. Here, we propose that noise possibly due to uncertainty in filter position or orientation occurs at a “second stage”, after combination of information from the oriented filters. Adding the noise at a second stage has two consequences. It produces a multiplicative effect (i.e. it will have a proportional effect at all contrast levels), and it can have an effect which is specific for vernier, but not for contrast detection and discrimination. SUMMARY AND CONCLUSIONS We used a simultaneous spatial masking paradigm (Waugh et al., 1993) to infer the spatial properties of the mechanisms underlying peripheral vernier acuity, and peripheral line detection. Our results show that the mechanisms which process vernier acuity in the periphery are qualitatively similar to those in the fovea, but are

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tuned to lower spatial frequencies. The shift in spatial scale is not sufficient to fully account for the decline in vernier thresholds. The additional loss of vernier acuity in the periphery may be a consequence of increased positional noise at a stage following the combination of filter responses. REFERENCES

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Ac~no~~ed~emenfs-We are grateful to Stan Klein, Srimant Tripathy and Hong Wang for helpful comments on an earlier version of the manuscript. We are indebted to Thorn Carney for assistance with the Venus, and to our observers, Cindy and True Nguyen and Jenny Tran for their many hours of observations. This research was supported by erant ROlEY01728 from the National Eye Institute.