discrimination of spatial phase in central and peripheral vision

V&ton Ra. Vol. 29, No. 4, pp. 43-5, 1989 0042-6989/89 S3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright 0 1989 Pergamon Press plc

DISCRIMINATION OF SYATIAL PHASE IN CENTRAL AND PERIPHERAL VISION

M. CONCETTA MORRONE,* DAVID C. BURR+ and DGNATELLA SPINELLI~

Department of Psychology, University of Western Australia, Nedlands, WA 6009, Australia

(Received 29 February 1988; in revised form 9 September 1988)

Abstract-Sensitivity to relative phase was measured for central and peripheral vision using stimuli comprising 256 harmonics, smoothly filtered in amplitude. With these stimuli, peripheral phase sensitivity was much higher than that previously reported with two-harmonic stimuli. Sensitivity did not depend on the average phase of the stimuli, nor on their second-order statistics, irrespective of the spatial frequency of the stimulus or the position in the visual field. After scaling for size, peripheral sensitivity was as high as central sensitivity. The scaling factor required to equate phase sensitivity was the same as that required to equate contrast sensitivity and grating acuity. These results suggest that phase sensitivity decreases with eccentricity at a similar rate as contrast sensitivity and grating acuity, much more slowly than the positional acuities. This is consistent with the suggestion that phase discrimination is mediated by discriminating the amplitude of the response. of quasi-linear filters, and does not require mechanisms that evaluate position. It is suggested that previous measurements on peripheral phase sensitivity may reflect positional uncertainty in the periphery, rather than a deficit in phase sensitivity per se.

Periphery Phase Edge-detector Cortical magnification

INTRODUCTION

Vision is poorer in the periphery than in the fovea. Snellen acuity, grating acuity, contrast sensitivity, vernier acuity and stereo acuity all fall off steadily with eccentricity. However, the rate of decrease in the so-called positional acuities (such as stereo, vernier and bisection acuity) is 34 times faster than grating acuity. A possible explanation for the difference is that grating acuity may be limited by retinal factors (such as photoreceptor and ganglion cell density) while positional acuities may be limited by cortical sampling density (Levi et al., 1985). Recent estimates suggest that the cortical representation of the fovea is magnified three to four times compared with that of the retina (Dow et al., 1981; Perry and Cowey, 1985).

In recent years there has been considerable interest in the ability of human observers to discriminate spatial phase (e.g. Burr, 1980; Lawden, 1983; Lawton, 1984, 1985). Many studies have suggested that phase sensitivity falls off with peripheral viewing far more rapidly than does contrast sensitivity, even when the

*Present address: Istituto di Neurofisiologia de1 CNR, via S. Zeno 51, Pisa 56100, Italy.

tOn leave from: Dipartimento di Psicologia, Universid di Roma, Italy.

peripheral stimuli are scaled appropriately (e.g. Hilz et al., 1981; Braddick, 1981; Klein and Tyler, 1981; Rentschler and Treutwein, 1985; Bennett and Banks, 1987). These results suggest that phase acuity varies with eccentricity like positional acuity rather than like grating acuity (see also Levi et al., 1985).

Rentschler and Treutwein (1985) reported that peripheral phase sensitivity was poor only for stimuli having matched second-order statistics (see Julesz, 1981). Phase discrimination between patterns with different second-order statistics was relatively good. Rentschler and Treutwein argue that when the second-order statistics vary, discrimination may be based on local contrast cues (Badcock, 1984a, b) rather than phase per se. For patterns with identical second-order statistics, they argue that the discrimination requires phase sensitive mechanisms, such as detectors with even- and odd-symmetric fields, which may be sparse or absent in peripheral retina.

A recent study by Bennett and Banks (1987) is consistent with this assertion. Using a technique introduced by Field and Nachmias (1984), they measured contrast thresholds for discriminating phase shifts of 180” in compound grating pairs comprising the first two harmonic components. By varying the relative phase of the harmonics, they varied the contribution

433

434 M. CONCETTA MORRONE et al.

of sine and cosine components at the points of the waveform where they assumed discrimination occurred. Discrimination thresholds for gratings with harmonics added in cosine phase were relatively independent of eccentricity, whereas discrimination thresholds for sine phase fell off rapidly with eccentricity. They concluded that detectors in sine phase (odd- symmetric receptive fields) were sparse in the periphery.

However, as discussed in the previous paper (Burr ef al., 1989), the technique of Field and Nachmias is open to certain criticisms, primarily the assumption that phase discrimination occurs only at the peaks of the fundamental. This is a convenient mathematical simplification, but difficult to justify on biological grounds. A further limitation is that a periodic grating comprising only two harmonics may not be the most appropriate stimulus to reveal the phase response of detectors (discussed further in the discussion section).

In this study we measure phase discrimination thresholds in central and peripheral vision using stimuli comprising 256 cosine components. Dis- crimination of these patterns is assumed to occur at the points where local energy is maxi- mum (Morrone and Burr, 1988) an assertion well supported by experimental evidence. As proved elsewhere (Morrone and Owens, 1987; Morrone and Burr, 1988), peaks in local energy occur where the arrival-phases of all harmonics are maximally similar. Thus, as well as being a biologically plausible assumption, the model leads to a convenient description of phase for multi-harmonic stimuli.

The study had two goals: to examine whether there exist in peripheral vision detectors with even- and odd-symmetric receptive fields (bar and edge detectors), using the approach described in the previous paper (Burr et al., 1989); and to measure, in central and peripheral vision, phase sensitivity for multi-harmonic stimuli. The results suggest that for these stimuli, phase sensitivity is as good in the periphery as in central vision, if stimuli are scaled to equate contrast sensitivity. We discuss the possibility that the results of previous studies may reflect positional uncertainty in the periphery rather than poor resolution of phase.

METHODS

The methods of this study were similar to those described in Burr et al. (1989), where the

reader is referred for full details of stimuli and procedures.

Stimuli

The stimuli for most of the experiments were vertical one-dimensional patterns, made up by summing 256 cosine harmonics. The amplitude spectrum of the patterns was multiplied by a Difference-of-Gaussian (DOG) function to attenuate smoothly both the high frequencies (to avoid ringing) and the low frequencies (that could give luminance cues for discrimination). The general equation of the luminance profile L(x) was:

256

L(x)=L,+a c

k=I

/T) - 4 I* DOW j/k, cos((2nk ‘X

where

DOG(k) = exp( -k2/2ai ) - exp(-k2/2d), (1)

for k odd integer. L, is the mean luminance, a a constant related to contrast, T the period (equal to 512 points) and 4 the phase at origin. aL and a,, are the space constants of the difference of Gaussian (equal to 4 and 128 cycles/period respectively).

Figure 2 of Burr et al. (1989) shows three examples of the multi-harmonic stimuli, for 4 = 0, 45 and 90”. The effect of varying 4 is to change the type of feature seen, from an edge, for 4 = 90”, to a line for 4 = 0. For inter- mediate phases such as 45”, the features seem to be a combination of edge and line.

For one experiment the stimuli comprised only two cosinusoidal components, one twice the spatial frequency of the other. The luminance profile L(x) was given by:

L(x) = L, + u(cos((2n .x/T)-4)

+0.5 cos(2~(2*n/T)) - 4)). (2)

For this stimulus, 2.4 cycles of grating were displayed, and the position of the grating was completely random from trial to trial. Other- wise, the experimental procedures were identical to those used for the multi-harmonic stimuli.

Stimuli were generated by Micro-vax computer and transferred to a smaller computer (Cromemco-Z2D). The Cromemco displayed stimuli on a Joyce Electronics oscilloscope via an 8 bit D/A port, at 100 frames/set, 624 lines/ frame. The signal was passed through a logarithmic digital attenuator (under computer

Discrimination of spatial phase 435

control), then multiplied analogically by a Gaussian envelope of time constant 100 msec (generated by a second D/A) to produce a temporal vignette of 5OOmsec total duration. 1.2 periods of stimulus were displayed. Cycle width was 24.6cm, on an oscilloscope face 30 cm wide by 20 cm high. On each presentation the position of the stimuli varied randomly over a region equal to l/16 cycle width, to minimize the possibility of basing the discrimination on local luminance cues. The screen was sur- rounded by white card 2 x 2m, floodlit to the same mean luminance as the screen (400 cd/m*).

For some experiments, a pedestal of fixed contrast was added to the test stimuli, and faded in and out with the test (see Burr et al., 1989 for details). The contrast of all stimuli was defined as the ratio of the standard deviation of the luminance profile to the mean luminance (see Burr et al., 1989 for justification).

Eccentricity was varied by positioning a fixation point away from the screen. For most experiments the fixation point was 10” above the upper extremity of screen, so the stimuli fell in the inferior field at 10” eccentricity. For one control experiment the fixation point was positioned 10” to the right of the screen and viewed with the right eye, so the stimulus fell 10” into the nasal field. Spatial frequency was varied by varying viewing distance. For spatial frequencies greater than 0.5 c/deg (only used for central viewing), stimuli were viewed through binoculars (Zeiss x 10) in reverse.

Phase

Contrast discrimination in the presence of an orthogonal pedestal can also be described as a phase discrimination task. Figure 1 illustrates the trigonometry. The combination of pedestal and test stimuli can be described by three parameters: contrast, given by the pythagorian sum of test and pedestal contrasts; mean phase, equal to pedestal phase; and threshold phase discrimination, given by twice the arc-tangent of the ratio of the test contrast at threshold to the pedestal contrast. The results of this study will be presented both as test contrast thresholds and as phase thresholds.

For one experiment (shown in Fig. 9), phase thresholds were measured as a function of spatial frequency for stimuli of constant contrast. For this experiment, the contrast of the com- bined test and mask stimuli was kept constant (although both individual components were varied) by attenuating the sum of the test and

90’

+ TESl

/O

270’

Fig. 1. Illustration of the phase and contrast of stimuli used in these experiments. In this example, the phase the harmonics of one test stimulus was 45”, the other 225”. Test stimuli presented alone are represented by the open symbols connected by a dashed line: phase is given by the angular co-ordinate and contrast by distance from the origin. The phase of the pedestal in this example is -45”. Test and pedestal sum (vectorially) to yield stimuli (solid symbols) that can be characterized by three parameters: contrast, C (the squareroot of the sum of squared test and pedestal stimuli); mean phase, given by the pedestal phase; and difference in phase, 8 (twice the arctangent of the ratio of

test to pedestal contrasts).

pedestal by a factor equal to ,/<l + (C,/C,)2), where C, is the contrast of the test at any given trial, and C, is the contrast of the pedestal. The attenuation was achieved by a digital logarithmic attenuator, inserted after the stimuli were summed. In practice, the correction factor was required only when the test contrast was more than half that of the pedestal (giving a phase difference of 58”): for lower test contrasts the correction factor was less than 1 dB.

Procedure

Contrast thresholds were measured for detecting multi-harmonic stimuli, for discriminating between pairs of compound stimuli of phase 4 and (4 + 180’7, and for making this discrimination in the presence of a pedestal of phase 4 f 90”. All thresholds were determined by two-alternative forced choice, guided by the QUEST procedure (Watson and Pelli, 1983) which homed in on the contrast that yielded 82% correct discrimination. Stimuli were presented on successive intervals, marked by a tone. For detection tasks, observers were required to identify the interval containing the stimulus (in the other interval, a blank stimulus

436 M. CONCETTA MORRONE er al.

was presented). For discrimination, observers were required to identify the interval containing the “target” stimulus. They were given no in- structions on how to perform the task, but were allowed several sessions to develop suit- able strategies. Usually observers based their judgements on the apparent polarity of edges and lines. For each condition, 5 sessions of 40 trials were run, yielding estimates of mean and standard error.

Two observers were used for all measurements, both corrected to 6/6 vision.

RESULTS

Contrast sensitivity

To examine the effect of eccentricity on the detectability of compound stimuli, contrast sensitivity functions were measured for central viewing, and 10” into the inferior field. For all spatial frequencies, the stimuli were 1.2 cycles wide by 0.8 cycles high.

Figure 2 plots contrast sensitivity against the fundamental spatial frequency of the stimuli. Closed symbols refer to central measurements, open symbols to peripheral measurements. The major difference between the two curves is a lateral shift of about 0.7 log units. That is to say, to obtain similar contrast sensitivities for central and eccentric viewing, spatial frequency must be about five times lower at 10” eccentricity. The shift does not equate the curves exactly; however, as peak sensitivity for central viewing was slightly higher than for peripheral viewing.

Note that peak sensitivity for these stimuli occurs at spatial frequencies about ten times lower than for pure sinewaves (e.g. Campbell and Robson, 1968; Virsu and Rovamo, 1979). This is because the spatial frequency reported here is that of fundamental, not of the components of highest amplitude. The stimuli were bandpass filtered, attenuating heavily the lower spatial frequencies (see amplitude spectrum in Fig. 2, Burr et al., 1989).

In this experiment, the phase (4 of equation 1) was always 90” (sine phase). However, other experiments show that varying the phase does not vary contrast thresholds, where contrast is expressed as ratio of standard deviation of the luminance profile to mean luminance (Morrone and Burr, 1989).

Sensitivity to contrast reversal

Following the procedure outlined in the previous paper (Burr et al., 1989), observers were

300

-Aq---+‘ ?OO

A, ‘if :\

z 30 5

MCM _ t ‘: $ 10 3 ( , ( , , ( , , , , , , , , , / , , , , , ,

101 I I,!,,, / I I,,,,,, I 1 I1

003 01 03 1 3

SPATIAL FREQUENCY Wdeg)

Fig. 2. Contrast sensitivity for detecting compound stimuli, for stimuli presented centrally (solid symbols) and lo” into the inferior visual field (open symbols). Spatial frequency was varied by varying viewing distance. Stimulus size was

1.2 cycles by 0.8 cycles high.

required to discriminate “target” stimuli with phase 4 from stimuli with phase 4 + 180” (re- versed in contrast). Stimuli were presented in the inferior field at 10” eccentricity. The fundamental spatial frequency was 0.092 c/deg, maxi- mizing contrast sensitivity at this eccentricity. Phase 4 varied between 0” and 90” in 15” steps. Contrast thresholds are plotted in Fig. 3 on polar coordinates. The angular co-ordinate represents 4, and vector length from the origin represents contrast at threshold (in linear units).

The results show that discrimination thresholds varied little with phase. At all phases thresholds were around 0.0024 for MCM and 0.0023 for DS, corresponding to contrast sensitivities of 420 and 430. Comparison with Fig. 2 shows that these discrimination sensitivities are very similar to detection sensitivity., The difference between detection and discrimination sensitivity was 1 or 2 dB at most.

Comparison with Fig. 5 of Burr et al. (1989) shows that discrimination thresholds at 10” eccentricity were not much higher than those for central vision. There was an advantage for


0.003 MCM

l

‘.‘: 0.002

0.00:

1 4=

I DS

0 0 0.001 0.002 0 0.001 0.002

CONTRAST OF COSINE CO’vlPONENT

Fig. 3. Polar plot of contrast thresholds for discrimination of compound stimuli differing in phase by 180”. The phase of the target stimulus varied from 0 to 90” (with its partner varying from 180” to 270”). Spatial frequency was O.O9c/deg, eccentricity 10” inferior. Phase is represented by the angular coordinate, and contrast at threshold by vector length. The Cartesian coordinates give the contrasts of the sine and cosine components of the stimuli. Error bars show f 1 SE. The inner curves are elipses passing through the

thresholds for sine and cosine phase.

central viewing of about 4dB for MCM, and 3 dB for DS, comparable to the difference in contrast sensitivity of the stimuli.

Thresholds could be well fit by an ellipse. This could suggest that for peripheral vision there may exist detectors tuned to all phases, all having roughly equal sensitivity. However, as mentioned in the previous paper, the difference between the ellipse and the predictions assuming probability summation between independent detectors tuned to sine and cosine phase is small, about 1 dB at most.

That discrimination thresholds did not depend on phase is surprising. Both Rentschler and Treutwein (1985) and Bennett and Banks (1989) reported that peripheral phase discriminations depended critically on the mean phase of the stimuli. To be certain that our results did not depend on the particular parameters chosen,

1000 MCM z 5

6 300

Z

w 1: y : 100

8

6 30

0 lb - * IOJ , I I

0 L5 90

the experiment were repeated with different spatial frequency and visual field.

Contrast reversal sensitivities are shown in Fig. 4, for phases ($) of 0,45 and 90”. The solid circles refer to vertical stimuli of 0.09 c/deg, positioned 10” in the inferior field (from Fig. 3). The filled triangles refer to vertical stimuli of 0.5 c/deg, again in the inferior field (10’). Note that 0.5 c/deg is very near the detection acuity for these stimuli (Fig. 2). Discrimination sensitivity was greatly reduced at this spatial frequency, but the reduction was similar at all phases. There was very little difference of sensitivity with phase.

The open squares refer to measurements with vertical stimuli of 0.09 c/deg, positioned 10” into the nasal visual field. Viewing was monocular, with the right eye. Sensitivities at all phases was about 7 dB lower than those for the same

DS

0 l

0 -0

c *

I I , 0 I.5 90

PHASE (deg 1

E 1000

- 300

= 100

-30

- 10

Fig. 4. Sensitivity for contrast reversal of multi-harmonic stimuli as a function of phase 4. Solid circles: vertical gratings of 0.09 c/deg, lo” inferior field (from Fig. 3). Open squares: vertical gratings of 0.09 c/deg, 10” nasal field, monocular viewing (right eye). Solid triangles: vertical gratings of 0.5 c/deg, 10” inferior

field. In all conditions, discrimination sensitivities were similar at all three phases.

438 M CONCETTA

stimuli viewed binocularly in the inferior field (solid circles), but the decrease was the same for all phases. Again, there was no dependence on stimulus phase. The decreased sensitivity prob- ably results partly from the monocular viewing, partly from the higher contrast sensitivity to radially oriented gratings. (Thibos and Ross, personal communication), and partly from the fact that the “features” were in fact more per- ipherai for tangential than for radial stimuli.

Berardi and Fiorentini (1988) and Bennett and Banks (1989) have observed that phase disc~mination (for stimuli comprising only two harmonics) depends on stimulus orientation. Discrimination sensitivity was higher for radially oriented gratings, more than could be ac- counted for by variation in contrast sensitivity. Furthermore, Bennett and Banks (1989) report that the difference between sine and cosine disc~minations disappear when stimuli point towards the fovea. Under the conditions of our experiments, we observed no such difference. Irrespective of the spatial frequency or position of the stimuli in the visual field, reversal discrimination sensitivity was independent of stimulus phase.

The results reported here differ markedly from those of Bennett and Banks (1987), yet the procedures were very similar. The major difference in the experiments was the spectral composition of the stimuli. Our stimuli comprised 256 odd harmonics, bandpass filtered, whereas those of Bennett and Banks comprised only two harmonics (1st plus 2nd). We therefore repeated our experiment with vertical stimuli made up by summing two cosine waves, one twice the frequency of the other (equation 2).

Fig. 5. Discrimination sensitivities for contrast reversal of vertical compound gratings comprising only two harmonics. The gratings were made up by adding two cosinusoidal waveforms (equation 2). Phase (represented by the abscissa) refers to the phase of both harmonics at origin (the point of phase congruence). Spatial frequency of the fundamental was 0.092 c/deg {open circles) and 0.53 c/deg (solid

triangles). Eccentricity was IO”, inferior field.

MORRONE et al.

The contrast of the second harmonic was always half that of the first harmonic (a slight variation from the procedure of Bennett and Banks). The measurement procedure was identical to that used for multi-harmonic stimuli.

Figure 5 plots the results as contrast sensitivity for discrimination (inverse of contrast at threshold) on a logarithmic axis, against phase l;b. The solid triangles show results for two-component stimuli of spatial frequency 0.5 c/deg (l/3 that used by Bennett and Banks at this eccentricity), the open symbols for the same stimuli at 0.09 c/deg. At the higher spatial frequency, our results were similar those of Bennett and Banks. Discrimination thresholds for gratings in sine phase (90”) were much higher than for those in cosine phase (00). The difference was 26 dB for MCM and 16 dB for DS. However, at the lower spatial frequency, the difference disappeared: thresholds for sine and cosine discriminations were similar, within 1 or 2dB.

Thus while we were able to confirm Bennett and Bank’s result under some conditions, it is clear that the difference between sine and cosine thresholds in the periphery depends strongly on the nature of the stimuli used. It occurred only for two-harmonic stimuli, at certain spatial frequencies. This result casts some doubt on the major conclusion of Bennett and Banks, that detectors in the peripheral field are pre- dominantly in cosine phase (even-symmetric receptive fields).

Facilitation

In the previous paper (Burr et al., 1989) the mechanisms subserving phase discrimination

DS 100


were investigated by measuring contrast reversal discrimination in the presence of a pedestal stimulus of orthogonal phase. This section reports similar measurements in the peripheral field (10” inferior). Contrast discrimination thresholds were measured for test stimulus pairs with phase $I of O-180”, 45-225” and 90-270”, in the presence of a pedestal of phase 4 90”, 315” and 0” respectively. Spatial frequency was 0.09 c/deg.

Figure 6 plots discrimination sensitivity for the three phases against pedestal contrast. The pattern of results is clearly different from that observed with central viewing. With central viewing, marked facilitation occurred only for 45-225” discriminations, whereas in the periphery the pedestal facilitated discrimination greatly at all phases.

The strategies used by observers to make the discrimination is of interest. All stimuli ap- peared to be edges, lines or combinations of both. Observers based their judgments on the apparent polarity of the lines or edges. The task was subjectively similar to the fovea1 measurements.

In the previous paper the selective facilitation was interpreted as evidence for the existence of independent detectors in sine and cosine phase. Applying the same logic here would suggest that in the periphery, detectors are tuned to phases other than sine and cosine. However, this conclusion is not supported by the subjective reports of the observers.

Phase discrimination

Phase can be studied either by measuring contrast thresholds for discriminating stimuli of a fixed phase difference (such as those described above), or by measuring phase discrimination thresholds for stimuli of fixed contrast. Both types of thresholds have been measured for stimuli comprising few harmonics (e.g. Burr, 1980; Lawden, 1983; Badcock, 1984a, b).

The discrimination thresholds in the presence of a pedestal can be expressed as phase discrimination thresholds (see Fig. 1 and methods section for details). Thus the results of the pedestal experiments of this and the previous paper can be replotted as phase thresholds as a function of stimulus contrast. Figure 7 shows phase discrimination thresholds for a stimulus of 0.25 c/deg, viewed centrally (from Fig. 6, Burr et al., 1989), and Fig. 8 for a stimulus of 0.09 c/deg, viewed lo” peripherally (from Fig. 6, this paper). The three separate curves plot thresholds measured at three mean phases (given by the pedestals: 0, 90 and 315”).

The results for central and peripheral viewing were similar. For all three average phase angles, phase discrimination improved greatly with increasing contrast. At low contrasts (near detection threshold), phase thresholds approached 180”. At higher contrasts, phase thresholds decreased steadily with contrast (as observed by Tyler and Gorea, 1986) to plateau below 10” for both central and peripheral viewing.

‘g

; 3oo wa z 100 I 8 h

+i_fi

p 3co & --------___ _

10oJ T, r ,111111, 1 ,,,in 0 0.001 aco3 0.01 0.03

PEDESTAL

T, I , ,,I ,,I, , , I ,,n 0 0.001 o.co3 0.01 0.03

CONTRAST

Fig. 6. Contrast sensitivity for discriminating contrast reversal of test gratings superimposed on pedestal gratings of orthogonal phase. For the upper curves, #J of the test grating phases was 0” and 180”, with the pedestal phase I$ = 90”; for the middle curves, test phases were 45 and 225”, pedestal 315”; for the

lower curves, test phases were 90 and 270”, pedestal 0”. The abssisca plots pedestal contrast.

“A. 29,4-E


1 i , . ..,..* 1.-.1

0001 0.0 1 0.1 0.001 0.01 01

CONTRAST

Fig. 7. Phase. sensitivity as a function of stimulus contrast, for multi-ha~onic gratings of 0.25 c/de&, viewed foveally. The data were taken from Fig. 6 Burr et 01. (1989), and reexpressed as phase thresholds (see Fig. 1, methods section). The mean phase was: 0” (open circles), PO” (open squares) or -45” (solid

triangles). Standard errors were about the size of the symbols.

Note that for average phases of 0 and 90” (cosine and sine pedestals), the two stimuli to be discriminated were mirror symmetric, and hence had identical second-order statistics. For the mean phase of -45”, however, the patterns were not mirror symmetric (one was more bar- like, the other more edge-like). With peripheral viewing, their was no significant difference between phase thresholds for the three mean phases. With central viewing, discrimination was slightly better for the -45” phase at the higher contrasts. This reflects the greater

j

MCM 300

facilitation of the 45-225” discrimination by a pedestal or orthogonal phase than was observed for the O-180” or 9s270” discriminations (see Fig. 6, Burr et al., 1989). These results are quite different from those of Rentschler and Treutwein (1985), who reported that discrimination thresholds of mirror symmetric patterns (comprising only two harmonics) was selectively impaired with peripheral viewing.

The spatial frequencies used for central and peripheral phase disc~mination thresholds were different. As the contrast sensitivity for de-

!-

-1w

-30

=lO

CONTRAST

Fig. 8. Phase ~n~ti~ty as a function of stim~us contrast, for m~ti-ha~oni~ gratings of O.~c~deg, viewed peripherally (10’ inferior field). The data were taken from Fig. 6 and reexpressed as phase thresholds (see Fig. 1, methods section). The mean phase was: 0” (open circles), PO” (open squares) or -45” (solid triangles). Note that for mean phases 0 and 90”, the gratings to be discriminated were mirror symmetric, and hence had the same second-order statistics. For mean phase -45”, the patterns were not

mirror symmetric. Standard errors were about the size of the symbols.


tection in the two conditions was not the same (see Fig. 2), it is difficult to parallel the two sets of results. For this reason we measured phase sensitivity as a function of spatial frequency, for central and eccentric viewing. The procedure was similar to that just described, except that the contrast of the stimulus (test plus pedestal) was kept constant throughout the experiment (see methods). Measurements were made at two contrasts, 0.01 and 0.02.

The results are shown in Fig. 9. Under all conditions, the curves had a similar form. Phase thresholds increased with spatial frequency, more rapidly as the stimulus approached acuity threshold. Both for central and peripheral viewing, the effect of stimulus contrast was to cause a vertical shift in the curves, decreasing phase thresholds.

The effect of eccentricity was interesting. At both contrasts, the sets of curves measured with fovea1 and eccentric viewing were similar in shape, but displaced horizontally along the abscissa. The displacement was about 0.7 log units, implying a multiplicative factor of about 5. This shift is similar to that required to match contrast sensitivity for central and 10” peripheral viewing. Thus, under the conditions of this experiment, phase thresholds scale with eccentricity in a similar way to contrast thresholds.

A

DISCUSSION

The major results of this paper can be sum- marized as follows:

(1) In peripheral vision, discrimination thresholds for contrast reversal of multi- harmonic stimuli were independent of the phase of the stimuli, and similar to detection thresholds.

(2) Phase discrimination thresholds in the periphery did not depend on the second-order statistics of the patterns.

(3) Addition of a pedestal stimulus, of phase orthogonal to the test stimuli, facilitated peripheral discrimination of contrast reversal. The amount of facilitation was independent of test phase.

(4) When appropriately scaled for spatial frequency, peripheral phase thresholds were identical to central phase thresholds. The scaling factor was the same as that required to equate contrast sensitivity.

The major difference between the results of this study (peripheral viewing) and those of Burr et al., 1989 (central viewing) was that in the periphery, addition of a pedestal of orthogonal phase always caused strong facilitation, whereas for central viewing, strong facilitation failed to occur for test stimuli of 0 or 90” phase. In the

SPATIAL FREQUENCY (c/deg)

Fig. 9. Phase discrimination thresholds as a function of spatial frequency. Closed symbols: fovea1 viewing; open symbols: 10” inferior field. Stimulus contrast was 0.01 for the upper curves, and 0.02 for the lower curves. Spatial frequency was varied by varying viewing distance. 1.2 cycles of grating were displayed. At both contrasts, the peripheral curves almost superimpose the central curves when shifted laterally by about

0.7 log units. Thus scaling for spatial frequency equates central and peripheral phase thresholds.


previous paper (Burr et al., 1989) it was argued that the absence of facilitation with 0 and 90” stimuli implied that the detectors responsible for the discrimination task were all of sine or cosine phase: i.e. had even- or odd-symmetric fields. By applying the same logic, facilitation for the 0 and 90” phase discriminations in peripheral viewing could imply the existence of detectors in the periphery tuned to phases other than sine or cosine: i.e. detectors with asymmetric receptive fields.

However, this does not agree with subjective reports of observers, Both for central and peripheral discriminations, the strategy employed was to look for lines and edges, and try to identify their strength or polarity. The appearance of the stimuli did not change with eccentricity. Thus while it is possible that the peripheral discrimination tasks were mediated by detectors with asymmetric receptive fields, the perceptual impression remains one of lines and edges. We cannot exclude the possibility that coma-like optical aberrations in the periphery caused small phase shifts in the stimuli, leading to this result.

The most surprising aspect of this study was that phase discrimination thresholds were very good at 10” eccentricity, and they did not depend on stimulus phase. These results are contrary to those reported by both Rentschler and Treutwein (1985) and Bennett and Banks (1987). Rentschler and Treutwein reported that peripheral phase discrimination thresholds depended critically on the mean phase of the stimuli (for stimuli comprising 1st plus 3rd harmonics). At 2” eccentricity, phase discrimination was impossible around mean phases* of 0 or 90”: for these mean phases, the patterns to be discriminated were mirror symmetric, and thus have identical second-order statistics (Julesz, 1981). The same argument applies for our stimuli, as they also contained only odd harmonics. Stimuli with mean phases of 0 or 90” were mirror symmetric, while those with mean phase 45” were not. Yet discrimination thresholds in the periphery were similar for all three mean phases (Fig. 8). For central viewing there was a slight advantage for 45” mean phase at

*Rents&ler and Treutwein used a different definition of

phase from that described here. They referred to the phase of the third sinusoidal harmonic at the point where the fundamental sinusoidal harmonic had phase zero (rather than the phase of the cosine harmonics at the point where all phases were identical). 0” by their definition becomes k 90” by our definition; 90” becomes 45 or 225”; and 180” becomes 0 or 180”.

some contrasts (Fig. 7), reflecting the greater

facilitation that occurred in that condition.

Similarly, Bennett and Banks reported that discrimination of 180” phase shifts in stimuli comprising the first and second harmonics increased dramatically with eccentricity when the harmonics were in sine phase, whereas thresholds for cosine discriminations remained relatively constant. For their stimuli (which have an even harmonic), patterns in ksine phase are mirror symmetric, while those in + cosine phase (or any other phase) are not. In this respect, their results were similar to those of Rentschler and Treutwein. We were able to replicate Bennett and Bank’s results with two-harmonic stimuli, but only at certain spatial frequencies. At low spatial frequencies, the difference between sine and cosine discriminations thresholds vanished. For multi-harmonic stimuli, the phase of the stimuli had no effect on discrimination thresholds, at any resolvable spatial frequency.

These results question the conclusions drawn by both Rentschler and Treutwein and Bennett and Banks: that phase sensitive mechanisms are deficient or lacking in the periphery. When stimuli were appropriately scaled in spatial frequency, phase sensitivity in the periphery was as good as that for central vision. The scaling factor necessary to equate the two was identical to that required to align contrast sensitivity. Thus it would seem to be more probable that the results obtained with two-harmonic stimuli were peculiar to the type of stimuli chosen, and cannot be generalized to reflect visual phase sensitive mechanisms. The question remains as to why these stimuli cause difficulties for peripheral vision.

Phase and position have often been loosely equated (e.g. Klein and Tyler, 1981; Hilz et al.,

1981; Julesz, 1981; Tyler and Gorea, 1986). However, except for pure sinewaves, phase does not imply position or vice versa. For example, the stimuli of this study varied in phase but not in position. As Fig. 1 of Burr et al. 1989 shows, variation in phase changed the nature of the stimulus (from edge to bar), but caused no apparent displacement of the feature (see also Morrone and Burr, 1988). The use of this type of stimulus clearly distinguishes phase from relative position. However, the stimuli of many previous studies do not distinguish the two so clearly. It therefore is possible that the supposed poor peripheral phase resolution reported by previous investigators is more a consequence of


positional uncertainty in the periphery, rather than a deficit in phase sensitive mechanisms per se.

There exists evidence to suggest that human observers are uncertain about the spatial location of peripheral targets but not fovea1 targets. For peripheral viewing, experimentally introduced positional uncertainty has little effect on detection threshold: thresholds for targets presented at a single and constant location are the same as for targets whose position is randomized from trial to trial over an extensive area (Mertens, 1956; Shiffrin et al., 1976; Pelli, 1981). This suggests that the peripheral retina has high intrinsic positional uncertainty, so adding further uncertainty has little effect. In the fovea, however, randomizing the position of target presentation over 160 non-overlapping positions raises thresholds by a factor of 10 (Cohn and Wardlaw, 1985), implying low intrinsic positional uncertainty in central vision. Levi et al. (1987) draw a similar conclusion from measurements of bisection acuity. Coarse sampling of the targets (increasing uncertainty) had little effect on fovea1 discriminations, but increased signifi- cantly peripheral discrimination thresholds. They suggest that the positional uncertainty may result from cortical under-sampling in the periphery.

Positional uncertainty could impede phase discrimination under some circumstances, particularly for periodic stimuli with few harmonics. For example, Fig. la of Rentschler and Treutwein (1985) shows that for mean phase 90”, the patterns are squarewave-like with light and dark bars superimposed on the edges. To distinguish between these two patterns observers must be able to localize the various edges and bars in space. When the mean phase of the cosine harmonics is 45”, however, the patterns to be discriminated are quite different (Fig. lb, Rentschler and Treutwein): one is edge-like, the other bar-like. This discrimination could be made on a global basis, without the need to localize particular features of the stimulus. A similar argument applies to stimuli comprised of the 1st and 2nd harmonic, used by Bennett and Banks.

The multi-harmonic stimuli of this study should reduce positional uncertainty. Only two “features” were displayed, separated by extensive blank patches (see Fig. 2, Burr et al., 1989). Because of the bandpass filtering, the periodicity of the patterns was large compared

with the weighted-mean spatial frequency. This may have aided spatial localization, reducing any detrimental effect resulting from peripheral positional uncertainty.

The repetitive nature of two-harmonic stimuli (with the periodicity of the repetition at a similar frequency of that of the component harmonics) may also cause spatial interference with the discrimination task. Many spatial discrimination tasks are impaired when the test stimuli are flanked by other stimuli, positioned at appropriate distances, particularly for peripheral viewing (e.g. Westheimer and Hauske, 1975; Bouma, 1970; Banks et al., 1979). In this study, 90-270” phase discrimination of two harmonic stimuli was selectively impaired for stimuli of 0.53 c/deg (periodicity 11 min), but not for stimuli of 0.092 c/deg (periodicity 114 min). This is quantitatively consistent with recent measurements of spatial interference of vernier (Levi et al., 1985) and bisection acuities (Yap et al., 1987b). At 10” eccentricity, interference extends to about 60 min arc.

Bennett and Banks (1989) have recently reported that phase discrimination depends strongly on stimulus orientation. When stimuli are oriented radially with respect to the fovea, the difference between sine and cosine discrimination thresholds is much reduced. We did not replicate this finding with multi-harmonic stimuli. Discrimination thresholds did not depend on mean phase, either for radially or tangentially oriented stimuli. Again the difference in the results suggest that the orientation dependent effect reported by Bennett and Banks may reflect positional uncertainty rather than phase insensitivity. It is possible, for example, that with radially oriented stimuli, observers can make use of the fovea as a reference point, reducing positional uncertainty. With tangentially oriented stimuli, the fovea would be a less useful reference. Interestingly, acuity for curvature detection and for line bisection both depend on stimulus orientation (Fahle, 1986; Yap et al., 1987a). This may be a general property of the positional acuities.

In many respects, the vision of amblyopes resembles that of the periphery of normal observers (Levi and Klein, 1985), and it has been claimed that amblyopes have poor phase sensitivity (Lawden et al., 1982). However, these studies have used periodic stimuli with only two harmonic components, which may present problems such as spatial interference, discussed

444 M. CONCETTA Mc

above. It is possible that the high thresholds for phase discrimination of amblyopes to these stimuli does not reflect a real impediment of phase sensitive mechanisms. It would be worth- while to measure phase selectivity with stimuli such as those used in this study.

To conclude, the experiments of this study show that peripheral phase discrimination thresholds are similar to fovea1 thresholds, pro- vided that the stimuli are scaled appropriately. This result holds irrespective of the mean phase or second-order statistics of the stimuli. The amount of spatial scaling required to equate central and peripheral phase sensitivity is the same as that required to equate contrast sensitivity. Phase sensitivity varies with retinal eccentricity at a rate commensurate with contrast sensitivity and grating acuity, much less than positional acuities. This is consistent with the suggestion that phase discriminations are mediated by discriminating the amplitude of the response of quasi-linear filters. As thresholds for discrimination of 180” phase differences were similar to detection thresholds, it is plausible that the same filters mediate both tasks (cf. Tyler and Gorea, 1986).

Acknowledgements-We thank Professor John Ross for fruitful discussions during these experiments and Dr Adriana Fiorentini for helpful comments on the manuscript. DB was supported by the Australian NH&MRC, MCM by the Australian Department of Science and DS by the Italian CNR.

REFERENCES

Badcock D. R. (1984a) Spatial phase or luminence profile discrimination? Vision Res. 24, 613623.

Badcock D. R. (1984b) How do we discriminate spatial phase? Vision Res. 24, 1847.

Banks W. P., Larsen D. W. and Prinzmetal W. (1979) Asymmetry of visual interference. Percept. Psychophys.

25, 447456.

Bennett P. J. and Banks M. S. (1987) Sensitivity loss in odd-symmetric mechanisms underlies phase anomolies in peripheral vision. Nature, Lond. 326, 873-876.

Bennett P. J. and Banks M. S. (1989) Personal communication. Vision Res. (Submitted).

Berardi N. and Fiorentini A. (1988) Laterization and orientation bias in the discrimination of mirror symmetric complex gratings (abstr.). Perception (In press).

Bouma H. (1970) Interaction effects in parafoveal letter recognition. Nature, Lond. 226, 177-178.

Braddick 0. J. (1981) Is spatial phase degraded in peripheral vision and visual pathology? In Pathophysiology of the

visual sysrem (Edited by Maffei L.). Junk, The Hague. Burr D. C. (1980) Sensitivity to spatial phase. Vision Res. 20,

391-396.

Burr D. C., Morrone M. C. and Spinelli D. (1989) Evidence for edge and bar detectors in human vision. Vision Res.

29, 419431.

NUtONE et al.

CamPbell F. W. and Robson J. G. (1968) On the apphcatton of Fourier analysis to the visibility of gratings. J. Phy.rio(.. Lond. 197, 551-556.

Cohn T. E. and Wardlaw J. C. (1985) Effect of large spatial uncertainty on fovea1 luminance increment detectability. J. opt. Sot. Am A2, 820-825.

Dow B. M., Snyder R. G., Vautin R. G. and Bauer R. (1981) Magnification factor and receptive field size in fovea1 striate cortex of the monkey. Expl Brain Res. 44,

213-228.

Fable M. (1986) Curvature detection in the visual field and a possible physiological correlate. Expl Brain Res. 63, 113-124.

Field D. J. and Nachmias J. (1984) Phase reversal discrimination Vision Res. 24, 333-340.

Hilz R., Rentschler I. and Brettel H. (1981) Insensitivity of peripheral vision to spatial phase. Expl Brain Res. 43,

111-114.

Julesz B. (1981) Textons, the elements of texture perception, and their interactions. Nafure, Lond. 290, 91-97.

Klein S. A. and Tyler C. W. (1981) Phase discrimination of single and compound gratings. Invest. Ophthal. visual Sci.

S20, 124.

Lawden M. C. (1983) An investigation of the ability of the human visual system to encode spatial phase relationships. Vision Res. 23, 145 l--1463.

Lawden M. C., Hess R. F. and Campbell F. W. (1982) The discrimination of spatial phase relationships in amblyopia. Vision Res. 22, 1005-1016.

Lawton T. B. (1984) The effect of phase structures on spatial phase discriminations. Vision Res. 24, 139-148.

Lawton T. B. (I 985) Spatial-frequency spectrum of patterns changes the visibility of spatial-phase differences. J. opt.

Sot. Am. AZ, 114@-1152.

Levi D. and Klein S. A. (1985) Vernier acuity, crowding and amblyopia. Vision Res. 25, 979-991.

Levi D. M. and Klein S. A. (1986) Sampling in spatial

vision. Nature, Lond. 320, 360-362.

Levi D. M., Klein S. A. and Aitsebaomo A. P. (1985) Vernier acuity, crowding and cortical magnification. Vision Res. 25, 963-977.

Levi D. M., Klein S. A. and Yap Y. L. (1987) Positional uncertainty in peripheral and amblyopic vision. Vision

Res. 27, 581b591.

Mertens J. J. (1956) Influence of knowledge of target location upon the probability of observation of peripherally observable test flashes. J. opt. Sot. Am. 46,

1069-1070.

Morrone M. C. and Burr D. C. (1988) Feature detection in human vision: a phase dependent energy model. Proc. R.

Sot. Lond. B235, 221-245.

Morrone M. C. and Burr D. C. (1989) Predicting contrast thresholds from local energy. (In preparation).

Morrone M. C. and Owens R. (1987) Feature detection from local energy. Pattern Rec. Lett. 1, 103-I 13.

Pelli D. G. (1981) The effect of uncertainty: detecting a signal at one of ten-thousand possible times and places. Invest. Opthal. visual Sci. S20, 178.

Perry V. H. and Cowey A. (1985) The ganglion cell and cone distributions in the monkey’s retina: implications for

central magnification factors. Vision Res. 25, 1795

1810. Rentschler I. and Treutwein B. (1985) LOSS of spatial phase

relationships in extrafoveal vision. Nature Land. 31%

308-310. 8hifffin B. M., MacKay D. P. and ShafTer W. 0.


(1976) Attending to forty-nine positions at once. J. exp. Psychol. 2, 14-22.

Tyler C. W. and Gorea A. (1986) Different encoding mechanisms for phase and contrast. Vision Res. 26, 1073-1082.

Virsu V. and Rovamo J. (1979) Visual resolution, contrast sensitivity, and the cortical magnification factor. Expl Brain Res. 37, 475-494.

Watson A. B. and Pelli D. G. (1983) QUEST: a bayesian adaptive psychometric method. Percept. Psychophys. 33, 113-120.

Westheimer G. and Hauske, G. (1975) Temporal and spatial interference with vernier acuity. Vision Res. 15, 1137-1141.

Yap Y. L., Levi D. M. and Klein S. A. (1987a) Peripheral hyperacuity: isoeccentric bisection is better than radial bisection. J. opt. Sot. Am. A. 4, 1562-1567.

Yap Y. L., Levi D. M. and Klein S. A. (1987b) Peripheral hyperacuity: 3-dot bisection scales to a single factor from O-10 degrees. J. opt. Sot. Am. A. 4, 1562-1567.

discrimination of spatial phase in central and peripheral vision

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