The use of different cues in vernier acuity

b'kron F&L Vol. 23, No. IO. pp. 991~-995. 1983 Printed in Grear Britam. Ail rights reserved

0042-6989.83 $3.00 +O.OO

CopyrIght c 1983 Pergamon Press Ltd

THE USE OF DIFFERENT R. J. Department

WATT,

M.

of Psychology,

CUES IN VERNIER

J. MORGAN

University

and R. M. College,

(Receilled 8 October 1982; in recised,form

Cower

ACUITY

WARD*

Street.

London

I February 1983)

Abstract-The roles of the various cues in the traditional vernier target are examined. We conclude that there are at least two mechanisms by which vernier acuities of the order of 5 set arc may be obtained. The two cues are the overall slope of the target, and the relative positional differences. By using vernier targets that are degraded in two different ways, we can demonstrate each mechanism. Vernier

Corner

blur

Orthoaxial

Orientation

position

INTRODUCTION

The vernier target is rich in cues for response and there are many ways in which an offset might be detected. We shall consider three important cues. First, one could separately assess the position of each bar in a direction at right angles to the target axis, and then compare the two. This we shall call the relutire position cue. Secondly, one could assess the overall slope of the target, for example by obtaining the best fitting linear regression to the target. The direction of this slope away from the vertical would code the offset direction. This we shall call the absolute orientution cue. Lastly, one could assess the slope of the component bars and compare with the overall slope of the target, or with the slope of an imaginary line joining the two inner ends of the bars (if a gap is present). This we shall call the relative orientution cue. Sullivan et nl. (1972) have compared the performance of vernier acuity (their own data). curvature detection (data from Ogilvie and Daicar, 1967), and three dot alignment (data from Ludvigh, l953), and conclude that performance in each case is limited by the accuracy with which orientation cues are represented in the visual system. In order to reach this conclusion, they make a number of geometric assumptions about the orientation cue used. They plot threshold slope distortion (defined separately for each task) as a function of line length, and claim that the functions obtained for the various tasks coincide. Westheimer (Westheimer and McKee, 1977b; Westheimer, 1981) has also recently attempted to formulate a single hypothesis to account for the various pattern acuities. He suggests that the underlying principle is that the location of any two features may be related with high accuracy, provided that they are not more than 5 min arc apart. In support of this, the effects of gap size and line length on vernier acuity, criterion separation on separation discrimination and target size on slope acuity are marshalled together. *Universite du Quebec “R

23’10

t

a Trois

Rivieres,

Quebec,

Canada. 991

Andrews et al. (1973) compared vernier acuity, curvature detection, chevron detection and three dot alignment and contrasted the similarities between the performance of these tasks with that of slope comparison. Their major conclusion is that slope sensitivity is not high enough, particularly for longer lines, for the use of slope cues in curvature detection, chevron detection and three dash alignment. They also argue that vernier acuity (without a gap) is only in part consistent with the use of an absolute slope cue. Relative efficiency for the performance of the former four tasks follows approximately the same function with increasing line length. Relative efficiency is approximately constant for lengths up to 25-30min arc, and then falls rapidly. In contrast, relative efficiency for line slope discrimination remains high for line lengths up to only 10 min arc. This discrepancy is interpreted as indicating two different sources of information. One is orientation; the other they describe as “collinearity failure”, but reserve judgment about the usefulness of such a label. Watt and Andrews (1982) have suggested that there are at least two (and perhaps three or more) independent mechanisms, each of which supports a range of tasks with high precision. One is a system that analyses positional information within a limited region of space and only across the axis of a nearly straight target. This information they term “orthoaxial” and they argue that coaxial position is not available in the output from this system. Orthoaxial position information is analyzed with uniform efficiency (or weighting) over a range of 20min arc. A second system would be a slope and position analyser, to provide slope and curvature comparisons. We have produced a series of vernier targets with the abruptness of the corner break or offset degraded by varying amounts in order to examine these conflicting views in the following fashion. (I) The suggestion of restricted usefulness of the absolute slope cue in vernier acuity was tested and confirmed by comparing performance when the over-

all slope was fixed or varied from trial to trial. For the more highly degraded stimuli, performance was worse when the slope was not fixed, thereby demonstrating the use of the absolue slope cue. For the less highly degraded stimuli, performance was the same in both conditions. indicating an alternative cue. (2) We then examined the quantitative effect of the degradation on acuity, and found it to be more consistent with relative position than relative orientation cues. METHODS

The observers were two of the authors (R.J.W., M.J.M.), who have normal uncorrected vision.

is removed from the target. The appearance of a classical vernier target is contrasted with one having corner blur in Fig. I. The overall length of the target was 30 min arc and two basic conditions were employed. Thresholds were measured either with the overall orientation of the target fixed (horizontal) from trial to trial, or with it randomly assigned within the interval k4 of horirental. For values of oH greater than about 7.5 min arc, the corner blur function will not reach 0 and 100°C,within the length, but in all cases quoted thresholds refer to the displacement between the ends of the line, and are thus smaller than the threshold expansion c factor for these large blur cases. information

.4ppuratus

Targets with a snot

were generated

on a display

si7e of less than

oscilloscope

0 3 mm (Hewlett-Pgrkgrrl

1333a) and a fast decay PI 5 phosphor. For a description of the MTF of this display see Morgan and Watt (1982). Viewing was from a distance of 114 cm and was binocular. The display was controlled by digital to analogue converters (DACs) from a CA1 LSI 2120G minicomputer and refresh rate was 200 Hz. Luminance of the bars (40 ft-L) was established by a microphotometer (United Detector Technology) and was controlled by an additional DAC connected to the Z-modulation input of the oscilloscope. Details of the method used to produce corner blur in the target are given in a separate Appendix. Observers lay supine and observed the display through a mirror placed at 45 above their head. Ordinary room lighting (fluorescence tubes) provided background illumination, ensuring that all observations were carried out at photopic levels.

The observer’s task on each trial was to report, by pressing the appropriate one of two switches, whether the left half of the target was above or below the right half of the target, taking into consideration (in the variable slope condition) any random rotation of the entire target away from horizontal. Over a series of 80 trials, preceded by 20 practice trials, the cue was randomly varied in sign and magnitude, in order to obtain a psychometric function. An adaptive version of the Method of Constant Stimuli (APE) was used (see Watt and Andrews, I98 I for details), and Probit Analysis (Finney. 1971) was used to determine the standard deviation of the psychometric function (83”,, correct point), defined as the threshold. Four independent thresholds were determined for each condition and each final datum represents the RMS of these estimates. with the standard deviation of their distribution serving as the standard error (typically less than 15”,, of the standard deviation).

Stimuli

The classical vernier step function in space

target can be described

T(.u) = 1./2

(O
T(S)=

(-15
-c/2

&pearance

as a

< 15min)

where c is the size of the offset cue, the direction of which the subject is required to detect. One can easily generalize from this stimulus to any displacement function, and we have chosen the series of normal cumulative sigmoid functions

I

---:.7 Y

i

I(-l5
X

< 15min).

When gB equals zero this defines the classical target. Increasing the corner blur, as we shall term this constant. has many effects: the range of orientations present is reduced; the size of the offset cue at points separated by 5 min arc is reduced; and positional

Fig. I. The figure illustrates the appearance of the stimuli used in the present study. one with a corner blur of zero and the other

with il moderate

corner

blur.

993

The use of different cues in vernier acuity MJH

25

/

/

/

/

/

/

/

/

S,Op

-0

FandO”,

x-x

fixed slope

2.5j !!I

5

lk

lb

CORNER BLUR SD. IMINd RJW ,

/

2.51 b

5

e

1%

CORNER 6LUR S.D (MIN.1

Fig. 2. Thresholds for offset as a function of corner blur, for the two conditions of fixed and random slope. Error bars represent & 1SE. Note the log scale.

When sharp corner detail is present, performance is unaffected by randomising overall target orientation, but when it is absent, performance is adversely affected. In the latter condition, subjects judged the overall slope of the target, when this was helpful, but had to use an alternative cue when it was not. Our major conclusion then is that there are two cues available and used, in vernier acuity. The first is the overall orientation cue, which provides higher precision than the second only when the target has been considerably degraded. The trend in acuity as corner blur is increased is informative and allows us to seek this second cue. Consider first the relative orientation cue, a possibility raised by Sullivan ef al. (1972). In Fig. 3, we show the difference between the two extreme orientations contained in each of our stimuli, at the threshold offset we have measured. This amounts to the largest available relative orientation cue in the stimulus at threshold offset. From the hypothesis of Sullivan es al., the function should be constant, or near constant at a rotation angle of about 20 min rotation. But, our data show that the subjects failed to detect much larger cues than this in some conditions, and succeeding in detecting much smaller cues in other conditions. Some small discrepancy at the smallest corner blur might be expected from the effects of optical blur, but this does not account for the major trends of the figure. Thus, the local slope hypothesis cannot account for our data. It therefore follows that relative position is the second cue. We are further able to discriminate between the two alternative accounts for the sensitivity to relative position, that of Westheimer and that of Andrews. The basic hypothesis of Westheimer is that hyperacuity is governed by the distance between separate features, the optimum distance being 5 min arc. In

RESULTS

Thresholds for the two observers as a function of corner blur are shown in Fig. 2. The two conditions of fixed and random slope are plotted together. Error bars represent + 1 SE. Thresholds are not different in the two slope conditions up to corner blurs of 6.5 min arc. Up to this point, log threshold rises linearly with increasing blur. Beyond this point, there is no further increase in threshold for the fixed slope condition, but further linear increases in log threshold for the random slope condition. The plateau threshold in the fixed slope condition has the value 10sec arc, and corresponds to an absolute orientation cue of 20 min rotation.

B

si !z t-

10

\

e

d CDRNER BLURSD. fMIN.ARCl

DISCUSSION

Vernier acuity is adversely affected by any degree of corner blur and the highest acuity is obtained only when sharp corner detail is present in the target.

Fig. 3. The value of the maximum orientation cue available to the subject at threshold, as a function of corner blur, for the random slope condition. The cue is expressed as minutes of angular rotation. The cue varies considerably and it may

be concluded that it does not control performance.

K. J. WATT 01ril

994

our targets, the only separate features are the far ends of the targels. separated in all conditions by a distance of 30 min arc. Performance should be low. but unaffected by corner blur, quite unlike the results we have obtained. Clearly, Westheimer intends something dllferent by his hypothesis, since he ubes it to explain the high acuity obtained for vernier acuity targets (with sharp corners). The implication is that thcsc is a comparator with a span of 5 mm arc, that does not need feature separation. This hypothesis may be examined by calculating the largest spatial offset cue available to the subject, at his threshold, between two points separated by S min arc, for each of the conditions of corner blur. The resultant function is shown in Fig 4. Were the spatial distance hypothesis correct, this function should bc flat at 3.5 set arc (the baseline threshold in our data). The obtained function is not flat and in particular, a position comparator with a span of 5 min arc fails to detect olfsets that are much ~FPU~PF than 3.5 set arc. both when slope is fixed and randomly varying. Thcrc are therefore objections to the hypothesis of a spatially limited comparison process. Finally we turn to the hypothesis of Andrews ef ui. (1973) and its subsequent revision by Watt and Andrews (lY82). This hypothesis postulates that orthoaxial position information is collected and efficiently combined over a range of 30 min a!-c, enabling a subject to detect collineanty failure. The size of the orthoaxial position cue is obtained as follows. The stimulus is defined with respect to its own axis thus

o

MJtl

o-1

I 5

I

i

0

f

CORNER BLW4 SO.

1

1

10

15

(MIN.1

Fig. 5. The value of the integraled orthoaxial positlon cue available to the subject at threshold, as a function of stlmuluscornerblur The unttsemployed are square mmutes and the quantity is equivalent to the area between the target and Its linear regression axIs. There is little variation m the xx of the cut as corner blur changes, and it is concluded that orthoaxial position is the cue employed by the subjects.

The linear regression is defined thus

Orthoaxial

axis of the target, with slope U,

position

is then given by

O(x) = T(x) - A (x) and

the size of the orthoaxial

position

cue is obtained

from 15 10(-r) I .d.y

CC,= s

I(

This quantity was calculated numerically and its value at threshold for each of the subjects. as a function of corner blur is shown in Fig. 5. There is little effect of corner blur and it is hkely that orthoaxial position information controls performance in this task.

CONCLUSIONS

x

r-l t

b

s

*

RJW

0

MJM

1

rb

l\

CORNERBLUR[MFI.ARCI Fig. 4. The value of the maximum spatial displacement cue between two pomts separated by 5 min arc, available to the subject at threshold. Data for the random slope condltmn alone are shown. If the vtsual system were capable ofmakmg localional comparisons with a precision of 3.5 set arc (the baseline condition), between two points separated by 5 min MC. then the function should bc flat. In fact, III the larger corner blur conditions, a considerably larger cue IS needed.

(I) There are two distinct mechanisms involved in vernier acuity. (2) One is responsible for the discrimination of absolute slope cues in the target. (3) The other appears to operate on orthoaxial position information, as suggested by Andrews et al. (1973) and Watt and Andrews (1982). Arkno~~l~d~emenl-This work was supported bq Grant G979/870/N from the Medical Research Council REFERENCES

Andrcws D. P. (1967) Perception of contour orientation m the central fovea. Part 11. Spatial Integration. r/ision Res. 7.999-1013.

995

The use of different cues in vernier acuity Andrews D. P., Butcher A. K. and Buckley B. R. (1973) Acuities for spatial arrangement in line figures: Human and ideal observers compared. Vision Res. 13, 599620. Averili H. L. and Weymouth F. W. (1925) Visual perception and the retinal mosaic. II. The influence of eye movements on the displacement threshold. J. camp. Physiol. 5, 147-176.

Finney D. J. (1971) Probit Analysis, 3rd edn. Cambridge Univ. Press. Ludvigh E. (1953) Direction sense of the eye. Am. J. ~pb~hal. 36, 1399143. Morgan M. J. and Watt R. J. (1982) The modulation transfer function of a display oscilloscope: measurements and comments. Vision Res. 22, 1083-1085. Ogilvie J. and Daicar E. (1967) The perception of curvature. Can. J. Psychol. 21, 521-525. Tyler C. W. (1973) Periodic vernier acuity. J. Physiol., Land. 228, 637-647. Sullivan G. D., Oatley K. and Sutherland N. S. (1972) Vernier acuity as affected by target length and separation. Percept. Psychophys. 12, 438-444.

Watt R. J. and Andrews D. P. (I 98 1) APE: Adaptive probit estimation of psychometric functions. Curr. Psvchol. Rev.

stimulus position to fractions of a second of arc. We assume that the perceived location of a spot may be adequately described-by the centroid of its iigh~disper~ion‘ West~eime~ and McKee (1977a) and Watt and Morean (1983) have demonstrated‘that this is a valid approximation for narrow bars. Centroid location may be moved in two different ways. The first method is simply to move the position of the dot, and is limited by the resolution of the D to A converters. An alternative method is to compose each notional point on the display by two neighbouring unresolved spots on the screen, and to change the centroid position by altering their relative luminance. Because fine luminance control is available, effective shifts of centroid position corresponding to fractions of a second of arc can be readily achieved. To demonstrate the equivalence between these two methods of controlling position, Fig. 6 shows a comparison between them for one observer (R.J.W.) over the range of corner blurs used in the main experiment.

RJW

2

1, 205-214.

Watt R. J. and Andrews D. P. (1982) Contour curvature analysis: hy~ra~uities in the disc~mination of detailed shape. Vision Res. 22, 449-460. Watt R. J. and Morgan M. J. (1983) The assessment of visual location: theory and evidence. k’ision Res. 23, 97-109. Westheimer G. (1981) Visual hyperacuity. In Progress in Sensory Physiology I. Springer, Berlin. Westheimer G. and McKee S. P. (1977a)Integration regions for visual hyperacuity. Vision Res. 17, 89-93. Westheimer G. and McKee S. P. (1977b) Spatial configurations for visual hyperacuity. Vision RPS. 17, 941-947.

0

ii

lb

1%

CORNER BLUR S.D.(MIN.1

APPENDIX Methods .for producing corner blur The manipulation

2.51

of corner blur requires the control of

Fig. 6. Thresholds for offset for observer R.J.W., as a function of corner blur, for the two methods of stimulus generation.