Vuion Res. Vol. 32, No. 7, pp. 1319-1339, Printed in Great Britain

1992

0042-6989/92 $5.00 + 0.00 Pergamon Press Ltd

The Spatial Localization Deficit in Amblyopia ROBERT

F.

HESS,*

Received 20 September

IAN

E. HOLLIDAY*

1991

There have now been numerous reports of a spatial localization deficit in amhlyopia but none so far have tackled (1) the relationship between the contrast sensitivity and spatial localization deficits and (2) whether the spatial localization deficit is best described in units of visual angle or in terms of the underlying filter size. These issues are germane because they lie at the very heart of our understanding of the underlying deficit in amblyopia. To answer these questions we use spatially bandpass stimuli so that we can readily compare detection and localization for the same stimuli at each of a number of spatial scales. For some amblyopes (all strabismics and a minority of anisometropes) the contrast sensitivity defect neither underlies nor covaries with the spatial localization deficit. In the majority of anisometropic amblyopes, the contrast sensitivity loss is a complete description. The spatial localization deficit in amblyopia is of two independent kinds; positional inaccuracy and positional distortion. The positional inaccuracy deficit which can occur in varying degrees in both strabismic and anisometropic amblyopia, affects all spatial scales equally and therefore is best thought of in terms of a constant fraction of the underlying filter size in the space-frequency plane. The positional distortion deficit which can also occur to varying degrees in both strabismic and anisometropic forms can not be easily understood within this metric at least for strabismics. Amblyopia

Spatial

localization

Contrast

sensitivity

INTRODUCTION

The nature of the neural deficit underlying amblyopia has been keenly sought during the past two decades. This is because it has been realized that such an understanding would extend beyond the specific clinical condition to more basic areas of normal visual processing and in particular to its early development. There is general agreement on some issues and disagreement on others. It is generally agreed that human amblyopes have, to varying degrees, reduced threshold contrast sensitivity and spatial resolution (Levi & Harwerth, 1977; Hess & Howell, 1977 among others). This we will henceforth refer to as the contrast sensitivity deficit. It is also generally agreed that human amblyopia is a heterogeneous category having at least two main subdivisions: strabismic and anisometropic (Hess, Campbell & Zimmern, 1980; Hess, Bradley & Piotrowski, 1983; Hess & Pointer, 1985; Sireteanu & Fronius, 1981; Levi & Klein, 1982, 1985, 1990b). What is not generally agreed is whether or not this contrast sensitivity loss (with its associated suprathreshold consequences-see Hess & Bradley, 1980) represents the complete picture of the amblyopic deficit (Bradley & Freeman, 1985). To address this issue a number of investigators have assessed “positional accuracy” or “spatial localization” on the rationale that this

*McGill Vision Research Center, Department of Ophthalmology, McGill University, H4-14, 687 Pine Avenue West, Montreal, Quebec. Canada H3A 1Al.

Distortion

Spatial

scale invariance

represents a visual process that is fundamentally different from that which underlies contrast sensitivity. Some of these studies argue that the deficit is positional accuracy in amblyopia is explicable in terms of the known contrast sensitivity loss (Flom, Bedell & Barbeito, 1985-for anisometropic amblyopes; Levi & Klein, 1982, 1985, 1990bfor anisometropic amblyopes; Bradley & Freeman, 1985-for strabismic and anisometropic amblyopes; Wilson, 1986) whereas others argue that there is an additional defect in spatial coding (Hess, 1982-for both anisometropic and strabismic amblyopes; Watt & Hess, 1987-for anisometropic amblyopes; Levi & Klein, 1985, 1990b; Levi, Klein & Yap, 1987-for strabismic only; Sireteanu & Fronius, 1981; Fronius & Sireteanu, 1989; Lagreze & Sireteanu, 1991for strabismics only; Wilson, 199 l-for strabismics only). The explanation for this discord lies in two things. First, different studies have used different experimental approaches, not all of which have provided unambiguous measures of spatial localization. In most cases positional misalignment can be deduced from local spatial contrast cues. Not surprisingly in these cases the loss in spatial accuracy has been found to be explicable in terms of the known contrast sensitivity loss (Bradley & Freeman, 1985). Second, all stimuli so far used in these studies have been spatially broad-band (at least in the region where alignment is assessed) and this further complicates any understanding of the possible relationship between the contrast sensitivity and spatial localization deficits because one can never be sure that the same spatial mechanisms are responsible for detection of the

1319

I.720

ROBERI‘

F. HESS rind IAN

stimulus and for its spatial localization. This has in turn also lead to the default belief that the deficit in positional accuracy is purely spatial in nature and therefore best described in terms of a visual angle. These deficiencies have resulted in some confusion regarding what we think are two fundamental issues in this area; first, j,s the contrast sensitivity deficit the complete picture qf amhlyopia or are there independent deficits in spatial coding? Second, ly there is a separate deficit in spatial coding i.~ this best described in units of visual angle as it would [fit were a purely spatial akjicit or in relative units of the underlying filter size as it would if it were a space--frequency akjicit? In the present study we have set out to answer these questions concerning spatial localization deficits in amblyopia. To accomplish this we use (I) a task which is devoid of local spatial contrast cues so that a pure measure of spatial localizaton can be obtained (Toe& 1987; Hess & Holliday, 1992); and (2) spatially narrowband stimuli to ensure that the same spatial mechanisms underlie detection and localization of the stimuli. The results suggest that there exists in amblyopia (in all strabismics and some anisometropes) a true loss of spatial localization which is independent of the threshold contrast sensitivity for the same stimuli. This deficit can be subdivided into one concerning positional inaccuracy and another concerning positional distortion. The deficit in positional accuracy is scale invariant (i.e. it is best described in units of the spatial scale under which it is measured rather than in min of arc) in both strabismic and in the few anisometropes who display it, where as the positional distortion deficit is not easily understood in these terms (in strabismic amblyopia). METHODS Psychophysics All the stimuli were presented on a Joyce Electronics display screen with a P40 phosphor. The display was refreshed at 99 Hz, and had a vertical 100 kHz raster. The dimensions of the display area were 30 x 20 cm. The mean luminance of the display was 300cd/m’. The stimuli were generated by a Cambridge Research Systems VSG/Z graphics display controller (TMS34010/ TMS32OC25). The host was a Compaq 386/20. The display was viewed monocularly by the subjects in a room lit from above by tungsten light. Care was taken to eliminate reflections. In all the experiments the subjects responded to the stimuli by depressing the buttons of a Logitech “mouse”. Stimuli The stimuli were all patches of sinusoidal grating enveloped in both the x- and y-dimensions by a Gaussian envelope (see Fig. 1). These stimuli are referred to commonly as “Gabor” patches. The orientation of the grating component of the stimuli was vertical (see Fig. 1). stimuli of different spatial frequencies were scaled replicas of one another and hence are plotted and referred to by spatial scale. Similarly, the envelope was

E. HOLLIDA‘t

circularly symmetric. The form of the Ciabor functions was thus: G(x) = A

sin(x) exp[ --(x2 +_r’)i(>‘)]

ill

where A is the amplitude of the function, and s is the standard deviation of the Gaussian envelope defining the patch. The choice of sinusoidal modulation at sine phase ensures that there is no mean luminance component in the stimulus. The spread and spatial frequency of the patch was manipulated by changing the viewing distance to the screen. For viewing distances greater than 4 m the display was viewed using a mirror. Alignment accuracy In the experiments we measured the accuracy with which a single Gabor patch could be localized on the horizontal bisector of the mid-point of the line joining the centers of two outer vertically aligned patches (subpixel spatial accuracy was achieved by recomputing each newly located stimulus instead of simply repositioning the stimulus in the frame store). The measurements were derived either by a method of adjustment technique (unlimited viewing time) or by the method of constant stimuli in which the temporal presentation time was limited (Gaussian temporal window with a spread 200 msec). There are advantages and disadvantages to each technique. In the case of the method of adjustment, the subjects directly controlled the position of the central patch using the left/right mouse buttons. indicating when they had found a satisfactory alignment by pressing the central button. They quickly learn to make accurate settings, and a range of conditions can be studied in short time. The mean and standard deviation of the settings were calculated. the standard deviation being taken as the measure of the accuracy of alignment. In the method of constant stimuli, a set of stimuli (10 displacements) covering the range of interest is used, which in our case was the range over which the central patch was seen to change from being to the left to being to the right of alignment with the reference patches. The stimuli were presented repeatedly in randomized order using a one interval temporal forced choice (IIFC) technique. The observers’ task was to identify on each trial (consisting of one interval) whether the central stimulus was positioned to the right or the left of the two outside stimuli (see Fig. 1). From the resulting psychometric function the threshold was found by fitting the error function, ERX (x), of the form P(x) = A {O.S+ 0.5 ERF [(x - B)/(sqrt (2.O)*C)]}

(2)

where A is the number of presentations per stimulus condition, B is the offset of the function relative to zero. and C is the slope parameter of the function, which corresponds to the standard deviation in the case of a Gaussian. The slope is the measure of the accuracy of alignment. The absolute position of the stimuli on the display screen was randomized from trial to trial so that correct performance could not be based on the absolute position of the central Gabor.

SPATIAL LOCALIZATION

DEFICIT

IN AMBLYOPIA

1321

Contrast thresholds

Patients

Detection thresholds were determined for the central stimulus alone (central fixation) and for the two peripheral stimuli jointly (central fixation). This was done either using a method of adjustment (10-20 settings) or by a two temporal forced choice approach (10-20 presentations at each of 10 contrast values) using the method of constant stimuli (in both cases the presentation time Gaussian was 200 msec). Contrast was controlled by varying a (14 bit) voltage from the digital signal generator and multiplying it with the Gabor stimuli output from the frame store, the contrast of which could also be scaled (8 bit resolution). This provided accurate estimates of contrast threshold as the Joyce display screen has a linear Z-amplifier. The resultant psychometric functions were fitted with a Weibull function of the form

The clinical details of the patients tested are given in Table 1 for the strabismic (including mixed anisometropic/strabismic patients) and Table 2 for purely anisometropic subjects. We chose this group of patients because for each of them we had a complete ophthalmic and ophthalmological history from the date of the first eye examination where the anisometropia or strabismus or amblyopia was first detected including all subsequent therapy between then and adulthood.

Y(db) = 50 + .50(1 - exp[-(IO(-b(db-n)i20)])

(3)

where h is the slope of the psychometric function and a is the threshold corresponding to 82% correct. Solutions were found with both of these parameters free to vary.

RESULTS 1. Strabismic Amhiyopia (a) Positional accuracy The two main issues addressed in this study concern firstly the role of the contrast sensitivity -deficit in amblyopic spatial localization judgments and secondly if there is an independent spatial localization deficit in amblyopia how is it best described, in space or in frequency. To answer these questions we use spatial bandpass stimuli so that the contrast sensitivity deficit

FIGURE 1. Illustration of the stimuli used in the present experiments. All stimulus are spatial scaled versions of one another and the task involves a spatial alignment of the middle Gabor.

ROBERT 1~. HESS and IAN E. HOLLIDAY

1327

can be measured and accounted for at each spatial scale at which the spatial localization accuracy was assessed. The results illustrated in Figs 2-3 compare the alignment accuracy of the normal and fellow amblyopic eye of a group of strabismic amblyopes (for their clinical details see Table 1). The task is the horizontal alignment of a central spatial Gabor patch between two outer Gabor patches. The local orientation of each Gabor patch is vertical and the inter-Gabor separation is 10 times its standard deviation (for illustration see Fig. 1). It is important to realize that, using identical procedures, we measured the contrast detection thresholds separately for the centrally and peripherally located narrow-band stimuli. The contrast of each Gabor was then set to bc a fixed number of decibels above the contrast threshold. thus all the spatial Gabors comprising the stimulus were at a constant suprurhreshold contrast so that valid comparisons could be made across scale and between eyes. This ensured that the stimuli which were to be aligned were not only at the same suprathreshold contrast but also equi-visible to the normal and fellow amblyopic eye (Hess & Bradley. 1980). In these initial experiments the suprathreshold level was either 4 or 8 dB (8 dB unless otherwise specified) above threshold. In Figs 2-3 the standard deviation of the alignment setting in min of arc is plotted against the spatial scale of the stimuli expressed in terms of the standard deviation of its Gaussian envelope, in min of arc. The stimuli when viewed from a distance of 1 m had a Gaussian standard deviation of 25 min and a peak spatial frequency of I c/deg (this is plotted as a spatial scale of

25min on the abscissa). The separation of the Gabors was 10 x 25 min. All other stimulus configurations were scaled replicas of this, obtained by altering viewing distance (see Fig. 1). The individual results in Figs 2 3 have been ordered in terms of the severity of the alignment deficit, Fig. 2 having more severe examples than Fig. 3. A number of points are noteworthy. First, normal and ambiyopic eyes display the same form of relationship between spatial alignment accuracy and spatial scale as found for normal observers, namely a linear dependence (Toet, 1987; Hess & Holliday, 1992). The solid lines in each figure have unity slope. Second, strabismic amblyopes display a loss of spatial alignment accuracy which, since all of the stimuli are well within their individual resolution limits and of equal suprathreshold contrast are therefore independent of their contrast sensitivity deficit for the same stimuli. The spatial localization deficits ranged from a factor of around 2 in the mildest case to a factor of around 25 in the most severe. Lastly, the amblyopic spatial localization deficit in all cases excepting that in Fig. 2(A) also scales, that is. it is a constant fraction of the spatial scales at which it is measured. The lack of scaling exhibited for the deficit in patient ST. [illustrated in Fig. ?(a)] was repeatable with both methods of adjustment and constant stimuli and was unaffected by the suprathreshold contrast level used, we therefore believe that this is a real effect. A similar trend was evident in the results of patient A.R. In order to ascertain the importance of the contrast parameter we further investigated this in four patients.

TABLE I. Strabismic patients Name

Refraction

R.C.

R +O.SO/-1.00 x I20 L -0.25;- 1.00 x 55

P.S.

R L R L

B.T.

+3.00/-1.00 x 120 +4.25/- 1.OOx 40 +0.25/‘-0.50 x 5 +I.00

*A.R.

R +3.00/-0.75 L +0.75

F.F.

R L R L

CF.

R -0.25/-0.50 L co.50

lM.H

R L R L R L R L

A.F. +F.B.

x 100

PLAN0 PLANO/-0.50 x 130 +4.50/-0.50 x 180 t4.25

ST.

M.S.

Clinical data

x I10

+0.75 c2.00 PLAN0 PLANO/-0.25 x 100 -2.50/-1.50x 170 - 1.25/- 1.00 x 10 +0.25!-0.75 x 85 -3.25

*Mixed smblyopes

10 deg R esotrope Steady centraf Steady fixation 5 deg L esotrope Central fixation L esotropia in childhood Now 2 deg exotropia Central fixation 15 deg R exotropia 5 deg R hypertropia Central unsteady fixation 8 deg L esotropia Steady central fixation 20 deg L exotropia I5 deg eccentric Unsteady fixation IO deg L esotropia 10 deg eccentric Unsteady fixation IO deg L esotropia Central fixation 5 dcg L esotropia Steady central fixation 5 deg R esotropia Unsteady central fixation 2 deg R exotropia Steady central fixation

History

Corrected acuity

No surgery, occlusion therapy only

R 6:18 L 6i6+ +

No surgery, occlusion therapy only Multiple surgery

R L R L

Surgery at Syr

R 6/24 L 69

Congenital esotrope surgery and patching First R, at 6 yr surgery at 8yr

R L R L

No surgery, occlusion therapy

R 615 L Ii60

Esotropia as child, surgery at 3 yr Surgery at 8yr

R L R L R L R L

No surgery, occlusion therapy Surgery at 5yr

6;s 6il8 6/6 6:36

6/5 6136 6;s 260

6i6 6/12 615 6;18 6:‘18 6,5 6:‘2I 6:5

SPATIAL

DEFICIT

LOCALIZATION

Name J.P. J.H. B.M. D.L.

J.S.S. E.D. P.W. R.S. J.S. G.Mc. N.N. S.M. N.C. G.T. G.D. S.H. K.K. SDS. L.C. L.C. M.K.

Refraction R L R L R L R L

- 1.00 +7.00/-2.00 ~4.50 +8.75/-2.00 PLAN0 -2.00/-4.00 PLANO/-0.50 +4.00/ - 3.00

R L R L R L R L R L R L R L R L R L R L R L R L R L R L R L R L R L

-5.00 + 1.25/-0.25 x 25 +lO.OO/-5.75 x 90 +9.00/-7.00x 180 f0.75 +4.75/1.25 x 50 -1.25/-1.00x 90 PLAN0 f4.25 +0.75/-0.25 x 90 +4.75/1.00 x 80 f1.50 PLAN0 -0.75/-2.5 x 10 +6.50 PLAN0 +S.OO/-1.00 x 60 f1.00 PLAN0 +3.50 PLAN0 +S.OO/-1.50 x 35 -6.50/-33.00 x 180 - 5.00/ -0.75 x 85 -3.15 +0.50 +1.75/-0.75 x 110 PLANO/ -0.75 x 80 PLAN0 +5.50 -2.25 PLANO/-2.75 x 101 +7.00/-2.00 x 120 PLANO/-0.50 x 90

Figures 5 and 6 display the spatial offsets (equivalent to the constant error measure of Bedell & Flom, 1981) for these spatial alignments for normal and amblyopic eyes of all subjects. These offsets are plotted in min of arc as a function of the spatial scale at which they were measured. The error bars represent twice the standard error (approx. 95% confidence interval) and relate to the positional accuracy described above for these subjects. Three points are noteworthy; first the majority of strabismic amblyopes exhibit significant spatial offsets for alignment and therefore show evidence of spatial distortion. Second, there is a great deal of individual variability on how this varies as a function of spatial scale. Third, in some cases and for some spatial scales the variability can be equal to or greater than the offset. This underscores the importance of obtaining good estimates

2. Anisometropic

Clinical Parafoveal

1323

(B) Positional offset

Again as in the previous experiment contrast thresholds were measured individually for central and peripheral Gabor stimuli and their contrasts were individually set to a constant suprathreshold level which was itself variable. The results showing the relationship between the spatial alignment deficit in amblyopia and the suprathreshold contrast of the stimuli are displayed in Fig. 4. In correspondence with the results of normal subjects (Hess & Holliday, 1992) the accuracy with which spatially narrow-band stimuli can be localized by the normal and fellow amblyopic eyes of strabismic amblyopes is not greatly affected by the suprathreshold contrast level of the stimuli. This results in the deficit being unaffected by the suprathreshold contrast level at which it is measured. The solid lines which correspond to a slope of 0.25 (4th-root of the contrast) were found to adequately describe similar results for normal observers (Hess & Holliday, 1992). TABLE

IN AMBLYOPIA

patients

data

Clinical

fixation

history

First R, at IOyr

x 30 Central

fixation

Central

fixation

x 180 x 180 x 180 x 90

Bilateral Holmes-Adies pupil No other defect Central fixation Central unsteady fixation

First R, at 7 yr Occlusion therapy First R, at 8 yr Occlusion therapy First R, at 9 yr Part-time occlusion

Central

fixation

First R, at 36 yr No treatment First R, at 6 yr

Central

fixation

First R, at 22 yr

Central

fixation

First R, at 7 yr

Unsteady

central

fixation

First R, at 6 yr

Unsteady

central

fixation

First R, at 7 yr Part-time occlusion First R, at 6 yr

Central

steady

fixation

Central

steady

fixation

Central

unsteady

Central

fixation

Central

fixation

Central

fixation

Unsteady

central

fixation

fixation

First R, at 6 yr Occlusion therapy First R, at 6 yr Occlusion therapy First XAR, at 5 yr Occlusion therapy No R, until 6 yr Occlusion at 6 yr First R, at 5 yr

Central

fixation

First R, at 5 yr Occlusion therapy First R, at 9 yr

Central

fixation

First R, at 7 yr

Unsteady Central

central fixation

fixation

First R, at 7 yr Occlusion therapy First R, at 14 yr No therapy

Corrected acuity R L R L

615 4160 615 6,I12

R L R L

6/6+ 6112 615 6112

R L R L R L R L R L R L R L R L R L R L R L R

2:‘60 6/5 615 6;12 6/46/9+ + 6/126/4619 6:5 6/12 6,i5 6/6 6/24 616 6/461’24 6,;6 615 616 614 6,‘18+ t 6,:36

L R L R L R L R L R L

6/6-t + 616 6130 6112 6/h 616 6!‘30 615 6/18 6/60 614

1324

ROBERT F. HESS and IAN E. HOLIDAY

of the variabiIity before considering the significance or otherwise of large offsets. In the strabismic group as a whole we found no evidence for abnormal spatial offsets which show the same type of spatial scaling previously described for the positional accuracy measure. Such an effect would be presented by a negatively sloping line on these axes.

(A) Pusiliunaf nccuracy In Figs 7-9 are displayed for the positional accuracy for a group of anisometropic amblyopes (see Table 2 for clinical details) as a function of spatial scale for the previously described spatial alignment task. As for the

S.T. 100

10

1

SPATfAt

SCALE

fmfnj

F.F. 1

E 2

e

5 2

100

IO

SPATIAL

SCALE

SPATIAL SCALE (mfn)

(m&Q

100

to

3 Y II

1

ii

VI ii

MS. .1 1

10

SPATfAt

SCALE

1

(min)

1

10

SPATfAL

SCALE

too

(mfrq

FHXJRE 2. Alignment accuracy in mire of arc is plotted against the spatial scale of the stimuli used for alignment. All stimuli were set to be 8dB above their individual contrast thresholds. Normal (open symbois) and fellow amblyopic eyes (solid symbols) of 6 strabismic amblyopes are compared. The solid line has a slope of unity.

SPATIAL

LOCALIZATION

DEFICIT

strabismics, contrast thresholds were first measured for the normal and fellow amblyopic eyes and for the central and peripheral Gabor stimuli. All stimuli were set at the same suprathreshold level (usually 8 db but occasionally 4 db above threshold). These results are similar to the strabismics in that, for some patients there is a deficit in positional accuracy

A

1; g

IN AMBLYOPIA

1325

even when the contrast sensitivity deficit has been compensated for and this deficit also exhibits spatial scaling. Unlike the previously described results for strabismic amblyopes, the magnitude of the deficit in spatial alignment is much reduced. For the majority of anisometropes (not necessarily the least severe cases) there is no significant difference between the normal and

loor

8

loo3

g

1 I

10

1

A.F. .I

,

rr

I

1

.I

SPATIAL SCALE

IO

SPATIAL SCALE

(min)

c

I

I

1

100

100

fmin)

D

C

1

10

SPATIAL

100

SCALE

:

1

(min)

10

SPATIAL

.‘.~I 1

SPATIAL

10

SCALE

SCALE

100

(min)

100

(mint

FIGURE 3. Alignment accuracy in min of arc is plotted against the spatial scale of the stimuli used for alignment. were set to be 8dB above their individual contrast thresholds. Normal (open symbols) and fellow amblyopic symbols) of 5 strabismic amblyopes are compared. The solid line has a slope of unity.

All stimuli eyes (solid

1326

ROBERT F HESS and IAN E. HOLLIDAY

0 CONTRAST

d CONTRAST

IO

(db

10 (db

20 above

20 above

30 threshold)

30 threshold)

CONTRAST

0

CONTRAST

(db

10

(db

above

20 above

threshold)

30 threshold)

FIGURE 4. Alignment accuracy in min of arc is plotted against the supra-threshold contrast of the stimuli. The contrast thresholds for each Gabor stimulus was previously determined. Normal (open symbols) and fellow amblyopic eyes (solid symbols) of 4 strabismic amblyopes are compared. The solid line has a slope of 0.25.

amblyopiceyes (e.g. patients L.C., P.W., S.M., D.L., J.S. and N.N.). For these anisometropes the contrast sensitivity loss is a complete description. For the other anisometropes, the largest deficit in positional accuracy was of the order of a factor of 2. This difference is not due to the fact that the spatial frequency composition of our stimuli relative to the resolution limit of the amblyepic eye differed in the strabismic and anisometropic groups because for all patients this was individually adjusted so that the finest scale tested was a factor of 2 lower than the resolution limit. To ascertain whether the particular suprathreshold contrast level chosen for these experiments (8 db above the threshold for each stimuli) was in any way crucial we investigated how the positional accuracy deficit varied with the suprathreshold contrast in two patients. These results are displayed in Fig. 10, the solid lines represent the slope expected for this relationship for normal observers (Hess & Holliday, 1992). It can be seen that the deficits which are small do not change significantly as a function of the suprathreshold contrast at which they are measured. It is interesting to note at this stage

that, at least in the case of spatially narrowband stimuli the relationship between spatial localization and contrast is similar for normal vision, strabismic amblyopia and anisometropic amblyopia. (B) Positional ofset

Some anisometropic amblyopic exhibited significant spatial offsets for alignment and others did not. A selection (12 out of 21) of the anisometropic results illustrating this is shown in Figs 11 and 12. In each, the offset is plotted against the spatial scale at which it was measured with the error bars representing twice the standard error of the mean (approx. 95% confidence limit). The results in Fig. I1 show that for any particular patient a significant offset may be found at some scales and not at others. However, it would seem on the basis of this limited set of results (these 6 patients were the only ones out of our anisometropic patient group of 21 who exhibited sign&ant offset at any spatial scale) that the positional offset does depend on the spatial scale of the stimuli used to measure it, for all patients the lower

SPATIAL

LOCALIZATION

DEFICIT

the scale the greater the offset. The solid curve in each of these diagrams represent the spatial scaling prediction and the results are consistent with these. The remaining anisometropic amblyopes (results for 6 of which are displayed in Fig. 12) showed no significant offset when their positional inaccuracy was taken into account. Thus for

SPATIAL

SCALE

132.7

the majority of anisometropes, the contrast sensitivity can be considered a complete description of their loss. 3. Strabismic and Anisometropic Amblyopia Compared There appear to be some clear differences in the spatial localization deficits in these two forms of amblyopia.

100

14.3

(mln)

SPATIAL

SCALE

(min)

SPATIAL

SCALE

(mln)

I

T

0

IN AMBLYOPIA

!I!

-10 i

!

-20 -

FF -30 ,

L

1

10 SPATlAL

SCALE

II

100 10

(mfn)

100

IF

10

5

0

I

-5

2

MS

ZE

-10 1

10

SPATIAL

SCALE

100

(min)

10

1

SPATIAL

SCALE

(min)

FIGURE 5. Mean offset in min of arc is plotted against the spatial scale of the stimuli used for alignment. All stimuli were set to be 8 dB above their individ~ai contrast thresholds. Normal (open symbols) and fellow amblyopic eyes (solid symbols) of 6 strabismic amblyopes are compared. The error bars represent twice the standard error of the mean.

ROBERT F. HESS and IAN E. HOLLIDAY

1328

First, it is apparent from a comparison of Figs 2 and 3 with their counterparts in Figs 7-9 that the spatial deficit in anisometropia is generally of lesser magnitude and, in the majority of anisometropes, not present at all. This difference is brought out more forcibly in Fig. 13 where the alignments of the whole patient group are compared. This type of comparison is only possible because the deficits in both groups exhibited scaling (excepting those

of patient S.T. which is not plotted here) enabling the deficit across scale to be represented by a single number. As a group, strabismic amblyopes exhibit more severe positional inaccuracy than found for their anisometropic colleagues. Furthermore, while only some members of both groups exhibit significant positional offset for the present stimulus arrangement, there does appear to be a difference in the way in which positional offset varies with spatial scale. Greater offsets were found at greater

B

15

10

10 5-

5

T

0

I

II

I

*

-5 -10

i

0

d

I 1

*

1

10 SPATIAL

-5 ;f

A.F.

R.C. n

-10

160

SCALE

SPATIAL

I 10 SCALE

SPATIAL

1 10 SCALE

1

(mln)

#l 100 (min)

15 10 -

0

-5 1 SPATIAL

10 SCALE

100

1

(mln)

-8 -

F.B. s-l 100 (mln)

P.S.

-10 1 SPATIAL

I 10 SCALE

89 100 (mln)

FIGURE 6. Mean offset in min of arc is plotted against the spatial scale of the stimuli used for alignment. All stimuli were set to be 8 dB above their individual contrast thresholds. Normal (open symbols) and fellow amblyopic eyes (solid symbols) of 5 strabismic amblyopes are compared. The error bars represent twice the standard error.

SPATIAL L~~ALIZATIUN

spatial scales for the anisometropes whereas no common relationship at all was apparent in the strabismic results. One obvious question is whether the strabismic and anisometropic patient groups were equivalent in other respects, for example in terms of their Snellen visual acuity and contrast sensitivity deficits. If it turns out that they are not then the reported differences in positional

DEFICIT

t329

II? AMBLYOPIA

accuracy and positional offset could follow as a trivial consequence. in Fig. 14 the visual acuity (A) and contrast sensitivity (B) deficits for the strabismic and anisometropic groups are compared. Each of these distributions is normally distributed (KoImo~orov-~m~rnov test @ 0.01 level) and the acuity of each is significantly different from normal (that is in

A

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FIGIJRE 7. Alignment accuracy in min of arc is plotted against the spatial scale of the stimuli used for alignment. All stimuli were set to be 8 dB above their individual contrast thresholds. Normal (open symbols) and fellow amblyopic eyes (solid symbols) of 5 anisometropic amblyopes are compared. The solid line has a slope of unity.

1330

ROBERT

F. HESS and IAN

the case of acuity from 1, and in the case of contrast sensitivity from 0). Each patient distribution (strabismic and anisometropic) for acuity and contrast sensitivity was statistically indistinguishabIe (see Table 3 for statistical analyses). Comparable distributions

E. HOLLIDAY

for the two groups are shown for the measures 01 positional accuracy [Fig. 15(A)] and positional offset [Fig. 15(B)], the latter was taken for the highest scale tested. In all cases the results which were normally distributed (Kolmogorov-Smirnov test (a, 0.01 level)

I ;i.‘_

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S.D.S. 100

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FIGURE 8. Alignment accuracy in min of arc is plotted against the spatial scale of the stimuli used for alignment. A11stimuli were set to be 8dB above their individual contrast threshe2ds. Normal (open symbols) and fellow amblyopic eyes (solid symbols) of 5 a~isometropic amblyopes are compared. The solid line has a stope of unity.

ALlGNMENT

ACCURACY

(m&j

cl

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ROBERT F. HESS and IAN E. HOLLIDAY

of spatially task.

broad-band

stimuli or to the particular

DISCUSSION

concerns whether the contrast sensitivity deficit is a complete description of the amblyopic visual loss. The second concerns how any subsequent purely spatial loss should be best described. 1. Is the contrast sensitivity loss a complete description?

questions which have not previously amblyopia.

The first of these

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FIGURE 10. Alignment accuracy in min of arc is plotted against the supra-threshold contrast of the stimuli. The contrast thresholds for each Gabor stimulus was previously determined. Normal (open symbols) and fellow amblyopic eyes (s&9 symbols) of 2 anisometmpic amblyopes are compared. The solid line has a slope of 0.25.

Strabismic amblyopia. This can only be answered if narrow-band stimuli are used because one can only then be sure that the spatial mechanisms responsible for detection are the same as those underlying localization. In this study the detection thresholds for all stimuli were measured so that all stimuli were presented at a constant suprathreshold contrast, thereby compensating for any threshold deficit. Any remaining localization deficit (in positional accuracy and or positional offset) for these stimuli cannot therefore be attributed to the associated contrast threshold deficit. All the strabismic subjects tested exhibited such a deficit in positional accuracy (and in some cases also for positional offset). It could be argued that one needs to consider not only the thresholds of the underlying filters but also their suprathreshold gain. Three findings argue that the localization deficit (in positional accuracy and positional offset) in amblyopia is not due to a decreased visibility of the stimuli due to reduced suprathreshold gain of amblyopic filters. First, Hess and Bradley (1980) have previously shown that strabismic amblyopes have veridical contrast perception above threshold. Thus stimuli of equal suprathreshold contrast appear equally visible to the amblyopic eye. Second, the localization deficit does not vary as a function of the level of suprathreshold contrast. Third, we checked informally with each patient that all stimuli were indeed equally visible to the normal and fellow amblyopic eyes. On the basis of this we conclude that the spatial localization deficits in accuracy and offset reported here do not follow as a consequence of the known contrast sensitivity losses. Even though this is not a particularly controversial conclusion, Levi and Klein (1991) come to a similar conclusion although admittedly Bradley and Freeman (1985) do not, it should be realized that such a claim could not be forceably made by any previous study (Bradley & Freeman, 1985; Levi & Klein, 1985; Watt & Hess, 1987) because either the spatial localization tasks that were used depended on local contrast cues or the stimuli were spatially broadband. In either case this invalidates such a comparison between contrast sensitivity and spatial localization for the underlying mechan~s~~s. ~n~sometro~~a. The deficits in positional accuracy (and to a lesser extent positional offset) are much reduced in anisometropic amblyopia and one must therefore proceed carefully before coming to similar conclusions to that arrived at for the strabismics above. First, it is clear that when the contrast sensitivity deficit has been taken into account (as it can only be done for spatially narrow-band stimuli) then the majority of anisometropic amblyopes do not display either an abnormality for positional accuracy or offset. For these subjects, in the absence of other information, the contrast sensitivity loss can be regarded as a complete

SPATIAL

LOCALIZATION

description. These would fall into the category which Levi and Klein (1991) describe in terms of an elevated internal blur because in terms of the narrow-band stimuli blur translates to a contrast sensitivity deficit at a particular scale. There are however some anisometropic amblyopes (and usually not only the severe cases) who

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display small but statistically significant deficits (in Table 3 these are statistically analyzed in terms of a population statistic) in positional accuracy and offset (not necessarily related, for some patients exhibit one without the other, e.g. see results for L.C.) which can not be explained in terms of the contrast sensitivity deficit. It is a

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FIGURE 11. Mean offset in min of arc is plotted against the spatial scale of the stimuli used for alignment. All stimuli were set to be 8 dB above their individual contrast thresholds. Fellow amblyopic eyes (solid symbols) of 6 anisometropic amblyopes are compared. The error bars represent twice the standard error of the mean. The solid curve represents an offset deficit which spatially scales.

I334

ROBERT F. HESS

and

possibility that the small residual positional accuracy deficit is due to a difference in the suprathreshold gain of the filters which remains uncorrected even after compensating for the contrast threshold. Informally this did not appear ta be the case since our attempts to balance the perceived contrast between the normal and amblyopic eyes did not greatly affect the magnitude of the localization deficit. Furthermore, it was not limited to severe amblyopes and was always spatial scale invari-

“I5

IAN E. HULLIDAY

ant. None of these factors make an explanation for this deficit in terms of reduced suprathreshold gain of the filters very appealing, However, because these deficits are small and not all of our anisometropic sample exhibited them we remain guarded in our conclusion as to their significance. In terms of positional offset the conclusions are more clear cut in that only a small percentage of anisometropic amblyopes exhibits such deficits, the deficits were sizeable, they exhibit spatial scaling and the

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FIGURE 12, Mean offset in tin of arc is plotted against the spatial scale of the stimuli used for aEgnment. All stimuli were set to be 8 dB above their individual contrast thresholds. Fellow ambfyopic eyes (solid symbols) of 6 anisometropic amblyopes are compared. The error bars represent twice the standard error of the mean.

SPATIAL LOCALIZATlON

DEFICIT

patients involved are not necessarily the severe amblyopes (in this study some had acuities of 6/6, and 6/ 12 and 619, others had 6130, 6136 and 2/60).

30

It is not immediately obvious what would be the best metric (Hess, Field & Watt, 1990) to use to understand spatial localizaton deficits within a visual system which we know uses a space-frequency code (or codes) of some description. Imagine that the spatial localization problem is a purely spatial one. It would be best specified in terms of visual angle and would as a consequence result from a more severe disruption of neurons with small receptive fields compared with those having large receptive fields. This is the implicit assumption of all previous studies in this area (e.g. Levi & Klein, 1990b; Wilson, 1991; Watt & Hess, 1987; among others). On the other hand, the localization deficit could affect all spatial scales equally resulting in a loss best described in terms of a fraction of a filter size for a stimulus at a particular scale (Hess et al., 1990). In this case neurons with large and small receptive fields would be aflected equally. The findings of this study of positional accuracy suggest that, in the majority of amblyopes (all but one strabismic and all the anisometropes exhibiting a deficit in positional accuracy), all spatial scales are equally affected so that

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the localizaton deficit is not a purely spatial one but one dependent on spatial scale. This underlines how essential it is to use bandpass spatial stimuli not only in relating localizaton and contrast sensitivity deficits as

6

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FIGURE 13. The ratio of the alignment accuracy between the normal and fellow amblyopic eye (averaged across scale) is plotted against the contrast sensitivity deficit at the finest scale for each amblyopic patient. Strabismic (open squares) and anisometropic (sofid symbols) amblyopes are compared.

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ROBERT F. HESS and IAN E. HOLLlDAY

1336

strabismics

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14(B)

FIGURE 14. Acuity in min of arc (A) and contrast sensitivity (B) histograms for the strabismic and anisometropic populations See Table 3 for their statistical evaluation.

described above but also in specifying the localization deficit per se within a meaningful metric. The situation is somewhat different when it comes to the deficits in positional offset for the strabismic and anisometropic groups. In anisometropic amblyopia a small proportion of amblyopes exhibited a significant offset abnormality which was worse in absolute terms at lower spatial scales which amounts to a spatial scaling similar to that observed in the same group (and in some cases the same individuals) for positional accuracy. In strabismic amblyopia, only some patients exhibit significant abnormalities in positional offset (that is when one takes into account their deficit in positional accuracy which in some cases can be quite large). Unlike their positional inaccuracies, these were not found to scale with stimulus spatial frequency. This suggests that there are two independent spatial deficits (relative positional inaccuracy and local positional offset or distortion) in amblyopia either occurring along quite different metrics or being different in different individuals. It should be noted that some tasks that purport to measure spatial accuracy are in fact measuring local contrast sensitivity, i.e. abutting vernier tasks and as

such their results do not bear on the issues that he at the heart of the present study. In terms of amblyopia such measures are directly correlated with, and in fact determined by, the contrast sensitivity deficit (Bradley & Freeman, 1985; also see Levi & Klein, 1992). Relationship to previous studies. The conclusions that the spatial localization deficit in amblyopia is scale invariant and its subsequent ramifications are unique to this study. All other studies have used spatially broadband stimuli and as such their results cannot address this issue. Furthermore, all previous studies have concentrated on understanding the deficit associated with the smallest filters under the assumption that these filters underlie our limiting positional accuracy (Levi & Klein, 1990a; Wilson, 1991). This emphasis not only limits one’s understanding of the amblyopic spatial deficit, as described above but also may be incorrect even for normal vision (Hess & Holhday, 1992). The conclusion that strabismics, unlike most anisometropes, display a spatial localization deficit which cannot be attributed to their known contrast sensitivity deficit is controversial (Levi & Klein, 1990b are in agreement whereas Bradley & Freeman, 1985 are not).

SPATIAL LOCALIZATION

DEFICIT

IN AMBLYOPIA

1337

TABLE 3. Population statistics Contrast sensitivity

I H,: contrast sensitivity loss in strabismic amblyopia is not significantly different from zero. One-tailed t-test; t = 6.868; reject H, (ii P = 0.001 2 H,: contrast sensitivity loss in anisometropic amblyopia is not significantly different from zero. One-tailed t-test; t = 5.8; reject H, (a P = 0.001 3 H,: the contrast sensitivity deficits are the same in strabismic and anisometropic ambiyopia. Two-tailed paired r-test; f = 0.1433; accept H, (@ P =O.Ol Positional offsets

1 H,: strabismic amblyopes as a population do not exhibit significant positional offsets (e.g. U, = 0) at the highest scale. One-tailed t-test; t =2.1; reject H, @ P =0.03 2 H,: anisometropic amblyopes as a population do not exhibit significant positional offsets (e.g. U, = 0) at the highest scale. One-tailed t-test; f = 4.5; reject H, (3 P = 0.001 3 H,: the positional offset abnormality are the same in strabismic and anisometropic amblyopia. Two-tailed paired t-test; t = 1.953; accept H, @ P = 0.01 Positional accuracy

1 H,: strabismic amblyopes do not exhibit a deficit in positional accuracy (averaged across scale). One-tailed t-test; I = 3.161; reject H, (~1P = 0.01 amblyopes do not exhibit a deficit in positional accuracy (averaged across scale). One-tailed t-test; f = 9.908; reject H,

2 H,: anisometropic (& P =O.Ol

3 H,: the positional accuracy deficit is the same in anisometropic and strabismic amblyopia. Two-tailed paired r-test: f = 3.8; reject H, (~1 P = 0.01 Acuity

1 H,: strabismic amblyopes do not exhibit an acuity deficit. One-tailed l-test; t = 2.06; reject H, @j P = 0.03 2 H,: anisometropic amblyopes do not exhibit an acuity deficit. One-tailed t-test; t = 3.24; reject H, @ P = 0.01 3 H,: the acuity deficits in anisometropic and strabismic amblyopia are the same. Two-tailed paired f-test; t = 1.056; accept Ho (ns P = 0.01

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ROBERT F. HESS and IAN E. HOLLIDAY

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FIGURE 15(B) FIGURE 15. Positional accuracy (A) and positional offset (B) histograms in min of arc for the strabismic and anisometropic populations. See Table 3 for their statistical evaluation.

Our approach is more direct than previous studies in that since our stimuli are spatially narrow-band the contrast sensitivity deficit can be exactly compensated for at the spatial scale at which the positional judgments occur (unlike that for spatially broad-band stimuli since detection and positional discrimination may occur at different scales even for the same stimuli). In this way we have been able to measure any residual spatial deficit that remains for stimuli that are in all respects equally detectable. Other studies have not only used broad-band stimuli but also have only been able to infer the possible importance of contrast by showing, through its arbitrary adjustment that conditions can be found where spatial accuracy in normal and amblyopic eyes can be made equivalent. This does not prove that the spatial deficit is due to a residual deficit in contrast only that it has a contrast dependence. The same criticism can be leveled at the study by Watt and Hess (1987) because their stimuli were also spatially broad-band. They argued that anisometropic amblyopes in general display a spatial deficit that is better understood in terms of positional uncertainty than it is in terms of the known contrast sensitivity deficit. In contradistinction to their conclusions we find by a more

direct approach that the majority of anisometropes, even the most severe do not exhibit spatial deficits once the contrast sensitivity loss at the particular spatial scale under investigation has been compensated for. We had the opportunity of including in our sample three of the patients (P.W., N.N. and J.S. see Figs 8 and 9) previously studied by Watt and Hess (1987) and our results suggest that once the contrast sensitivity deficit is corrected at the spatial scale of the discrimination no additional abnormality was detected. We leave open the possibility that a minority of anisometropes (not necessarily the most severe) may display a purely spatial deficit unassociated with the contrast loss however it is very small and therefore of questionable significance to their visual problem. Model of localization and of the underlying loss. The process of spatial localization can be thought of as the result of a number of separate stages (see Hess 8z Holliday, 1992 for more details); stimulus representation by self-similar arrays of linear filters, contrast energy extraction and feature localization. Our claim to have factored out the contrast threshold deficit by the use of spatially narrow-band stimuli rests on our belief that the raised contrast thresholds are associated with the

SPATIAL

early

stage

LOCALIZATION

of

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Hess, R. F. & Pointer, J. S. (1985). Differences in the neural basis of human amblyopia; the distribution of the anomaly across the visual field. Vision Research, 25, 1577-1594. Hess, R. F., Bradley, A. & Piotrowski. L. (1983). Contrast coding in amblyopia-I. Differences in the neural basis of human amblyopia. Proceedings of the Royal Society of London B, 217, 309-330. Hess, R. F., Campbell, F. W. & Zimmern, R. (1980). Differences in the neural basis of human amblyopias; the effect of mean luminance. Vision Research, 20, 295-305. Hess, R. F., Field, D. J. & Watt, R. J. (1990). The puzzle of amblyopia. In Blakemore, C. (Ed.), Vision: Coding and t$iciencJ (Chap. 25, pp. 267-280). Cambridge: Cambridge University Press. Lagreze, W.-D. & Sireteanu, R. (1991). Two dimensional spatial distortions in human strabismic amblyopia. Vision Research, 3/, 1271-1288. Levi, D. M. & Harwerth, R. S. (1977). Spatio-temporal interactions in anisometropic and strabismic amblyopia. Imwtigatiw Ophthalmology and Visual Science, 16, 90-95. Levi, D. M. & Klein. S. A. (1982). Hyperacuity and amblyopia. Nature (London), 198, 268-270. Levi, D. M. & Klein, S. A. (1985). Vernier acuity, crowding and amblyopia. Vision Research, 25, 979-991. Levi, D. M. & Klein, S. A. (1990a). Equivalent intrinsic blur in spatial vision. Vision Research, 30, 1971 -1993. Levi, D. M. & Klein, S. A. (1990b). Equivalent intrinsic blur in amblyopia. Vision Research, 30, 1995-2022. Levi, D. M. & Klein, S. A. (1992). The role of local contrast in the visual deficits of humans with naturally occurring amblyopia. Neuroscience Letters. In press. Levi, D. M., Klein. S. A. & Yap, Y. L. (1987). Positional uncertainty in peripheral and amblyopic vision. Vision Research. 27, 581-597. Sireteanu, R. & Fronius, M. (1981). Naso-temporal asymmetries inhuman amblyopias: Consequences of long term interocular suppression. Vision Research, 21, 1055-1063. Toet, A. (1987). Visual perception of spatial order. PhD thesis, Utrecht. Watt. R. J. & Hess, R. F. (1987). Spatial information and uncertainty in anisometropic amblyopia. Vision Research. 27, 661-674. Wilson, H. R. (1986). Model of peripheral and amblyopic hyperacuity. Inoestigalioe Ophthalmologic and Visual Science (SuppI.). 27, 95. Wilson, H. R. (1991). Model of peripheral and amblyopic hyperacuity. Vision Research, 31, 967?996.

Acknowledgements-This work was supported by the Medical Research Council of Canada (project grant # MT- 108 18). We wish to thank Dennis Levi for a constructive review and for drawing our attention to his paper with Stan Klein in press in Neuroscience Letters.