www.elsevier.com/locate/visres

Vision Research 44 (2004) 2475–2482

Perception of mirror symmetry in amblyopic vision

Dennis M. Levi a,*, Jussi Saarinen b

a School of Optometry, Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94720-2020, USAb Department of Psychology, University of Helsinki, Finland

Received 24 December 2003; received in revised form 7 May 2004

Abstract

Mirror symmetry is ubiquitous in natural visual scenes, and detection of mirror symmetry seems to be a global, automatic, effort-

less and important aspect of visual perception. The perception of mirror symmetry has not been studied in humans with amblyopia.

In this paper we measured and quantified the detection of mirror symmetry in adults with naturally occurring amblyopia. Our re-

sults show that amblyopia may severely impair the detection of mirror symmetry, and that this impairment is not simply a conse-

quence of reduced stimulus visibility. Rather, we suggest that this loss may reflect, at least in part, a deficit in the integration of local

orientation information.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Human spatial vision; Amblyopia; Orientation integration; Long-range perceptual interactions; Perception of mirror-symmetry; Psyc-

hophysics

1. Introduction

Mirror symmetry is ubiquitous in natural visual

scenes, and detection of mirror symmetry seems to be

a global, automatic, effortless and important aspect of

visual perception (Barlow & Reeves, 1979; Dakin &Hess, 1997; Dakin & Watt, 1994; Julesz & Chang,

1979; Tyler, 1999; Wagemans, 1995; Wilson & Wilkin-

son, 2002).

Perception of mirror symmetry has not been studied

in humans with amblyopia; however, there are a number

of reasons to suspect that it might be compromised: first,

there is a good deal of evidence that perception of mir-

ror symmetry is based on positional comparisons be-tween the local stimulus elements or their groups

forming a symmetric global pattern (Barlow & Reeves,

1979; Dakin & Hess, 1997; Dakin & Watt, 1994; Julesz

0042-6989/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.visres.2004.05.011

* Corresponding author. Fax: +1-510-642-7806.

E-mail address: dlevi@berkeley.edu (D.M. Levi).

& Chang, 1979; Wagemans, 1995), and strabismic am-

blyopes have a high degree of positional uncertainty

(Hess & Holliday, 1992; Wang, Levi, & Klein, 1998).

In addition, random undersampling (Levi & Klein,

1985) would effectively reduce the correspondence be-

tween the two half-images, resulting in symmetrical pat-terns being perceived as non-symmetrical. Second, in a

recent study, we found that perception of mirror sym-

metry in normal vision is strongly influenced by the local

orientations of the targets (Saarinen & Levi, 2000), and

suggested that perception of mirror symmetry may in-

volve long-range interconnections between cortical fil-

ters with similar orientation specificity. Previous work

calls into question the integrity of long-range neuralconnections in amblyopia (Polat, Sagi, & Norcia,

1997). Third, functional imaging studies (Tyler, Basse-

ler, & Wandell, 1998) suggest that a bilateral region of

the occipital cortex may selectively respond to mirror

symmetry, i.e., symmetry perception may involve higher

cortical regions. Recent psychophysical (Sharma, Levi,

& Klein, 2000) and imaging studies (Barnes, Hess, Du-

moulin, Achtman, & Pike, 2001; Demer, 1993; Imamura

Fig. 1. Illustration of the visual patterns used to measure symmetry

2476 D.M. Levi, J. Saarinen / Vision Research 44 (2004) 2475–2482

et al., 1997) suggest that strabismic amblyopia may also

damage higher cortical regions, in addition to area V1.

Although the precise mechanism for detecting mirror

symmetry in normal vision is not well understood, there

are now several models (e.g. Barlow & Reeves, 1979;

Dakin & Hess, 1997; Rainville & Kingdom, 2000; Hu-ang & Pashler, 2002) and there may well be more than

one mechanism for detecting symmetry (see e.g., Wilson

& Wilkinson, 2002). A number of studies (Julesz &

Chang, 1979; Dakin & Watt, 1994; Dakin & Hess,

1997) have demonstrated that rapid and effortless sym-

metry perception can be based on the comparison of a

small number of low-pass filtered clusters of elements.

However, there must be a (long-range) neural mechan-ism to compare the positions of the ‘‘blob’’ centroids;

moreover, recent results show an important role for ori-

entation. For example, Rainville and Kingdom (2000)

showed that masking of symmetry perception was

strongest when the mask and test had similar orienta-

tions, and Saarinen and Levi (2000) showed that symme-

try perception is most acute when the orientations of the

‘‘matches’’ are similar.In this paper we measured and quantified the percep-

tion of mirror symmetry in adults with naturally occur-

ring amblyopia. Our results show that amblyopia may

severely impair the perception of mirror symmetry,

and that this is not simply a consequence of reduced

stimulus visibility. Rather, we suggest that this loss

may reflect a deficit in the integration of local orienta-

tion information.

thresholds. This example shows N=24 patches in which the proportion

of symmetrically positioned paired patches is 25%, 50%, 75% or 100%.

The lower panels show the mixed-matching and mixed-opposing

orientation conditions in which the patch orientations were randomly

both vertical and horizontal, but mirror-symmetric pairs were either

matching (left panel) or orthogonal (right panel).

2. Methods

Our stimuli and methods are similar to those of Saar-

inen and Levi (2000) and are described briefly below.

2.1. Stimuli

Stimuli, composed of N Gabor patches (where N var-

ied between 8 and 48 in separate blocks of trials––Fig.

1), were briefly displayed (�150 ms) on the face of a

Mitsubishi Diamond Scan 21TX monitor with a mean

luminance of 56 cd/m2 using a Cambridge Research Sys-

tems VSG 2/3 graphics card with 15 bit contrast resolu-

tion, housed in a Pentium computer. The Gabor patcheswere constructed to contain 0.5 cycles/standard devia-

tion, i.e., a spatial frequency bandwidth of �1.2 octaves,

and except for the ‘‘vary contrast experiment’’ the con-

trast was set to 90%.

To construct the global symmetry patterns, we de-

fined a circular area with a vertical line of symmetry.

On each trial, the Gabor patches were randomly placed

in one half of the circular region (with the constraintsthat the centers of the patches must be at least 3 SD

from the stimulus region boundary (the �forbidden

zone�), and the minimum distance between patches was

3 SD). Symmetry was generated by reflecting the posi-

tions of the patch centers across the vertical axis. A

pre-specified proportion of patches was in mirror-sym-

metric positions––with the remaining patches placed atrandom positions within the defined area: the propor-

tion of symmetrically positioned paired patches was

either 100% (a perfectly mirror-symmetric global pat-

tern), 75%, 50%, 25%, or 0% (no mirror-symmetric

pairs) presented in random order. Fig. 1 shows examples

of N=24 with symmetry varying from 25% to 100%. In

most of the experiments all of the Gabor patches had

vertical carriers; however we also made some measure-ments in which the carrier of each patch in one half

was randomly either vertical or horizontal, and the car-

riers of the corresponding mirror symmetric patches in

the other half were either the same orientation (mixed-

matched––lower left panel of Fig. 1; data shown in

Fig. 4) or were orthogonal (mixed-opposing––lower

right panel of Fig. 1; data shown in Fig. 4). A fixation

D.M. Levi, J. Saarinen / Vision Research 44 (2004) 2475–2482 2477

point (a black square of 0.5�) was constantly present at

the center of the display area in all stimulus conditions.

2.2. Psychophysical procedure

We used a rating-scale method of constant stimuli toquantify the perception of mirror symmetry. The obser-

ver�s task was to rate the proportion of mirror symmetry

(0%, 25%, 50%, 75%, or 100%) by pressing one of five

buttons indicating the degree of symmetry, and was then

given auditory feedback about the actual proportion

presented. Symmetry detection thresholds (specified at

d0=1) were calculated using signal detection methodol-

ogy. These thresholds represent the proportion of mir-ror-symmetric pairs required to discriminate mirror

symmetry from the 0% symmetry condition at the 84%

correct level. The final threshold estimates represent

the weighted average of at least four blocks of 125 tri-

als/block, and the error bars are the 95% confidence

interval.

Between blocks we varied (1) the number of Gabor

patches (N) in a fixed radius stimulus field (N varied be-tween 8 and 48), (2) patch contrast (from 30% to 90%),

and (3) viewing distance (from 50 cm to 4 m) which var-

ied the spatial scale (i.e., the carrier spatial frequency,

envelope SD, radius, the angular size of the forbidden

zone and the angular separation between neighbouring

patches).

2.3. Observers

We tested two normal observers (one of the authors

and one naive as to the purpose of these experiments)

Table 1

Visual characteristics of amblyopic observers

Age Sex Eye

Observer Rx.

Anisometropic

AM 23 F O.D. +2.50/�1.0·005O.S. �0.25 DS

SL 26 M O.D. +6.25

O.S. +2.25

Strabismic

RH 32 M O.D. �1.00/�0.50·170O.S. �1.50/�1.50·10

Strabismic and Anisometropic

DS 26 M O.D. +2.25 DS

O.S. +0.50 DS

DM 40 F O.D. �0.50/�0.25·92O.S. +2.50/�1.0·160

DN 24 F O.D. +0.50

O.S. +2.75/�0.25·180AJ 27 F O.D. +5.50/�2.50·20

O.S. �0.25

a 75% correct on Davidson–Eskridge charts.b Fixation determined with haidinger�s brushes and visuoscopy.

and seven amblyopes (see Table 1). All of the observers

were highly practiced on psychophysical tasks in general

and our rating scale method in particular. Not all

observers were tested in all conditions. Observers viewed

the screen monocularly (with the untested eye occluded

with a black patch). All observers wore appropriateoptical correction and all were highly experienced in

making psychophysical judgements. The observers were

given several hundred practice trials in the symmetry

perception task, and we report thresholds after the ob-

server reached asymptotic performance.

3. Results

3.1. Vary viewing distance

We first measured symmetry detection thresholds for

a fixed number of patches (24) with a fixed contrast of

90% over a range of viewing distance. For amblyopic

observers the range of distances was limited by the visi-

bility of the patches (i.e., we required that the individualpatches be above threshold). Thus RH and DS were able

to perform the task at distances up to 4 m (15 c/deg)

whereas DM was limited to 1.33 m (5 c/deg). While nor-

mal and non-amblyopic eyes require about 30% corre-

spondence independent of target spatial frequency, in

order to discriminate mirror symmetry (Fig. 2––open

symbols), symmetry thresholds of all of the amblyopic

eyes begin to rise as spatial frequency increases (filledsymbols, Fig. 2). The thick lines in Fig. 2 are the best fit-

ting power functions fit to the data of the normal

observers (grey-dotted) and the non-amblyopic eyes

Acuitya Fixationb Strabismus

20/45 Central None

20/20 Central

20/38 Central

20/15 Central None

20/15 Central

20/59 Unsteady Microtropia l. et., 2D

20/40 2� nasal Constant r. et., 8D

20/20 Central

20/20 Central

20/80 0.50� nasal Constant l. xt., 3D

20/20 Central

20/52 1� nasal Constant l. et., 5D

20/60 1.5� temporal Constant r. xt., 4D

20/15 Central

Fig. 2. Symmetry detection thresholds as a function of patch spatial

frequency (lower abscissa) and patch Gaussian standard deviation

(upper abscissa). Target size and spatial frequency were manipulated

by varying the viewing distance. N was 24 and patch contrast 90%. The

open circles are thresholds of the normal observers, and open squares

the thresholds of the preferred eyes of amblyopes. Filled symbols show

the amblyopic eyes of seven amblyopes. Error bars are the 95%

confidence intervals. The lines are the best fitting power functions to

the normal (gray dotted line) and preferred (black dotted line) eyes.

2478 D.M. Levi, J. Saarinen / Vision Research 44 (2004) 2475–2482

(black dotted). These power functions take the form:

Th=Tha*[SF/1.88]n where Tha is the asymptotic thresh-

old at a spatial frequency [SF] of 1.88 c/deg and n is the

exponent (the slope of the line on log–log coordinates).

We use an asymptotic spatial frequency of 1.88 c/deg inorder to limit the fit to the range over which we actually

made measurements. For the normal and non-amblyo-

pic eyes, the slopes were effectively zero (0.04±0.03

and 0.006±0.06, respectively) indicating that symmetry

detection in normal vision is spatial frequency independ-

ent over this range. The amblyopic eyes show little or no

deficit in symmetry detection at low spatial frequencies,

but the deficits becoming increasingly apparent as thespatial frequency increases. 1 Below we examine, in

three highly experienced amblyopic observers, the nat-

ure of the deficit in symmetry detection.

1 The slope of the best fitting power function to the data of all

amblyopic eyes (not shown) was significantly different from zero

(0.23±0.06 p=0.0017). Restricting the fit to spatial frequencies below

10 c/deg still results in a highly significant increase in slope

(0.19±0.09). While the power function provides a reasonable descrip-

tion of the trend for the amblyopic observers as a group, over the range

of spatial frequencies tested, it ignores the clear individual differences.

The reader should judge the significance of individual differences based

on the error bars indicating the 95% confidence intervals.

3.2. Vary patch number and contrast

The elevated thresholds of the amblyopic eyes were

nearly independent of the number of patches (Fig. 3a)

or contrast (Fig. 3b), measured at the spatial frequencies

that were well within the observers� spatial frequencypass-band, and where the observers showed elevated

symmetry thresholds in Fig. 2 (i.e., 5 c/deg for DM,

7.5 c/deg for RH and 10 c/deg for DS). Importantly,

the contrast invariance indicates that the deficit is not

simply due to reduced stimulus visibility. The small ele-

vation in RH�s amblyopic eye symmetry threshold at

contrast near 50% is because the target contrast is close

to the individual patch detection threshold (48% meas-

Fig. 3. (a) Symmetry detection thresholds as a function of the number

of patches (N) and (b) symmetry detection thresholds as a function of

the patch contrast. Error bars are the 95% confidence intervals. Other

details as in Fig. 2.

D.M. Levi, J. Saarinen / Vision Research 44 (2004) 2475–2482 2479

ured in control experiments). Although the increased

threshold at the very highest spatial frequency in Fig.

2 may be in part due to poor visibility, the significant

threshold increase at 7.5 c/deg for observers SL, AM,

DN, and RH, at 6 c/deg for AJ, at 5 c/deg for DM

and at 10 c/deg for DS are not simply a consequenceof reduced contrast sensitivity.

4. Discussion

Our results show that when viewing with their ambly-

opic eyes, amblyopes have elevated symmetry detection

thresholds, and these are not solely a consequence of re-duced stimulus visibility. Our previous experiments (Sa-

arinen & Levi, 2000) showed that the perception of

global symmetry in normal vision was more difficult

when the carrier orientations of element pairs were or-

thogonal than when they were matched, suggesting that

the visual system performs symmetry detection most effi-

ciently by integrating information about the local orien-

tations in symmetric element pairs. This phenomenon isshown for normal observers in Fig. 4 (top panel): thresh-

olds for orthogonal orientations (mixed-opposing) are,

on average, 24% and 30% higher than for vertical and

for mixed-matched orientations respectively when

N=12, and 66% and 78% higher when N=48. Interest-

ingly, the amblyopic eyes have symmetry thresholds

for vertically oriented and mixed-matched patches that,

on average, are remarkably similar to those of normaleyes when the corresponding patches have orthogonal

orientations. It is as if the amblyopic eyes were unable

to make the local orientation matches required for opti-

mal symmetry detection.

In our experiments, the global pattern was mirror

symmetric with respect to the vertical meridian of the

visual field. However, we also made some measurements

of mirror symmetry with respect to the horizontalmeridian, and found that the amblyopic eyes showed

similarly elevated thresholds. Thus, the abnormal sym-

metry perception cannot be explained on the basis of

abnormal properties of the neurons in the corpus callo-

sum, which selectively interconnects cortical filters with

identical orientation specificity (Antonini, Berlucchi, &

Lepore, 1983; Schmidt, Kim, Singer, Bonhoeffer, &

Lowel, 1997).

4.1. Mechanisms of symmetry detection in normal vision

The mechanisms underlying symmetry detection in

normal vision are not well understood; however, Rain-

ville and Kingdom (2000) provide evidence that the neu-

ral coding of symmetry involves the integration of

oriented (low-level) spatial filters into ‘‘symmetry detec-tion units’’ (these are collections of self-similar oriented

filters) followed by some form of comparison (e.g. cross-

correlation) of the spatial contents from one side of the

axis, with the mirror image of the other side. Our finding

that symmetry detection is worse for orthogonal pairs

(Saarinen & Levi, 2000 and Fig. 4) is consistent with this

notion.

The comparison process required for accurate sym-metry detection can occur across substantial distances

(Barlow & Reeves, 1979; Tyler, Hardage, & Miller,

1995). The perception of mirror symmetry is not just

based on the features close to the vertical symmetry axis.

Our previous calculations (see Table 1 of Saarinen &

Levi, 2000), suggest that it is rather unlikely that single-

synapse connections in any of the early visual areas (V1,

V2, or V4) would mediate the comparison process sincethe extent of the intrinsic horizontal connections in these

areas is too short to convey the signals required for the

integration of local orientation in mirror-symmetric

pairs. Rather, we speculated that ‘‘higher’’ visual areas

may play an important role in the instant and effortless

perception of symmetry. Tyler (1999) has recently sug-

gested that the non-retinotopic region around the mid-

dle occipital gyrus on the lateral surface could mediatesymmetry perception. It is also possible that the ‘‘elabo-

rate neurons’’ (Tanaka, 1992) in the anterior inferotem-

poral cortex could detect symmetry in visual shapes.

These neurons tend to have large receptive fields and

can code positional relationships between stimulus fea-

tures.

It is also interesting to note that thresholds for the

mixed-matching condition shown in Fig. 4 are about30%––similar to thresholds obtained with all of the

patches vertical (see also Saarinen & Levi, 2000). Thus

the poor thresholds obtained in the mixed-opposing case

are not simply a result of having to separately scan two

feature maps (horizontal and vertical––e.g., Huang &

Pashler, 2002) but a consequence of the orientation spe-

cificity of the comparison process. Presumably with

mixed-opposing stimuli, the observer must use a lessacute, non-orientation dependent mechanism or strat-

egy.

4.2. Deficits in symmetry detection in amblyopia

The present results suggest that one can add to the list

of amblyopic deficits, reduced symmetry perception. We

note that both the strabismic and anisometropic am-blyopes in our sample showed reduced symmetry detec-

tion, and our results suggest further that this deficit is

not due to reduced stimulus visibility. How can the am-

blyopic losses be explained?

If the outline of the neural encoding of symmetry

detection outlined above is correct, then amblyopia

could produce deficits at several stages: (1) in the low-le-

vel filters, (2) in the integration process required to formsymmetry detection units, or (3) in the comparison

stage. Although we cannot rule out abnormalities in

Fig. 4. Symmetry detection thresholds for all vertical patches, mixed-matching and mixed-opposing patches. The top panel shows the normal eye

mean for N=12 and for N=48. The lower two panels are for each eye of amblyopes RH (N=12) and DS (N=48). The error bars are the 95%

confidence intervals. Note that for the amblyopic eyes, but not the normal or non-amblyopic eyes, vertical and mixed-matching thresholds are

elevated, and are close to thresholds for the mixed-opposing condition.

2480 D.M. Levi, J. Saarinen / Vision Research 44 (2004) 2475–2482

the low-level filters, we note that our stimuli were

highly visible, and well within the bandpass of the

amblyopes� visual systems. Moreover, the deficit is

contrast independent. Simply lowering the contrast

does not result in normal observers behaving likeamblyopes (Fig. 3). It is more difficult to rule out

low-level explanations such as undersampling and/or in-

creased topographical jitter. Thus, as discussed in

the Introduction, either low-level random undersam-

pling or increased jitter might be expected to elevate

symmetry thresholds for similarly oriented pairs of

patches. However, previous studies suggest that symme-

try detection is quite robust to spatial jitter (Barlow &

Reeves, 1979; Rainville & Kingdom, 2000), and

counter to our results (see Fig. 4), both low-level

undersampling and increased jitter would be expectedto also raise thresholds for orthogonally oriented

pairs.

We speculate that the amblyopic brain does not inte-

grate local orientations normally to form symmetry de-

tection units. Thus, when viewing with the amblyopic

eye, rather than using the highly acute orientation sym-

D.M. Levi, J. Saarinen / Vision Research 44 (2004) 2475–2482 2481

metry mechanisms, the observer uses the less acute, non-

orientation dependent mechanism or strategy (which is

not impaired). Thus performance with vertical or

mixed-matching stimuli is compromised, while perfor-

mance with mixed-opposing stimuli is more or less nor-

mal. While the similarity of the amblyopes� thresholdsfor vertical, mixed-matching and mixed-opposing stim-

uli may be coincidental, this is precisely what our spec-

ulation would predict. This speculation is consistent

with several other bits of evidence for anomalies in inte-

gration of orientation. First, while ‘‘crowding’’ in nor-

mal foveal vision only occurs with similar target and

flank orientations, some amblyopes show crowding

effects with cross-oriented targets and flanks (Levi,Hariharan, & Klein, 2002), suggesting that amblyopic

crowding, which extends over long distances, is qualita-

tively different from crowding in the normal fovea, and

that it may reflect abnormal pooling of information be-

yond the initial stage of feature extraction. Second,

some amblyopes show abnormalities in contour integra-

tion (Hess, McIlhagga, & Field, 1997; Mussap & Levi,

2000; Popple & Levi, 2000). For example, Levi, Klein,and Sharma (1999) showed that strabismic amblyopes

require more samples to be present in order to represent

a contour (an E-like figure) than did normal observers,

even though the individual samples were highly visible.

Like the present study, the deficit increased with spatial

frequency. Likewise, strabismic amblyopes undercount

the number of Gabor patches and the number of missing

patches, pointing to a deficit beyond the initial filteringstage (Sharma et al., 2000). Perhaps more relevant to

the present study, Popple and Levi (2000) showed

abnormalities in the perception of illusory tilts in tex-

tures of Gabor patches in both strabismic and anisome-

tropic amblyopes. These results could not be easily

modeled by low-level (filter stage) deficits, but could

be modeled by abnormalities at the level of second-stage

orientation grouping. Similar abnormalities in orienta-tion integration in both strabismic and anisometropic

amblyopes have been recently reported by Simmers

and Bex (2004). We suggest that the deficit in symmetry

detection described here can be understood similarly as

an abnormality in integration of local orientation in the

visual cortex of amblyopes.

Our results do not enable us to localize the abnormal-

ity in symmetry perception. Brain-imaging studies (PETand fMRI) have been rather inconclusive. Although

some imaging studies have suggested that the deficits

occur downstream of V1 (e.g. Imamura et al., 1997) oth-

ers show a clear deficit in V1 (Barnes et al., 2001; Good-

year, Nicolle, Humphrey, & Menon, 2000). To our

knowledge there have not been any functional imaging

studies addressing symmetry perception in amblyopia.

However imaging studies of symmetry perception innormal observers point to areas downstream of V1 (Ty-

ler et al., 1998; Wilkinson & Halligan, 2003). Interest-

ingly, some of these areas, e.g. the right anterior

cingulate gyrus, are associated with a variety of higher

level attentional functions (Wilkinson & Halligan,

2003).

If indeed, as we speculate, the deficit occurs beyond

V1, one might wonder why the deficit is not also presentin the non-amblyopic eye, since later stages of visual pro-

cessing are considered to be indifferent to the eye of sti-

mulation. Indeed, several ‘‘higher order’’ anomalies

have been reported which affect both eyes of amblyopes

(although to a greater extent in the amblyopic eye). These

include detection of second-order patterns (Wong, Levi,

& McGraw, 2001), abnormalities in orientation integra-

tion (Simmers & Bex, 2004). Thus the apparently normalthresholds of the preferred eye�s of amblyopes represents

a puzzle. We note that there are several unknowns. First,

while it is clear that higher visual areas are overwhelm-

ingly binocular in the normal visual system, there is little

evidence to suggest that this is also true in cases of abnor-

mal visual development which leads to a dramatic loss

of excitatory binocular visual connections in primate

V1 (Kumagami, Zhang, Smith, & Chino, 2000; Smithet al., 1997). Second, there may be specific tasks (e.g. sec-

ond-order detection tasks) in which performance of the

preferred eye is more sensitive to input (such as noise)

from the amblyopic eye than our symmetry task.

5. Conclusion

The instant and effortless perception of mirror sym-

metry in normal vision is strongly influenced by the local

orientations of the features. Our results suggest that mir-

ror symmetry perception is compromised in the ambly-

opic visual system, and we speculate that this may

reflect an abnormality in integration of local orientation

in the visual cortex of amblyopes.

Acknowledgments

We are grateful to Hope Marcotte-Queener for pro-

gramming the experiments, and to Roger Li for his help-

ful comments and suggestions. The research was

supported by a grant (RO1 EY 01728) from the Na-

tional Eye Institute.

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