Fusional limits for a large random-dot stereogram

t’ision Rex Vol. 28, No. 2, pp. 345-353, 1988 Printed in Great Britain. All rights reserved

0042-6989/88 $3.00 + 0.00 Copyright 0 1988 Pergamon Journals Ltd

FUSIONAL LIMITS FOR A LARGE RANDOM-DOT STEREOGRAM

CASPER J. ERKELENS

Department of Physiology I, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands

(Received 8 January 1987; in revised form 7 May 1987)

Ahstraet-Fusional limits of absolute retinal disparity between the two half-images of a large random-dot stereogram have been measured. The stereogram was viewed with disparity clamped at selected values (vergence loop opened), but without stabilization against conjugate eye movements, allowing the subject to look freely to different parts of the stereogram. Movements of both eyes were measured with a scleral coil technique. Limits for acquisition and retention of fusion were similar for the large stereogram. Total fusional ranges between 128 and 175 min arc were found in the different subjects. Limits for acquisition of fusion were smaller when fusion was preceded by prolonged stimulation with a large disparity (exceeding the fusional range) of the same direction (crossed or uncrossed). Thus, hysteresis between acquisition and retention was absent and the hysteresis present between loss of fusion and refusion was due to a reduction of the refusional limit. Probably this reduction is related to the recent history of binocular rivalry. Inspection of ocular vergence movements made during stimulation with constant or slowly changing disparity shows that neural remapping of retinal correspondence is rather unlikely.

Binocular vision Fusion Retinal disparity Fusional hysteresis

INTRODUCTION divergence (Hyson et al., 1983; Erkelens and Collewijn, 1985a).

Establishing and maintaining fusion of binocu- From these large fusional limits Fender and larly perceived images involves the contribution Julesz (1967) concluded that hysteresis is present of the sensory fusional mechanism as well as of in the fusional process. This hysteresis was the vergence system. Whenever disparity be- attributed to a capability of the visual system to tween similar images in the two eyes increases, enlarge its fusional range, whenever the object ocular vergence movements will reduce it as far had previously been projected within Panum’s as possible, keeping it within limits tolerated by fusional area. Fender and Julesz (1967) showed the fusional process. For fovea1 targets these that if the pulling of the random-dot half- limits amount to about 7 min arc of crossed or images exceeded the 2 deg limit, or if the stimu- uncrossed disparity (Mitchell, 1966). Under the lus was occluded briefly, fusion was lost until special condition that contributions to fusion by the half-images were brought within Panum’s ocular vergence movements were prevented by fusional area. Piantanida (1986), however, re- horizontal stabilization of the two images on the ported that refusion of two vertical lines as well foveae, Fender and Julesz (1967) found that as of two random-dot half-images occurred far fusion of two vertical lines (size 60 x 13 min arc) outside of Panum’s area and attributed the was maintained up to 65 min arc of uncrossed difference between his results and those of disparity, provided the disparity between the Fender and Julesz (1967) to the absence of lines was increased very slowly (2 min arc/set). fiducial marks in his experiments. Refusional By using a random-dot stereogram (size ranges of 44 min arc disparity at least for both 3.43 x 3.43 deg) the fusional zone was extended targets might indicate that the fusional zone for even further to 120 min arc of uncrossed dis- horizontally stabilized targets is far larger than parity. Recently, these findings were confirmed Panum’s area. If this is the case, it has important and extended to similar limits for crossed dis- implications for fusional hysteresis. However, a parity (Piantanida, 1986). Similar results were complicating factor could be the establishing of obtained under normal viewing conditions by a memory for recently viewed stereograms. If pulling the half-images beyond the limits of this plays a role, the recent history of viewing a

345

346 CASPEK J. ERKELENS

stereogram in fusion or rivalry might affect the refusional process. This point was not addressed in the experiments of Piantanida (1986).

On the basis of the presence of hysteresis in the fusional process, Hyson et al. (1983) pro- posed the hypothesis that correspondence be- tween similar images is not limited to retino- topically corresponding areas, but can be redefined to non-corresponding retinal loci. The neural mechanism operating the process of redefinition was called “neural remapping”. Piantanida (1986) adhered to this view and argued that no data were available opposing this hypothesis. Reliable information about the existence of neural remapping related to fusion might be obtained from ocular vergence re- sponses. The reasoning is that neural remapping is most likely to be accompanied by an arrest of ocular vergence movements, because, under normal viewing conditions, ongoing vergence movements would interfere with the correspon- dence just established.

The present report describes experiments sim- ilar to those performed by Fender and Julesz (1967) and Piantanida (1986). In addition, half- images were presented at constant absolute dis- parities under open-loop viewing conditions without a recent history of fusion or rivalry. Fusional limits for slowly changing absolute disparity show that hysteresis is also present in the fusional process when large parts of the retinae are stimulated. This hysteresis, however, is caused by reduction of the fusional zone after prolonged viewing of a stereogram in rivalry, and not by an extension of the fusional range during slow accumulation of disparity. Ongoing vergence responses as long as fusion is preserved do not favour the concept of neural remapping.

Subjects

METHODS

Four subjects participated in the experiments. All had 20/20 visual acuity or better, without (two subjects) or with correction. None of them showed any ocular or oculomotor pathologies other than refraction anomalies. Two of the subjects, an emmetropic male (HS.) and a myopic male (C.E.) wearing contact lenses for correction, were experienced in the viewing of stereograms with retinal disparity clamped. The two other subjects, a myopic female (J.N.)

wearing glasses and an emmetropic male (M.P.), served in such experiments for the first time.

Apparatus

Horizontal and vertical eye movements of both eyes were measured with induction coils mounted in scleral annuli in an a.c. magnetic field as first described by Robinson (1963) and modified and refined by Collewijn et al. (1975). The dynamic range of the recording system was d.c. to better than 100Hz (3 dB down), noise level less than 1 min arc and deviation from linearity less than 0.5%. Head movements were minimized by supports under the chin and around the skull.

The stimulus patterns were backprojected on a translucent screen (93 x 82 deg) at a distance of 1.43 m in front of the subject. Each pattern consisted of two half-images viewed by the left and right eye, and separated by colour filters mounted on the projectors and on spectacles (Cinemoid, primary green and primary red). Light separation between the red and green images was better than 99%. The luminance of the images was adjusted to equal brightness for the subject’s two eyes. Luminances of 14 cd/m* for light target elements and of 1 cd/m* for dark target elements were typical values. Subjects viewed the left and right half-images of a Julesz random-dot stereogram (30 x 30deg). With binocular viewing the random dots of the stereogram (Julesz, 1978; Fig. 6) were seen in two depth planes; the centre in the shape of a diamond was seen in front of the surround. The disparity between figure and background was 36 min arc. All targets were viewed without a visual frame of reference. Target vergence (Rashbass, 198 1) of these dichoptically presented images was defined as the angle sub- tended between the lines passing through the centre of each half-image and the nodal point of that eye by which it is viewed.

A minicomputer (PDP 11/73), used for stimu- lus generation, data collection and data anal- ysis, controlled the horizontal movements of the two half-images independently, by rotating two servo-controlled mirrors (General Scanning, Watertown, Mass.), mounted in the light path- ways. Half of the ocular vergence signal, com- puted from the difference between the measured horizontal eye positions, was fed to each of the two mirrors. As a result, any change in the ocular vergence angle was accompanied by a similar change in target vergence, keeping a constant retinal disparity between the half-

Fusional limits for random-dot stereogram 347

images. Thus, the retinal disparity between the half-images was stabilized for disparity. By addi- tional deflection of the mirrors by chosen values the retinal disparity of the half-images could be changed and clamped at any desired angle. The conjugate component of eye movements did not affect the mirror angles, so that the subject could freely scan the stereogram.

Procedure

The sensitivity of the eye movement recorder was adjusted at the start of each experimental session. A calibration target containing three fixation marks spaced at 10deg intervals was presented, and the subjects fixated on each mark in turn while gain and offset of the eye position signals were adjusted. The quality of the cali- bration was checked by opening the vergence feedback loop for disparity, while the subject scanned the depth plane in the centre of the Julesz stereogram. Whenever the angle of ocular vergence started to drift, the calibration pro- cedure was repeated. As a result of proper calibration the foveally viewed part of the stereogram was projected at corresponding retinal locations. All subjects could very easily fuse the stereogram and, moreover, could not tell whether it was viewed under normal or stabilized disparity conditions. Fusion was stable and intermittent disappearance of the cyclopean figure, as reported by Fender and Julesz (1967) and Piantanida (1986) who used complete stabilization of each half-image, was never observed.

Experiment 1

Essentially, this was a replication of the clas- sic experiment performed by Fender and Julesz (1967). In a sequence of 8 measurements, each lasting 32.8 set, the half-images of the stereo- gram were slowly pulled across the retinae in opposite horizontal directions. Vergence stabil- ization was switched on at the start of the first measurement and an uncrossed disparity was presented which increased from zero up to 197 min arc disparity with a velocity of 6 min arc/set. During a period of about 30 set after the measurement vergence remained stabilized and disparity was held constant at the ampli- tude of 197 min arc. At this high level of dis- parity the stereogram was perceived in binocu- lar rivalry by all subjects. The disparity amplitude was decreased to zero with the same speed in the second measurement. Subse- quently, these two measurements were repeated

but now for crossed disparity. Finally, the total sequence of 4 measurements was repeated once. During the full period of the measurements the subject indicated the presence of fusion by keeping a joystick in the utter right position and swinging it to the left whenever loss of fusion was experienced.

Piantanida (1986) reported that the maximal disparity at which the central figure was per- ceived in a depth plane different from the surround did not coincide with the disparity beyond which the half-images were perceived diplopic. The subjects in the present experiment confirmed this observation while viewing a stereogram with a linear size 10 times larger than the stereogram used by Piantanida (1986). Near the fusional limits the central figure re- ceded into the background, Shortly after depth had disappeared the ster~~am ~sintegrated and the half-images were seen in binocular rivalry. The visibility of the stereoscopic figure was a much easier criterion for fusion than the single vision of indi~dual dots. Therefore, the percept of a central diamond figure standing out in depth relative to the surround of the stereo- gram was used as the single criterion for fusion. This choice implied that the presence of fusion as indicated by the subjects was to some extent an underestimate of their fusional zones.

Exper~ent 2

In this experiment the half-images were presented at constant disparities without a re- cent history of fusion or rivalry. S~ulation with the half-images of the stereogram under stabilized conditions for vergence was inter- leaved with presentation of a line stereogram under normal viewing conditions by means of a shutter. The two lines forming the stereogram, each of which was viewed by one eye only, were 10 deg high and 25 min arc wide and subtended a target convergence of 4 deg. The pre~ntation of this target lasted 1 min at least during which the subject had to fuse the line. After this period the experimenter switched to the stabilized stimulus, provided that the subject perceived the line targets in binocular fusion. This procedure guaranteed that each presentation of the stimu- lus started at the same angle (4 deg) of ocular convergence. During the period that the subject viewed the line, an offset was superimposed on the positions of the half-images forming the random-dot stereogram. As a result, this stereo- gram was viewed with a constant disparity during the full period of presentation. During

348 CASPER J

such periods of 8.2 set the subject indicated the presence of fusion with use of the joystick. Crossed and uncrossed disparities up to 3 deg were presented in a randomized order. The experiment was replicated on different days for all subjects.

Experiment 3

In this experiment the half-images of the random-dot stereogram were viewed under sta- bilized conditions for vergence during the entire experiment. For periods of 20 see the stimulus was viewed with 4deg crossed or uncrossed disparity. From these starting conditions, in which the half-images were perceived in binocu- lar rivalry, the disparity was changed in a single step to a new fixed value between 3 deg of crossed and 3 deg of uncrossed disparity. During the following period of 8.2 set, in which the disparity remained constant, the subject indicated the state of fusion. Subsequently the disparity was set at 4 deg of either crossed or uncrossed disparity, selected randomly. The amplitudes of the test disparities were also presented in a random order.

Horizontal eye position signals were digitized on-line at a frequency of 125 Hz (resolution 0.8 min arc, 8 msec) after low-pass filtering with a cut-off frequency of 62.5 Hz, and then stored on disk.

Target vergence was calculated from the ex- perimental data by subtracting the position of the centre of the right half-image from the position of the centre of the left half-image. Ocular vergence was calculated in a similar way by subtracting the right horizontal eye position from the left horizontal eye position. Zero

ERKELENS

values corresponded to fixation of a point at infinity.

The vergence error (i.e. absolute disparity of the fixated depth plane) was calculated by sub- tracting the ocular vergence from the target vergence. Under stabilized conditions the ver- gence error was equal to the externally imposed disparity. Thus comparison of the calculated disparity signal with the imposed disparity pro- vided an off-line check on the quality of the stabilization.

RESULTS

Fusional limits under three d@erent experimental conditions

Figure 1 comprises the fusional limits ob- tained from Experiments 1 and 2. The fusional limits shown for slowly increasing and de- creasing disparity are the mean values from two trials. Generally, the difference between similar trials was smaller than 10 min arc for increasing disparity. Differences tended to be slightly larger for decreasing disparity indicating that subjects were less confident about refusion than about loss of fusion of the stereogram. In- spection of the joystick signals confirmed this impression. These signals showed considerably slower speeds and even interruptions of manual movements in refusion trials indicating more uncertainty of the subjects about the moment that the change from rivalry to fusion took place. The fusional limits for constant dis- parities which were measured on two occasions were well defined and very reproducible. The subject reported fusion for all disparities below the limit value, and loss of fusion for larger

Subject Oisparlty (min arc)

uncrossed crossed I__-___---__-_I___-_____-____-_-_________* 50 0 100

H.P.

J.N.

&<__-___---_--_--_---___-___---_------,1&f increasing ___>35--__---_____-__-________--_-----92___ decreasing

~&-----_-_----------___--__-_----_______*~~ constant

3,<___--_-_--______________->,O __->I,_---_-________S~<--_

46----------------__-_--__-__-__-_@

54<--_--__---__---------___-_----_______>I()3

H.S. ___>,S-___--_-______-53<---

S7----------____-_______________-__-__--____~~~

Fig. 1. Fusional limits for slowly increasing disparity, slowly decreasing disparity, and constant disparity between the half-images of the stereogram.

Fusional limits for random-dot stereogram 349

Table 1. Total fusional ranges of absolute retinal disparity expressed in min arc. The data were obtained from two trials

Increasing Decreasing Constant Subject disparity disparity disparity

M.P. 146 132 156 154 121 160

J.N. 102 58 125 112 72 132

H.S. 154 69 179 160 75 170

C.E. 155 92 168 150 84 162

Means f SD 142 & 22 88&226 156 f I9

disparities. After the experiment the subjects stated that the stereogram had been perceived in binocular rivalry in most of the cases in which they had signalled loss of fusion. The range of uncertainty around the limits, therefore, was within the in~~ment of 6min arc in disparity between stimulus presentations. Figure 1 shows that fusional limits for crossed and uncrossed disparity were rather different. They were at least 30 min arc larger for crossed disparity in all subjects and under all the three experimental conditions.

Table 1 shows the total fusional ranges for the stereogram under the three conditions. Sur- prisingly, the range was largest when the stereo- gram was presented without a recent history of fusion or rivalry. Averaged over the 4 subjects it amounted to 156 min arc. At an average of 142 min arc the fusional range was slightly smaller for the slowly increasing disparity con- dition Fusional ranges were rather smaller for slowly decreasing disparity. In this condition the total range amounted to an average value of only 88 min arc.

Influence of the recent fusional history on the fusional limits

An obvious reason for the smaller fusional ranges in the slowly decreasing disparity condi- tion would be the uncertainty displayed by the subjects. It was unclear, however, whether the smaller ranges were fully explained by this hesitation of the subjects in indicating refusion of the stereogram. To answer this question Experiment 3 was carried out, In this experi- ment decision time did not afkct the results, because the full period of 8.2 set in which the stereogram was presented with a constant dis- parity was available to the subject to decide about the state of fusion. The fusional limits for the condition that a constant disparity during

Subject Disparity bin arc)

uncrassed crossed *____-__--_--_~_______-----_______.._---__~

50 0 100

5i<_____----___________---____________-__,iOQ

H.P. --->~,_-_-____________--_-__-_______-_95<~-- ~~____---------_----__-_--_____-_______-_~*~

~~<____-_-_________-_-----_-______>~*

J.N. --,3~____________--_______54(-___ &___-___---____-__-__----____-_-__OZ

55<_____--_----__---__----______-__-___->*O~

H.S. ___>2&------_---__---_______--_79<-_--

6,__-____--___________--_________________-__*O~

5O<______--_--_______-__--____----______>gO

C.E. ___>pj____-----_______-_--__--_61(-___

6O_____-__---________________-__________-_*O$j

Fig. 2. Fusional limits for constant disparity preceded by stimulation with 4 deg of crossed (<-- -) or uncrossed (--->) disparity, or without (---) preceding disparity stimulation. Thus, for each subject the data in the upper row are fusional limits for constant disparity preceded by dis- parity of opposite polarity, and the data in the second row are fusional limits for constant disparity preceded by dis-

parity of the same polarity.

the test period was preceded by a larger dis- parity of 4deg are shown in Fig. 2.

The fusional limits appeared to fall into two groups depending on whether the disparity of 4deg and the disparity during the test period were both crossed or uncrossed or were opposite in direction. Whenever the disparities were op- posite in direction, the fusional limits well matched those found under the conditions that, disparity was either increased slowly (Experi- ment I) or presented abruptly (Ex~~ment 2). When, however, disparities were similar in di- rection, fusional limits agreed best with the limits found for slowly decreasing disparity. This means that the smaller fusional limits for slowly decreasing disparity were not just the result of the subject’s decision time. On the contrary, Table 2 shows that exposure to a large (non-fusable) disparity appears to induce a real

Table 2. Differences between fusional ranges for constant disparity with and without preceding stimulation with 4deg of crossed or uncrossed

disparity (min arc)

Preceding Preceding stimulation stimulation similar in opposite in

Subject direction direction

M.P. -26 2 J.N. -32 2 H.S. -68 -18 C.E. -66 -9 Means f SD -48f22 -6+10

350 CASPER J

reduction of the fusional range in the same (crossed or uncrossed) direction, but not in the opposite direction.

A control experiment for eflects of memory

At the beginning of all experiments the stereo- gram was viewed with zero disparity during the calibration procedure. This means that the stereogram was binocularly fused and, there- fore, known to the subject. One could argue that the fusional limits measured in Experiment 2 were not the maximal disparities at which fusion is acquired when the stereogram is viewed for the first time (initial fusion) but rather the disparities at which fusion is regained after a short loss of fusion (refusion). To find out whether memory affected the fusional limits, a Julesz random-dot stereogram was made resem- bling the one that was normally used. The internal structure and the hidden figure, how- ever, were different and unknown to the subject. After the calibration procedure, carried out with the normally used Julesz stereogram, the newly made stereogram was presented directly under stabilized viewing conditions at an uncrossed disparity just below the fusional limit measured for the same subject in Experiment 2. The two subjects (M.P. and C.E.) who participated in this experiment could fuse the stereogram and see the hidden figure within a few seconds. This result strongly suggests that the fusional limits measured in Experiment 2 are representative for initial fusion, and do not depend on memory of the previously viewed stereogram.

Ocular vergence movements

The constant or slowly changing disparities in the experiments induced ocular vergence move- ments. Uncrossed disparity evoked diverging movements and crossed disparity converging movements. The vergence movements in both directions were limited by the physiological limit of divergence or convergence. Consequently, converging eye movements were larger than diverging eye movements. Typical examples of converging eye movements in response to a constant disparity, or to a slowly increasing or decreasing disparity are shown in Fig. 3.

Sections of measurements are displayed in which the stereogram was perceived in binocu- lar fusion. Constant disparity induced ocular vergence movements the speed of which was related to the amplitude of disparity. The move- ments saturated at the limit of convergence or divergence. Ocular vergence remained near that

ERKELENS

limit as long as fusion was maintained, although it showed fluctuations of a few degrees at the limit of convergence in particular. Ocular ver- gence responded to slowly increasing disparity like to constant disparity by moving rather smoothly from the initial angle of 4deg of convergence to the limit of convergence or divergence. During stimulation with slowly de- creasing disparity, ocular vergence remained near its physiological limit until the end of the measurements.

DISCIJSSION

The results presented in this report confirm the findings of Fender and Julesz (1967) and Piantanida (1986) that fusional limits for slowly increasing disparity are larger than refusional limits for slowly decreasing disparity. Absolute disparity between stabilized images in the two eyes can be increased to about 2 deg without loss of fusion. These limits are not a special feature of the stabilized viewing condition, be- cause similar limits were also observed under normal viewing conditions (Hyson et al., 1983; Erkelens and Collewijn, 1985a). Refusional limits were in better agreement with those of Piantanida (1986) than those of Fender and Julesz (1967). Similar results were obtained de- spite the fact that free conjugate eye movements were permitted in the present experiments while the stereogram was completely stabilized in the

r- 0'

Fig. 3. Ocular vergeace movements (continuous lines) in- duced by a crossed absoiute retinal disparity (dotted line) between the half-images of the stereogram. The crossed disparity was constant (top figure), slowly increasing (mid- dle figure), or siowly decreasing (bottom figure). The left scale is for ocular vergence and the right scale for retinal

disparity.

Fusional limits for random-dot stereogram 351

experiments of Fender and Julesz (1967) and Piantanida (1986). This might indicate that con- jugate eye movements do not play an important role in the fusional process. In view of the relation between the size of Panum’s fusional area and target size, it is remarkable, though, that the fusional ranges for slowly changing disparity were about the same for stereograms as small as 3 x 3 deg and as large as 30 x 30 deg.

The limits measured for initial fusion (Experi- ment 2) throw a new light on the inte~~tation of hysteresis found in the fusional process. The ability to fuse a random-dot stereogram seen for the first time at a disparity just below the fusional limit provided evidence that the limits measured in Experiment 2 were truly limits for initial fusion. The finding that these limits were about the same as those for loss of fusion (Experiment 1) showed that for large-sized stereograms the fusional range is not stretched when disparity is slowly increased. Fusion of large corresponding retinal images is acquired and retained up to the same disparity limits. The lower refusional limits for slowly decreasing disparity seem to contradict this conclusion. Experiment 3 showed that refusional limits were only lower after a period of stim~ation with a disparity larger than the fusional limit of the same polarity (crossed or uncrossed). This sug- gests that during stimulation with slowly de- creasing disparity, fusion is hampered by the preceding stimulation with disparities above the fusional limit, during which the stereogram is perceived in binocular rivalry. At this point one can only speculate about the presence of fusion- al hysteresis for small fovea1 targets. Fender and Julesz (1967) investigated initial fusion by briefly occluding the eyes and found very low limits. However, they also found very low re- fusional limits. As was pointed out by Piantanida (1986) the low values of these limits could be caused by the presence of fiducial marks. Piantanida (1986) did not measure limits for initial fusion. Thus, there are two options for hysteresis between acquisition and retention of fusion; it does not exist at all or it is only manifest when the disparity between small reti- nal images is very slowly increased. Under nor- mal viewing conditions this stimulus is rather unrealistic. Small retinal images can only be experienced in darkness and slowly changing disparity implies an almost absence of ocular vergence movements. Fusional hysteresis for small targets was observed between disparities of about 1 and 2 deg (Piantanida, 1986). Ocular

vergence movements have speeds between 7 and 15 deg/sec (Rashbass and Westheimer, 1961; Erkelens and Collewijn, 1985b) in this disparity range. Such high speeds of ocular vergence make retinal disparity speeds of only a few minutes of arc@ under non-stabilized condi- tions rather unlikely. Thus, it is questionable whether hysteresis between acquisition and re- tention of fusion, if ever present, is a feature of normal binocular vision.

As was mentioned before, refusional limits during stimulation with slowly decreasing dis- parity appeared to be lower than the limits for initial fusion. It was concluded that a relatively long period of stimulation with large disparities, at which the stereogram is perceived in binocu- lar rivalry, prevented fusion to emerge at its nearby lying normal disparity limit. This effect may be related to the stimulus adaptation that was found in ocular vergence (Erkelens, 1987). When the vergence system was stimulated with a large constant disparity at which the retinal images could not be fused, the ocular vergence response to a range of disparities around the stimulus disparity gradually declined. It was hypothesized then that stimulation of binocular neurons responding to large disparities affected the response characteristics of neurons re- sponding to neighbouring disparities. Such a behaviour of binocular neurons would also ex- plain the lower refusional limits. To test this hypothesis, insight in the temporal character- istics of binocular neurons is essential. Un- fortunately, at present no substantial informa- tion is available on the temporal aspects of binocular neuron activity.

Lower limits for fusion after stimulation with large disparities in combination with adaptation of ocular vergence to large disparities may have implications for abnormal binocular vision. Both phenomena predict that the combined effort undertaken by the visual and the oculo- motor system to acquire single binocular vision declines whenever this goal is not reached within a short period of time. This situation may occur in some patients with comitant strabismus, whose retinal images cannot easily be brought within a fusable range by ocular vergence move- ments. The response of the visual and oculo- motor system to longstanding large and small disparities suggests that the heterotropia of such patients might be changed by decreasing the overall disparity between the two retinal images to within a range between 0 and 2 deg with help of prisms. In this range of disparity the two

352 CASPER J. ERKELENS

brought within Panum’s fusional area. This statement suggests that the disparity limits for matching are identical to the limits for fusion of a random-dot stereogram. This view, however, completely overlooks the contribution of ver- gence. Erkelens and Collewijn (1985a) showed that after a prolonged absence of fusion, efforts of the vergence system to reduce absolute dis- parity restarted at disparities of about 4 deg. Thus, the range in which vergence operated extended by far the range in which stereopsis was achieved. At least a part of the matching problem has to be solved prior to the initiation of vergence movements. This means that the disparity limits for matching are better related to the disparity limits of vergence than to the limits of fusion. I believe that stereopsis does not emerge as soon as the matching problem has been solved, but that another problem has to be solved before it can become manifest; namely how can a series of matched dots or forms with different disparities be related to each other and be fitted in a single stereoscopic percept. Appar- ently, this problem can only be solved for small absolute disparities. The relative disparity be- tween points in the stereograms that were used in the hysteresis experiments were fixed. With increasing absolute disparity this fixed relative disparity failed to lead to stereopsis whenever absolute disparity exceeded values of about 2 deg, although corresponding points could still be matched as indicated by the ongoing ver- gence efforts. This suggests that stereopsis is not limited by the inability to match corresponding points, but by the inability to relate correspond- ing points or shapes with different disparities to each other. The fact that binocular depth per- ception is based on relative disparity between objects, but that ocular vergence is driven by absolute disparity, i.e. differences in retinal locus (Erkelens and Collewijn, 1985b; Regan et al., 1986) may support this view.

retinal images might be fused and the vergence effort sustained, so that the eyes may be forced into a smaller vergence angle resulting in prism adaptation (Schor, 1979). Longlasting stimu- lation might change the amount of tonic con- vergence (Ogle and Prangen, 1953) and conse- quently change phoria to an angle between the initial heterotropia of the patient and ortho- phoria. If that situation should occur the pro- cedure could be repeated with weaker prisms until the phoria of the patient is minimized and finally might reach orthophoria.

A possible interpretation of fusional hyster- esis, as it was found for small targets, is the concept of neural remapping. In this view the fusional range is not stretched for slowly in- creasing disparity. The size of the fusional range would remain constant and shift along with the slowly changing disparity. Thus, the centre of the fusional range would not be fixed to retinal correspondence. This implies that absolute reti- nal disparity would not be a measurable entity. It would not be equal to the difference between target vergence and ocular vergence, but depend on the alignment of the “neural maps” at that time. For ocular vergence this would mean that a certain absolute retinal disparity might induce a converging movement at one time, no move- ment or even a diverging movement at other times. Such ocular movements, however, have not been reported in the literature and were not observed in the present experiments (Fig. 3). Once disparity drove ocular vergence to one of its physiological limits, it stayed there provided that fusion was maintained. This would not occur if the driving disparity had been interpre- ted as a zero input as a consequence of neural remapping, because without any drive ocular vergence is only stable between about 0 and 10 deg of convergence (Erkelens, 1987). Neural remapping was also not observed under normal viewing conditions in experiments in which the half-images of a stereogram were slowly pulled beyond the limits of divergence (Erkelens and Collewijn, 1985a). From the ocular vergence movements it is clear that neural remapping of retinal correspondence is rather unlikely. More- over, the need for invoking it seems no longer to exist, because equal limits were found for acquisition and retention of fusion of large retinal images.

Authors of papers on fusional limits (Fender and Julesz, 1967; Hyson et al., 1983; Piantanida, 1986) have stated that for solving the matching of corresponding dots, a stereopair has to be

Acknowledgements-This research was partly supported by the Foundation for Medical Research MEDIGON (grant no. 900-550-092). I am indebted to Professor H. Collewijn for valuable advice and discussion.

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