fusional limits for a large random-dot stereogram - Science Direct

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, The Netherlands

P.O. Box 1738, 3000 DR Rotterdam,

(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

INTRODUCTION

Establishing and maintaining fusion of binocularly perceived images involves the contribution of the sensory fusional mechanism as well as of the vergence system. Whenever disparity between similar images in the two eyes increases, ocular vergence movements will reduce it as far as possible, keeping it within limits tolerated by the fusional process. For fovea1 targets these limits amount to about 7 min arc of crossed or uncrossed disparity (Mitchell, 1966). Under the special condition that contributions to fusion by ocular vergence movements were prevented by horizontal stabilization of the two images on the foveae, Fender and Julesz (1967) found that fusion of two vertical lines (size 60 x 13 min arc) was maintained up to 65 min arc of uncrossed disparity, provided the disparity between the lines was increased very slowly (2 min arc/set). By using a random-dot stereogram (size 3.43 x 3.43 deg) the fusional zone was extended even further to 120 min arc of uncrossed disparity. Recently, these findings were confirmed and extended to similar limits for crossed disparity (Piantanida, 1986). Similar results were obtained under normal viewing conditions by pulling the half-images beyond the limits of

Fusional hysteresis

divergence (Hyson et al., 1983; Erkelens and Collewijn, 1985a). From these large fusional limits Fender and Julesz (1967) concluded that hysteresis is present in the fusional process. This hysteresis was attributed to a capability of the visual system to enlarge its fusional range, whenever the object had previously been projected within Panum’s fusional area. Fender and Julesz (1967) showed that if the pulling of the random-dot halfimages exceeded the 2 deg limit, or if the stimulus was occluded briefly, fusion was lost until the half-images were brought within Panum’s fusional area. Piantanida (1986), however, reported that refusion of two vertical lines as well as of two random-dot half-images occurred far outside of Panum’s area and attributed the difference between his results and those of Fender and Julesz (1967) to the absence of fiducial marks in his experiments. Refusional ranges of 44 min arc disparity at least for both targets might indicate that the fusional zone for horizontally stabilized targets is far larger than Panum’s area. If this is the case, it has important implications for fusional hysteresis. However, a complicating factor could be the establishing of a memory for recently viewed stereograms. If this plays a role, the recent history of viewing a 345

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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) proposed the hypothesis that correspondence between similar images is not limited to retinotopically 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 responses. 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 correspondence just established. The present report describes experiments similar to those performed by Fender and Julesz (1967) and Piantanida (1986). In addition, halfimages were presented at constant absolute disparities 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.

METHODS

Subjects 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 subtended 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 stimulus generation, data collection and data analysis, controlled the horizontal movements of the two half-images independently, by rotating two servo-controlled mirrors (General Scanning, Watertown, Mass.), mounted in the light pathways. Half of the ocular vergence signal, computed 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

images. Thus, the retinal disparity between the half-images was stabilized for disparity. By additional 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 calibration 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 procedure 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 classic experiment performed by Fender and Julesz (1967). In a sequence of 8 measurements, each lasting 32.8 set, the half-images of the stereogram were slowly pulled across the retinae in opposite horizontal directions. Vergence stabilization 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 amplitude of 197 min arc. At this high level of disparity the stereogram was perceived in binocular rivalry by all subjects. The disparity amplitude was decreased to zero with the same speed in the second measurement. Subsequently, these two measurements were repeated

stereogram

347

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 perceived 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 receded 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 stereogram 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 recent history of fusion or rivalry. S~ulation with the half-images of the stereogram under stabilized conditions for vergence was interleaved 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 stimulus 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 stereogram was viewed with a constant disparity during the full period of presentation. During

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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 stabilized 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 binocular 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 experimental 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 Oisparlty

Subject

values corresponded to fixation of a point at infinity. The vergence error (i.e. absolute disparity of the fixated depth plane) was calculated by subtracting the ocular vergence from the target vergence. Under stabilized conditions the vergence error was equal to the externally imposed disparity. Thus comparison of the calculated disparity signal with the imposed disparity provided 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 obtained from Experiments 1 and 2. The fusional limits shown for slowly increasing and decreasing 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. Inspection 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 disparities 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 (min arc)

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