Depth attraction and repulsion in random dot stereograms

Yirlon Res. Vol. 31. No. 5. pp. 805-813. 1991 Printed in Great Britain. All rights mcrvai

mM2-6989:91 53.00 f 0.00

Copyright6 1991 PergamonRW

DEPTH ATTRACTION AND REPULSION DOT STEREOGRAMS SCOrr B. STEVENSON, LAURENCE K.

CORMACK and

pk

IN RANDOM

CLETON

M. SCH~R

School of Optometry, University of California. Rerkeley, CA 94720, U.S.A. (Receired 31 January 1990; in reuircd form 19 July

l9!20)

At&met-Ptevious studies of perceived attraction or repulsion of adjacent visual targets have used local targets whose positions were varied in both depth and direction. We have measured these effects in three subjects using dynamic random-dot stereograms to isolate depth-axis effects. Results show that both attraction and repulsion effects can occur for overlapping, positively correlated. randomdot surfaces. The results were quantitatively similar to those reported previously for local targets. Manipulation of interocular correlation confirmed that the effects are produced by binocular interactions. Results are explained as accurate judgments based on the stimulus at the cyclopean ievel. Stereopsis

Random dots

Cross-correlation

INTRODUCTION

When visual targets are placed in close proximity to one another, whether in depth or in direction, their perccivcd positions arc shifted relative to their actual positions by as much as I min arc. These effects have been termed attractions and repulsions (Canz, 1964; Westheimcr, 1986), indicating the shift of a test target toward or away from an inducing target. While results vary with the individual subject, there is generally an attraction effect for test and inducing separations of less than 5 min arc, and a repulsion efTeet for larger separations. Westheimer (1986) and Westheimer and Levi (1987) have specilically addressed the question of whether the effects seen in the depth domain are completely accounted for by monocular effects which shift the visual direction of targets before they are combined at a subsequent binocular stage. Their results indicate that a depth axis effect occurs in addition to the changes in monocular visual direction, but their studies all involved local targets (points or lines) which necessarily have a combination of lateral separations and depth separations. We sought to examine the depth-axis component of attraction and repulsion effects with a stimulus-the dynamic random-dot stereogram-that allows for changes in target depth without changes in the monocular stimulus. We produced stereograms which portrayed two overlapped surfaces of random dots in the bottom half of the visual field serving as test and

Disparity

Averaging

inducing targets. A single surface in the top half served as an adjustable probe target (Fig. I). Changes in the disparity of thcsc surfaces are visible only in the binocular view. The monocular stimuli remain virtually unchanged, because each frame displays a new, random pattern of dots, providing no info~ation about the lateral image shifts which produce disparity (Julcsz, 1971). Thus, if any interactions occur between individual dots in the monocular stimuli, they will be constant across all binocular conditions and so any attraction or repulsion effects measured will reflect depth-axis inte~ctions only. The manipulation of interocular correlation provides another means of ensuring that binocular effects are isolated from monocular ones since it alters the visibility of binocular (cyclopean) surfaces without changing the monocular images in any detectable way. Interocular correlation is a measure of the degree to which the two monocular views match one another at a particular disparity. It is essentially a description of the signal strength of a random-dot surface. An interocular correlation of zero means that matches between the two monocular views are completely random. An interocular correlation of positive one means that the monocular views match exactly. An interocular correlation of negative one means that the monocular views are exactly opposite (every black dot is matched to a white dot and vice versa).

Scol-r 8.

806

SEVENSON

Fig. 1. Schematic depiction of subject’s task. Subject viewed a dynamic random-dot stereogram display containing three surfaces. labelled “adjustable probe.” “test” and “inducing” in the figure. The test and inducing surfaces were overlaid and appeared in the lower half of a circular 1I deg field. The depth separation of the test and inducing surfaces. and the correlation of the inducing surface were set by the experimenter. Probe and test surfaces were always positively correlated. The probe appeared in the upper half of the display and was adjusted by the subject to match the depth of the test surface. Configuration for the “inducing far” condition is shown. EXPERIMENT

1

We began our studies by testing for attraction and repulsion cffccts with positively correiatcd random-dot surfaces.

Stimuli. The stimuli used in ail our stud& wcrc dynamic random-dot stcrcograms which were displayed on video monitors (TSD modci HR,M, 60 Hz nonintcrlaccd) and viewed in a front-surface mirror haploscope. The dots wcrc generated by a pseudo-random noise generator that consisted of a 32 bit shift register, running at 7 MHz. with a NOT XOR combination of bits 23 and 30 fed back to the input. In this configuration, the resulting stream of bits repeats itself about every 2 min with equal numbers of on and off bits. Positive interocular correlation was produced by sending identical bit streams to the two video monitors. Negative interocular correlation was produced by inverting the sign of one of these bit streams. Zero interocular correlation was produced by sending independent bit streams to the two monitors. Disparity was manipulated by introducing a variable delay into the bit stream going to the left monitor. The output of the shift register was delay line (Data Delay fed into a programmable Devices model PDU- 13256). and the amount of delay was controlled by an AT clone computer. Upper and lower half-fields of the display were independently controlled by changing disparity and correlation at a fixed location in each video frame. OverIapped surfaces with different

et

al.

depths were independently controlled by alternating between two values of disparity and correlation on alternate video frames. The rapid (60 Hz) exchange between two disparity values which produced overlapped surfaces was never visible to the subject as such: neither motion in depth nor flicker were ever perceived. The resuiting stereograms portrayed three independent surfaces: a single one in the upper half-field and two overlapped ones in the lower half-field. Figure I shows a cartoon intended to represent approximately what the subjects saw when viewing the display. Appmzrus. The stereograms were viewed in a mirror haploscope arrangement at a distance of 57.3 cm. Convergence angle was set to match the viewing distance. Opaque circular apertures Ii deg in diameter masked the edges of the display. A horizontal black line subtending 3 min arc covered the center of the field where depth and correlation transitions occurred. The dots were 5 min arc wide, the contrast was about 80% (measured on a static dot pattern) and the mean luminance was about SOcd/m*. The AT computer controlled the disparity and correlation of the three surfaces and subjects made ~~~ijustm~nt settings by pressing keys on the computer keyboard. Prodwe. The apparent attraction or repuision of the overiappcd test and inducing surfaces in the lower half-field was measured by having subjects adjust the disparity of the probe surface in the upper half-field so that there appeared to be no depth difference between the probe and the test sufaccs. Ten adjustment settings were made for each depth separation of test and inducing surfaces. Each setting began with the probe at a randomly selected disparity. The difference between the mean of the 10 settings of the probe surface and the actual disparity of the test surface was used as an index of the attraction or repulsion for that condition. For most conditions, separate runs were made with the inducing surface nearer than and farther than the test surface. For small depth separations of the test and inducing surfaces, the gap between them is not visible and they appear as a single, thick surface (Stevenson, Cormack & Schor, 1989). In these situations the subjects were instructed to adjust the probe to match the depth of this single surface. Subjects. Subjects were two of the authors (SBS and LKC) and an undergraduate who was naive to the purpose of the experiments

Depth attraction and repulsion

(GSEG). Two were emmetropic and one wore contact lens correction. Complete data sets were collected on SBS and GSEG, and the basic results for expts I and III were confirmed on subject LKC. Results The attraction and repulsion effects measured in expt I are shown in Fig. 2. For each subject, the disparity difference between the test surface and the mean of the probe surface settings is plotted against the disparity difference between test and inducing surfaces. Attraction is represented as positive values on the vertical axis, repulsion as negative values. The horizontal line

807

which intersects the vertical axis at zero represents the expected result if no attraction or repulsion occurred. Symbols represent the mean of the 10 settings and error bars represent f 1 SD. The open and solid symbols represent the conditions in which the inducing surface was near and far, respectively. From all three subjects’ data it is clear that both attraction and repulsion effects occur under the conditions we have used. When the depth separation is zero, subjects align the probe to the same disparity as the combined test and inducing surfaces with high precision and accuracy. As the separation is increased, the probe settings indicate an attraction effect which

Interaction of random-dot surfaces both positive correlation

1

LKC

.o

05

^u b .s E

1.0

0.5

.A

0

z5 0

u ._,

-0.5

z ;

-1.0

0.

1.0

-

0.5

-

GSEG

Oj

-1.5+

0

,

,

,

)

2

4

6

6

Separation Fig. 2. Data

.

(

,

10

12

.

, 14

_ 16

(min arc)

for three subjects from cxpt I. in which the inducing

surface was positively correlated.

Perceived shift of test surface is plotted on the vertical axis against disparity separation of test and inducing surfaces on the horizontal are for “inducing disparity

near.”

axis. Solid symbols show data for “inducing Attraction

specifies. are plotted as positive values on the vertical negative values. Error

far” configuration,

open symbols

effects, in which test is perceived as closer to inducing surface than bars represent

axis. Repulsion

f I SD of the IO adjustment

efkcts settings.

are plotted

as

SCOTT

808

8. %TW!BsoN

peaks at 2-3 min arc of sepaqtion and returns to baseline at 4-6 min arc. Further separations reveal a repulsion effect which is maximum at 6-8 min arc of separation and returns to baseline at lO-12min arc. While there are some individual differences apparent in these data, the general result is the same for all three subjects. In addition, these results are in agreement with results reported previously for attraction and repulsion interactions for targets separated in depth and/or in visual direction (Westheimer, 1986; Westheimer & Levi, 1987). EXPERIMENT

et

al.

Intrmctionof rundam-dot zero correlation

swkcas control

15, 4

1.0

1 .r

0

f -0.5

f

-151

II

Methods

The next experiment was conducted as a control to ensure that the effects measured in expt I were due to binocular interactions, and not to interactions among elements in the monocular stimuli. While the use of random-dot stercograms should ensure this, we took the conservative approach of testing this assumption with a control experiment. The conditions were the same as in expt I except that the inducing surface was given zero correlation instead of positive corrciation. Thus, our procedure went through all the manipulations for prcscnting an inducing surface, but there was no binocular information to specify the surface. Under these conditions we expect no attraction or repulsion effects. Stimrli. The stimuli were the same as in expt I, except that the left and right monitors received statistically independent bit streams while the inducing surface was being displayed. This was achieved by having the computer switch an electronic gate at the same time it changed the disparity to that of the inducing surface. The gate determined whether the right monitor received the same bit stream as the left monitor or received a bit stream generated by an XOR combination of two different bits of the shift register. Subjects and apparatus were the same as in expt I. Proced4re. Since the inducing surface had zero correlation, it was not visible to the subject and therefore the lower half-field of the display always had a single, unambiguous surface to which the probe could be matched. Reslrlts

The results of expt II are shown in Fig. 3, plotted on the same axes as in Fig. 2. It is clear

-1.5-I

1 0

1

,

2

4

,

6

,

,

e

10

Separation (mln arc) Fig. 3. Data

for two subjects from cxpt II, in which the

inducing surface had zero correlation.

Axes and symbols are

the same as in Fig. 2.

from these results that no attraction or repulsion effects occurred when a zero-correlation inducing surface was used. Subjects always made an accurate and precise match of the probe and test disparities for all separations of test and inducing surfaces, with no evidence of any constant errors that would indicate attraction or repulsion.

EXPERIMENT

III

The next experiment sought to further explore the role of interocular correlation in the generation of the attraction and repulsion effects. Instead of a positively correlated inducing surface, we used a negatively correlated inducing surface. The probe and test surfaces were positively correlated as before. While we had no specific predictions of the outcome of this experiment, we reasoned that if interocular correlation is an accurate descriptor of the binocular stimuli whose interactions we measured in expt I, then a negative inducing stimulus should produce essentially opposite results.

Depth attraction Metho& Stimuli. The stimuli were the same as in expt I and II except that the left and right monitors received exactly opposite bit streams while the inducing surface was being displayed. As before. the computer switched an electronic gate at the same time it changed the disparity to that of the inducing surface. This gate determined whether the right monitor received the same bit stream as the left monitor or received a digitally inverted version of the bit stream. Subjects and apparatus were the same as in expts I and II. Procedure. For small separations of test and inducing surfaces, the presence of the negatively correlated inducing surface tended to cancel the positively correlated test surface, making it

and repulsion

809

difficult or impossible for the subjects to perform the task. This was generally true for separations below l-2 min arc. so settings were not made for separations in this range. For larger separations, the positively correlated test surface was not cancelled by the negatively correlated inducing surface and the standard procedure was used. Results The results from expt III are shown in Fig. 4, plotted on the same axes as in Figs 2 and 3 except that the scale has changed on the vertical axis. All three subjects show a repulsion effect that is greatest for small separations of test and inducing surfaces and tapers off to baseline at about 10 min arc. Note that the results are

Intoration of random-dot surfacer positive and negative correlation 21

, 1

LKC

-

-31

=a

-1

2

s

a;

-2

-3 2

GSEG

1

0

-1

-2

0

2

4

6

a

10

12

14

?6

Separation Imin arc) Fig. 4. Data for three subjects from expt Ill, in which the inducing surface was negatively correlated. and symbols are the same as for Figs 2 and 3. except for the vertical scale.

Axes

?iCOl-K 8. STEVENSON et d.

810

generally but not exactly the opposite of the results from expt I. Small separations produce a repulsion effect instead of an attraction effect, but in most cases, larger separations do not produce an attraction effect where repulsion occurred in expt I. Note also that the variability of the settings, as indicated by the error bars, is very high for small separations. This is in agreement with the observation that the test and inducing surface tend to cancel at small separations, making the task more difficult.

lus, the visual system responds to a proximal one that has been filtered by the optics of the eye and, in this case, processed by monocular stages of vision before some matching process extracts the information required to perform the task. With this in mind we performed a computer simulation designed to describe the information available to the “cyclopean retina” (Julesz, 1971) under the conditions of our experiments. This information was then used to determine how subjects would be expected to perform in the tasks based on the information provided to their binocular visual mechanisms. Any departure from this performance would indicate central interactions among the processes involved, assuming an accurate stimulus description.

DISCUSSION

The results of these three experiments indicate that attraction and repulsion effects do occur for stimuli which isolate depth-axis changes from monocular visual direction changes. This confirms the conclusions of Westheimer (1986) and Westheimer and Levi (1987) that the depthaxis effects are not due simply to monocular interactions, and it extends the generality of their findings to include random dot stereograms in the list of stimuli which show these interactions. In particular, the powerful effect of intcrocular correlation on these interactions is strong cvidcncc that the interactions arc occurring in the cyclopean domain; that is. at the level of binocular interaction in the visual system. HIMULATION

Methods

Figure 5 illustrates our approach to the simulation. On the left-hand side is a cartoon intended to represent the stages of vision involved. The images are generated on the video monitors, blurred by optics, imaged on the two retinas, processed through some monocular stages of vision, combined by binocular mechanisms and then analyzed by “downstream processcs” to dctcrmine the relative depths of image fcaturcs. On the right-hand side of Fig. 5 is a parallel structure describing our simulation of thcsc events. First, left- and right-eye “image” arrays of 5 min arc dots were constructed with a simulation of the pseudo-random noise generator. These were then smoothed (blurred) with a sine-squared function and added to a realvalued “retinal” array with 0.5 min arc receptor

I

In order to better understand these effects. it is necessary to start with a complete description of the stimulus to the cyclopean Icvel of vision. While our methodology specifies a distal stimu-

Simulatron

Visual Stages

E!!!La

Image

Array

Smoothing

Optics Monocular

Differencing,

Call.S

Averaging

Binocular

Cross Correlation

Cells

Localization

Decision I Fig. 5. Schematic

outline of rationale

for simulation.

processing presumed to occur on viewing a dynamic stages of the computer

simulation

The left panel represents stages of visual image

random-dot

intended

stereogram.

to parallel

The right panel represents

the visual stages.

Depth

5

E.,.,1

c

Cm*r-cormlaUontunctlon mlnsre dots. 4 mtnsm blur

0

-10 dlrpsrlly

Fig. 6. Cross-correlation ated random-dot in depth.

10

In

function

mln of smoothed,

images which portray

Interocular

attraction

correlation

vertical axis against disparity

differenti-

a single. flat surface

product

is plotted on the

in min arc on the horizontal

axis. Dot size for this simulation

was 5 min arc, as in the

actual

were

experiments.

sine-squared

Dot

function

arrays

smoothed

with

a

whose full width was 4 min arc.

spacing. This process was repeated for 1 set of model time, to simulate time-averaging over several video frames. These arrays were then converted to their first-difference functions, to simulate edge extraction in the visual system. The resulting left- and right-eye arrays were cross-correlated over a range of horizontal disparity to yield functions of intcrocular correlation vs horizontal disparity. Finally, statistics arc computed on thcsc functions to localize fcaturcs in them.

Figure 6 shows the result of this simulation for the case in which test and inducing surfaces were both positively correlated and had zero separation. (This is equivalent to a single, flat, positively correlated random-dot surface.) Interocular correlation. or matching strength of the random-dot pattern is plotted on the vertical axis as a function of horizontal disparity on the horizontal axis. The function shows a broad peak of correlation at zero disparity, negative side-lobes at a distance of one pixel on either side of the peak, and zero correlation for all other disparities. The breadth of the cross-correlation function on the disparity axis is largely determined by the amount of blur introduced by the optics, which we have simulated by smoothing the image arrays. The high correlation at zero disparity occurs because identical patterns were used for the right and left eye images. The zero correlation at most other disparities occurs because the dot patterns are random and the simulation averaged over a large enough region that spurious matches (“false targets”) were cancelled out.

and repulsion

811

The side-lobes of negative correlation are the result of having matched edge information in the random dot stereograms. Binary-valued random-dot patterns have two constraints which give rise to these negative side-lobes. First, the spatial quantization into pixels constrains the shortest distance between edges in the random dot image. Second, a rising (or falling) luminance edge in the image is always adjacent to either no edge (0 correlation) or a falling (rising) edge (- 1 correlation) one pixel away. Thus, at a disparity equal to one pixel’s width on either side of a correlated surface where all edges match, on average there is a correlation of -0.5. Side-lobes with some amount of negative correlation usually occur (when edge information is matched) for images that have been quantized into pixels. They also occur for spatially broadband natural images that have been low-pass filtered, by optics for example (Nishihara. 1989). Negative side-lobes do not usually occur if gray-level (zero order) luminance information in the images are matched, instead of edge (first order) information. A bright dot is always adjacent to either a bright dot (+ I correlation) or to a dark dot (- I correlation), producing an average correlation of zero. The function in Fig. 6 simulates the information available to the subjects in our task to specify the location in depth of a single randomdot surface. Figure 7 shows a series of cross-

-10

10

0 Disparity IminI

Fig.

7. Series of cross-correlation

two overlaid,

positively correlated

varying disparity separation. The

top-most

function

functions

representing

random-dot

surfaces of

Axes are the same as in Fig. 6.

represents

surfaces with zero dis-

parity difference, and is the same as the function in Fig. 6. Functions

for progressively

larger separations

are plotted

with vertical offsets for clarity. One surface is placed at zero disparity

in every function,

while

the other

is placed at

successively larger negative disparity values in steps of arc. The simulated

I min

subject’s task was to locate the “test

surface” peak near zero disparity

in each function without

regard to the position of the “inducing

surface.”

2 shows good agreement between our simulation and the data collected in expt 1. The simulation shows an attraction effect for small separations of test and inducing surface, a crossover at about 5 min arc of disparity separation and a repulsion for still larger separations.

Slmulrtlon

SIML‘LATION 0

2

4

6 SeporatIon

6

10

12

14

16

fmln ofd

Fig. 8. Results of Simulation I in which test and inducing surfaces are both positively correlated. The predicted shift of the test surface in min arc is plotted on the vertical axis against the disparity separation of test and inducing surfaces on the horizontal axis. E&h function represents the value of a statistic computed on the cross-correlation functions shown in Fig. 7 to localize the peak near zero disparity. Heavy curve represents the location of local maximum (mode) nearest zero disparity in eztch cross-correlation function. Lighter curves represent mean and median values computed for the region bounded by nearest minima in the cross-correlation functions. Comparison to Fig. 2 shows goad agrrrment between data and simulation.

correlation functions simulating two randomdot surfaces with varying amounts of depth separation. The function at the top of the figure is the same as that plotted in Fig. 6, and represents zero disparity dilTerence between test and inducing surface. The placement of the functions is such that the component produced by the test surface is always in the same position, running straight down the page, while the component produced by the inducing surface is displaced incr~~lsingly to the left in steps of I min arc of disparity. As the depth separation between test and inducing surface is increased, the cross-correlation function becomes broader and then splits into two clearly discriminablc components. Since the subjects’ task was to locate the position of the test surface, the last stage of our simulation was to localize the test component in the cross-corrclotion functions of Fig. 7. We computed the mean, median and mode of each function in the region surrounding zero disparity. The mean and median were computed for the region bounded by local minima on either side of zero disparity. Figure 8 shows the location of the computed mean, median and mode values as a function of the disparity difference between test and inducing surfaces in our simulation. The mode values are plotted with a heavier line for emphasis because they involve fewer assumptions than the mean and median values and because they seem to fit the data best. A comparison of Figs 8 and

II

Experiment II, the control condition in which the inducing surface had zero correlation, was not simulated. Since the zero-correlated inducing surface produces no signal in the crosscorrelation function, only the test surface is visible and no attraction or repulsion effects are expected. SIhllJLATfON

iI1

in order to simulate the results of expt III, in which a negatively correlated inducing surface was used, we followed all the same steps as above except that the image array values for one eye were inverted on the appropriate frames. The cross-correlation function for a single, negatively correlated random-dot surface is exactly the inverse of the function shown in Fig. 6, with high negative correlation at the disparity of the surface and positive side-lobes on either side. The simulation was carried out for a range of disparity separations of the positive test and negative inducing surfaces. The same rules described above for Simulation I were applied in order to localize the test component for each separation of test and inducing surface. RWdlS Figure 9 shows a series of cross-correlation functions representing a positively correlated o-2

-

-4

-6

-

-8

+

0

-30 Disparity

30

lminl

Fig. 9. Series of cross-correlation functions as in Fig. 7. but with a negatively correlated inducing surface. Test surface is placed at zero disparity in each function, while inducing surface is placed at successively larger negative disparity values in steps of I min arc. Note that the top-most function is flat. due to complete cancellation of overlaid positive test and negative inducing surfaces at zero disparity separation.

Depth

Sepomtlon Fig. 10. Results of Simulation

attraction

(mtn an)

111 in which inducing surface

was negatively correlated, for comparison to data in Fig. 3. Axes and functions are the same as in Fig. 8.

test surface with fixed disparity and a negatively correlated inducing surface which is displaced increasingly to the right in steps of 1 min arc of disparity. Figure IO is a plot of the mean, median and mode values as a function of the disparity separation of the two components. The values for the mode are once again plotted with a heavier line for emphasis. A comparison to the data in Fig. 4 indicates that the experimental and simulation results arc in good agreement for expt 111as they were for expt I. The simulation shows the most repulsion for small separations and shows a gradual decrease in the effect up to 8-10 min arc of separation. DISCUSSION

Given the assumptions of our simulation, that the visual system matches edge information in blurred images averaged over space and time, it appears that subjects made accurate judgments of the location of the test surfaces. That is, their responses reflect the information they were given. We have found no evidence of a shifting of perceived position due to central interactions. The attraction and repulsion effects seen in the data are consistent with identification of the peak or some other centroid in the cross-correlation function, with the effects being caused by the interaction of the profiles of the two component cross-correlation functions. In particular. the negative side-lobes in these profiles give rise to the repulsion effects found in the data. Perhaps previous suggestions of lateral inhibition were based on an intuitive realization that some negative side-lobes were required in order to account for repulsions. Our finding is that these side-lobes occur in the stimulus, if one

and repulsion

813

assumes that edge information is used in the binocular matching process. If one assumes instead that gray-level (zero order) luminance information is used, these side-lobes do not occur and the repulsion effects are not predicted. Such a model might then involve inhibition among central, binocular units in order to account for all the experimental results. Given that cortical visual neurons in nonhuman primates are known to respond to edge information, our assumptions seem most reasonable in this regard. Thus, while inhibitory interactions certainly occur at many levels of the visual system (probably including the processes which extract edge information), our results suggest that inhibitory interactions at the central level are not causing the depth attraction and repulsion effects we have measured. In summary, we have measured the perceived position of a test surface in random-dot stereograms in the presence of an inducing surface whose depth and correlation were varied. We found attraction and repulsion effects like those reported by others for local targets, confirming that the interactions which produce these effects occur at binocular levels of the visual system in the disparity domain. A simulation of the information available to this level of the visual system suggests that the interactions occur due to summation of the cross-correlation profiles of the surfaces. Acknow/e&e~enr~-The her cooperation.

authors thanks subject GSEG

This work was supported

for

by NE1 NRSA

grant no. EY-06045.

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und

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