Temporal aspects of depth contrast

~2-6989193 $6.00 + 0.00 Copyright Q 1993 Pergamon Press Ltd

Vision Rex Vol. 33, No. 7, pp. 941-957, 1993 Printed in Great Britain. Al1 rights reserved

Temporal Aspects of Depth Contrast T. KUMAR,*

DONALD

A. GLASER*

Received 7 October 1991; in revised form 4 February 1992; in final form 2 October 1992

Depth contrast is a contrasting change in the depth of a feature that results from changes in the disparities of other objects in the field of view, even though the disparity of the original feature remains unchanged. Depth contrast effects decrease during continuous viewing of the stimuli and may disappear altogether after several minutes unless the disparities of the inducing features change with time. This fading occurs wbenever the inducing features have constant disparity, whether they are stationary or oscillating laterally. Depth contrast effects occur whenever the ind~ing features are visible within half a second before or after presentation of the test features. When test features are enclosed by a rectangle which is just inside of a circumscribing outer trapezoid, the inner rectangle “shields” the test features front the depth-inducing effects of the outer trapezoid. Surprisingly, this shielding effect persists if the inner rectangle and outer trapezoid have the Sante slant direction, but fades with time if the slants are opposite in direction. Stereopsis

Binocular

vision

Depth

contrast

Disparity

In reporting his experiments on depth contrast,? Werner stated that, “At the beginning of each single observation, the contrast effect appears generally to be more pronounced than it does as the observation continues” (Werner, 1937, p. 112). Informal observations during our previous studies on depth contrast (Kumar & Glaser, 1991, 1992) confirm Werner’s report. We have quantified Werner’s observation and find that the perceived depth does not settle down to the value predicted by the disparities of the test features alone, but remains influenced by surrounding inducing features. In our earlier investigations on depth contrast (Kumar & Glaser, 1991, 1992) observation times were < 100 msec which ruled out mechanisms involving changes in either the direction of gaze (Werner’s solution) or cyclotorsional movements (Ogle’s explanation). In Werner’s experiments, however, significantly longer observation *Department of Molecular and Cell Biology, Neurobiology Division and Department of Physics, c/o Stanley/Dormer ASU, 337 Stanley Hall, University of California, Berkeley, CA 94720, U.S.A. tWe have followed the lead of Werner, Ogle, Wallach (Wallach & Lindaur, 1961) and others [see Nelson (1977) for other references and history] in referring to the phenomenon under study as the depth contrast effect. Nelson (1977) called the depth contrast effect “simultaneous contrast in disparity” to distinguish it from depth after-effects which he classified under successive contrast. However, nearly all the stimuli used in this paper are similar to the ones used by Werner and for the sake of historical continuity and simplicity we followed Werner’s terminology. He used depth contrast when the depth induced in the test features was in contrast to the primary depth of the frame. Test features that appear at equal depth when seen by themselves are seen at different depths in the presence of depth inducing features and compensating disparity has to be imparted to the test features for them to be seen at equal depths in the presence of inducing features.

Depth

perception

times were used so that changes in eye ~sition during the observations could play a role. The goal of our investigation is to understand this reduction in the depth contrast effect which follows continued observation. Our experiments were designed to address the following questions: can this reduction be due to changes in eye position or to some other mechanism? Does this compensation for the depth inducing effect require that the image be relatively stationary on the retina? Do the inducing and test features have to be presented simultaneously to produce depth contrast, and if not, what is the effect of asynchrony between the inducing and test features? For stimuli with multiple inducing features, what is the effect of the prolonged display of some of the inducing features and brief presentation of others? Is depth contrast the result of a complex cognitive process in which disparity processing is but one of the minor contributing events? In this paper we describe seven experiments that address these questions. In the first experiment we varied the presentation time to quantify Werner’s observations and found that the depth contrast effect is about half as large for viewing times >500msec as it is for 10 msec, but remains significant even for viewing times of 1.5 sec. In the second experiment we found that the depth contrast effect fades for briefly seen test features when the inducing features are visible for extended periods of time even when these inducing features are oscillating laterally. However, if it is the disparity of the inducing features that oscillates during a long viewing time, the induction effect does not fade for briefly seen test features but is the same as would result from some time-averaged “effective” disparity. The third experiment showed that fading of the depth contrast effect does not depend on the shape of the inducing features.

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The inducing pattern can be a trapezoidal frame, a uniform grid of dots or a single dot. In the fourth experiment, we measured the effect of asynchrony between briefly presented test and inducing features. Depth contrast effects were found to decrease with increasing asynchrony and are evident whenever the inducing features are shown within less than about 500 msec before or after presenting the test features. The fifth experiment showed that a dark, empty field displayed for 1 set between 2 see presentations of the inducing features is sufficient to prevent the cumulative fading of the depth contrast effect which results from extended viewing of the inducing features. The sixth experiment used two enclosing frames, a trapezoidal frame with inducing disparity and a rectangular frame in the frontoparallel plane with zero inducing disparity shown for extended periods of time (Fig. 1, stimuli I and J). When the rectangular frame was inside of the trapezoidal frame, it reduced the depth contrast effect significantly for brief and extended observation times, but had a negligible effect when it was the outer frame. In the seventh

experiment both the inner rectangle and other outer trapezoid had inducing disparity. As before, the inner rectangle determines the depth contrast effect with the disparity of the outer frame apparently contributing very little to the result. This dominance of the inner rectangle persists if the continuously shown inner rectangle and briefly presented outer trapezoid have the same slant direction but fades with time if the slants are opposite in direction. Thus, the temporal aspects of depth contrast effect cannot be characterized simply with one or two time constants. METHODS We will describe the experimental arrangement and procedure briefly since they have been reported in detail already (Kumar & Glaser, 1991). The stereoscopic stimuli were presented on two identical Hewlett-Packard vector oscilloscopes (HP-1345A) fitted with Polaroid polarizers so that observers could see only one oscilloscope with each eye. The frontal

view of the two test

FIGURE 1 ficing page). Description of stimuli. The frontal view of the stimuli used in the various experiments are shown. All the stimuliexceptA, C, D, E and F are to the same scale, let us say I unit to 1 deg of arc. Stimulus A is drawn to a scale of 1 unit to 2.5 deg of arc and stimuli C, D, E and F are drawn to a scale of 1 unit to 0.5 deg of arc. The left and the right eyes’ views have been superposed with the dashed lines and open dots representing items shown to the left eye and the solid lines and solid dots representing items shown to the right eye. Configurations I and II of stimuli B and H-L are shown explicitly. The configuration not shown for stimuli A, C, D, E, F and G is obtained by exchanging the right and the left eyes’ views. The two central vertical lines or dots represent test features in the various stimuli and are shown with zero disparity; hence only the solid lines and solid dots are shown. (A) The inducing rectangle was 9.36 deg high and 12.44 deg wide in one eye’s view and 9.36 deg high and 10.44 deg wide in the other eye’s view, giving a magnification of 12.44/10.44 or 19%. The test features were two dots 5 min arc in diameter, 21.6 min arc apart horizontally and located on the horizontal axis symmetrically in the center of the rectangular frames. The dots in the remaining stimuli were all < 1 arc min in diameter. Results for this stimulus are shown in Fig. 2. (Bj The inducing trapezoid was 60 min arc wide in one eye and 50 min arc in the other, giving a magnification of 20%. The central two vertical test lines were both 20 min arc long and 8 min arc apart. (C) The inducing feature was a single 1 min arc dot and the test features were again dots 1 min arc in diameter, 8 min arc apart and 2 min arc vertically below the depth inducing dots. The horizontal separation between the inducing and test dots was varied during the presentation. A more complete description of the stimulus and results for stimuli B, C and I3 are given in the legend for Table I. (D) Dots with diameters somewhat less than 1 min arc were arranged in 1I coIumnsand 6 rows separated by 8 min arc. The disparity increment was 1 min arc per column, with the outermost columns having 5 min arc crossed and uncrossed disparities, giving a 12% horizontal magnification. The test lines were 24 min arc apart and 20min arc long, placed symmetrically around the center of the grid of dots (each line was 12 min arc horizontally away from the central column). (E) The stimulus consisted of four dots on a horizontal axis; the central two dots were the test dots whose relative depth was reported by the observers; the outermost two dots were inducing dots. The separation between the inducing dots was 40 min arc in one eye and 32 min arc in the other eye, giving a magnification of 25%. The separation between the test dots was 12 min arc. (F) The separation between the central two test dots was 12 min arc as for (E). The separation between the outer inducing dots was 38 min arc in one eye and 34 min arc in the other, giving a reification of 12%. (G) The separation between the outer inducing dots was 339 min arc in one eye and 262 min arc in the other eye, giving a magnification of 29%. The separation between the central two test dots was 15 min arc. The results for stimuli E, F and G are shown in Figs 3 and 4. (H) The inducing feature was a trapezoidal frame that was 2.05 deg wide in one eye and 1.72 deg wide in the other giving a magnification of 19%. The vertical edges of the trapezoid were l.SSdeg and 0.81 deg high. The central test lines were both 10min arc long and 15 min arc apart, positioned s~rnetri~ly in the middle of the trapezoidaf frame. The results using this stimulus are shown in Fig. 5. (I) A rectangular frame 1.33 deg wide and 0.81 deg high in both eyes was interposed between a trapezoidal inducing frame and the test lines. Only the solid lines for the rectangular frame are shown. The dimensions of the trapezoidal frame and the test lines were the same as in stimulus H. (J) A trapezoidal frame 1.45 deg wide in one eye and 1.22 deg wide in the other eye, with identical height in both eyes of the vertical edges of 0.81 and 6.8 min arc was enclosed in a rectangle 2.05 deg wide and 1.58 deg high in both eyes. This corresponds to a magnification of 19% for the trapezoidal frame. Again, only the solid lines are shown for the rectangular frame. The test lines were each 10 min arc long and 15 min arc apart horizontally and placed at the center of the enclosing frames. The results for stimuli I and J are shown in Table 2. (K) The trapezoids and the test lines were the same dimension as in H. A rectangle of height of 0.81 deg in both eyes and 1.45 deg wide in one eye and 1.23 deg wide in the other eye ~~~ifi~tion of 18%) was interposed between the inducing trapezoidal frame and the test lines. (L) All the dimensions were the same as in K. The wider trapezoid and rectangle were shown to the right eye in configuration 2 in K and were shown to the left eye in configuration 1 in L. The slants of the trapezoid and the rectangle were in the same direction for these two cases and were in the opposite direction in configuration 1 in K and configuration 2 in L. The results for stimuli K and L are shown in Fig. 6.

DEPTH CONTRAST

features and the depth inducing features used in the various experiments are shown in Fig. 1 and the dimensions of these stimuli are described in the figure legend. Two test features and some nearby depth-inducing features were displayed and observers reported whether the left test feature appeared closer to them or farther away than the right test feature. The observers were given no indication whether their responses were “correct” although their continuing participation in the experiment indicated that their responses were felt to be useful. The disparity of the right feature was always zero with respect to the frames of the oscilloscopes, whereas the disparity of the left feature was selected randomly from a set of six disparities, chosen so that the observers’ responses spanned the range from almost always “closer” to almost always “farther”. A preliminary run was sometimes necessary to determine a suitable range of disparities for each individual observer, but data from this preliminary run were discarded. Each run was long enough to insure that there was an average of 30 responses for each of the six disparity values of the test feature for a given configuration of the depth inducing features. The percent of total responses called “closer” was fitted to a psychometric function chosen to be the integral of a Gaussian using the probit method to compute a mean and a slope of the curve. The mean of the psychometric curve was the point for which the responses were equally divided between the “left test feature reported closer” and “left test feature reported

farther away” than the right test feature, and it can therefore be considered as an estimate of the disparity of the left test feature needed for it to appear at equal depth to the right test feature. The slope of the psychometric curve was used to obtain the conventional estimate of the stereoscopic acuity for the particular configuration of the stimulus. A minimum of four runs was conducted to obtain the average of the mean and of the threshold. Additional runs were carried out if there was any evidence of training. The results presented are based on the average of the last four runs which exhibited asymptotic performance. In the absence of depth-inducing features the mean of the fitted curve was within a few arc seconds of zero disparity for all the observers tested. However, when depth inducing features were added, compensating disparity had to be given to the test features in order that the observers perceive the two features at equal depth. This was reflected in a change in the mean of the psychometric function to a value significantly different from zero. Since the quantity of interest was a change in the mean of the psychometric function, two different (but related) configurations of the inducing features were presented at random during any given run. The configurations were chosen so that the expected compensating disparity was uncrossed in one configuration and crossed but of about the same magnitude in the other. By convention we refer to crossed disparity as positive and uncrossed disparity as negative in this paper. The two H

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1

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T. KUMAR and DONALD A. GLASER

configurations of the inducing features were obtained by interchanging the two eyes’ views except when the inducing frame was trapezoidal in shape (Fig. 1). When the inducing feature is a rectangular frame or grid of dots (Fig. l., stimuli A, C, D, E, F and G), the wider frame was shown to the left eye in configuration 1 and the narrower frame shown to the right eye and vice versa for configuration 2. We will refer to configuration 1 as having negative frame disparity and configuration 2 as having positive frame disparity. For configuration I, the right vertical edge of the frame was perceived closer than the left vertical edge. In this case, consistent with the depth contrast effect, the left dot of the central test dots shown in the center of the frame appeared closer than the right one, although both dots had zero disparity and should have appeared to be at the same depth. The left dot had to be given uncrossed disparity in order for it to appear at the same depth as the right dot. For configuration 2, the left dot had to be assigned crossed disparity in order for the two dots to appear equidistant. For the trapezoidal inducing frame, perspective information and disparity information supported each other and, as before, the left test feature had to be assigned uncrossed disparity for configuration 1 and crossed disparity for configuration 2. The frontal view of these stimuli (B and H-L) for both configurations is shown in Fig. 1. When the sign of the compensating disparity given to the left test feature is the same as that of the inducing frame, the situation is consistent with the conventional depth contrast effect. Except in Expts 6 and 7 the magnitude of the required compensating disparity was essentially the same for the two configurations and the value reported is the average of the compensating disparities measured for the two configurations. In previous studies (Kumar & Glaser, 1991, 1992) we showed that the required compensating disparity was roughly proportional to the separation between the test features, proportional to the disparity of the surrounding frame for some range of disparity values

*The lines and dots used to draw the various frames and test features are not magnified; only the separation between these features is changed. A frame of width L shown with disparity D means that the width of the frame in one eye was L + 1D l/2 and the width in the other eye was L - 1D l/2 where 1.1is the absolute value of the enclosed quantity. Magnification of the frame is then defined as (L + 1D l/2)/(,5 - 1D l/2) which is always > 1. The magnification factor is defined as the above quantity minus 1, which is ID l/(L - ID l/2). Similarly the magnification factor of the test features is Idl/(a - [d//2) where d is the measured compensating disparity and a is the horizontal separation between the test features. Using the sign convention that disparity D is positive when the width of the inducing frame is larger in the right eye and negative when it is narrower in the left eye, and disparity d of the left test feature is positive for crossed disparity and negative for uncrossed, the percent magnification factors may be written as 100 D/(L - 1D l/2) and 100 d/(a - Id l/2). The CMF is the ratio of these 2% magnification factors x 100: 100 (d/(a - IdIP))/ (D/(L - ID l/2)). To be consistent with the conventional use of contrast in the depth contrast effect, CMF should be positive, i.e. d and D should have the same sign.

and inversely proportional to the width of the surrounding frame. The shape of the inducing pattern as well as its location and disparities had a large effect on the compensating disparity. For example, a rectangular inducing frame required a compensating disparity 2-3 times larger than that required by the vertical sides alone, although they had the same disparity information as the whole rectangular frame. A trapezoidal frame required a larger compensating disparity than a rectangular frame of comparable size. The depth contrast effect clearly depends on more than the disparities of the features and their horizontal separations. A measure which perhaps captures the magnitude of the depth contrast effect better than compensating disparity alone is the compensating magnification factor (CMF).* In previous studies (Kumar & Glaser, 199 1, 1992) we varied the dimensions of the inducing and test features and found no abrupt changes in the induced depth as the dimensions of a given configuration were varied. In this study we examined the temporal properties of the depth contrast effect while varying the dimensions and geometry of the stimuli considerably while keeping the magnification of the inducing frame fairly constant (see Fig. 1 legend). We don’t know of any studies that show that variations in the dimensions and geometry of the stimuli have a large effect on the temporal properties of disparity processing or the depth contrast effect. Since Expt 4 suggests that such an effect cannot be ruled out, we measured the compensating disparity for simultaneous presentation of inducing and test features for each stimulus so that temporal changes could be compared unambiguously with the corresponding situation with no time delays. The dots and lines making up the stimulus appeared bright against a dark background in all of the experiments. The observers had normal vision with standard corrective glasses or contact lenses and were selected on the basis of their performance on a stereo acuity task using a stimulus consisting of three parallel vertical lines 15 min arc long and 15 min arc apart. They reported whether the middle line appeared closer or farther than the outer two lines and were selected if their initial stereo acuity threshold was t40 set arc.

EXPERIMENTS

Efect

AND RESULTS

of presentation time on the depth contrast effect

The dimensions of the stimulus [Fig. l(A)] were identical to those of the principal stimulus used in our earlier report (Kumar & Glaser, 1991). In this experiment we measured the dependence of the depth contrast effect on the duration of the presentation time. For four observers, the depth contrast effect shown in Fig. 2 is reduced by about half for presentation times > 500 msec when compared with the results for 10 msec. It is significant even for presentation times of 1.5 sec. In the next experiment we measured the effect of displaying the inducing features for times much longer than 1.5 sec.

DEPTH CONTRAST

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50

Presentation Time (msec ) FIGURE 2. The effect of duration of presentation time of inducing frame and test dots on depth contrast. The dimensions of stimulus are given in the legend for Fig. l(A). In a singie trial the rectangle and the central dots were presented sim~~neo~ly for the iength of time indicated and preceded and followed by a dark empty visual field presented for 250 msec. For the remaining time a single dot was shown in the center of the visual field to help maintain convergence. The total time for a trial was 4 set when the presentation time of the rectangular frame and the test dots was > 1set; total trial time in all other cases was 3 sec.

E#ect of extended presentation times of stationary and moving inducing features We studied the effect of displaying the inducing features continuously during an entire run. Under these conditions the inducing stimulus used in Expt I induced a negligible change in the depth of the test features. If the inducing features move on the retina while being viewed for long times and again induce a negligible change in the depth of briefly presented test features, the depth contrast effect cannot be due to fine tuning of eye position as required by Werner’s (1937) or Ogle’s (1946) explanation even for these long observation times. Retinal coordinates are therefore not expected to play a major role in explaining depth contrast. It was not possible to do that experiment with a stimulus of the size used in Expt 1 since the active drawing area of our oscilloscopes is 12.6 deg wide x 9.65 deg high at 50 cm viewing distance, barely larger than the stationary stimulus itself. Using an inducing frame 60 min arc wide by 50 min arc high [Fig. l(B)] viewed at a distance of 3 m, the active drawing area subtended just over 2 deg of visual angle and we could move the inducing frame right and left horizontally with an amplitude of 30min arc (see the legend of Fig. 1 for stimulus details). At this viewing distance we could reliably measure changes of a few seconds of arc in the mean of the psychometric function. Since a trapezoidal inducing frame requires more com~nsating disparity than any other shape we “R33,7--D

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have tested (Kumar & Glaser, 1992), we could measure any residual depth contrast effect consistently for different observers under these new stimulus conditions. Depth contrast effects essentially vanish after extended viewing whether the frame is stationary (Table 1, column 6, rows 1 and 4) or moving to and fro horizontally (Table 1, column 4, rows 1 and 4). For comparison, we also measured the effect of presenting both the test and inducing patterns simultaneously for 102 msec (Table 1, column 3, rows 1 and 4) and found a very significant amount of compensating disparity was required. However, when the disparity of the frame was made to oscillate with time, the depth contrast effect was reduced by about half (Table 1, column 5, rows 1 and 4) compared with that obtained for a brief static presentation at the maximum disparity of the oscillating display. In earlier studies we found that the shape of the inducing features had considerable effect on the size of the depth contrast effect (Kumar & Glaser, 1992) and in the next experiment we tested two additional shapes for the inducing feature in order to determine whether the fading of depth contrast measured in this experiment depended upon the shape of the inducing features. Eflect of extendedpre~entation of various shapes

times of inducing features

Two additional shapes were used: a single dot as the minimal inducing feature [Fig. l(C)] and a grid of uniformly spaced dots [Fig. l(D)]. The grid of dots with the inducing disparity distributed over the entire pattern, was the stimulus that ~itchison and Westheimer (1984) used (see their Figs 3 and 4) when they found that “its tilt out of the fronto-parallel plane is almost impossible to detect”, but the mean compensating disparity for frontoparallelism of the pair of test lines depended nevertheless on the tilt of the background sheet of dots. In comparison, the depth corresponding to the inducing disparity of a single dot was readily detectable and the trapezoidal frame in Expt 2 above always appeared tilted. Displaying the grid of dots for 1 set before presenting the test lines allows an observer enough time to achieve a stable depth percept for this stimulus configuration which is inherently susceptible to the “wallpaper effect”. Therefore, the grid was not moved and its disparity was not changed during the experiment. As in Expt 2 above, the single dot was made to oscillate in position or in disparity and was visible continuously during an entire run while the test features were presented only briefly (102 msec). The depth contrast effect was again negligible when the inducing features were shown for extended times (Table 1, column 4 and 6) and was somewhat reduced when the disparity of the inducing dot varied periodically (Table 1, column 4). During the 102 msec that the test features were being shown, the stimulus configuration was identical for the various conditions of stimulus presentation listed in Table 1 and described above. Inducing features that are seen for more than a few seconds lose their influence on the perceived depths of other items whether or not they are stationa~ in retinal coordinates. Perhaps this fading or

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T. KUMAR and DONALD A. GLASER TABLE 1.Threedifferent types of inducing frames were tested for extended presentation times and two were tested while moving to and fro horizontally with constant frame disparity (frame oscillating laterally), or while stationary but with their disparities varying ~riodically (frame with oscillating disparity) CMF

Observer KV

TK

Frame type (stimulus) Trapezoid (B) Single dot (Cl Grid 0) Trapezoid (B) Single dot (Cl Grid (D)

Frame flashed Oil

169 k 10 56+4

Frame oscillating laterally

Oscillating frame disparity

Frame always on

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5+-3

7&5

37&2

6&4

54 + 5

254

9726

9+3

58 & 6

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37 & 5

614

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The first inducing frame was a trapezoid [stimulus Fig. l(B)]. The test lines were positioned symmetrically in the center of the trapezoidal frame and shown for 100 msec. Sinusoidal horizontal translation oscillations of amplitude 30 min arc and frequency of 1 Hz were approximated by horizontally displacing the frame through a series of positions 6 min arc apart in the same direction in each eye and presenting the frame for a varying amount of time at each position. The lengths of time in msec that the frames were shown at different positions starting from an extreme position on the left to an extreme position on the right were 102, 46, 37, 33, 32, 32, 32, 33, 37, 46 and 102. The cycle was completed by running this sequence backwards (note that the time spent at an extreme position is IO2 and not 204 msec). The test lines were presented at the same position on the oscilloscope for 102 msec every third cycle when the frame was at the leftmost position of its motion. For the remaining time a single fixation dot was shown at the position which corresponded to the midway point between the test lines when they were presented. An identical sequence of times was used to present oscillations in disparity of the inducing feature. The extreme positions of the oscillations corresponded to (1) 5 min arc crossed disparity of one of the vertical edges with 5 min arc uncrossed disparity of the other vertical edge of the trapezoidal frame and (2) 5 min arc uncrossed disparity of the first edge with 5 min arc crossed disparity of the second edge. The displacement in disparity of each edge was 1 min arc for each new value of disparity shown in the sequence of presentation times given above. The second type of inducing feature tested was a single 1 min arc dot [Fig. l(C)] which was shown in our previous study (Kumar & Glaser, 1991) to be able to induce a depth contrast effect. The third type of inducing feature tested was a grid of dots [see Fig. l(C) for dimensions]. The test features for stimulus C were again dots I min arc in diameter, 8 min arc apart horizontally and 2 min arc vertically below and about 30 min arc laterally away from the depth-inducing dot. The motion and displacement of this feature were identical to those of the trapezoidal frame described above, since this stimulus was generated from the above by showing only a 1min arc segment from the left vertical edge of the trapezoidal frame and the same test lines.

“adaptation” affects some internal representation of depths in the environment and is inde~ndent of whether or not the depth profile of the inducing features is easily detected. The effect is the same when the inducing disparity is localized in a single dot or uniformly distributed in a grid of dots. EJJ;ectof asynchrony between briefly presented test features and depth -inducing features How long does the influence of a briefly presented inducing feature last? We investigated this question by displaying the inducing dots for 50 msec and the test dots for 25 msec. A dark empty field was interposed between them when the asynchrony was < 200 msec or a single dot was presented in the center of the visual field when the asynchrony was > 200 msec to help maintain convergence. Asynchrony is defined here as the time interval

between the. of&et of the first dot pair shown and the onset of the second pair. This ~~c~ony is called positive when the inducing dots precede the test dots and negative when the test dots precede the inducing dots. The stimulus consisted of four dots on a horizontal axis. Observers were asked to report the relative depth of the two central test dots and the two outermost dots were the inducing dots [Fig. 1 (E, F, G)]. The total time for a singie trial was 3 set and a single dot in the center of the field was shown during the inter-stim~us time interval. All the dots were about 1 min arc in diameter. We selected this arrangement as the stimulus because very few parameters are needed to specify it and the effect of varying the spacing between the dots can be investigated without worrying about the accompanying shape changes possible for more complicated inducing features. The separation at zero disparity between the

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DEPTH CONTRAST test dots was 12 min arc for E and F and 1.5min arc for G. The average of the separations between the inducing dots in the two eyes was 36min arc for E and F and 300 min arc for G; the differences between their separations in the two eyes was 8 min arc for E, 4 min arc for F and 77 min arc for G. This gives magnifications of 25% for the inducing dots of E, 12% for F and 29% for G. Results for two observers are given in Figs 3 and 4. Depth judgments of the test dots are found to be influenced by the inducing dots if they are displayed in the time interval between 500msec before to 200msec after the test dots appear. The observers reported a strong sense of apparent motion for stimulus F in Figs 3 and 4 for async~onies > 100 msec, which interfered seriously with the observers’ ability to perceive depth and produced larger errors for those conditions. We did not test whether negative values of CMF were always accompanied by perception of motion, although that is possible. In investigating the spatial distribution of disparity inter~tions, Westheimer (1986) and Westheimer and Levi (1987) reported an “attraction” or a “repulsion” effect: features less than about 6 min arc apart laterally appear to “pool” their disparities and are perceived closer to each other as if attracting each other while features farther away laterally are perceived as if repelling each other. In this notation the usual depth contrast effect or positive CMF corresponds to the repulsion effect and negative CMF to the attraction effect. We do not know the relationship between the disparity interactions reported here and those that

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FIGURE 3. The effect of asynchrony in the presentation of inducing dot and test dots. CMF as a function of synchrony for two observers is shown. The stimuhzs arrangement used is shown in E, F and G of Fig. I. Asynchrony is defined to be positive when the central pair of test dots are shown after showing the outer two in’ducing dots and negative when the inducing dots are shown after showing the central test dots. CMF is positive by definition when the perception of the depth of the test dots is consistent with the usual depth contrast effect and negative when it is not (see main text for additional description).

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Westheimer reported. Westheimer (1986) reports only a very small temporal after-effect; when the inducing disparity features are shown before the test features, the spatial pattern of attraction or repulsion remained unchanged (see his Fig. 5). Our data show a much stronger temporal after-effect. Induction effects are found in our expe~ments to depend on the positions of items and their disparities and also strongly on time. Since our stimulus arrangement and Westheimer’s were very simple (only four dots on the horizontal axis in our experiment), the differences between our results and Westheimer’s are unlikely to depend on high level shapedependent cognitive processes. The only difference between the stimuli E and F is that the disparity of the inducing dots for E is twice that of those for F. If the CMF measure were able to capture the depth contrast effect completely, one would expect the ratio of CMF for F to that for E to be about 2. The measured value is not 2, except maybe for zero asynchrony. Separations between the features for stimuli E or F was quite different than for stimulus G. CMF values for stimuli E or F are negative for negative asynchrony, but are positive for stimulus G for the same asynchrony. This difference implies a time-dependent spatial effect requiring a reversal of sign of the compensating disparity which extends our earlier rule that the required compensating disparity is inversely proportional to the width of the simultaneously presented inducing frame. This suggests that the temporal properties of depth contrast might depend significantly on the geometry of the inducing features. Effect of a time delay between the onsets of inducing features and briefy shown test features Depth contrast fades slowly when the inducing features are displayed continuously and test items are

954

T. KUMAR and DONALD A. GLASER

presented briefly as in Expts 2 and 3. What is the timecourse of this fading? We attempted to measure this by presenting the inducing features [Fig. l(H)] for 2 set and the test features for 100 msec beginning after some delay, T, from the onset of the inducing features. The total time for a single trial was 3 set, with a single dot being shown in the 1 set inter-stimulus interval. The CMF for two observers is shown in Fig. 5 as a function of the delay time, T. We found that observers do not “adapt” to the depth of the inducing frame shown this way and there is no apparent slow cumulative adaptation when the same configuration is shown every 3 set for 2 set at a time. The time constant for fading appears to be much longer than a few seconds. Thus, both the inducing frame and the test features have to be shown simultaneously for the entire presentation time to produce the reduction in the depth contrast effect seen in Expt I and the inducing frame has to be shown continuously for extended times to produce fading of depth contrast. Repeated exposure to the inducing frame does not produce a “cumulative” fading of the depth contrast effect.

-B-

EO

-%--

K”

FRAME ON FOR 2 SEC. TEST LINES ON FOR 100 MSEC AFTER T MSEC

al

TIME 2 SEC 0

i 0

I

I 500

vmo

l5cul

‘T’MSEC

FIGURE 5. Effect of time delay between onsets of presentation of inducing trapezoid and test dots. The stimulus dimension and arrangement is shown in Fig. l(H). The central test lines were shown for 100 msec after a delay of T set from the onset of the inducing frame. The frame was shown for 2 set beginning every 3 set; 3 set was the total time for one trial. Data were first collected when the two configurations were randomly interdigitated during a run; later, data were collected for each configuration separately. The effect was independent of whether the configurations were run intermixed or separately and the results given are averages over all the data collected in both ways. The CMFs are given for two observers as a function of delay time. For comparison, the solid symbols show the results (same as those given in Table 2, row 2, under stimulus I) when the inducing trapezoidal frame and the test lines were shown simultaneously for IOOmsec.

Inner and outer inducing features While studying depth contrast, Ogle (1946) found that observers showed a markedly different response to inducing features when there were items located between the test features and the original inducing features. Mitchison and Westheimer (1984) reported a “shielding” effect due to intervening features. Since it appears that temporal proximity is necessary to “bind” the visual effect of inducing features to the test features over large visual angles, an important question is, does the effect of the intervening features fade if they are shown for extended periods of time? We investigated this question by comparing the depth contrast effect of two types of stimulus geometry shown as stimulus I and J in Fig. 1. Stimulus I had an outer trapezoidal frame that was slanted with respect to the frontoparallel plane and enclosed a rectangular frame in the frontoparallel plane. Stimulus J had a rectangular frame in the frontoparallel plane enclosing a trapezoidal frame which was slanted with respect to the frontoparallel plane. The test lines were shown symmetrically in the center of the frames for both stimuli. The idea was to determine if a rectangle in the frontoparallel plane that is shown all the time participates in the depth contrast effect, whether it intervenes between the depth-inducing trapezoidal frame and the test lines or encloses both the trapezoid and the test lines. The results of two observers for the six different conditions under which the effect was measured are given in Table 2. When the inducing trapezoidal frame is in the frontoparallel plane (row 1), the induced depth, if any, is very small compared with the situation in which the frame is slanted with respect to the frontoparallel plane and shown simultaneously with the test lines (row 2). When the trapezoidal frame is shown all the time and no rectangle is shown, the depth contrast effect essentially disappears (row 4). When the rectangle in the frontoparallel plane is shown simultaneously with the inducing trapezoidal frame and the test lines, the depth contrast effect is insignificant when the rectangle is between the inducing frame and the test lines (row 3, stimulus I) and essentially unaffected by the rectangle when it encloses both the inducing frame and the test lines (row 3, stimulus J). These results are consistent with the “shielding” concept proposed by Mitchison and Westheimer (1984) and the observations by Ogle (1946). If the trapezoidal frame is shown all the time and the rectangle and the test lines are presented for 100 msec, there is no measurable depth contrast effect when the frame encloses the rectangle and the test lines (row 5, I) and perhaps a very small effect when the inducing frame was between the test lines and the rectangle (row 5, J; cf. row 4, J). A feature shown all the time seems to contribute little to the depth contrast effect in these experiments, leading to the expectation that when a continuously shown rectangle is between the inducing frame and the test lines, it would not “shield” out the depth contrast effect seen for the test lines. Surprisingly, the shielding effect persists even when the intervening rectangle is

955

DEPTH CONTRAST TABLE 2. Stimulus configurations shown in Fig. 1 (I, J) CMF KV

EO Condition Only a trapezoidal frame with zero disparity and the test lines were shown simultaneously for lOOmsee Only a trapezoidal frame with given disparity and the test lines were shown simul~neously for 100 msec Trapezoidal frame with disparity, the rectangle and the test lines were all shown simultaneously for 100 msec Trapezoidal frame with disparity is shown all the time and the test lines are shown for 100 tnsec (rectangle not shown) Trapezoidal frame with disparity is shown all the time and the rectangle and the test lines are shown simultaneously for 100 msec Rectangle is shown all the time and the trapezoidal frame with disparity and the test lines are shown simultaneously for 100 msec

I

J

I

J

2,2

2t2

4+3

3+2

60*3

59 &-2

54&3

51%4

3&2

60 + 3

142

61+4

1+2

I+2

l&2.

2_+3

1*2

4&2

l&3

6*2

10+2

72+4

122

73+4

The trial time was 3 set and a fixation dot was shown midway between the usual positions of the test lines when the test lines were not being shown. There was an interval of 250 msec before and after the presentation of the test lines and the fixation dot during which only the continuously shown feature was visible. When no feature was shown continuously, the 250msec interval was occupied by a dark, empty visual field.

displayed continuously, and the depth contrast effect was rather small compared with the condition in which no rectangle was shown (compare row 6, I to row 2, I). Observer EO, unlike KV, showed a slightly increased CMF for the continuously displayed intervening rectangle when compared to the simultaneously presented one (cf. row 6, I to row 3, I) indicating perhaps slightly less shielding by the continuously displayed rectangle than the simultaneously presented one. The important fact is that the required compensating disparity for both of these conditions was small indicating considerable shielding. The differences between them were also small and might not be significant. When the rectangle enclosing the inducing frame and the test lines and was shown all the time, the measured induced depth appeared to be slightly larger than when the frame was not shown at all (cf. row 6, J to row 2, J). These surprising changes in CMF indicate a temporally dynamic interaction between the rectangle and the trapezoidal frame more complex than the original expectation that a continuously displayed feature becomes transparent to depth contrast “binding” after some time. Perhaps the intervening rectangle having a zero disparity was a special case; in the next experiment, the intervening rectangle itself was slanted. Intervening slanted rectangle In this experiment the disparity of the inducing trapezoidal frame was varied while the disparity of the continuously displayed intervening rectangle was held constant (Fig. 1, stimulus K and L). Data for two observers are shown in Fig. 6, including configurations in which the rectangular frame was not shown at all and also those in which the rectangular frame was presented simultaneously with the trapezoidal frame and the test lines for 100 msec. The separation between a vertical edge of the rectangle and the trapezoidal frame was about 15 min arc in these stimuli and the trapezoidal frame had a disparity of 20 min arc. Some of the data were also collected at a viewing distance of 1 m instead

of 3 m to determine whether the results were influenced by the small separations between the two frames. The stimulus dimensions on the oscilloscope were left unchanged, resulting in a factor of three in angular dimensions. The results for these stimulus dimensions are given in Table 3. When the rectangle is not shown, CMF is always positive (Table 3, row 1, triangle symbol Fig. 6) in agreement with the conventional depth contrast effect in which the depth of the test features are seen in contrast to the depth of the inducing trapezoidal frame. The CMFs have been calculated using the magnification of the trapezoidal frame that was being varied. When the rectangle is shown simultaneously and briefly (Table 3, rows 2 and 3; x , + , $ and () symbols in Fig. 6), the sign of CMF is the sign of the disparity of the trapezoidal frame for negative rectangular frame disparity @j and ZJ, Fig. 6) and it is opposite to the sign of the disparity of the trapezoidal frame when the disparity of the rectangular frame is positive ( x and -t- in Fig. 6). Since the sign of CMF is determined by d/D (see footnote on p. 950), this means that the sign of the com~nsating disparity is the sign of the rectangular frame. When the rectangle is shown simultaneously and briefly, the depth of the test features is seen in contrast to the depth of the rectangle and not to that of the outer trapezoid. When the rectangle is displayed continuously, it is not expected to influence the depth contrast effect and the results should be comparable to those obtained when the rectangle was absent. This was not the case, The results look more similar to the case when the rectangle was simultaneously and briefly shown than when the rectangle was absent (Fig. 6). Although the sign of the compensating disparity was determined by the sign of the rectangle’s disparity, the CMF was much smaller (mostly near zero) when the frame and the continuously displayed rectangle had disparities of opposite sign (configuration 1 of stimulus F and configuration 2 of stimulus G) than when these disparities had the same sign (confi~ration 2 of stimulus K and

956

T. KUMAR and DONALD A. GLASER KV

TK

NOT SHOWNi

.__._ A ____.

RECTANGLE

@1+13-J ON SlMULlANEOU8Ly:

RECYANQLE

(b-15’)

.--+._-_

RECTANQLE

ON SMlJLTANEOUSLy:

RECTANOLE

(D=+13‘) ALWAYS ON:

RECTANGLE

(D-r133 ALWAYS ON:

-20

-10

t

n I-I n

0

A

ii @

Ill

?a

TRAPEZOIDAL FRAME PERCENT MAGNlFlCATlON

FIGURE 6. Temporal effects in “shielding”. The stimuli are shown in Fig. 1 (K, L). The difference in widths of the rectangular frames (13.2 min arc) seen by the two eyes is listed as D and was + 13 min arc for both configurations of stimulus F and - 13 min arc for both configurations of stimulus G. The sign of the disparity of the rectangular frame or the trapezoidal frame is called positive when the wider frame was shown to the right eye and negative when the wider frame was shown to the left eye. The trapezoidal frame disparity is the difference between the widths of the trapezoidal frames shown to the two eyes. The trial time was 3 set and the rectangular frame with either 13.2 min arc positive or negative disparity was shown all the time. The trapezoidal frame and the test lines were shown simultaneously for 1OOmsec. The disparity of the trapezoid was constant in magnitude throughout a run, but its sign was randomly selected from trial to trial. As described in the Methods section, the disparity of the left test line was randomly selected from a finite and appropriately preselected set of values. For comparison, data are also plotted for the case in which the intervening rectangle was not shown or was shown simultaneously for 1OOmsec when the test lines and the trapezoidal frame had a magnification of k 19% and +4%.

configuration 1 of stimulus L). If a slanted rectangle is displayed all the time, an external briefly flashed trapezoidal frame with a slant “opposite” to that of the rectangle induces much less depth in the central test lines

than a trapezoid with a slant that “matches” the slant of the rectangle. An intervening continuously displayed rectangle “shielded” much less when the slants of the rectangle and the outer frame matched than when the slants of the rectangle and the trapezoidal frame were opposite. If effects of the trapezoidal frame and the rectangle are combined by taking the simple arithmetic average of the magnification factors of the two figures as the “effective” magnification factor of the combination, then the effective combined percent magnification factor is about 0.5 when disparities of the frame and rectangle are of opposite sign. When the disparities of the two figures are of the same sign the combined percent magnification factor is large and between 10 and 19. An equivalent way to combine the effects of the two figures is to treat the midpoint of the left or the right vertical edges of the figures as the location of the edges of the inducing feature. Then the required compensating disparity is expected to be less when the inducing magnification is negligible and large when the inducing magnification is large. What is surprising is that edges that are quite far apart (for viewing distance of 1 m) may be being “pooled” to arrive at some net inducing feature when the inner rectangle has been continuously displayed and not when it is shown simultaneously and briefly. This suggests that although the depth contrast effect by a continuously displayed inducing feature fades, its inducing disparity “interacts” with the disparity of briefly shown inducing features as measured by their effect on the central test features. Do these “pooling” effects of features relatively far apart indicate that interaction among underlying disparity mechanisms changes with time? Only further experiments can help answer that.

DISCUSSION

Stereo acuity is known to improve with prolonged viewing (Ogle & Weil, 1958) and depth judgments appear to involve averaging disparities over time (Richards, 1972). In this paper we have shown that there are stereopsis “interactions” that take place over distinctly different time scales ranging from 200 msec to many minutes. Explanations of depth contrast that rely on the dynamics of eye position are insufficient to account for these effects. The depth contrast effect is

TABLE 3 CMF TK

KV Condition Rectangle not shown Rectangle on simultaneously (D = +40min arc) (D = -4Omin arc) Rectangle always on (D = + 40min arc) (D = -40min arc)

Frame D=+l” 69 + 8 36 + 4 -37+4 40*5 2&4

Frame DE-1” -65k6 21* 5 -5255 -3&-5 -35+6

Frame D=+l”

54 f 6

Frame D=-1’

-52+6

38 + 4 -6456

33+4 -43k6

30 * 3 3+3

3+5 -32+4

957

DEPTH CONTRAST

most pronounced for short times and diminishes as the observation time increases, essentially disappearing after a few minutes. Viewing times used in our experiments extend up to several minutes, much longer than times associated with vergence and cyclotorsional movements. When inducing features and test features appear simultaneously, the perceived depths of the test features are related to the entire configuration of all the features and not simply to some hypothetical frontoparallel plane. Inducing and test features which are widely separated spatially but very close in time seem to be treated as a single object. If the inducing features are displayed continuously beginning long before the appearance of the test features, they seem to have no role in determining the depth of the test features unless their disparity changes with time or they are “reinforced” by matching slant features as in Expt 7. Werner sought to explain dynamical effects in terms of changing correspondence by invoking “secondary corresponding points”. As demonstrated by Expt 4, outermost boundaries that are visible for a long time do not even have to be stationary in retinal coordinates in order to have no effect on the depth of the test features. We suggested previously that “a relative depth map is not identical to a relative disparity map of the features in the visual field, which implies that observers make an assumption of some ‘local reference frame’ with respect to which they use disparity to obtain a depth map. The assumptions regarding this frame are probably very observer dependent” (Kumar & Glaser, 1991, p. 1698). Our depth contrast experiments suggest to us that this internal reference system for representation of depths depends on more than establishing corresponding points on the retina in relation to eye position, or on interactions in terms of disparities even though the local reference system must use retinotopic information. This coordinate system is probably established early in disparity processing and leads to “shielding” and other effects which produce a CMF proportional to the separation between the test features and inversely proportional to the width of the frame, but only if the inducing and test features are presented within half a second of each other. Minimal stimuli containing only three or four dots produce results qualitatively similar to those obtained with more complex inducing shapes, which suggests that even processing of simple stimuli may reflect cognitive mechanisms.

Provisional models of depth perception using local filters or wavelets may be useful, but a fuller explanation of the dependence of depth on disparity and other image parameters will involve more complex mechanisms that vary considerably among subjects. Our knowledge of the neurophysiology of the human visual system is not yet sufficient to lead us to an explanation of how a depth reference system could be established. We believe, however, that many of the phenomena demonstrated here for the depth contrast effect will have counterparts in other percepts that depend on disparity. Careful measurements of these expected effects may bring us closer to understanding internal representations of depth and its reference systems.

REFERENCES Kumar,T. & Glaser, D. A. (1991). Influence of remote objects on local depth perception. Vision Research, 31, 1687-1699. Kumar, T. & Glaser, D. A. (1992). Shape analysis and stereopsis for human depth perception. Vision Research, 32, 499-512. Mitchison, G. J. & Westheimer, G. (1984). The perception of depth in simple figures. Vision Research, 24, 1063-1073. Nelson, J. I. (1977). The plasticity of correspondence: After-effects, illusions and horopter shifts in depth perception. Journal of Theoretical Biology, 66, 203-266.

Ogle, K. N. (1946). The binocular depth contrast phenomenon. American Journal of Psychology, 59, 11I-126. Ogle, K. N. & Weil, M. P. (1958). Stereoscopic vision and the duration of the stimulus. Archives of Ophthalmology, 59, 417. Richards, W. (1972). Response functions for sine- and square-wave modulations of disparity. Journal of the Optical Society of America, A, 62, 907-911.

Wallach, H. & Lindaur, J. (1961). On the definition of retinal disparity. Psychologische Beitrage, 6, S-530.

Werner, H. (1937). Dynamics in binocular depth perception. Psychology Monograph, 49, 129.

Westheimer, G. (1986). Spatial interactions in the domain of disparity signals in human stereoscopic vision. Journal of Physiology, London, 370, 619629.

Westheimer, G. & Levi, D. (1987). Depth attraction and repulsion of disparate fovea1 stimuli. Vision Research, 27, 1361-1368.

Acknowledgements-This

work was supported in part by the U.S. Office of Naval Research, Contract No. NOfNJl4-85-K-0692 and Grant No. NOOOl4-90-J-1251. We also wish to acknowledge the very useful comments and suggestions by two anonymous reviewers who obviously spent a significant amount of their time on the original draft.