Randolph Blake was sup- ported by National Science Foundation Grant BNS 8418731. We would like to thankCynthia Owsley for comments on an earlier draft ...
Perception & Psychophysics
1987, 42 (6), 569-575
Perceptually unequal spatial frequencies do not yield stereoscopic tilt MICHAEL E. SLOANE University of Alabama, Birmingham, Alabama and RANDOLPH BLAKE Northwestern University, Evanston, Illinois Stereoscopic tilt can be obtained by presenting vertical grating patterns differing in their spatial frequencies to the two eyes (Blakemore, 1970). Following monocular adaptation, the perceived spatial frequency of a test grating is different in the adapted and unadapted eyes by an amount that would yield stereoscopic tilt if corresponding physical spatial frequencies were presented (Experiment 1). Perceptually unequal (but physically identical) gratings presented to the two eyes do not yield stereoscopic tilt, but tilt is obtained if differences in physical spatial frequency exist (Experiment 2). Changes in perceived spatial frequency for a binocular test grating following monocular adaptation are smaller than those measured in the adapted eye but larger than those in the unadapted eye (Experiment 3). These results suggest that (1) stereopsis is immune to perceptual distortions of the monocular stimuli, and (2) perceived spatial frequency reflects the pooled activity of monocular and binocular neurons.
When two vertical gratings of the same spatial frequency are presented stereoscopically to the two eyes, the fused binocular image lies in the frontal plane. If the frequency of one of the gratings is slightly higher than that of the other, the fused binocular image appears to be tilted around its vertical axis (Blakemore, 1970). The side of the fused grating appearing further away corresponds to the eye receiving the lower spatial frequency. The angle of tilt increases with relative frequency difference, up to interocular frequency differences of about 20 %, beyond which stereoscopic fusion breaks down. The question addressed in the present study was whether one could obtain stereoscopic tilt using dichoptically presented gratings whose apparent (rather than physical) spatial frequencies differed by an amount that would typically yield tilt. There exists a variety of stimulus conditions that affect the perceived spatial frequency of a grating, including luminance (Virsu, 1974), stimulus duration (Georgeson, 1980; Kulikowski, 1975; Tynan & Sekuler, 1974), temporal modulation (Gelb & Wilson, 1983a; A. J. Parker, 1983), stimulus masking (Gelb & Wilson, 1983b), and contrast (Gelb & Wilson, 1983a). In the present study, perceived spatial frequency was altered using an adaptation paradigm ftrst described by Blakemore and Sutton Michael Sloane was supported by National Institutes of Health Grants EY04838, AG05515, and EY03039 (CORE). Randolph Blake was supported by National Science Foundation Grant BNS 8418731. We would like to thank Cynthia Owsley for comments on an earlier draft of this manuscript. Requests for reprints should be sent to Michael Sloane, Department of Psychology, University of Alabama at Birmingham, Birmingham, AL 35294.
(1969). For example, in this adaptation paradigm, test gratings of a somewhat lower spatial frequency than the adapting grating were perceived to have a lower spatial frequency than their true frequency. This spatial frequency effect transfers interocularly, the magnitude of the effect being reduced 50% (Blakemore, Nachmias, & Sutton, 1970). One can achieve a frequency shift of up to 20 % to 25% in the adapted eye, and if this is reduced by 50% in the unadapted eye, the apparent spatial frequency of the test grating will differ by about 10% between the two eyes. Stereoscopic fusion of gratings differing in their physical spatial frequencies by 10% yields a robust stereoscopic tilt. The question addressed in the present study was whether stereoscopic tilt could be generated following monocular adaptation designed to induce similar differences in apparent spatial frequency. If, following monocular adaptation, dichoptically viewed gratings of the same physical spatial frequency (but perceptually different frequencies) generate stereoscopic tilt, one may conclude that the site of the perceived spatial frequency shift is prior to that of stereoscopic fusion, that is, stereopsis depends on the apparent spatial frequencies of the gratings rather than on their physical spatial frequencies. If, on the other hand, one observes no stereoscopic tilt under these conditions, one might conclude that stereopsis is based on the physical spatial frequencies of the gratings and that the site of the frequency-shift aftereffect follows that of, or is parallel to, stereoscopic fusion. If the latter is true, then dichoptically viewing perceptually equal gratings following monocular adaptation should generate stereoscopic tilt, since the gratings would differ in their physical spatial
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frequencies. The relative loci of stereopsis and the frequency-shift effect have not been directly addressed previously. It is known, however, that the magnitude of the frequency-shift effect is not affected by phenomenal absence of the adapting grating during binocular rivalry suppression (Blake & Fox, 1974), suggesting that the generation of the aftereffect precedes the stage ofbinocular rivalry. In a series of experiments, A. J. Parker (1980, 1981) has shown that the threshold elevation aftereffect is specific to the physical rather than the perceived spatial frequency of a temporal modulated adapting grating, whereas the frequency-shift aftereffect is specific to the perceived frequency of the adapting grating. It would seem, therefore, that for certain types of visual phenomena neural mechanisms signaling the veridical spatial frequency of the stimulus are being tapped.
EXPERIMENT 1 The purpose of this experiment was to confirm that monocular adaptation does indeed produce sufficiently large differences in perceived spatial frequency between the adapted and unadapted eyes. (By "sufficiently large" we mean differences comparable to real frequency differences yielding reliable stereoscopic tilt.) The magnitude of the frequency-shift aftereffect was measured following monocular adaptation in the adapted eye (direct condition) and in the unadapted eye (interocular condition).
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After nine practice trials, baseline frequency matches were obtained for vertical sine-wave gratings of 4,5,6, and 7 cycles/degree S2, _ (cpd) with 40% contrast. Thirty matches were obtained for SI, S2, S3, and S4) were tested. All had good stereopsis, as assessed by and S4 on the same day; 30 matches were obtained for S3 on each the RDE Stereotest (Stereo Optical Co.), the test figures of Julesz of 3 consecutive days. In the baseline condition, there was a 2-min (1971), and the stereopsis test in the Bausch and Lomb Orthorater. blank period during which the left and right halves of the fused No subject had significant vertical or lateral phorias as assessed image were homogeneous. This was followed by a 5-sec test interby the Orthorater. val, which, in turn, was followed by a return to homogeneous fields. Apparatus. A custom-built mirror stereoscope enclosed in a dark This cycle of a 5-sec test interval and a lO-sec blank interval was booth was used for viewing. The subject's head was maintained continued until the subject had made six frequency matches. The in a steady position by means of a dental impression board. The adaptation conditions followed the same temporal course as the baseleft and right fields of the stereoscope were brought into binocular line condition, with the blank intervals being replaced by a highalignment by appropriate adjustment of the outer two mirrors. contrast (80%) 7-epd adapting grating. Thus there was an initial Stimuli were displayed on two matched Tektronix 608 monitors 2-min adaptation period and lO-sec refresher adapting periods inusing P31 phosphors. Vertical sinusoidal grating patterns were serted between the 5-sec test intervals. A schematic of the stimulus generated by conventional means (Campbell & Green, 1965). The conditions is shown in Figure 1. In the adaptation conditions, a 7average luminance of the display was 34.3 cd/m-, and this was uncpd grating of 80% contrast was presented in the right half of the affected by changes in contrast or spatial frequency of the grating. right CRT. The test grating was presented in the right half of either At the viewing distance of 94 cm, each CRT screen subtended a the right CRT (direct condition) or the left CRT (interocular convisual angle of 6.16° x 9.21 0. The screen of each CRT was split dition). The binocular test condition shown in Figure I was used electronically so that gratings of different spatial frequency could only in Experiment 3. The subject adjusted the frequency of the be presented in the two half-fields. The screens were divided in comparison grating (indicated by"?" in Figure I). In separate conequal halves. A vertical strip of black paper (subtending 0.125° ditions, frequency matches were made for test gratings of 4,5,6, x 5°) was placed in the center of the screen, providing an addiand 7 cpd following adaptation to a 7-cpd grating. Each adaptation tional fusion contour as well as a fixation marker during simulta- condition produced 6 frequency matches for a given test frequency. neous frequency matching. A total of 12 matches were obtained for each test grating, with 6 Procedure. While fixating the center of the vertical black stripe, matches being made on each of two occasions. Adequate time the subject adjusted the spatial frequency of the comparison gratelapsed between adaptation sessions to allow the effects of adaptaing on the left to match that of the test grating on the right. The tion to dissipate fully. subject used a lO-turn potentiometer to adjust the frequency of the comparison grating. The test and comparison gratings were Results presented simultaneously for 5 sec. The subject was not constrained The results of this experiment are shown in Figure 2. to produce a frequency match within a given 5-sec test interval, Spatial frequency ratios (real over matched) are shown although he/she was not encouraged to deliberate too long on any for the four test frequencies for each subject. All four obgiven frequency match.
Method Subjects. Four experienced psychophysical observers (SI,
PERCEIVED FREQUENCY SHIFT AND STEREOSCOPIC TILT servers were very consistent in making frequency matches. Subject 3, who was tested in the direct condition on 3 successive days, showed no statistically significant differences between successive measurements. As expected, there was little shift in perceived spatial frequency at the adapting frequency for any subject. In the baseline conditions, the subjects tended to overestimate slightly the frequency of the test grating. Left-right hemispheric or nasotemporal asymmetries in frequency matching have been reported previously (Brown, 1953). The subjects differed in the strength of the frequency-shift aftereffect at different test frequencies, but there was a consistent trend among the subjects. The averaged results for the 4 subjects are shown in Figure 3. As expected, for a given test frequency, there were large differences in apparent spatial frequency as measured in the adapted and unadapted eyes. With a few exceptions, the differences in perceived spatial frequency in the adapted and unadapted eyes were very similar for two test frequencies of 5 and 6 cpd. This was the rationale for choosing a test frequency of 5.5 cpd in Experiments 2 and 3. The question remains as to whether these differences in apparent spatial frequency between each eye's view are sufficient to produce stereoscopic tilt if corresponding physical frequencies were used. To determine this empirically, a control experiment was carried out to assess the range of frequency differences yielding stereoscopic tilt for each of the 4 subjects. The split-screen procedure was not used. Instead, both screens were masked to a cirS#2
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cular 4 0 aperture. The subjects were presented with 20 pairs of gratings differing in spatial frequency from 0.25% to 21.5 % in random order. The reference frequency was 5.5 cpd, and all gratings had 40% contrast. The subject's task was to report the presence or .absence of tilt and, if present, its direction. If tilt was seen, the subject was then asked to manipulate the frequency of one eye's view until the tilt was nulled. If no tilt was seen,the subject altered the frequency until he/she perceived stereoscopic tilt and then nulled that tilt. Three subjects obtained tilt in both directions with spatial frequency differences in the two eyes of up to 21.5 %. The fourth subject obtained tilt with this disparity only when the tilt was to the right. This subject could perceive tilt to the left only when the frequency difference was 10% or less. The subjects reported difficulty in fusing frequency differences as large as 21.5%, yet, when fusion was obtained, tilt was easily perceived. The subjects also showed high sensitivity for stereoscopic tilt produced by very small differences in spatial frequency. Two subjects could detect tilt with a 0.25% difference, whereas the other 2 observers needed a difference of O. 78 % and 2.1 %, respectively. These measurements did not attempt to examine the limits of stereoscopic tilt discrimination, but were simply an attempt to show sufficient sensitivity for participation in Experiment 2.
Discussion The results of Experiment 1 show that (1) one can reliably create differences in perceived spatial frequency in the two eyes following monocular adaptation, and (2) the magnitude of these differences is more than adequate to produce a robust stereoscopic tilt effect for all subjects when using true spatial frequency differences. These
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results were expected, inasmuch as Blakemore et al. (1970) had reported about a 50% decrement in the magnitude of this aftereffect in the unadapted eye. On the basis of the results of Experiment I, a binocularly presented test grating of 5.5 cpd presented after monocular adaptation to a 7.0-cpd grating will appear to have a lower spatial frequency in the adapted eye than in the unadapted eye. If stereoscopic tilt is based on the physical spatial frequency of the gratings presented to each eye, then no tilt should be perceived. If, however, perceived spatial frequency provides input for stereoscopic fusion, then subjects should perceive tilt and should have to lower the spatial frequency of the unadapted eye to cancel the resultant stereoscopic tilt. Experiment 2 was designed to examine these alternatives.
this experiment. A one-tailed t test for correlated samples was performed on the data pooled across subjects. No significant difference was found [t(74) = 1.64, P > .05]. The subjects did not report any depth after adaptation. When forced to choose the direction of tilt, they responded with "left side further" and "right side further" with equal frequency. The difference in null settings between the adapted and unadapted conditions was about half the standard deviation of the null settings in the adapted conditions. One-tailed t tests for correlated samples were also carried out on the data for each individual [SI, t(19) = 1.49, P > .05; S2, t(19) = 1.89, .025 < P < .05; S3, t(19) = 0.39, p > .05; S6, t(19) = 2.39, .01 < P < .05]. There was a shift in the null frequency for S2 and S4, which was significant at the .05 level. For S4, who showed the larger change in null setting, the difference was outside her stereoscopic limit, as EXPERIMENT 2 measured in the preliminary tests. For both of these observers, the shift in null frequency was toward a higher Method Subjects. The same 4 subjects were used in this experiment. frequency. This was curious in that it was in the direcStimuli. To avoid the difficult task of matching stereoscopic tilt tion opposite to what might be predicted. Since the right of two half-fields while fixating a center line, both CRT screens eye was being adapted, a greater shift in apparent spatial were masked down to a central circular area subtending 4 frequency would obtain in this eye than in the unadapted Procedure. The sequence of adaptation and testing was identileft eye. Hence, the subject would have to decrease rather cal to that of Experiment I, except that during adaptation the subthan increase the frequency of the grating in the left eye ject was allowed to scan the 7-cpd grating. FoIlowing the 2-rnin initial adaptation, test gratings of physically equal spatial frequency to perceive a grating in the frontal plane. One possible (5.5 cpd) were presented to the two eyes. A schematic of the stimuexplanation for the paradoxical direction of the shift in lus conditions is shown in Figure 4. The subject's task was to adnull settings was the hypothesis of Fiorentini and Maffei just the spatial frequency of the grating presented to the nonadapted (1971) that a contrast disparity between gratings of equal eye so that any stereoscopic tilt was nuIled and the fused grating spatial frequency may produce stereoscopic tilt. They arlay in the frontopara1Ielplane. If no tilt was perceived, the observers adjusted the spatial frequency of one eye's view until stereoscopic gued that the grating of lower contrast appears to be of tilt was obtained. They then proceeded to null this tilt. The subject a higher spatial frequency, and thus, when fused with a adjusted the frequency either during the refresher adapt interval or higher contrast grating of equal spatial frequency, the gratduring a brief eye closure during the test interval. Each subject paring appears to be tilted away from the eye receiving the ticipated in four sessions, each yielding five null settings. lower contrast. Blake and Cormack (1979) failed to find evidence of stereoscopic tilt based on contrast disparity Results alone. In our experiment, any stereoscopic tilt produced To assess the effects of adaptation, the unadapted null by contrast disparity would be in a direction opposite to settings of the previous control experiment were compared that produced by differences in apparent spatial frequency. with the null settings made after monocular adaptation in Thus, according to Fiorentini and Maffei (1971), the effects of the experimental manipulation could have been SCHEMATIC OF STIMULUS CONDITIONS negated by the presence of stereoscopic tilt produced by contrast disparity, itself produced by adaptation (the familiar threshold elevation effect). To test the contribution of contrast disparity, 3 subjects LEFT EYE RIGHT EYE (SI, S2, S3) were run in a control condition in which any stereoscopic tilt produced by contrast disparity and shift ADAPT in apparent spatial frequency following adaptation would be in the same direction. The only change necessary was to alter the frequency of the adapting grating from 7 to 4.32 cpd while keeping the test frequency at 5.5 cpd. Adapting the right eye and testing with a higher spatial TEST frequency should result in a greater shift in apparent spatial frequency in the right eye than in the left eye, thus producing a grating tilted to the left. In terms of contrast disparity, the test grating in the adapted right eye would PHYSICALLY EQUAL SF appear to have a lower contrast and thus a higher spatial Figure 4. Stimulus conditions of Experiment 2. frequency, which would also produce, according to 0
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PERCEIVED FREQUENCY SHIFT AND STEREOSCOPIC TILT Fiorentini and Maffei, a grating tilting away to the right. Thus, the two potential sources of stereoscopic tilt would facilitate, rather than cancel, each other. If either or both sources led to the perception of tilt, one would expect a difference in the null settings between pre- and postadaptation. A one-tailed I test for matched samples was performed on each subject's data. No significant differences were found [SI, 1(9) = 0.9127; S2, 1(9) = 0.832; S3, 1(9) = l. 47; all ps > .05], and no depth was reported after adaptation. It would appear, therefore, that contrast disparity following adaptation had no influence on the outcome of the main experiment. The results of this control experiment confirm those of the main experiment in finding no evidence of stereoscopic tilt after monocular adaptation, despite the fact that there are sufficient differences in perceived spatial frequency to yield robust stereoscopic tilt effects. In a corollary, albeit informal, experiment, we presented gratings that were perceptually equal (and hence physically unequal) to the two eyes following monocular adaptation. The spatial frequencies were interpolated from the postadaptation frequency matches of Experiment I. Although the two monocular spatial frequencies appeared equal, subjects always reported seeing stereoscopic tilt in the predicted direction, and they had no difficulty in canceling the tilt by altering the spatial frequency of one eye's grating pattern. Discussion Experiment 2 showed that: (I) following monocular adaptation, perceptually unequal, but physically equal, spatial frequencies presented to the two eyes do not yield stereoscopic tilt; (2) failure to obtain stereoscopic tilt was not affected by any contrast disparity generated by the adaptation procedure itself; and (3) stereoscopic tilt was observed following monocular adaptation when perceptually equal, but physically unequal, spatial frequencies were dichoptically presented. Stereopsis is unaffected, therefore, by distortions of perceived spatial frequency. This finding suggests that the site of the frequency-shift aftereffect is at either a later or a parallel stage of visual processing. If the perceived spatial frequencies of the grating patterns in each eye's view are not labeled independently, then one would not expect any stereoscopic tilt. That is, perceived frequency may result from the pooled responses of monocular and binocular neurons. Previous studies have argued that the magnitude of adaptation aftereffects is a function of the pooled responses of tested neurons (Blake, Overton, & Lema-Stem, 1981; Moulden, 1980; Sloane & Blake, 1984). Thus, in the interocular transfer condition, some neurons (monocular) that have not been adapted and others (binocular) that have been adapted are being tested. The inclusion of unadapted neurons serves to reduce the size of the interocular aftereffect relative to that measured in the adapted eye. In the case of Experiment 2, in which both eyes were presented with grat-
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ings of physically equal spatial frequency, the perceived frequency may well have been determined by a large pool of neurons containing not only the adapted monocular and binocular neurons, but also the unadapted monocular neurons that respond to the unadapted eye. If this is the case, then a binocularly measured frequency-shift effect following monocular adaptation should be intermediate between the effect measured in the adapted eye and that measured in the unadapted eye. If, on the other hand, the perceived spatial-frequency effect is determined by the least adapted or most sensitive neurons, then the binocularly measured effect should be similar in magnitude to that measured in the unadapted eye. One could also argue that the binocular test grating would be processed by binocular AND neurons (Wolfe & Held, 1981), which are activated only by simultaneous presentation of identical stimuli to the two eyes. Wolfe and Held found a binocularly measured adaptation aftereffect that was smaller than that measured in the unadapted eye. They suggested that, since monocular adaptation would not affect the binocular AND neurons, the activation of this unadapted set of neurons by a binocular test would serve to reduce aftereffect magnitude. Since their pattern of results does not obtain when test patterns are at threshold, Wolfe and Held argued that suprathreshold test stimuli are needed to activate the binocular AND neurons. The next experiment used binocularly presented suprathreshold test stimuli. Based on Wolfe and Held (1981), the expectation would be that the binocularly measured frequency shift would be lower than that measured in the unadapted eye. This final experiment examined the relative magnitudes of the spatial frequency-shift effect following monocular adaptation using monocular and binocular test gratings.
EXPERIMENT 3 Method
Subjects. Three of the 4 previously involved subjects participated in this experiment (81,82, and 83). Stimuli. The split-screenconfigurationof Experiment I was used. Monocular adaptationagain was to a 7-epd vertical sinusoidalgrating of 80% contrast. The test grating was a 5.5-cpd grating of 40% contrast. The latter was presented to the adapted eye (direct condition), to the unadapted eye (interocular condition), or to both (binocular condition). Procedure. Ten preadaptation baseline measures were obtained for each subject. Two adaptation sessions, each yielding six frequency matches, were run for each subject for the direct, interocular, and binocular test conditions. For 83, binocular test gratings of 5 and 6 cpd were also run.
Results Spatial frequency ratios for direct, interocular, and binocular test conditions are shown in Figure 5. For each subject, the magnitude of the binocularly measured spatialfrequency shift was between the magnitudes measured in the adapted and unadapted eyes. This was also true for the additional test frequencies examined for S3. These results support the pooling hypothesis, namely that aftereffect magnitude is determined by the pooled sensitiv-
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ity of the tested neurons, and argue against the involvement of binocular AND neurons. GENERAL DISCUSSION Following monocular adaptation, the differences in perceived spatial frequency in the adapted and unadapted eyes would be more than adequate to produce a robust stereoscopic tilt if corresponding physical frequencies were used. Despite the difference in perceived spatial frequency in the two eyes, no stereoscopic tilt was found when gratings of equal physical frequency were binocularly presented following monocular adaptation. Our findings substantiate a similar observation made by Blakemore (mentioned in Julesz, 1971). Stereoscopic tilt was produced only with fusion of gratings differing in their physical frequencies. One instance of this was where the gratings were matched for perceived spatial frequency in the two eyes (a perceptual match necessitated a mismatch of physical spatial frequencies). These results suggest that the output of mechanisms responsible for the spatial frequency-shift effect do not feed into the stereoscopic mechanisms. Rather, stereopsis utilizes the undistorted physical frequencies of the monocular patterns. Given the number of stimulus conditions that affect perceived spatial frequency, it is fortunate that stereopsis is immune to any perceptual changes in the monocular views. It is not difficult to find conditions in which stimulus contrast or retinal illuminance would differ between the two eyes. If the resultant alterations in perceived spatial frequency affected stereopsis, then spurious stereoscopic tilt effects would obtain. In preliminary work, we noted that altering the perceived spatial frequency of one eye's grating using simultaneous induction (surrounding a patch of grating in one eye with a grating of different spatial frequency) also fails to yield a stereoscopic tilt. Westheimer (1986) recently showed that altering the perceived orientation of lines in one eye's view (by means of a geometrical opti-
cal illusion) did not result in any three-dimensional tilt effect. Blakemore and Sutton (1969) suggested that, following adaptation, test gratings with a spatial frequency close to that of the adapting grating will produce a neural response distribution whose peak (or other measure of central tendency) is skewed away from the adapting frequency, since the maximum decrease in sensitivity (i.e., threshold elevation) occurs at the adapting frequency. Thus, the apparent spatial frequency of the test grating .. will appear shifted away from the adapted frequency. Such a distribution shift model (see also Gilinski & Mayo, 1971; Marshak & Sekuler, 1979; Mather & Moulden, 1980) necessitates that the magnitude of shift in perceived spatial frequency be directly related to the degree of threshold elevation. However, Klein, Stromeyer, and Ganz (1974) showed that threshold elevation and spatial frequency-shift aftereffects are dissociable. They illustrated that equal shifts in perceived spatial frequency can be produced by adaptation and simultaneous induction, but that only adaptation yields threshold elevation. Also supporting this idea of dissociability, A. J. Parker (1981) demonstrated that the spatial frequency specificity of threshold elevation and frequency-shift aftereffects were distinct. More specifically, the threshold elevation centered around the true spatial frequency of a temporally modulated adapting pattern, while the frequency shift aftereffect was centered around the apparent spatial frequency of the adapting pattern. Other evidence for the dissociability of threshold elevation and frequency-shift aftereffects was offered by Heeley (1979), who found shifts in perceived frequency for test gratings orthogonal to the adapting grating. As one would expect, no threshold elevation was found for the orthogonal test patterns. Klein et al. (1974) proposed a two-stage neural model of the frequency-shift aftereffect. The initial stage is a set of "analyzers" tuned to various orientations and spatial frequencies that feed into a detection pooling mechanism.
PERCEIVED FREQUENCY SHIFT AND STEREOSCOPIC TILT
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A second output goes to a set of "integrators" that have CAMPBELL, F. W., &; GREEN, D. G. (1965). Optical and retinal factors affecting visual resolution. Journal of Physiology, 181, 576-593. broader tuning. Perception of spatial frequency stems from some measure of central tendency of the response FIORENTINI, A., &; MAFFEI, L. (1971). Binocular depth perception without geometrical cues. Vision Research, 11, 1299-1305. distribution of these "integrators." Heeley's (1979) find- GELB, D. J., &; WILSON, H. R. (1983a). Shifts in perceived size as a ing of a frequency shift at orthogonal orientations sugfunction of contrast and temporal modulation. Vision Research, 23, 71-82. gests that perceived frequency relies on the response distribution of mechanisms that differ widely in their orien- GELB, D. J., &; WILSON, H. R (1983b). Shifts in perceived size due to masking. Vision Research, 23, 589-597. tation preference. In the final experiment of the present GEORGESON, M. A. (1980). Spatial frequency analysis in early visual study, it was shown that the shift in perceived frequency processing. Philosophical Transactions ofthe Royal Society ofLondon, Series B, 290, 11-22. of a binocularly presented test grating following monocular adaptation was intermediate between the shifts in per- GIUNSKl, A. S., & MAYO, J. M. (1971). Inhibitory effects of orientationa! adaptation. Journal of the Optical Society of America, 61, ceived frequency measured in the adapted and unadapted 1710-1716. eyes. This result suggests that perceived frequency relies HEELEY, D. W. (1979). A perceived spatial frequency shift at orientaon a pooling of responses between monocular and binocutions orthogonal to the adapting gratings. Vision Research, 19, 1229-1236. lar neurons. It may well be, therefore, that the coding of perceived spatial frequency involves a generalized pool- JULESZ, B. (1971). Foundations of cyclopean perception. Chicago: University of Chicago Press. ing of responses across the orientation and ocular KLEIN, S., STROMEYER, C. F., &; GANZ, L. (1974). The simultaneous dominance domains, in addition to the critical dimension spatial frequency shift: A dissociation between the detection and perof spatial frequency. In a similar vein, D. M. Parker ception of gratings. Vision Research, 14, 1421-1432. (1972) obtained changes in perceived orientation of a test KUUKOWSKl, J. J. (1975). Apparent fineness of briefly presented gratings: Balance between movement and pattern channels. Vision grating following adaptation that were equally strong for Research, 15, 673-680. test gratings equal to, or one octave on either side of, the MARSHAK, W., & SEKULER, R. W. (1979). Mutual repulsion between adapting frequency. We suggest that perceptual dimenmoving targets. Science, 205, 1399-1401. sions of spatial patterns reflect some central tendency mea- MATHER, G., & MOULDEN, B. (1980). A simultaneous shift in apparent direction: Further evidence for a "distribution-shift" model of sure of a response distribution that involves the responses direction coding. Quarterly Journal ofExperimental Psychology, 32, of mechanisms differing in their ocular dominance, spa325-333. tial frequency, and orientation tuning. The more global MOULDEN, B. (1980). Aftereffects and the integration of patterns of distribution (across space) of these local distributions will neural selectivity within a channel. Philosophical Transactions ofthe Royal Society of London, Series B, 290, 3-55. also playa role (e.g., Gelb & Wilson, 1983a, 1983b). For basic visual processes, such as stereopsis, it is criti- PARKER, A. J. (1980). Responses ofthe human visual system to the spatial structure ofstimuli. Unpublished doctoral thesis, University of Camcal that the system can extract neural signals that carry bridge, Cambridge, England. information about the veridical orientation and spatial fre- PARKER, A. J. (1981). Shifts in perceived periodicity induced by temporal modulation and their influence on the spatial frequency tuning quency of spatial stimuli. The present paper has shown of two aftereffects. Vision Research, 21, 1739-1747. that, indeed, the stereoscopic mechanisms remain unperPARKER, A. J. (1983). The effects of temporal modulation on the perturbed by perceptual characteristics of the stimuli. ceived spatialstructureof sine-wavegratings. Perception, 12, 663-682. REFERENCES
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(Manuscript received January 21, 1987; revision accepted for publication June 5, 1987.)
