Viricw~Rrs. Vol. 30, No. IO. pp. 1467-1474, 1990 Printed in Great Britain. All rights reserved
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THE INFLUENCE OF SPATIAL FREQUENCY PERCEIVED TEMPORAL FREQUENCY AND PERCEIVED SPEED
0042&X9/90 53.00 + 0.00 1990 Pergamon Press pk
ON
A. T. SMITHand G. K. EDGAR Department of Psychology, University of Wales College of Cardiff, Cardiff CFl 3YG, Wales, U.K. (Received 8 August 1989; in revised form 26 February 1990)
AMraet-Speed matching experiments were conducted using drifting gratings of different spatial frequencies in order to assess the influence of spatial frequency on perceived speed. It was found that gratings of high spatial frequency appear to drift more slowly than low spatial frequency gratings of the same actual velocity. The perceived temporal frequency of a counterphase grating similarly declines as spatial frequency increases. The previously reported effect of temporal frequency on perceived spatial frquency probably does not contribute to these phenomena. Our results suggest that the motion sensors thought to operate within different spatial frequency ranges have different velocity transfer functions, a fact not incorporated in existing computational models of motion perception. Motion
Velocity
Temporal frequency
Spatial frquency
lNTRODUClION
Numerous studies have provided evidence that early visual processing occurs within a number of largely independent channels each sensitive only to a restricted range of spatial frequencies. Consequently, theories of the way in which velocity of image motion might be encoded have naturally tended to incorporate the idea that velocity might be computed within such spatially restricted channels. The theoretical models of Watson and Ahumada (1985), Adelson and Bergen (1985) and Harris (1986) provide differing suggestions as to how velocity might be computed, but all three involve derivation of velocity signals within spatially restricted channels. There is also some empirical support for such a system; for example Watson (1986) found that apparent motion with gratings occurs only when the successively presented stationary gratings are of similar spatial frequency. Presumably, in such a system, a moving spatially complex pattern generates a range of separate velocity signals in different spatial channels. In this case the question arises of how these velocity signals are combined to give a percept of rigid motion at a single perceived velocity. This question has not been addressed in detail in the models cited above. In the model of Harris (1986) a spatially complex moving stimulus generates identical velocity outputs in
all spatial channels. Similarly, Watson and Ahumada (1985) assume that temporal frequency is encoded in a way that is quantitatively consistent across spatial frequencies so that combination of velocity outputs, although not made explicit in the model, could be straightforward. However, we show here that neither temporal frequency nor velocity is perceived in a way that is consistent across spatial frequencies. This suggests that it cannot be assumed that different spatial channels produce identical velocity outputs in response to a rigidly moving complex pattern.
APPARATUS
All stimuli were vertically oriented sinewave gratings generated by a “Constable” CRT image generator under computer control and presented on a single CRT display (HP1332A with white phosphor). The mean luminance of the display was 70 cdm-r and the frame rate was 122 Hz. The display was masked to leave two 5 deg square apertures, one to the right and one to the left of a small fixation spot. The adjacent edges of the apertures were separated horizontally by 1 deg. Gratings with independently programmable contrast and spatial frequency could be presented separately in each aperture; these could be stationary, drifting or counter-phased.
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In the case of drifting gratings the direction of drift was centripetal (towards the fixation point) to aid fixation. Pilot studies had indicated that this technique yields identical matches to those obtained when both patterns drift in the same direction. The latter procedure, however, yields greater variance (perhaps due to poorer fixation), and so centripetal motion was considered preferable. Strictly, therefore, the task is speed matching not velocity matching (velocity being defined as speed in a particular direction). EXPERIMENT
1: SPEED
MATCHING
The purpose of this experiment was to examine the effect, if any, of spatial frequency on the perceived speed of a drifting grating in order to establish whether different spatial channels all generate the same velocity signal in response to a given fixed velocity. Procedure
The perceived speed of a 1 c/deg drifting grating (referred to as the match) presented in one aperture was matched to that of a second grating (referred to as the standard) presented simultaneously in the other aperture. Within any one run the spatial frequency and drift velocity of the standard grating were constant. In separate runs, the 1 c/deg match grating was matched for speed to standards of spatial frequency 0.5, 1, 2 and 4 c/deg and at each spatial frequency matches were made for each of a range of standard speeds. In each run the subject fixated the fixation point between the two apertures. A twoalternative forced-choice (ZAFC) procedure was used. For 1 min at the start of each run the two apertures were blank, their luminance equal to the mean luminance of the grating stimuli. The standard grating was then presented for I set in one aperture while the match grating was presented simultaneously in the other. After each such trial the subject indicated which of the two gratings appeared to be drifting faster. Following each response there was a 3 set interval in which the screen was blank, followed by presentation of the next pair of gratings. The drift speed of the match grating on each trial depended upon the previous responses of the subject and was determined using a PEST routine (Taylor & Creelman, 1967). The parameters of the PEST routine were set to give a 50% correct performance level, i.e. the level at
which the subject was unable to distinguish between the speeds of the standard and match gratings. This procedure was repeated four times for each spatial frequency and speed of the standard and the mean speed match calculated. In two of the runs the standard was presented on the left and in the other two it was presented on the right. Thus any hemifield differences in perceived speed (Smith & Hammond, 1986) were counterbalanced. In order to minimize differences (other than speed and spatial frequency) between the match and standard gratings, the two patterns always had subjectively equal contrast. In a pilot experiment the contrast of each ‘grating used was subjectively matched to that of a 1 c/deg grating of 20% contrast drifting at 0.5 deg/sec, and the contrast values so obtained were then used in the main experiment. Since perceived contrast is inversely related to speed, this meant that the physical contrast of both patterns increased as speed increased. Three subjects were used: the two authors and a naive observer. All practised the task before the experiment commenced and none was aware of the results obtained by the others. Resulw and discussion
The results are shown separately for the three subjects in Fig. 1 (upper). When the standard and match gratings have the same spatial frequency, the speed matching function is linear and has unity slope, as expected. This is also the case for standard gratings of spatial frequency 0.5 c/deg. However, at higher standard spatial frequencies the matching function departs from linearity. At low speeds the expected matches are made but as standard speed increases match speed increases more slowly than standard speed. Thus, at high spatial frequencies, and particularly at high velocities, speed is underestimated relative to the speed of a I c/deg grating of the same actual velocity. In view of the fact that physical (though not perceived) contrast varied across conditions involving different standard speeds it was felt necessary to check that this did not in itself produce the observed results. Thompson (1982) reports that, at low contrast, perceived speed depends on contrast. It was not expected that contrast would affect the speed matches made in this experiment since, firstly, we have found in unpublished experiments that perceived speed is essentially independent of contrast above about 10% contrast, and secondly the match and
lhe influence of spatial frequency
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Fig. I. Speed matches obtained by matching a drifting grating of spatial frequency 1 c/deg to standards of 0.5 (squares), I (open circles), 2 (solid circles) and 4 (triangles) c/dog drifting at each of a range of speeds. Results for three subjects are shown separately. The upper plots show the data presented in terms of the velocity of the standard grating, the lower plots show the same data presented in terms of the temporal frequency of the standard. Error bars show f I SE. Regression lines reflect either linear or logarithmic regressions as appropriate.
standard always had broadly similar contrasts in any run despite the variations across speed conditions. Nonetheless, the condition yielding the greatest underestimation of speed (4 c/deg) was repeated using a fixed contrast of 40% throughout. The results were very similar to those in Fig. 1 showing that contrast is not an important factor. As a check on the validity of the use of opposite directions of motion for the standard and match we repeated the experiment with one subject (GKE) using the same method except that both patterns drifted in the same direction (leftward in half the trials, rightward in the others). The results were similar to those shown in Fig. 1, though they were slightly more variable (see Introduction). It therefore seems that perceived speed is not dependent on direction and that speed comparisons can readily be made across directions, at least for motion in the two directions along the same axis. The distinction between speed and velocity appears to be unimportant in this context.
A problem that can arise when making speed matches between patterns of different spatial frequencies is that subjects might tend towards the use of a temporal frequency criterion, i.e. to “count” the cycles passing a given point in the image. We have found in other experiments that after considerable practice subjects can use either criterion at will, but not perfectly: temporal frequency matches tend to be influenced by velocity and vice versa. We cannot rule out the possibility that our data reflect the use of a criterion which is not a pure speed criterion but is influenced to some degree by temporal frequency. However, it should be noted that the use of a temporal frequency criterion in a speed matching task would result in overesfimates of perceived speed where, as in our experiments, the spatial frequency of the standard is higher than that of the match. Our finding of reduced perceived speed therefore cannot be explained in this way. If anything, the effect of spatial frequency on perceived speed must be greater than our data indicate, not less.
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The main conclusion drawn from the results is that if velocity perception is derived from multiple velocity sensors each of which operates within a single spatial frequency mechanism, it would seem that the different velocity sensors do not have identical velocity transfer functions. Generally, the higher the spatial frequency the lower the velocity signalled. However the relationship is not linear: the effect is more marked at high spatial frequencies. While a one octave increase in spatial frequency from 2 to 4c/deg has a marked effect on speed matches, a one octave increase from 0.5 to 1 c/deg has no measurable effect. This asymmetry is not related to the choice of match spatial frequency (1 c/deg), which is essentially arbitrary; we have found that the same result occurs with other match spatial frequencies. EXPERIMENT
2: TEMPORAL MATCHING
FREQUENCY
In Experiment 1 it was shown that perceived speed depends on spatial frequency, and that it is not always a linear function of physical speed. One plausible way in which perception of speed might be derived (e.g. Watson & Ahumada, 1985) is by measuring temporal frequency within a labelled spatial frequency mechanism and computing speed by dividing the measured temporal frequency by the spatial frequency signalled by that spatial mechanism. In this case, there are two separate possible sources of the effects of spatial frequency and speed demonstrated in Experiment 1. Firstly, the temporal frequency sensors might have non-linear frequency transfer characteristics, and might have different transfer characteristics in different spatial channels, so that in some cases a distorted temporal frequency signal is divided by a correct spatial frequency to give a distorted speed. That is, speed might be underestimated because temporal frequency is underestimated. This possibility is examined in Experiment 2. Secondly, the spatial frequency mechanisms themselves might carry spatial frequency labels bearing a different relationship to each other than the spatial frequencies of the gratings that stimulate them optimally, or (perhaps more likely) they might carry fixed spatial frequency labels while having optimum spatial frequencies that vary with temporal frequency. In this case the correct temporal frequency might be divided by a distorted spatial frequency to give a distorted speed. That is, speed might be underestimated because spatial frequency is
overestimated. This possibility will be examined in Experiment 3. The purpose of Experiment 2 was thus to examine the effects of spatial frequency on perceived temporal frequency. This was done using counterphase gratings. Procedure
The procedure was similar to that of Experiment 1 except that the standard and match gratings did not drift but instead were temporally modulated in sinusoidal counterphase. The standard gratings used were of the same spatial frequencies as those used in Experiment 1, and they were modulated at one of a range of temporal frequencies equivalent to those used in Experiment 1 (up to 24 Hz). The task of the subjects was to identify the grating with the higher temporal frequency, and frequency matches were estimated using the same PEST routine used in Experiment 1, the temporal frequency of the match grating in each trial depending on the previous responses of the subject. The apparent contrasts (modulation depths) of the standard and match gratings were again matched and any hemifield differences were counterbalanced in the same way as in Experiment 1. The subjects, who were the same as for Experiment 1, were given practice in the task before the experiment commenced. No subject was aware of the results obtained by the others. Results and discussion
The results for temporal frequency matching are shown in Fig. 2. The pattern of results is broadly similar to that obtained for speed matching in Experiment 1. For standard gratings of low spatial frequency, match temporal frequency is a linear function of standard temporary frequency and the function has unity slope. But as the spatial frequency of the standard increases, its temporal frequency is progressively underestimated relative to that of the 1 c/deg match grating, particularly at high temporal frequencies. In order to see the extent to which the speed matching functions of Experiment 1 can be explained in terms of the underestimation of temporal frequency shown in Experiment 2, the results of Experiment 1 are replotted in Fig. 1 (lower) with the speed of the standard expressed in terms of temporal frequency. In this form, the data are directly comparable to those of Experiment 2. When Fig. 1 (lower) is compared with Fig. 2 it can be seen that the extent of the underestimation is similar in the two cases.
The influence of spatial frequency
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Fig. 2. Temporal frequency matches obtained by matching a counterphase grating of spatial frequency 1c/deg to standards of 0.5 (squares), 1 (open circles), 2 (solid circles) and 4 (triangles) c/deg for each of a range of counterphase frequencies.
The effect is rather greater for speed than for counterphase frequency in the case of GKE, rather greater for frequency than speed in the case of PAC, and similar in the two cases for ATS. This suggests that the temporal frequency effect of Experiment 2 and the speed effect shown in Experiment 1 have the same root cause.
EXPERIMENT
j: SPATIAL FREQUENCY MATCHING
A possible contributory cause of the nonlinear velocity transfer functions of Experiment 1 is that the spatial frequency encoded by the visual system in response to a given grating might vary with the temporal properties of the stimulus, which would affect the velocity code if computed from separate signals representing the temporal and spatial frequencies of the pattern. Several studies have shown that perceived spatial frequency is influenced by temporal modulation. The best known example is spatial frequency doubling during high-frequency modulation (Kelly, 1966), thought to be caused by a brightness non-linearity in the visual system. More relevant to our investigation is the finding (Virsu & Nyman, 1974) that relatively low temporal frequencies cause an increase in the perceived spatial frequency of a counterphased grating. Virsu and Nyman suggested that this results from decreased effectiveness of the inhibitory surrounds of visual neurons so that receptive field sizes increase. Parker (1983) also reports that perceived spatial frequency is markedly affected by temporal modulation of the stimulus. For both drifting and counterphase gratings, the perceived spatial frequency (as measured by matching to a standard spatial
frequency) of a grating of fixed spatial frequency increases as the drift rate or counterphase frequency increases. Taken together with physiological evidence that the optimum spatial frequencies of neurones in area 18 of cat cerebral cortex shift towards lower spatial frequencies as temporal frequency increases (Bisti, Carmignotto, Galli & Maffei; 1985), these findings suggest that the different spatial mechanisms in human cortex may carry fixed spatial frequency labels while having optimal spatial frequencies that change with temporal frequency. This would give rise not only to the increases in perceived spatial frequency observed by Parker but also to reductions in perceived velocity if the latter is computed by dividing temporal frequency by perceived (encoded) spatial frequency. Within such a scheme, perceived temporal frequency might be independent of changes in perceived spatial frequency, in which case temporal frequency matches should show less marked spatial frequency effects than speed matches. This was not the case in Experiment 2. speed matches between drifting However, gratings of different spatial frequencies will only be influenced by the reported rise in perceived spatial frequency with velocity if the perceived spatial frequencies of the standard and match gratings are d@kenrially affected by motion. If gratings of all spatial frequencies are equally affected (in percentage terms), the perceived spatial frequency effect will not influence speed marches made across spatial frequencies since standard and match gratings will be equally affected. The speed matches made should then mirror the corresponding temporal frequency matches despite the perceived spatial frequency effect. Parker found that gratings of different
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spatial frequencies are indeed differentially affected by velocity, but his results suggest that they are approximately equally affected by temporal frequency. Perceived spatial frequency is linearly related to stimulus temporal frequency and the slope of the function is similar for all spatial frequencies and similar for drift and counterphase. If this is so, no difference is predicted between speed matches expressed in temporal frequency terms (Fig. 1, lower) and temporal frequency matches (Fig. 2). We wished to re-examine the perceived spatial frequency effect using the same methods, stimulus conditions and subjects used in Experiments 1 and 2 in order to allow a quantitative assessment of its possible contribution to changes in perceived velocity across spatial frequencies. We wished to confirm that perceived spatial frequency is a linear function of temporal frequency as Parker has found, and to test whether the slope of the function is the same for different standard spatial frequencies and whether it is the same for drifting and for counterphase gratings. Prmedure Viewing conditions were identical to those used in Experiments 1 and 2. The procedure used for spatial frequency matching was similar to that used for speed and temporal frequency matching in the earlier experiments. The experiment was in two parts. In the first part the standard grating was a drifting sine grating; in the second part the standard grating was sinusoidaliy counterphased. In both cases the match grating was a stationary sine grating with a contrast of 20% and the subject’s task was to identify the grating that appeared to have the higher spatial frequency. Standard gratings of two spatial frequencies, 1.O and 2.0 c/deg, were used, and for each spatial frequency a range of drift velocities or counterphase frequencies was tested. The spatial frequency of the stationary match grating varied from trial to trial in small steps under the control of a PEST routine which estimated the point at which the match and standard gratings had the same perceived spatial frequency. The drifting or counterphased standard grating was matched for apparent contrast to the stationary match grating. The two authors acted as subjects and the main trends were confirmed with a naive subject. Any hemiheld differences in perceived spatial frequency (Georgeson, 1985; Edgar & Smith, 1990) were counterbalanced by repeating each condition
twice with the standard on the left and twice with it on the right and taking the mean. Results and d~cussio~ The results for spatial frequency matching with both drifting and counterphase gratings are shown in Fig. 3. The results for drifting gratings are plotted in terms of the temporal frequency, rather than the velocity, of the standard grating to allow direct comparison with the results for counter-phase gratings, In all cases, perceived spatial frequency, as measured by matching, increases linearly as the temporal frequency of the standard increases. When the results for the two spatial frequencies are compared it can be seen that the slopes of the two functions are similar, as reported by Parker. Comparison of results for drift and counterphase show that the slopes are similar, although slightly lower for counter-phase than for drift. Thus, the perceived spatial frequency of a counterphase grating may be influenced by temporal frequency to a slightly lesser extent than is that of a drifting grating. This is reminiscent of the much more marked finding of Bisti et al. (1985) that the shift in optimal spatial frequency seen in neurones of cat area 18 stimulated with drifting gratings does not occur with counterphase gratings. The significance of the results of Experiment 3 in relation to the results of Experiments 1 and 2 is discussed below. GENERALDISCUSSION The central question of interest in this paper is whether or not velocity (or temporal frequency) is encoded in quantitatively the same way within different spatial channeis. If it is not, ail existing models of velocity coding involving temppral frequency sensors within spatial &annels rquire modification to incorporate that fact, and the way in which the differing velocity outputs from different spatial ranges are combined to give perception of rigid movement of spatially complex targets needs to be made explicit. The results of Experiment 1 show clearly that the perceived speed of a drifting sine grating declines markedly as spatial frequency is increased, suggesting strongly that speed is not encoded in the same way in al1 spatial channels. Two other studies have investigated the efiects of spatial frequency on perceived speed. Firstly, Diener, Wist, Dichgans and Brandt (1976), using a magnitude estimation technique, report that
The influence of spatial frequency
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Fig. 3. Spatial frequency matches obtained by matching a stationary grating to a drifting (circles) or counterphase (squares) grating at each of a range of temporal frequencies. Results for two standard spatial frequencies, 1 and 2 c/deg, are shown separately.
perceived speed increases with spatial frequency. However their study was confined to extremely low spatial frequencies (0.01-0.07 c/deg), and so there is no direct conflict with our results. It is in any case possible that the subjects in this study were influenced by temporal frequency. With magnitude estimation, as with our technique (see earlier), this would result in overestimation of perceived velocity. Secondly, Campbell and Maffei (198 1) used rotating gratings to estimate the effects of spatial frequency on perceived speed. They found, using a matching technique with a 1 c/deg match, that as spatial frequency was increased, perceived speed first increased (up to 4c/deg) and then progressively decreased, reaching zero (“stopped motion”) at very high spatial frequencies. Thus, although they obtained a pronounced effect in the same direction as ours, it occurred only at higher spatial frequencies. At low spatial frequencies their effect was in the opposite direction to ours. Importantly, however, their results were confined to very low speeds: their 5 deg dia. disk rotated at 1 rpm, giving a maximum speed (on the rim. of the disk) of about
0.25 deg/sec. At our lowest speeds high spatial frequencies did not appear slower than low, and indeed there is an indication, clearest in Fig. 1 (lower), that in some cases they appeared faster, in accord with Campbell and Maffei. However, it must again be borne in mind that the use of a criterion influenced by temporal frequency could produce this result artifactally. Similarly, the results of Experiment 2 show that temporal frequency is not encoded in the same way at all spatial frequencies. The interpretation of this result depends on the conceptual framework adopted. Within the framework of the Watson and Ahumada (1985) model, in which velocity is derived from temporal frequency, it might suggest that the velocity effect of Experiment 1 is a knock-on effect of the temporal frequency effect found in Experiment 2. But if it is the case, as McKee, Silverman and Nakayama (1986) have suggested, that temporal frequency perception derives from velocity perception rather than vice versa, then the temporal frequency effect could be seen as a knock-on effect of the velocity effect. If it is assumed that temporal frequency perception
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and speed perception are derived independently in parallel from the same initial temporal filtering stage (Wilson, 1985) then our results suggest that there is a failure of temporal frequency constancy across spatial frequencies at the initial filtering stage, and that this causes the observed effects of spatial frequency on both velocity and temporal frequency. The contribution to the result for velocity of the fact that spatial frequency is encoded differently at different temporal frequencies (Experiment 3) may be minimal. As stated earlier, the spatial frequency effect examined in Experiment 3 will only affect the matches made in Experiments 1 and 2 if it affects the standard and match gratings differentially. Since the slopes of the functions in Fig. 3 are constant across spatial frequencies, it seems likely that at any given temporal frequency the standard and match are equally affected and that the spatial frequency shift therefore does not affect speed or temporal frequency matches. The spatial frequency effect may well influence the way velocity is perceived, but not in a spatial frequency dependent manner. In conclusion, the temporal frequency transfer function and the velocity transfer function of the visual system both vary markedly with spatial frequency. The two functions can be seen approximately to co-vary. The assumption made by some existing models of velocity perception (Watson & Ahumada, 1985; Harris, 1986) that temporal frequency coding is quantitatively similar at all spatial frequencies is therefore incorrect. We are conducting further experiments to ascertain how discrepant velocity signals may be resolved to give coherent drift. One possibility is that low spatial frequency motion signals may “capture” erroneous motion signals in high spatial frequency channels (Ramachandran & Cavanagh, 1987). Acknowledgemenr-Financial support from The Wcllcome Trust is gratefully acknowledged.
EDGAR
REFERENCES Adelson, E. H. & Bergen, J. R. (1985). Spatiotemporal models for the perception of motion. Journal of the Optical Society of America, AZ, 284-299. Bisti, S., Carmignotto, G., Galli, L. & Maffei, L. (1985). Spatial frequency characteristics of neurons of area I8 in the cat: Dependence on the velocity of the stimulus. JOWMI of Physiology, Landon, 359, 259-268.
Campbell, F. W. & Maffei, L. (1981). The influence of spatial frequency and contrast on the perception of moving patterns. Vision Research 21, 713-721. Diener, H. C., Wist, E. R., Dichgans. J. & Brandt, Th. (1976). The spatial frequency effect on perceived velocity. Vition Research,
16, 169-176.
Edgar, G. K. Jr Smith, A. T. (1990)Hemifield diflerences in perceived spatial frequency. Perception, in press. Georgeson, M. A. (1985). Apparent spatial frequency and contrast of gratings: Separate effects of contrast and duration. Vision Research, 25, 172 l- 1727. Harris, M. G. (1986). The perception of moving stimuli: A model of spatiotemporal coding in human vision. Vision Research, 26, I28
I - 1287.
Kelly, D. H. (1966). Frequency doubling in visual responses. Journal of the Optical Society of America, Js, 1628-l 633. McKee, S. P., Silverman, G. H. 8c Nakayama, K. (1986). Precise velocity discrimination despite random variations in temporal frequency and contast. Vision Research, 26, 605619.
Parker, A. (1983). The effects of temporal modulation on the perceived spatial structure of sine-wave gratings. Perceprion,
12, 663-682.
Ramachandran, V. S. & Cavanagh, P. (1987). Motion capture anisotropy. Virion Research, 27, 97-106. Smith, A. T. & Hammond, P. (1986). Hemifield differences in perceived velocity. Perception. 15, I I I-1 17. Taylor, M. M. & Creelman. C. D. (1967). PEST: EtBcient estimates on probability functions. Journal ofthe Acourrical Society of America, 41, 182-787.
Thompson, P. (1982). Perceived rate of movement depends on contrast. Vi&n Research, 22, 377-380. Virsu, V. & Nyman, G. (1974). Monophasic temporal increases apparent spatial frequency. modulation Perception, 3, 337-353.
Watson, A. B. (1986). Apparent motion occurs only between similar spatial frequencies. Vision Research, 26, 1727-l 730.
Watson, A. B. & Ahumada, A. J. (1985). Model of human visual-motion sensing. Journal of the Optical Society of America, AT, 322-342.
Wilson, H. R. (1985). A model for direction selectivity in threshold motion peraption. Biological Cybemelics. 51. 213-222.
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THE INFLUENCE OF SPATIAL FREQUENCY PERCEIVED TEMPORAL FREQUENCY AND PERCEIVED SPEED
0042&X9/90 53.00 + 0.00 1990 Pergamon Press pk
ON
A. T. SMITHand G. K. EDGAR Department of Psychology, University of Wales College of Cardiff, Cardiff CFl 3YG, Wales, U.K. (Received 8 August 1989; in revised form 26 February 1990)
AMraet-Speed matching experiments were conducted using drifting gratings of different spatial frequencies in order to assess the influence of spatial frequency on perceived speed. It was found that gratings of high spatial frequency appear to drift more slowly than low spatial frequency gratings of the same actual velocity. The perceived temporal frequency of a counterphase grating similarly declines as spatial frequency increases. The previously reported effect of temporal frequency on perceived spatial frquency probably does not contribute to these phenomena. Our results suggest that the motion sensors thought to operate within different spatial frequency ranges have different velocity transfer functions, a fact not incorporated in existing computational models of motion perception. Motion
Velocity
Temporal frequency
Spatial frquency
lNTRODUClION
Numerous studies have provided evidence that early visual processing occurs within a number of largely independent channels each sensitive only to a restricted range of spatial frequencies. Consequently, theories of the way in which velocity of image motion might be encoded have naturally tended to incorporate the idea that velocity might be computed within such spatially restricted channels. The theoretical models of Watson and Ahumada (1985), Adelson and Bergen (1985) and Harris (1986) provide differing suggestions as to how velocity might be computed, but all three involve derivation of velocity signals within spatially restricted channels. There is also some empirical support for such a system; for example Watson (1986) found that apparent motion with gratings occurs only when the successively presented stationary gratings are of similar spatial frequency. Presumably, in such a system, a moving spatially complex pattern generates a range of separate velocity signals in different spatial channels. In this case the question arises of how these velocity signals are combined to give a percept of rigid motion at a single perceived velocity. This question has not been addressed in detail in the models cited above. In the model of Harris (1986) a spatially complex moving stimulus generates identical velocity outputs in
all spatial channels. Similarly, Watson and Ahumada (1985) assume that temporal frequency is encoded in a way that is quantitatively consistent across spatial frequencies so that combination of velocity outputs, although not made explicit in the model, could be straightforward. However, we show here that neither temporal frequency nor velocity is perceived in a way that is consistent across spatial frequencies. This suggests that it cannot be assumed that different spatial channels produce identical velocity outputs in response to a rigidly moving complex pattern.
APPARATUS
All stimuli were vertically oriented sinewave gratings generated by a “Constable” CRT image generator under computer control and presented on a single CRT display (HP1332A with white phosphor). The mean luminance of the display was 70 cdm-r and the frame rate was 122 Hz. The display was masked to leave two 5 deg square apertures, one to the right and one to the left of a small fixation spot. The adjacent edges of the apertures were separated horizontally by 1 deg. Gratings with independently programmable contrast and spatial frequency could be presented separately in each aperture; these could be stationary, drifting or counter-phased.
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In the case of drifting gratings the direction of drift was centripetal (towards the fixation point) to aid fixation. Pilot studies had indicated that this technique yields identical matches to those obtained when both patterns drift in the same direction. The latter procedure, however, yields greater variance (perhaps due to poorer fixation), and so centripetal motion was considered preferable. Strictly, therefore, the task is speed matching not velocity matching (velocity being defined as speed in a particular direction). EXPERIMENT
1: SPEED
MATCHING
The purpose of this experiment was to examine the effect, if any, of spatial frequency on the perceived speed of a drifting grating in order to establish whether different spatial channels all generate the same velocity signal in response to a given fixed velocity. Procedure
The perceived speed of a 1 c/deg drifting grating (referred to as the match) presented in one aperture was matched to that of a second grating (referred to as the standard) presented simultaneously in the other aperture. Within any one run the spatial frequency and drift velocity of the standard grating were constant. In separate runs, the 1 c/deg match grating was matched for speed to standards of spatial frequency 0.5, 1, 2 and 4 c/deg and at each spatial frequency matches were made for each of a range of standard speeds. In each run the subject fixated the fixation point between the two apertures. A twoalternative forced-choice (ZAFC) procedure was used. For 1 min at the start of each run the two apertures were blank, their luminance equal to the mean luminance of the grating stimuli. The standard grating was then presented for I set in one aperture while the match grating was presented simultaneously in the other. After each such trial the subject indicated which of the two gratings appeared to be drifting faster. Following each response there was a 3 set interval in which the screen was blank, followed by presentation of the next pair of gratings. The drift speed of the match grating on each trial depended upon the previous responses of the subject and was determined using a PEST routine (Taylor & Creelman, 1967). The parameters of the PEST routine were set to give a 50% correct performance level, i.e. the level at
which the subject was unable to distinguish between the speeds of the standard and match gratings. This procedure was repeated four times for each spatial frequency and speed of the standard and the mean speed match calculated. In two of the runs the standard was presented on the left and in the other two it was presented on the right. Thus any hemifield differences in perceived speed (Smith & Hammond, 1986) were counterbalanced. In order to minimize differences (other than speed and spatial frequency) between the match and standard gratings, the two patterns always had subjectively equal contrast. In a pilot experiment the contrast of each ‘grating used was subjectively matched to that of a 1 c/deg grating of 20% contrast drifting at 0.5 deg/sec, and the contrast values so obtained were then used in the main experiment. Since perceived contrast is inversely related to speed, this meant that the physical contrast of both patterns increased as speed increased. Three subjects were used: the two authors and a naive observer. All practised the task before the experiment commenced and none was aware of the results obtained by the others. Resulw and discussion
The results are shown separately for the three subjects in Fig. 1 (upper). When the standard and match gratings have the same spatial frequency, the speed matching function is linear and has unity slope, as expected. This is also the case for standard gratings of spatial frequency 0.5 c/deg. However, at higher standard spatial frequencies the matching function departs from linearity. At low speeds the expected matches are made but as standard speed increases match speed increases more slowly than standard speed. Thus, at high spatial frequencies, and particularly at high velocities, speed is underestimated relative to the speed of a I c/deg grating of the same actual velocity. In view of the fact that physical (though not perceived) contrast varied across conditions involving different standard speeds it was felt necessary to check that this did not in itself produce the observed results. Thompson (1982) reports that, at low contrast, perceived speed depends on contrast. It was not expected that contrast would affect the speed matches made in this experiment since, firstly, we have found in unpublished experiments that perceived speed is essentially independent of contrast above about 10% contrast, and secondly the match and
lhe influence of spatial frequency
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Fig. I. Speed matches obtained by matching a drifting grating of spatial frequency 1 c/deg to standards of 0.5 (squares), I (open circles), 2 (solid circles) and 4 (triangles) c/dog drifting at each of a range of speeds. Results for three subjects are shown separately. The upper plots show the data presented in terms of the velocity of the standard grating, the lower plots show the same data presented in terms of the temporal frequency of the standard. Error bars show f I SE. Regression lines reflect either linear or logarithmic regressions as appropriate.
standard always had broadly similar contrasts in any run despite the variations across speed conditions. Nonetheless, the condition yielding the greatest underestimation of speed (4 c/deg) was repeated using a fixed contrast of 40% throughout. The results were very similar to those in Fig. 1 showing that contrast is not an important factor. As a check on the validity of the use of opposite directions of motion for the standard and match we repeated the experiment with one subject (GKE) using the same method except that both patterns drifted in the same direction (leftward in half the trials, rightward in the others). The results were similar to those shown in Fig. 1, though they were slightly more variable (see Introduction). It therefore seems that perceived speed is not dependent on direction and that speed comparisons can readily be made across directions, at least for motion in the two directions along the same axis. The distinction between speed and velocity appears to be unimportant in this context.
A problem that can arise when making speed matches between patterns of different spatial frequencies is that subjects might tend towards the use of a temporal frequency criterion, i.e. to “count” the cycles passing a given point in the image. We have found in other experiments that after considerable practice subjects can use either criterion at will, but not perfectly: temporal frequency matches tend to be influenced by velocity and vice versa. We cannot rule out the possibility that our data reflect the use of a criterion which is not a pure speed criterion but is influenced to some degree by temporal frequency. However, it should be noted that the use of a temporal frequency criterion in a speed matching task would result in overesfimates of perceived speed where, as in our experiments, the spatial frequency of the standard is higher than that of the match. Our finding of reduced perceived speed therefore cannot be explained in this way. If anything, the effect of spatial frequency on perceived speed must be greater than our data indicate, not less.
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The main conclusion drawn from the results is that if velocity perception is derived from multiple velocity sensors each of which operates within a single spatial frequency mechanism, it would seem that the different velocity sensors do not have identical velocity transfer functions. Generally, the higher the spatial frequency the lower the velocity signalled. However the relationship is not linear: the effect is more marked at high spatial frequencies. While a one octave increase in spatial frequency from 2 to 4c/deg has a marked effect on speed matches, a one octave increase from 0.5 to 1 c/deg has no measurable effect. This asymmetry is not related to the choice of match spatial frequency (1 c/deg), which is essentially arbitrary; we have found that the same result occurs with other match spatial frequencies. EXPERIMENT
2: TEMPORAL MATCHING
FREQUENCY
In Experiment 1 it was shown that perceived speed depends on spatial frequency, and that it is not always a linear function of physical speed. One plausible way in which perception of speed might be derived (e.g. Watson & Ahumada, 1985) is by measuring temporal frequency within a labelled spatial frequency mechanism and computing speed by dividing the measured temporal frequency by the spatial frequency signalled by that spatial mechanism. In this case, there are two separate possible sources of the effects of spatial frequency and speed demonstrated in Experiment 1. Firstly, the temporal frequency sensors might have non-linear frequency transfer characteristics, and might have different transfer characteristics in different spatial channels, so that in some cases a distorted temporal frequency signal is divided by a correct spatial frequency to give a distorted speed. That is, speed might be underestimated because temporal frequency is underestimated. This possibility is examined in Experiment 2. Secondly, the spatial frequency mechanisms themselves might carry spatial frequency labels bearing a different relationship to each other than the spatial frequencies of the gratings that stimulate them optimally, or (perhaps more likely) they might carry fixed spatial frequency labels while having optimum spatial frequencies that vary with temporal frequency. In this case the correct temporal frequency might be divided by a distorted spatial frequency to give a distorted speed. That is, speed might be underestimated because spatial frequency is
overestimated. This possibility will be examined in Experiment 3. The purpose of Experiment 2 was thus to examine the effects of spatial frequency on perceived temporal frequency. This was done using counterphase gratings. Procedure
The procedure was similar to that of Experiment 1 except that the standard and match gratings did not drift but instead were temporally modulated in sinusoidal counterphase. The standard gratings used were of the same spatial frequencies as those used in Experiment 1, and they were modulated at one of a range of temporal frequencies equivalent to those used in Experiment 1 (up to 24 Hz). The task of the subjects was to identify the grating with the higher temporal frequency, and frequency matches were estimated using the same PEST routine used in Experiment 1, the temporal frequency of the match grating in each trial depending on the previous responses of the subject. The apparent contrasts (modulation depths) of the standard and match gratings were again matched and any hemifield differences were counterbalanced in the same way as in Experiment 1. The subjects, who were the same as for Experiment 1, were given practice in the task before the experiment commenced. No subject was aware of the results obtained by the others. Results and discussion
The results for temporal frequency matching are shown in Fig. 2. The pattern of results is broadly similar to that obtained for speed matching in Experiment 1. For standard gratings of low spatial frequency, match temporal frequency is a linear function of standard temporary frequency and the function has unity slope. But as the spatial frequency of the standard increases, its temporal frequency is progressively underestimated relative to that of the 1 c/deg match grating, particularly at high temporal frequencies. In order to see the extent to which the speed matching functions of Experiment 1 can be explained in terms of the underestimation of temporal frequency shown in Experiment 2, the results of Experiment 1 are replotted in Fig. 1 (lower) with the speed of the standard expressed in terms of temporal frequency. In this form, the data are directly comparable to those of Experiment 2. When Fig. 1 (lower) is compared with Fig. 2 it can be seen that the extent of the underestimation is similar in the two cases.
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Fig. 2. Temporal frequency matches obtained by matching a counterphase grating of spatial frequency 1c/deg to standards of 0.5 (squares), 1 (open circles), 2 (solid circles) and 4 (triangles) c/deg for each of a range of counterphase frequencies.
The effect is rather greater for speed than for counterphase frequency in the case of GKE, rather greater for frequency than speed in the case of PAC, and similar in the two cases for ATS. This suggests that the temporal frequency effect of Experiment 2 and the speed effect shown in Experiment 1 have the same root cause.
EXPERIMENT
j: SPATIAL FREQUENCY MATCHING
A possible contributory cause of the nonlinear velocity transfer functions of Experiment 1 is that the spatial frequency encoded by the visual system in response to a given grating might vary with the temporal properties of the stimulus, which would affect the velocity code if computed from separate signals representing the temporal and spatial frequencies of the pattern. Several studies have shown that perceived spatial frequency is influenced by temporal modulation. The best known example is spatial frequency doubling during high-frequency modulation (Kelly, 1966), thought to be caused by a brightness non-linearity in the visual system. More relevant to our investigation is the finding (Virsu & Nyman, 1974) that relatively low temporal frequencies cause an increase in the perceived spatial frequency of a counterphased grating. Virsu and Nyman suggested that this results from decreased effectiveness of the inhibitory surrounds of visual neurons so that receptive field sizes increase. Parker (1983) also reports that perceived spatial frequency is markedly affected by temporal modulation of the stimulus. For both drifting and counterphase gratings, the perceived spatial frequency (as measured by matching to a standard spatial
frequency) of a grating of fixed spatial frequency increases as the drift rate or counterphase frequency increases. Taken together with physiological evidence that the optimum spatial frequencies of neurones in area 18 of cat cerebral cortex shift towards lower spatial frequencies as temporal frequency increases (Bisti, Carmignotto, Galli & Maffei; 1985), these findings suggest that the different spatial mechanisms in human cortex may carry fixed spatial frequency labels while having optimal spatial frequencies that change with temporal frequency. This would give rise not only to the increases in perceived spatial frequency observed by Parker but also to reductions in perceived velocity if the latter is computed by dividing temporal frequency by perceived (encoded) spatial frequency. Within such a scheme, perceived temporal frequency might be independent of changes in perceived spatial frequency, in which case temporal frequency matches should show less marked spatial frequency effects than speed matches. This was not the case in Experiment 2. speed matches between drifting However, gratings of different spatial frequencies will only be influenced by the reported rise in perceived spatial frequency with velocity if the perceived spatial frequencies of the standard and match gratings are d@kenrially affected by motion. If gratings of all spatial frequencies are equally affected (in percentage terms), the perceived spatial frequency effect will not influence speed marches made across spatial frequencies since standard and match gratings will be equally affected. The speed matches made should then mirror the corresponding temporal frequency matches despite the perceived spatial frequency effect. Parker found that gratings of different
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spatial frequencies are indeed differentially affected by velocity, but his results suggest that they are approximately equally affected by temporal frequency. Perceived spatial frequency is linearly related to stimulus temporal frequency and the slope of the function is similar for all spatial frequencies and similar for drift and counterphase. If this is so, no difference is predicted between speed matches expressed in temporal frequency terms (Fig. 1, lower) and temporal frequency matches (Fig. 2). We wished to re-examine the perceived spatial frequency effect using the same methods, stimulus conditions and subjects used in Experiments 1 and 2 in order to allow a quantitative assessment of its possible contribution to changes in perceived velocity across spatial frequencies. We wished to confirm that perceived spatial frequency is a linear function of temporal frequency as Parker has found, and to test whether the slope of the function is the same for different standard spatial frequencies and whether it is the same for drifting and for counterphase gratings. Prmedure Viewing conditions were identical to those used in Experiments 1 and 2. The procedure used for spatial frequency matching was similar to that used for speed and temporal frequency matching in the earlier experiments. The experiment was in two parts. In the first part the standard grating was a drifting sine grating; in the second part the standard grating was sinusoidaliy counterphased. In both cases the match grating was a stationary sine grating with a contrast of 20% and the subject’s task was to identify the grating that appeared to have the higher spatial frequency. Standard gratings of two spatial frequencies, 1.O and 2.0 c/deg, were used, and for each spatial frequency a range of drift velocities or counterphase frequencies was tested. The spatial frequency of the stationary match grating varied from trial to trial in small steps under the control of a PEST routine which estimated the point at which the match and standard gratings had the same perceived spatial frequency. The drifting or counterphased standard grating was matched for apparent contrast to the stationary match grating. The two authors acted as subjects and the main trends were confirmed with a naive subject. Any hemiheld differences in perceived spatial frequency (Georgeson, 1985; Edgar & Smith, 1990) were counterbalanced by repeating each condition
twice with the standard on the left and twice with it on the right and taking the mean. Results and d~cussio~ The results for spatial frequency matching with both drifting and counterphase gratings are shown in Fig. 3. The results for drifting gratings are plotted in terms of the temporal frequency, rather than the velocity, of the standard grating to allow direct comparison with the results for counter-phase gratings, In all cases, perceived spatial frequency, as measured by matching, increases linearly as the temporal frequency of the standard increases. When the results for the two spatial frequencies are compared it can be seen that the slopes of the two functions are similar, as reported by Parker. Comparison of results for drift and counterphase show that the slopes are similar, although slightly lower for counter-phase than for drift. Thus, the perceived spatial frequency of a counterphase grating may be influenced by temporal frequency to a slightly lesser extent than is that of a drifting grating. This is reminiscent of the much more marked finding of Bisti et al. (1985) that the shift in optimal spatial frequency seen in neurones of cat area 18 stimulated with drifting gratings does not occur with counterphase gratings. The significance of the results of Experiment 3 in relation to the results of Experiments 1 and 2 is discussed below. GENERALDISCUSSION The central question of interest in this paper is whether or not velocity (or temporal frequency) is encoded in quantitatively the same way within different spatial channeis. If it is not, ail existing models of velocity coding involving temppral frequency sensors within spatial &annels rquire modification to incorporate that fact, and the way in which the differing velocity outputs from different spatial ranges are combined to give perception of rigid movement of spatially complex targets needs to be made explicit. The results of Experiment 1 show clearly that the perceived speed of a drifting sine grating declines markedly as spatial frequency is increased, suggesting strongly that speed is not encoded in the same way in al1 spatial channels. Two other studies have investigated the efiects of spatial frequency on perceived speed. Firstly, Diener, Wist, Dichgans and Brandt (1976), using a magnitude estimation technique, report that
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Fig. 3. Spatial frequency matches obtained by matching a stationary grating to a drifting (circles) or counterphase (squares) grating at each of a range of temporal frequencies. Results for two standard spatial frequencies, 1 and 2 c/deg, are shown separately.
perceived speed increases with spatial frequency. However their study was confined to extremely low spatial frequencies (0.01-0.07 c/deg), and so there is no direct conflict with our results. It is in any case possible that the subjects in this study were influenced by temporal frequency. With magnitude estimation, as with our technique (see earlier), this would result in overestimation of perceived velocity. Secondly, Campbell and Maffei (198 1) used rotating gratings to estimate the effects of spatial frequency on perceived speed. They found, using a matching technique with a 1 c/deg match, that as spatial frequency was increased, perceived speed first increased (up to 4c/deg) and then progressively decreased, reaching zero (“stopped motion”) at very high spatial frequencies. Thus, although they obtained a pronounced effect in the same direction as ours, it occurred only at higher spatial frequencies. At low spatial frequencies their effect was in the opposite direction to ours. Importantly, however, their results were confined to very low speeds: their 5 deg dia. disk rotated at 1 rpm, giving a maximum speed (on the rim. of the disk) of about
0.25 deg/sec. At our lowest speeds high spatial frequencies did not appear slower than low, and indeed there is an indication, clearest in Fig. 1 (lower), that in some cases they appeared faster, in accord with Campbell and Maffei. However, it must again be borne in mind that the use of a criterion influenced by temporal frequency could produce this result artifactally. Similarly, the results of Experiment 2 show that temporal frequency is not encoded in the same way at all spatial frequencies. The interpretation of this result depends on the conceptual framework adopted. Within the framework of the Watson and Ahumada (1985) model, in which velocity is derived from temporal frequency, it might suggest that the velocity effect of Experiment 1 is a knock-on effect of the temporal frequency effect found in Experiment 2. But if it is the case, as McKee, Silverman and Nakayama (1986) have suggested, that temporal frequency perception derives from velocity perception rather than vice versa, then the temporal frequency effect could be seen as a knock-on effect of the velocity effect. If it is assumed that temporal frequency perception
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and speed perception are derived independently in parallel from the same initial temporal filtering stage (Wilson, 1985) then our results suggest that there is a failure of temporal frequency constancy across spatial frequencies at the initial filtering stage, and that this causes the observed effects of spatial frequency on both velocity and temporal frequency. The contribution to the result for velocity of the fact that spatial frequency is encoded differently at different temporal frequencies (Experiment 3) may be minimal. As stated earlier, the spatial frequency effect examined in Experiment 3 will only affect the matches made in Experiments 1 and 2 if it affects the standard and match gratings differentially. Since the slopes of the functions in Fig. 3 are constant across spatial frequencies, it seems likely that at any given temporal frequency the standard and match are equally affected and that the spatial frequency shift therefore does not affect speed or temporal frequency matches. The spatial frequency effect may well influence the way velocity is perceived, but not in a spatial frequency dependent manner. In conclusion, the temporal frequency transfer function and the velocity transfer function of the visual system both vary markedly with spatial frequency. The two functions can be seen approximately to co-vary. The assumption made by some existing models of velocity perception (Watson & Ahumada, 1985; Harris, 1986) that temporal frequency coding is quantitatively similar at all spatial frequencies is therefore incorrect. We are conducting further experiments to ascertain how discrepant velocity signals may be resolved to give coherent drift. One possibility is that low spatial frequency motion signals may “capture” erroneous motion signals in high spatial frequency channels (Ramachandran & Cavanagh, 1987). Acknowledgemenr-Financial support from The Wcllcome Trust is gratefully acknowledged.
EDGAR
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Campbell, F. W. & Maffei, L. (1981). The influence of spatial frequency and contrast on the perception of moving patterns. Vision Research 21, 713-721. Diener, H. C., Wist, E. R., Dichgans. J. & Brandt, Th. (1976). The spatial frequency effect on perceived velocity. Vition Research,
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Edgar, G. K. Jr Smith, A. T. (1990)Hemifield diflerences in perceived spatial frequency. Perception, in press. Georgeson, M. A. (1985). Apparent spatial frequency and contrast of gratings: Separate effects of contrast and duration. Vision Research, 25, 172 l- 1727. Harris, M. G. (1986). The perception of moving stimuli: A model of spatiotemporal coding in human vision. Vision Research, 26, I28
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Kelly, D. H. (1966). Frequency doubling in visual responses. Journal of the Optical Society of America, Js, 1628-l 633. McKee, S. P., Silverman, G. H. 8c Nakayama, K. (1986). Precise velocity discrimination despite random variations in temporal frequency and contast. Vision Research, 26, 605619.
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Thompson, P. (1982). Perceived rate of movement depends on contrast. Vi&n Research, 22, 377-380. Virsu, V. & Nyman, G. (1974). Monophasic temporal increases apparent spatial frequency. modulation Perception, 3, 337-353.
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