Vi.kn Res. Vol. 32, NO. 7, pp. 1263-1269, 1992 Printed in Great Britain. All rights reserved

Copyright

~042.49~9~92 $5.00 t 0.00 I‘ 1992 Pergamon Press l.td

Moving Two-Dimensional Patterns Can Capture the Perceived Directions of Lower or Higher Spatial Frequency Gratings CHRISTOPHER Receked

2 February

YO,* HUGH R. WILSON* 1991; in rel~~~ed~orm 20 Not,ember

1991

Coherent plaid motion is produced by superimposing two one-dimensional gratings of the same spatial frequency moving f 60’ from the intersection-of-constraints (IOC) resultant direction. These moving plaids were found to change the perceived direction of a third one-dimensional grating, either 6-fold lower or higher in spatial frequency, from traveling in one of the plaid’s component direction to the IOC resultant direction. We describe this phenomenon as coherence capture. Coherence capture was found to be effective between plaids with 0.5, 1.0, and 1.5 c/deg components and gratings of 3.0, 6.0 and 9.0 cfdeg respectively. It was also found to be effective between plaids with 3.0 c/deg components and gratings of 0.5 c/deg. However, coherence capture between higher spatial frequency plaids and lower spatial frequency gratings became less effective when the ~orn~~nt spatial fr~uencies of the plaid increased. Aperture problem

Intersection-of-constraints

Plaid motion

INTRODUCTION When a high spatial frequency (SF) grating moves in a direction different from that of a low SF grating, the perceived overall direction is biased towards the low SF grating’s direction. This phenomenon was named “motion capture” by Ramachandran and Cavanagh (1987) who initially demonstrated that a low SF moving grating was able to capture the motion of uncorrelated dynamic random dots and make the percept indistinguishable from that of a correlated random dot pattern physically moving with the grating. The authors proposed that motion signals are separately extracted from spatial mechanisms tuned to different SFs. As the low SF features are more salient than high SF features during motion, signals from the former are able to block or inhibit those from the latter {Ramachandran & Cavanagh, 1987). The advantage of this strategy is that it disregards ambiguous or incorrect motion signals from high SF features. Therefore, solving for low SF motion first and then assuming the solution holds for the high SF features will be useful in attacking the correspondence problem during motion perception. Ramachandran (1985) also found that low spatial frequencies are not the only salient features that can generate motion capture; under certain situations, subjective contours can also generate vivid capture. Adelson and Movshon (1982) showed that in the case of two-dimensional patterns, the components have to be within 1S-2 octaves

*Visual

Sciences Center,

University

Chicago, IL 60637, U.S.A.

of Chicago,

939 East S7th Street,

Motion capture

for them to cohere. When the components are perceived as incoherent, the probability of coherence can be increased by increasing the components’ contrast. Kooi, Grosof, DeValois and DeValois (1988) showed that when two-dimensional motion was created by superimposing a 1 and 1.5 c/deg component gratings drifted in orthogonal directions, the perceived direction is biased towards the lower SF grating when the two gratings have been scaled for apparent contrast. However, the perceived direction could be shifted to the higher SF component by increasing the contrast of the higher SF component relative to that of the lower. Adelson and Movshon (1982) proposed that the synthesis of two-dimensional pattern motion from onedimensional component motions is accomplished in two stages. The first stage consists of component detectors which signal one-dimensional motion, and the second stage consists of pattern detectors which compute the two-dimensional image resultant motion. Subsequently, Welch (1989) performed speed discrimination experiments and showed that the discrimination thresholds of two-dimensional patterns reflected the discrimination thresholds at the component level. This further supports the two stage model by implying that the precision in the extraction of two-dimensional pattern speed is limited by noise at the component stage. Motion processing operates at different spatial scales. Each layer of the motion processing model shown in Fig. 1 depicts a SF scale. Two gratings moving perpendicularly to one another and differing by more than 1.5-2 octaves in SF will not cohere because they stimulate component units across different scales. This

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FIGURE 1. Spatial frequency selective motion processing layers, Each layer consists of two stages. Component selective units tuned to different direction feed into pattern selective units. Top layer is selective for high SF while the bottom layer is selective for low SF. The purpose of this paper is to investigate the interaction between layers tuned to different spatial scales.

will lead to the stimulation of pattern units in two different scales that are tuned to 90” apart in direction. Assuming that there is no facilitatory or inhibitory connection between the two scales, the resulting percep-

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cl : -60”; Variable contrast c2 : -60°; contrast = 0.2 c3 : +60”; contrast = 0.2

cl : -60”; Variable contrast c2 : -60”;contrast = 0.2 c3 : +60”;contrast = 0.2 FIGURE 2. Parameters used for measuring coherence fraction. Three components were presented. Two of the same spatial frequency, the other being 6 times higher or lower in spatial scale. Diagrams on the left show the velocity space construction of the three component vectors. Thick arrows indicate lower SF components, and thin arrows represent higher SF components. Components shown in gray were presented at variable contrasts during an experiment. All components were drifted 60” from the vertical direction at the same speed.

tion will be that of two gratings sliding transparently across each other. The goal of the research reported here was to determine the conditions under which interactions between spatial scales can occur. In these experiments, one set of gratings is 6 times higher in SF than the other; and they are drifted in directions that are 120” apart as shown in the velocity space constructions in Fig. 2. In this figure, thick arrows indicate the low SF component vectors and thin arrows indicate the high SF component vectors. Dark arrows represent components presented at a fixed contrast of 0.2 and gray arrows represent components presented at variable contrast from 0 to 0.2. In Experiment 1, the purpose is to test whether adding a low SF component to the high SF component will increase the probability of overall pattern coherence when the other component is low in SF. From the work of Ramachandran and Cavanagh (1987) and Kooi et al. (1988) it was expected that when the low SF components cohere, the plaid would alter the perceived direction of the high SF component. The control experiment for this test is to increase the contrast of the existing high SF component in the two-dimensional pattern todetermine whether it alone is sufficient to increase the probability of coherence. The

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reverse of the above experiments was also performed to test whether high SF components at f60” and 0.2 contrast can influence the perceived direction of the low SF component. Thus, a variable contrast high SF grating was superimposed on the existing high and low SF gratings. The surprising result from this study was that high SF gratings were found to be able to capture the perceived direction of a low SF grating so that all appeared to drift in the IOC resultant direction. METHODS Pattern display methods and equipment have been described elsewhere (Yo & Wilson, 1992). Viewing distances were 38, 76 and 114in., with circular display diameters equaling 8, 4 and 2.7” respectively. At the viewing distance of 38 in., the pixelsize was 72 arcsec. The velocity space construction for each pattern used in the four experiments is shown in Fig. 2. Components 1 and 2 of each pattern were displayed on odd horizontal pixel lines while component 3 was displayed on even horizontal pixel lines. In these experiments, two components always drifted 60” anticlockwise (-60”) to the vertical direction and the other always drifted 60” clockwise (+ 60”) to the vertical. Component drift speeds were 1.33”/sec at 114”, 2”/sec at 76”, 4”/sec at 38”. In Fig. 2, thick arrows indicate the lower SF (0.5, 1.0 and 1.5 c/deg) component vectors and thin arrows indicate the higher SF (3.0,6.0 and 9.0 c/deg) component vectors. Dark arrows represent components presented at a fixed contrast of 0.2 and gray arrows represent components presented at variable contrast from 0 to 0.2. All patterns had a fixation spot in the center and subjects were trained to fixate on the fixation target at all times. Each experiment consisted of 150 trials. In each trial, subjects pressed a mouse button to initiate pattern presentation. The subject’s task was to move the mouse to the left if the two-dimensional pattern and the onedimensional grating moved rigidly (coherentIy) in one direction, and move the mouse to the right if the pattern and the grating moved in different directions. Each test pattern could contain 1 of 5 possible contrasts for the variable component, and it was presented randomly 30 times in each experiment. Drift direction was randomized between upward and downward. A total of 4 subjects participated in this study, 2 of them naive. CY, RM and PJ used their right eyes. HRW used his left eye. Presentation duration for each pattern was 450 msec for all subjects. Every experiment was replicated at least three times. Control experiments were conducted at the highest three variable component contrasts in Experiments 1 and 2. RESULTS The fraction of patterns that appeared to be coherent is shown in Figs 3 and 4 as a function of the contrast of the variable component. The component spatial frequencies were at 0.5 and 3.0 c/deg. Solid triangular symbols represent data under test conditions in Experiments 1

and 2. Open circular symbols represent control data. The means of the test and the control data are connected by solid and dotted lines respectively. Results from Experiment 1 (Fig. 3) show that when the low SF (0.5 c/deg) component contrast increased from 0 to 0.2, mean coherence fraction increased to be well over 0.9. When the low SF (0.5 c/deg) component was not present, mean coherence fraction was below 0.1. To show that this increase in coherence perception was not due to contrast increase alone, the contrast of the isolated high SF (3.0 c/deg) component was increased. Mean coherence fraction measured under these conditions remained below 0.2 for both subjects (Fig. 3, open circles). In Experiment 2, the low SF and high SF components were again at 0.5 and 3.0 c/deg. Results displayed in Fig. 4 show that when the high SF component contrast increased from 0 to 0.2, mean coherence fraction increased to over 0.9. When the high SF component was not present, mean coherence fraction was below 0.2. To show that this increase in coherence perception was not due to contrast increase, the same contrasts added to the high SF component was added to the low SF component (refer to Fig. 2). Mean coherence fraction in the control experiment remained below 0.1 for both subjects (Fig. 4, open circles).

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FIGURE 3. Coherence capture by the lower SF components. Top panel shows data for subject CY and bottom panel shows data for subject PJ. A 0.5 and a 3.0 qdeg grating moved in directions differing by 120”. Symbols indicate actual data points whereas lines connect the averages of the data. When variabte amounts of the OSc/deg component contrast was superimposed onto the 3.0 c/deg component (x-axis), the fraction of patterns that looked coherent (y-axis) increased. In the control experiment, variable amounts of additional 3.0 c/deg component contrast was added to the existing 3.0c/deg component (x-axis), the fraction of patterns that appeared coherent remained unchanged.

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FIGURE 4. Coherence capture by the higher SF components. Top panel shows data for subject CY and bottom panel shows data for subject PJ. A 0.5 and a 3.0 c/deg grating moved in directions differing by 120”. Symbols indicate actual data points whereas lines connect the averages of the data. When variable amounts of the 3.0c/deg component contrast was added to the 0.5 c/deg component (x-axis), the fraction of patterns that looked coherent (y-axis) increased. In the control experiment, variable amounts of additional 0.5 c/deg component contrast was added to the existing 0.5cjdeg component (x-axis), the fraction of patterns that appeared coherent remained the same.

In order to compare the effectiveness of coherence capture by higher and lower SF plaids, we define the coherence threshold as the contrast at which the coherence fraction equaled 0.5. The data sets were fitted with the Quick function (Quick, 1974) using a maximum likelihood estimation procedure to estimate threshold contrast. The threshold contrast for the plaid’s lower SF component to induce coherence capture was 0.100 + 0.009 for subject CY and 0.113 f 0.018 for subject PJ. The threshold contrast for the plaid’s higher SF component to induce coherence capture was 0.077 f 0.016 and 0.047 f 0.033 for subjects CY and PJ respectively. The threshold contrasts of the higher SF component were significantly lower than the threshold contrasts of the lower SF component of the plaid for both subjects at the 0.05 level (t-test). Further variations in the stimulus parameters using components drifted 90” apart in direction, at different speeds, and with the three components drawn on three separate sets of horizontal pixel lines instead of two sets of pixel lines used in this study, produced essentially the same results (Yo, 1990). As low SF gratings were found to be able to capture a high SF grating, it is expected that the coherence

threshold will decrease as the low SF components approach the peak of the CSF. In the case of high SF gratings capturing a low SF grating, the coherence threshold will be expected to increase as the high SF components move further from the peak of the CSF. In Figs 5 and 6 we show data comparing the effectiveness of motion capture for three SF pairs. In these figures, top panels show data for experienced subjects CY and HRW; lower panels show data for naive subjects PJ and RM. Different spatial frequencies were produced by altering the viewing distance while the drift rate of the components were kept at 2 Hz. In Fig. 5, mean coherence fractions are shown for low SF components at 0.5, 1.O and 1.5 c/deg. The higher components were at 6 times higher in SF in each case. Solid circular symbols indicate averaged data when the lower SF component was 0.5 c/deg. Data under this condition for subjects CY and PJ were the same as those shown in Fig. 3. Dotted square and open triangular symbols indicate averaged data when the lower SF components were 1.0 and 1.5 c/deg respectively. When variable amounts of the lower SF component contrasts were superimposed onto the higher SF component (xaxis), the fraction of patterns that looked coherent (y-axis) increased across the tested SF range. The data show that there is a trend for coherence capture to be more effective when the lower SF component was closer to the peak of the CSF (1.5 c/deg). In Fig. 6, mean coherence fraction is shown for high SF components at 3.0, 6.0 and 9.0 c/deg. The lower SF components were at 6 times lower in SF in each case. Solid circular symbols indicate averaged data when the higher SF component was 3.0 c/deg. Data under this condition for subjects CY and PJ were the same as those shown in Fig. 4. Dotted square and open triangular symbols indicate averaged data when the higher SF components were 6.0 and 9.0 c/deg respectively. When variable amounts of the higher SF component contrasts were added to the lower SF component (x-axis), the fraction of patterns that looked coherent (_r-axis) increased most clearly for the case when the higher SF components were 3.0c/deg. The data show that coherence capture became less effective when the higher SF component was further away from the peak of the CSF (3.0 vs 9.0c/deg). For subject PJ, two-dimensional patterns consisting of 9.0 c/deg gratings were ineffective in capturing the 1.5 c/deg grating, and therefore the 1.5-9.0 c/deg pair of interaction was not tested on him. In order to illustrate the SF dependent nature of coherence capture, mean coherence fraction is plotted against SF of the two-dimensional pattern in Fig. 7. The segment of the graph on the left (0.5, 1.0, I .5 c/deg) shows the ability of lower SF plaids to capture gratings that are 6-fold higher in SF. The segment of the graph on the right (3, 6, 9 c/deg) shows the ability of higher SF plaids to capture gratings that are 6-fold lower in SF. Different symbols indicate the mean coherence fraction for different subjects. Mean coherence fraction for each subject represented the average of all coherence fractions measured with the variable components at and beyond

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FIGURE 5. Coherence capture by low SF components at 0.5, 1.0 and 1.5c/deg. The higher SF components were at 3.0, 6.0 and 9.0 c/deg respectively. Top panels show data for experienced subjects CY and HRW; bottom panels show data for naive subjects PJ and RM. Solid circular symbols indicate averaged data when the lower spatial frequency component was 0.5 c/deg. Data under this condition for subjects CY and PJ were the same as those shown in Fig. 3. Dotted square and open triangular symbols indicate averaged data when the lower spatial frequency components were at 1.0 and 1.5 c/deg respectively. When variable amounts of the lower SF component contrasts were superimposed onto the higher SF component (x-axis), the fraction of patterns that looked coherent (y-axis) increased across the tested spatial frequency range. The data show that there is a trend for coherence capture to be more effective when the lower SF component was nearer to the peak of the CSF. 1.0 0.8 -

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FIGURE 6. Coherence capture by high spatial frequency components at 3.0,6.0 and 9.0 c/deg. The lower SF components were at 0.5, 1.0 and 1.5 c/deg respectively. Top panels show data for experienced subjects CY and HRW; bottom panels show data for naive subjects PJ and RM. Solid circular symbols indicate averaged data when the higher spatial frequency component was 3.0 c/deg. Data under this condition for subjects CY and PJ were the same as those shown in Fig. 4. Dotted square and open triangular symbols indicate averaged data when the higher SF components were 6.0 and 9.0c/deg respectively. When variable amounts of the higher SF component contrasts were added to the lower SF component (x-axis), the fraction of patterns that looked coherent (y-axis) increased most clearly for the case when the higher SF components equaled 3.0 c/deg. The data show that coherence capture became less effective when the higher SF component was further from the peak of the CSF.

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Spatial Frequency (cpd) FIGURE 7. Spatialfrequency dependent nature ofcoherencecapture. Mean coherence fraction is plotted on the Y-axis. spatial frequency of the two-dimensional pattern is plotted on the X-axis. The segment of the graph on the left (0.5, I .O, 1.5 c/deg) shows the ability of lower SF two-dimensional patterns to capture gratings that are 6-fold higher in SF. The segment of the graph on the right (3, 6, 9c/deg) shows the ability of higher SF two-dimensional patterns to capture gratings that are 6-fold lower in SF. Different symbols indicate the mean coherence fraction for ditTerent subjects. The solid and dotted lines indicate the mean coherent fraction across subjects as a function of spatial frequency.

0.05 contrast. The solid and dotted lines indicate the mean coherent fraction across subjects as a function of SF. The sold line shows that as the SF of the twodimensional pattern increased from 0.5 to 1.5 c/deg, the ability to capture gratings that are 6-fold higher in SF increased. The dotted line shows that as the SF of the two-dimensional pattern increased from 3.0 to 9.0 c/deg, the ability to capture gratings that are 6-fold lower in SF decreased. DISCUSSION

The results indicate that when a two-dimensional pattern coheres, it is able to change the perceived direction of another grating of a different SF, which initially appeared to move in one of the component’s direction, into moving in the IOC resultant direction. Two-dimensional patterns consisting of 0.5. 1.0. or 1.5 c/deg component gratings were found to be effective in altering the perceived direction of 3.0. 6.0, and 9.0 c/deg gratings respectively. As the lower SF components approached the peak of CSF, they became more effective in altering the higher SF component’s perceived direction (Fig. 7). Two-dimensional patterns consisting of 3.0c/deg component gratings were found to be effective in changing a 0.5 c/deg one-dimensional grating’s apparent direction. This novel “coherence capture” phenomenon is similar to the “motion capture” that Ramachandran and Cavanagh (1987) described in that moving low SF features are able to alter the perceived motion of high SF features. The previous investigators also tested the effectiveness of motion capture between higher and lower SF gratings. They found that although a higher SF grating (2.67 c/deg) was able to capture the motion of a lower SF grating, the effectiveness of motion capture was at least an order of

magnitude less than that of a lower SF grating capturing a higher SF grating. We defined the threshold contrast for inducing coherence as the contrast corresponding to 50% fraction coherent. The threshold contrasts for the 3.0c;deg component of the plaid to capture a 0.5c.:deg grating were found to be significantly lower than the threshold contrasts for the 0.5 c/deg component of the plaid to capture a 3.0cldeg grating. This indicates that the coherence capture was more effective in the 3.0 to 0.5 cideg direction than in the 0.5 to 3.0 cideg direction. As the component SFs of the plaid increased, they became less effective in capturing a lower SF grating. In particular, the coherence fraction for all subjects tested with a 9.0 cjdeg plaid and a 1.5 c/deg grating never exceeded 0.6. Subject PJ’s coherence fraction did not even exceed 0.25 when tested with a 6.0 cideg plaid and a I .Oc/deg grating. These data suggest that the strength of coherence capture is determined by the contrast sensitivity function. The coherence capture phenomenon that we have described was tested with three component gratings all being consistent with one IOC resultant vector. In the motion capture experiments of Ramachandran and Cavanagh, the lower SF stimulus was a sinusoidal grating, the higher SF component was either a grating or a random dot pattern. The random dots either underwent coherent or incoherent motion, and the direction of the pattern being captured was either 0,90 or 180 from the other grating. Therefore the coherence capture phenomenon described here represents a special case of motion capture when all the components satisfy the conditions for rigid body movement, i.e. the components in a rigid body always maintain the same positions with respect to one another. Williams. Phillips and Sekuler (1986) hypothesized that the generation of a unique global motion percept from random dot movements relies upon cooperative behavior among interconnected direction selective units. The cooperative neural network they proposed consisted of non-linear excitatory interactions among units tuned to similar directions and non-linear inhibitory connections between units tuned to different directions. The results reported in this paper suggest that the excitatory interactions proposed by Williams et ul. (1986) may operate between different spatial scales in the two-stage motion system. The result of these facilitatory connections would allow pattern units in the different spatial scales tuned to similar directions to reinforce each other. This would be beneficial to an organism because such interactions can expedite the computation of rigidly moving two-dimensional patterns, as moving objects in the real world generally contain features spanning a wide SF range. Any moving feature that contains a SF that is nearer to the peak of the contrast sensitivity function will facilitate the same motion signal in other motion processing spatial scales. Ramachandran and Cavanagh (1987) used the moving leopard analogy to argue that low SF features consisting of the leopard’s outline are more salient during motion than the high SF features

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like the spots on the leopard’s skin. However, it can also be argued that when the same leopard is moving in a dense forest, orientation of the background objects like tree trunks or branches will be able to mask the outiine of the leopard. The moving high SF spots enable figure-ground segregation and define the border of the leopard. Under certain spatial-temporal conditions, the higher SF features may even be more effective than the lower SF features to induce coherence capture. In fact Ramachandran (1987) has emphasized that motion capture can be achieved by features other than low spatial frequencies. Under certain situations, even subjective contours and cyclopean edges can mediate capture (Ramachandran, 1985). Results from our study show that both high and low SF features can be equaily important in motion processing, and there is no reason why the visual system should ignore motion generated from high SF features.

Quick, R. F. (1974). A vector-magnitude model for contrast detection. Kybernetik, 16, 65567. Ramachandran, V. S. (1985). Apparent motion of subjective surfaces.

REFERENCES

Acknowledgements-This research was funded in part by NIH grant No. EY02158 to HRW. CY is supported in part by the Medical Scientist Training Program, PHS training grant No. 5 T32 GM0728 I. The authors would like to thank Dr Ramachandran for helpful comments. CY would like to thank his wife, Isabella, for encouragement and participation.

Adelson, E. H. & Movshon, J. A. (1982). Phenomenal coherence of moving visual patterns. Nature, 300, 523-525. Kooi, F. L., Grosof, D. H., DeValois, K. K. & DeValois, R. L. (1988). Optical Society of America, Technical Digest Series, 17, THS3.

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Ramachandran, V. S. (1987). Visual perception of surfaces: A biological theory. In Petry, S. & Myer, G. (Eds), The perception of illusory contaur~ (pp. 93-108). New York: Springer. Ramachandran, V. S. & Cavanagh, P. (1987). Motion capture anisotropy. Vision Research, 27. 97-106. Welch, L. (1989). The perception of moving plaids reveals two motion-processing stages. Nafure, 337, 734-736. Williams, D. W., Phillips, G. & Sekuler. R. (1986). Hysteresis in the perception of motion direction as evidence for neural cooperativity. Nature, 324, 253-255. Yo, C. (1990). Perceptual properties of two-dimensional

motion. PhD thesis, University of Chicago, Chicago, Ill., U.S.A. Yo, C. & Wilson, H. R. (1992). Perceived direction of moving two-dimensional patterns depends on duration, contrast and eccentricity. I%on Research, 32, 135-147.

Moving two-dimensional patterns can capture the perceived directions of lower or higher spatial frequency gratings.

Coherent plaid motion is produced by superimposing two one-dimensional gratings of the same spatial frequency moving +/- 60 degrees from the intersect...
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