The spatial frequency effect on perceived velocity

V&on KS. Vol.16.~~.169-l-6. PergamoaPress1976. PrimedtnGrearBritain.

THE SPATIAL FREQUENCY EFFECT PERCEIVED VELOCITY’ J. DICHGAYSand

H. C. DIENER, E. R. Wts?, Neurologische Universititsklinik,

TH.

ON

BRANDT

78 Freiburg im Breisgau. HansastraBe 9, W. Germany

(Received 28 January 1975) Abstract-The effect of the spatial frequency of a vertically oriented, horizontally moving stripe pattern on perceived speed was investigated. Perceived velocity increased linearly with both angular speed and spatial frequency. The spatial frequency effect was independent of the relative angular width of light and dark stripes and was also found to apply to the case of a single moving bar. Evidence for weighted frequency averaging was obtained for more complex patterns. The results are consistent with a model involving both a spatial frequency dependent input mediated by temporal frequency and an angular speed input relating to the movement of a single edge through the visual field.

This study is concerned with the question of whether’ or not the perceived velocity of visual patterns, depends upon their spatial frequency. Evidence consistent with both possibilities is suggested by the existing literature. In order to clarify the problem of accounting for the existence of such a relationship, some of the requirements for a model appropriate for adequate pursuit movements of the eyes as well as for afferent motion perception can be outlined. First, for stimulus adequate pursuit mOremerits of the eyes, it may be necessary that afferent information concerning the angular speed of the proximal stimulus be available. In order for this condition to be fulfilled, it must be assumed, for the simplest model, that movement detectors exist in the visual system which receive their information from at least two, spatially separated, retinal receptors. Movement information would result when these two receptors are successively stimulated by a moving contrast. Information concerning movement direction would be provided by the temporal order of stimulation of these receptors, as well as the orientation with respect to the retinal coordinates of the “line” connecting them. Furthermore, the angular speed of a contrast moving across the retina would be signalled on the basis of the spatial distance separating the two receptors and the temporal interval between their separate excitations. In the case of afluent motion perception, however, the existence of a constancy mechanism is known which is relatively insensitive to the changes in angular speed which result when contours moving at a constant linear speed vary their distance from the eyes (Brown, 1931a). Variation in the distance of a periodic stimulus pattern of constant physical size moving at *This study was financially supported by the Deutsche Forschungsgemeinschaft (SFB 70, ‘Hirnforschung und Sinnesphysiologie”). Please send reprint requests to Doz. Dr. J. Dichgans, Neurologische Universit&tsklinik. 78 Freiburg i. Br., Hansastr. 9a, W. Germany. ’ On leave of absence from The Whitely Psychology Laboratories, Franklin and Marshall College, Lancaster, Pa., U.S.A., as a “Senior U.S. Scientist Awardee” of the Alexander von Humboldt Foundation. \.i 162- I,

a constant linear speed results in a corresponding variation of the angular speed of the image on the retina but does not result in a variation of the temporal frequency of stimulation of a given retinal receptor (see Fig. 1). This occurs because with decreasing distance from the observer, the resulting increase in angular speed is compensated by a corresponding increase in spatial period. In order for the above model to be able to account for velocity constancy in this situation, it would have to be modified so that speed of movement would be signalled by the temporal frequency of which a given retinal receptor is stimulated. The direction of movement, however, would as before result from stimulation of two receptors successively. Thus, this modified model would indicate velocity of stimulus motion by measuring the number of moving contrasts per unit time at a single retinal locus. Both the model and its modification which might account for velocity constancy are extremely oversimplified and serve only as an aid in illuminating the problem and formulating hypotheses. Since with moving patterns temporal frequency is determined both by stimulus speed and the spatial frequency of the stimulus pattern its eventual influence on motion perception can be tested by varying spatial frequency. Consequently, in the experiments to be reported, the perceived speed of moving periodic stimulus patterns of various spatial period in man was investigated. If the initial version of the model were valid, then variation in the spatial period of stimuli moving at a constant angular velocity should result in no variation in perceived speed. In constrast, the modified model implies that if a change in the spatial period of a stimulus pattern is large enough, for example, to result in a doubling of temporal frequency, then a doubling of its perceived velocity ought to occur, provided the input-output relation were one to one. Evidence exists which supports the modified version of the model. It has been shown that the optomotor reaction of insects to moving stripe patterns is influenced by both the angular speed and the spatial period of such patterns (Hassenstein and Reichardt, 1956; Reichardt, 1957; Hassenstein, 1959; Vajti, 1959

169

H. C. DIEXR. E. R. WIST. J.

I:?1

\+4idealt~marmg ibirii light ones. 11 ;itde .~a\,ng 1.: IO0 deg set m J stimulus tieid of ertter 30’ \\lde h) 1x1 high in eupertmcnt I. or 50 x 50‘ in the subsequent experiments. The arbitrar) c~iuz of “30” uas assigned to this condition as ths modulus. In each experiment 16 different randomly ordered stimulus speeds i\ere presented. The slowest speed 1~~1s5 dry sec. and begmning with the nc.xt slo\vest speed of I!) dq set speed SJJ incremen:sd rn !I) dcg ‘set steps to 100 deg, set and therxfter in 20 deg;sec steps to the maximum speed of 200 deg sec. Ss were asked to base their estimates on the spsed with which a given stripe moved past the fixation point. ,411 estimates were made monocularly with the right eye fixated on the small disc in the center of the screen. Ss were exposed to the standard stimulus at the onset of all four experiments and thereafter it was represented after each block of eight magnitude estimations oi stripe speed. Both the standard and the stimulus whose speed was scaled were presented so that their movement direction changed ever]; 3 sec. This was necessary in order to prevent the occurrence of an optically induced apparent self movement which would reduce the perceived speed of the moving stripes themselves (Brandt. Wist and Dichgans. 1971). In preliminary experiments with 20 SS. it ‘*Lasfound that the direction of stripe movement (temporai or nasal) had no effect on perceived speed. and that the latency of occurrence of self-motion perception was greater than 5 sec. During all experiments the noise of the optokinetic projector motor was masked by means of enher white noise or music presented through earphones. 6

d= Distance from the

X-Spatial period

(deg)

w=Angularveloclty (deg /set) da

f,=Spatial k/deg

frquency

1

Fig. I. Schematic diagram showing the relationship between the spatial period of a periodic pattern and its distance from the eye.

for Ch/orophnnrrs; Fermi and Reichardt. 1963 and Eckert. 1973 for Muscn domesrica). Foster’s (1969. 1971 b) results on movement thresholds in man for rotating radially striped patterns presented foveally are also consistent with the second version. He found that movement thresholds were affected by both the temporal frequency and the spatial period of these patterns. Related effects of temporal frequency stimulation were obtained in motion adaption experiments by Breitmeyer (1973) and Pantle (1974). In the present study, in addition to the effect of spatial period, the effect of stimulus field size and location in the visual field on perceived speed was investigated, thus supplementing earlier work on motion thresholds (Aubert, 1886, and others reviewed in Graham, 1965 and Johansson, 1966) and on suprathreshold motion perception (Brown, 1927, 1931a). GEIVERAL.

METHOD

Apparatus Ss sat in front of a half-cylindrical projection screen at the same distance as its 795cm radius of curvature. The screen’s surface subtended a visual angle of 165” horizontally and 100” vertically. An optokinetic stimulus projector (Jung. 1953) mounted directly above the Ss head, allowed the presentation of continuously moving dark and light stripes of various spatial frequencies and light/dark ratios. Both left and right directions of motion could be presented and angular speeds could be continuously varied between 5 and loo0 deg’sec. The area and location of the stimulus pattern could be altered by means of movable apertures of various sizes located in the plane of the projector. A black fixation point, 1’ dia. was located in the center of the projection screen in the Ss median plane. The level of illumination in the experimental room was such that the outlines of the projection screen were visible. General

procedure

Perceived speeds were measured by means of the magnitude estimation technique (Stevens. 1961). The standard consisted of a periodic stimulus pattern of dark stripes.

Subjects c\ total of 100 Ss with refraction errors within normal limits and no visual anomalies were paid for their participation. All were students between the ages of 19 and 30 yr.

EXPERIXIEXT

In this experiment,

I

the effect oj‘ nimulus field

size

and its location within the visual field as well as the spatialfrequency of the stimulus pattern on perceived speed was investigated. Conditions

and procedure

Two different field sizes were emplo!_ed. The large field (A) filled the entire surface of the projection screen and was therefore 165” wide and loo” high. The small field was 30” wide and 40’ high and was located either symmetrically centered about the fixation point (B) or peripherally on the temporal retina (C) with its nearest edge 30’ from the fixation point. ,Magnitude estimates of stimulus speed for each of three spatial frequencies of the moving vertical stripe pattern were obtained for each of the above three stimulus fields. making a total of nine experimental conditions. The angular width of the dark stripes for each spatial frequency was held constant at 6’, while the width of the light stripes was either 54’. 24’ or 9” for the three spatial frequencies shown in the table. The term “spatial frequency”, strictly speaking, cannot be used for a square wave pattern. It may, however. be appreciable here if it is conceived of as the fundamental of the frequency spectrum constituting the square wave pattern. This conception allows for the case of light/dark ratios deviating from 14 as in the present study. Independent groups of Ss were empIoyed for each of the spatial frequencies listed in the table: 10 for frequency, I. and 20 each for frequencies II and III. The order of presentation of the three stimulus fields within each frequency condition was randomized and different for each S.

The spatial frequency effect

Results and co~enrs and standard deviations of the magnitude estimates of perceived speed were calculated for each of the 16 angular speeds presented within each condition. Regresiion slopes were calculated for each of the resulting nine functions and are Iisted in the tabIe (experiment I). It shoutd be noted that as a result of the particular number chosen as the modulus. a perfect linear relation between pcrceived speed and angular speed should result in a slope coefficient of 020. The exponents of the Steven’s power functions for Arithmetic

means

perceived t’elocity for all nine experimented conditions up~ro.~i~red 14.X Similar exponents have tien

obtained earlier under similar stimulus conditions (Khmer and Dichgans. 1967). Dichgans, Khmer and Voiet (1969) found that the slope of the standard fur&ion was 1.02. while the slope of the corresponding function in the present study, calculated in relation to their standard, was l-035. Earlier studies in which mostly smaller stimulus field sizes and angular speeds of less than 5 deg,kec were presented, or in which nonperiodic stimulus patterns were used have also obtained power function exponents of t.0 (Eisler and Ottlander, 1963; Kennedy, Yessenow and Wendt, 1972; Mashhour, 1964) and 0.8 (Rachlin, 1966). In these latter experiments, however, no clear separation was made between afferent (with fixations and efferent (smooth pursuit) motion perception, as was the case in the present study as well as in the earlier ones of Kijmer and Dichgans (1967) and Dichgans ef al. (1969). Besides revealing a linear relation between perceived speed and angular speed, the data also indicated a clear frequericy effect: Perceived speed increased with increasing spatial frequency (see Fig.2 and the table). The Krus~al-Wai~is (1952) H-test yielded significant differences between each of the spatial frequencies within each of the three stimuIus fields (P c 0401). The influence of spatial frequency on perceived speed will he investi~ted in the subsequent experiments as well; therefore, discussion of this finding will be deferred. By examining Fig. 3 and the table (under experiment I) it can be seen that perceived speeds are slower for ske large sr~mulus~e~doff rhan for the smaller fields (B,C), as indicated by the smatier slope coefkients for the former. Furthermore, perceived speed is slower in the periphery than in the central, smdl field. A

Friedman analysis of variance showed a significant etTect of stimulus field (A, B,C) on perceived speed for frequencies II C;C~ = 13437. df = 2, P < O-001) and III i&j = 2740, df = 2, P < 0401) but not for frequency I r;Ci = 3.78, df = 2). Multiple comparisons between the means using the Wilcoxon and Wilcox test (1964) showed that for all spatial frequencies sig nificant differences in the effect of stimulus field existed, except for those comparisons involving the large stimulus field (A) and the small, peripheral field (C). A decrease in perceived speed with increasing stimulus area has been reported by Brown (1931a) who explained this finding in terms of his transposition principle, according to which a doubling of all of the dimensions of the stimulus field shoufd lead to a halving of perceived speed. Brown (1931a) found in fact a 38% reduction. Reductions of 20-25% were

171

obtained in analogous experiments by Cohen (1964) and Oyama (1970). In the present experiment, a roughly &fold increase in stimulus dimensions resulted in an average reduction in perceived speed of only 27’1&which falls far short of the rou_&ly 75% reduction predicted by the tran~osition principle. The sirnikrity of the magnitude estimation mnctions for the large field and the small peripheral field, as opposed to the small, central field can be regarded as evidence that when the entire visual field is stimulated by a moving stimulus, its perceived speed is determined predominantly by the peripheral retina. The signifkance of the peripheral retina for the perception of visual orientation size and movement (Bechinger, RongehI and Kornhuber, 1973) as well as for dynamic spatial orientation (Brandt, Dichgans and Kiinig. 1973) has already been demonstrated. The dominance of the peripheral retina seems to hold for movement thresholds as well as suprathreshold perceived speed. Brown (1931b) found an increase in the movement threshold with increasing field size. while Aubert (1886) reported a similar increase with increasing retinal eccentricity of the motion stimulus. The possib~ity that movement threshold differences between the central and peripheral retina may be partially of dioptric rather than retinal or cerebral functional origin is suggested by the study of Leibowitz. Johnson and Isabeile (1972). Dioptric factors could not, however, account for the apparent velocity difference between center and periphery demonstrated here, since the motion stimulus speeds were welf beyond threshold.

EM’EPERlME~TII

This experiment had two purposes: first, to measure the foible con~ibut~~l of stationary border contrasts on the area-location e@zct on perceived speed found in experiment I, and secondly, to determine whether a spatial frequency effect is still apparent when a l~ln~tedcar of stripes is alloyed to pass rhrougk the visual field rather than a continuousty moving periodic pattern as in the first experiment. Conditionsand procedure An jllum~ated 50” square field was moved ho~on~lly through the entire 165’ visual field under one condition (D) or remained stationary and centered about the fixation point under a second condition (E). For the first condition (D), both the vertical stripe pattern and its borders moved together across the visual field. Thus no stationary contrasts were present. For condition E, however, the borders of the field were stationary while only the vertical stripes moved past them. Either 1, 2 or 3 dark stripes. 6’ in angular width, were present within each geld. These dark stripes were separated on either side from the vertical edges of the 50” field for condition D by two light areas 22” in width. When two or three stripes were present, they were separated from each other and from the borders by light areas of 12.66” and 8”. resnectivelv (see Fig. 4 inset). The resulting spatial frequencies and $&ds are shown in the table under experiment 11. It should be stressed that in this experiment, unlike the first, no continuous pattern of moving stripes was seen by S, but rather on a given sweep of the stimulus across the visual field, oniy 1,2 or 3 stripes were visible. Each of the 10 Ss received three of the resulting six stimulus conditions (2 fields x 3 spatial frequencies) in

I-’ a

H. C. DIF\ER. E R

_

LVIST.

random order on one day. folloued by the remainder on the following da!. As in experiment I. 16 randomI> ordered angular sveds of stimulus movement were presented for each condition. Results and cornmew Figure 1, which represents the data for the condition involving stationary borders (E), shokvs that perceiced speed increused with increasing spatial frequency. Even though the data points appear to

deviate from a linear function in the region between 50 and 100 deg/‘sec. such functions were fitted to these data (see table, experiment II). It should be noted that this deviation from linearity was observed only for conditions D and E of this experiment and not in any of the other experiments. Although the slopes of the functions for which stationary border contrasts (E) were present were greater than those for condition D where they were absent, no statisticall! significant differences were found between these condrtions (Multiple comparisons. Wilcoxon and Wilcox. 1963). This finding suggests that the significant difference between the scaling functions for the large field (.A) and the small, central field (IS) in experiment I was not simply due to the presence of stationary border contrasts in the latter condition. The increase in the slopes of the scaling functions with the increasing number of moving stripes was statistically significant for both conditions D and E (Friedman analysis of variance: ;ci =_j-k06, df = 5. P < OQOI). Thus. the~e~~~~ency effect obtairied in the first was verified in the second experiment even though a discrete number of stripes, rather than a continuous, uninterrupted stripe sequence was employed. The spatial frequencies of the standard stimulus (0.033 c/deg) and frequency 1 in experiment II (PO35 c deg) in Table 1 were almost identical. Correspondingly, the slopes of the scaling functions for these frequencies were almost identical (0.207 and 0.208, respectively). The possibility that estimates of perceived speed in experiment I were based simply on “counting” the number of stripes passing the fixation point per unit time can seemingly be rejected: in experiment II. for frequency 1. only a single stripe passed the

J point pr:or to each speed estimats. This line of reasoning would be more convincing if it ivere not for the fact that such a large discrepancy exists between the slopes of function B III in experhent I and E3 in experiment II. Although the spatial frequencies for these two functions were almost identical (0.066 and 0.071 c deg. respectively). rhs slope of the B III function of the first study (0.37-Q was much greater than that of the E3 function of the second study (0.270). An alternative explanation would be that in this case the total angular width of the moving field itself represents a half cycle of a much lower spatial frequency which decreases the apparent vetlocity. This “depressing” effect of the lower spatial frequency of the field itself is not apparent for the lower spatial frequencies (1 and 2) in Fig. 1. fisation

ESPERIMEST

The present experiment was designed co determine whether rhe cariarion in angular widrh ?/‘a single [ight stripe moving through the visual field is n sujicierrr condirion for producing II wiotiotl in prceiurd speed. On the basis of the preceding experiments, it was predicted that a wider light stripe would appear to move slower than a narrower one. Cotrdirions and procedure A single. moving. light stripe, either 50’ (4) or 20 (5) wide was projected onto the screen (see table 1. experiment III). These stripes either swept across the entire screen {F) or moved behind a square 50’ aperture (G). On the basis of the hypothesis that a single stripe can be considered to be orwholf of r/w spntia/ prriod of a periodic pattern. the spatial periods corresponding to these stripe widths were 100’ and 40’. respectively. The four stimulus conditions resulting from two stripe widths and two field sizes were presented in a different random order to each of 10 ss. Reszrlts and comments

The relationship between the angular speed of stimulus movement and scaled speed was linear for the four conditions. just as in the preceding experiments. The slopes obtained for the four functions are listed in the table under experiment 111and show that a ttarrobver swipe is perceived as mocitrg faster than

Table I. Slope coefficients of the velocity-scaling-functions Stimulus pattern characteristics

Experiment No.

Spatial frequency kdeg)

Spatial Period (deg)

I

0.033 III 0.016 0.066 III

30 60 15

II

O-035 0.053 21 0.071 3

28 18.67 II

III IV

0.025 0.010 0.011 0-0’2 0.0;; O-044

45 6 7 8 9

40 100 90 -15 30 22.5

III

for the four experiments

Stimulus field characteristics

Large field 163 x 100deg

Smal\ central field 3d x 4Odcg

8:;; @ 0.293 165 x ICOdeg

;:I;: @ 0.374 50 x 50 deg

0.179 0.228 0.231

0.270

0.138 0.113

0D

0F

;:;;;@ 0

0.179 G @123 0.135 O,lU 0.239 0.371

Small peripheral fieid 30 x 4Odeg

BI y=Ol58x-0.56

-I-

510 20

BlI y=O.207

40

60 Stimulus

x - 1.65

80

100

velocity,

120

140

160

180

deg lsec

Fig. 2. The etrect of spatial frequency on perceived speed for the small central 30’ :~:4O’stimulus field of experiment I. BI = 60’ spatial period (0.016 c/deg.), BlI = 30’ spatial period (0.033 c/deg.) and B1IL = IS” spatial period (0.066 cideg.). The arrow indicates the modulus whose spatial frequency was the same as that of BIT. The dark stripes are visible on the dark background surrounding the stimulus field for the sake of illustration only. For Ss, stripes were visible only within the bounds of the white central area. Vertical lines associated with each point represent standard deviations. IV = 20,

200

AID y=O293x

+I*20

80

20

510 20

40

60 Stimulus

100

80 velocity,

Fig. 3. The effect of stimulus field size and location spatialperiodof 15’ (spatial frequency 0066 c/deg.) B = central small field, 30’ x 40’, C = peripheral standard deviations. The arrow indicates the modulus 0.033 c/deg.).

120

140

160

180

deg/sec

on perceived speed for a stripe pattern with a in experiment I. A = large field 165’ :: 1001, small field of same size. Vertical lines represent whose spatial period was 30’ (spatial frequency :V = 20.

200

t2 v=0256

E3 y=027Ox 0 0

Stimulus

x - 1.67

-0.24

velocity,

deghec

Fig. 4. The effect of number of moving stripes on perceived speed For the small, central SO’ :c 50” stimulus field (experiment II@ El = one single stripe, El = two stripes, and E3 = three stripes. T& modulus indicated by the arrow is the same as in Figs. 2 and 3, The insert shows the appearance of Vertical lines represent the stimulus field nt the instant when tile stimulus patterns were centered. standard deviations. h’ = IO.

- 0.72

- I.24

Stimulus

velocity,

deg /see

Fig. 5. The effect of spatial frequency on perceived speed when the angular widths of light and dark stripes were equal for the small SO’ -: 50’ central stimulus field (experiment 111). 6 = 90’ spatial period CO.01I c/deg), 7 = 45’ spatial period (0.022 c:d:g), 8 = 33’ spatial period (0.033 c,‘dzg) and 9 = 22.5’ spatial period (ON4 c’deg). The arrow indicates the modulus (same as in preceding figures). Vertical lines represent standard deviations. The dark stripes are visible on the dark background surrounding the stimulus field only for the sake of illustration. For Ss stripes were visible onI> within the white central area. N = 10.

The spatial frequency e&t

a wider one moving at the same angular speed. This is consistent with the earlier finding of Brown (193 la), who varied both the vertical and horizontal dimensions of the moving stimulus together. An analysis of variance by ranks (Friedman, 1937) indicated that scaled speeds differed significantly for the four conditions (;ci = 32.12, df = 3, P < OGOL).Wicoxon’s multiple comparisons test revealed that only the scaled speeds for the two stripe widths differed significantly (P < 0.01). Thus, just as in experiment I, stationary border contrasts as such had no discernible effect on perceived speed. Consistent with the above result are the earlier observations of Bourdon (1902) and Brown (1931b) that the detection threshold for movement is higher for larger than for smaller moving objects. Further discussion of the implications of the present finding wilI be postponed until the general discussion.

EXPERIMEAT

1)

In experiments I and II, the spatial period or frequency of the stimulus was altered by varying the angular width of the light stripes while holding the size of the dark ones constant at 6”. Thus, the ratio of angular width of dark to light stripes covaried with spatial period. The purpose of the last experiment was to determine the effect of spatial period on perceived speed when this ratio was equal to one.

Four spatial periods which are listed in the table under experiment IV were employed. The angular widths of the dark and light stripes were equal for all four periods. They were presented in a centrally located 50” square field in different random orders to each of 10 Ss in a single session. The spatial period of 30’ (No. 8 in the table) was identical to that of the standard used for all experiments, making possible a direct comparison between the slopes of the scaling functions for equal and unequal widths of light and dark stripes.

173

of adjacent light and dark stripes). It should be noted that Ss always reported seeing dark stripes on a light ground regardless of the light-dark ratio except in experiment III where single light stripes were used. Thus a possible effect of figure-ground relations on perceived speed played no role here. In experiment III in which a singIe, light moving stripe was present, the hypothesis was offered that such a stimulus might be regarded as constituting one-half of a spatial period of twice the angular width of the stripe. The results of the present study allow a test of this hypothesis. If it is valid then the slope of the 20” stripe width function in experiment III should be the same as the slope of a function obtained with a periodic stimulus pattern with a spatial period of 40”. The slope of the 20’ function in experiment III was D179, while that of the 45’ function in experiment IV was @184. Similarly. the slope of the 50” function in experiment III (Dil3) was comparable to that of the 90” function (@125) of the present study.

.Lv .. . Spatial

period.

deq

Spatial

frequency.

/

c/deq

Results and comments

Figure 5 shows that the linear relationship between angular speed and perceived speed as well as the increase in perceiaed speed with increased spatial jiequency found in the preceding studies was replicated.

The slope coefficients are indicated in this figure .as well as in the table under experiment IV for comparison with those from the other experiments. A Friedman analysis of variance by ranks revealed a sign& cant effect of spatial period on perceived speed (;(i = 46.2, df = 3, P < 04lOl). Comparing the slopes of the function for the 30” spatial period (8) in this experiment with that of the standard stimulus condition of experiment I (frequency II), a greater slope for the former was found (0.239 and @207, respectively), although the actual perceived speeds for the two conditions did not differ significantly (t-test for independent samples, t = OG41, df = 30, n.s.). This finding suggests that within the limits of our experimental conditions, the relative angular width of adjacent light and dark stripes was not important in determining perceived speed, but rather spatial period (the sum of the angular widths

Fig. 6. The relationship between the slopes of the scaling functions and spatial period (a) spatial frequency, (b) and temporal frequency (c).The Roman numerals and numbers just above the abscissa in (a) and (b] refer to the spatial frequencies employed in experiments I, II and IV (see Table 1). The three functions in (a) Hnd (b) refer to data

obtained from the small central 30” x 40” or 50” x SO” fields (0). the small 30” x 40’ peripheral field (A), aad the large, 165’ x 100’ field (W). The functions in (a) were fitted by eye, while those in (b) represent linear lines of best fii 1; (c) the functions db&;d in experiments I and N (Figs. 3 and 5) have been replotted according to the temporal frequency in Hertz of the moving stimulus. For the sake of clarity, data points obtained at angular speeds of 50. 100 and 200 deg/sec only have been piotted.

SYSTHESIS

OF THE

-FREQLESCY

RESLLTS

OK THE

EFFECT’

Taken together, the results of the experiments show that perceiced speed increases wirh increasing spatial frequency

and is incrrsely

t&ted

to spuriul period.

These relationships can be clearly seen in Fig. 6, where the slope coeficients of experiments I. III and IV have been plotted against both spatial period (left panel) and spatial frequency (right panel). The co&icients for experiment II. in which a discrete moving stimulus was used, have been omitted from these plots because they were appreciably smaller than those of the other experiments. When plotted against spatial period, the functions for all three stimulus fields show an inverse, nonlinear relationship benveen the slopes of the scaling functions and period, which appears to be asymptotic af a spatial period of 90” or loo”. When plotted against spatial frequency, however, a clear. linear relationship between scaling function slopes and frequency emerges. Linear lines of best fit to these data yielded slope coefficients of 3.X. 341 and 439 for the large field. the small peripheral field. and the small, central field, respectively. Consequently. the difference between central and peripheral retinal velocity perception increases with higher spatial frequencies. Figure 6c illustrates that the frequency effect cannot be solely ascribed to temporal frequency detection, since each spatial frequency yields its own linear relationship between angular and perceived sp2ed. DISCUSSIOS

The spatial frequenc,v effect on perceived speed found in this study is independent of whether or not the ratio of the angular widths of light and dark stripes is one, since it was obtained in experiment I where this ratio varied as well as in experiment IV, where it was held constant at 1. This finding justifies the defnirion of spatial j-equency, as applied to velocity perception as the reciprocal of spatial period. The latter is constituted by the sum of the angular widths of an adjacent light and dark stripe. Furthermore, the experiments demonstrated that the frequency effect occurs whether a continuous sequence of moving stripes is viewed as in experiments I and IV or a single sweep of a field containing 1, 2 or 3 stripes occurs as in experiment II. Also, this effect is evident for both large and small visual fields as shown by experiments I and II. and appears not to be appreciably influenced by the presence of stationary border contrasts as shown by experiments II and III. In experiment III it was found that perceived speed was greater for an angularly narrow single light stripe, than for an angularly larger one. This finding is consistent with the possibility that the visual system treats single mooing srimuli as though they represent one-half cycle of a periodic stimulus with a light-dark ’ This value has not been taken directly from Fig. 6b, but rather has been calculated so that it is independent of the arbitrary value of the modulus chosen for the experiments. A comparable estimate of slope was also obtained in a supplementary experiment using five Ss and the method of magnitude reproduction.

ratio of one. This interpretation 1s supportzc: hk the fact that the slope oi ths functions relatine o~rce~~:ci and angular speed for the 20’ and Xi’ angul:ir stripe widths of this experiment tvere comparable in size to those obtained for the functions of experiment IV. whose spatial periods uere roughly double these values (45’ and 90. respectively). In view of Fig. 6a it seems, however, necessary to test and compare smaller stripes before d&nits conclusions are made. The data do not warrant the conclusion that the visual system in jm performs a frequency analysis of the motion stimulus. At this point. this kind of formal analysis can only be regarded as a convenient way of describing the motion stimulus. Given that single moving objects are treated bv the visual system as periodic stimuli with spatial peiiods of twice the object’s angular width. a further inference concerning the nature of the frequency analysis applied bq the visual system to moving stimuli can be made. In condition D of experiment I1 Lvhere I. 2 or 3 stripes contained within a 50’ squars field swept across the visual field, a usaker spatial frequency effect was found as compared to that for the large field condition of experiment I. This weaker frequency effect is plausible, if it is the case that the visual system extracts a weighted average of all spatial periods present in a moving stimulus favoring the lower frequency components. In experiment IID. two spatial periods were present for each moving stimulus: one provided by the dark and light stripes within the 50’ square moving field and the other bq the moving field itself. Its 50’ width would bs equivalent to that produced by a periodic stimulus with a spatial period of loo” (corresponding spatial frequency: 1 100 = 001 cideg). It is clear that if this latter spatial frequency is averaged together with that of the stripes the effect would be an attenuation oi the contribution of the high frequency components to perceived speed. The functional utility of such a frequency averaging mechanism in “real world” situations can be illustrated by considering the case of a zebra running past the observer. If the spatial frequency of its stripes and the spatial frequency corresponding to the animal’s overall angular width Lvere analysed independently. the paradoxical result would be that the zebra’s stripes would appear to be moving faster than the zebra itself. The spatial frequency characteristics of a single moving object or of a periodic pattern cannot be the sole determinant of its perceived speed. A single moving edge has a very definite perceived speed. This fact is reflected in Fig. 6b in that the slope ik) of the function relating perceived speed (M’) and angular speed (u), JI = kw 11) does not approach zero at the lowest spatial frequencies. Zero spatial frequency on the ordinate of this figure corresponds to the condition in which a single moving edge is present in the visual field. Consequently, k in Fig.6b is composed of two terms: b which corresponds to the Y-intercept in this figure and is spatial frequency independent andf, representing spatial frequency whose proportionality constant. 0.61 represents the mean slope of the three regression lines in this figure3. These relations may then be

The spatial frequency effect

expressed as follows: k=Q61f,-tb.

(3

Since A4’ = ko,

perceived speed may then be described by the following equations: M’ = (061f, + b)u

(3)

Or M’

=

wO*61f, -i- wb.

(4)

In the first and simplest model of motion perception described in the introduction, ~fo~tion concerning the speed of motion of a stimulus is provided by the temporal asynchrony in stimuiation (A r) between two spatially separated receptors. Such a model could be appropriate for the perceived velocity of a single moving edge and would be associated with the term w b in equation (4). The output of this model would be unaffected by the spatial frequency of the movement pattern as long as the spatial separation of the elements or the angular width of a single element of this pattern exceeded the spatial separation between the two receptors. Each element in a periodic moving pattern would be treated as a separate and independent movement stimulus. Since it was found that spatial frequency affects perceived speed, this simple model, by itself, is not tenable. The modified version of this model involves information concerning the time interval between successive stimulations of a given retinal receptor. This information would reflect the temporal frequency- of stimulation of this receptor (&). Since f, = w.A, the possible contribution of temporal frequency to perceived velocity can be represented by the term 00.61f, in equation (4). Thus, the formal properties of both the simple model and its modification are reflected in the data. It is possible that both operate jointly in determining perceived speed. According to this view, spatial frequency influences velocity perception onty in so far as it determines the temporal frequency in a system which possesses long time constants for averaging in the case of variable light-dark ratios as in experiment I and for combinations of different frequencies as in experiment III. It is difficult to conceive that the output of the retinal network would not reflect frequency information.4 A system, however, which analyses pattern characteristics in terms of spatial frequency to yield distance invariant velocity perception is not denied by our data. The existence of sensory channels specifically tuned to spatial frequency has been suggested by the work of Blakemore and Campbell (1969), Maffei and Fiorentini (1973), and Sachs, Nachmias and Robson (1971), and others. The Iikehhood that such a mechanism is involved in motion perception is much reduced by our observation that the pequency effect an perceived speed disappears during pursuit movements of the eyes. ’ Fischer and Kommtillet (1930) reported that an increase in the perceived spatial frequency of a moving stripe pattern produced by the partial binocular fusion of monocularly lower spatial frequencies resulted in an increase in perceived self-motion speed. This eflect must be supraretinal. But their result does not rule out a pure retinal mechanism for the results presented here. ’ These experiments were conducted in collaboration with John Allum in our laboratory.

175

In a previous study (W&t, Diener, Dichgans and Brandt, 1975) a central constancy mechunism in motion perception was demonstrated by the finding that the perceived distance of the motion stimulus affects perceived speed. Our data suggest that increasing spatial frequency serves a role analogous and complementary to that of perceived distance in motion constancy. As mentioned in the introduction, under normal environmental conditions, the angular speed of a pattern moving across the visual field at a constant linear speed decreases as its plane of motion increases in distance from the retina. With adequate distance info~tion available, a constant perceived speed results. Motion constancy, however, may also rely on increased spatial frequency resulting from an increase in distance. This interpretation is consistent with the finding of Rock, Hill and Fineman (1968) that a correlation exists between size constancy and perceived speed. The perceived distance contingent and the spatial frequency contingent mechanism may supplement each other for optimal motion constancy. It should be stressed, however, that the possible role of spatia1 frequency in motion constancy is limited to the case where fixation is maintained on a stable point in the visual field. Finally, it should be noted that we have been unable to obtain evidence that spatial frequency affects the angular speed of the slow phases of optokinetic nystagmus. Slow phase velocity remains constant as spatial frequency is increased while holding angular stimulus speed constant.5 Thus while spatial frequency affects afferent object-referred motion perception, it does not affect either pursuit movements of the eyes during the slow phases of OKN or velocity perception during smooth, pursuit eye movements. The present data make possible an explanation of the Aubert-Fleischl paradox which concerns the overestimation of pattern speed with fixation as compared to smooth pursuit eye movements. The magnitude of this overestimation was found to be about 1.7 (Dichgans et aZ., 1969). Since the spatial frequency effect exists when the eyes are fixated but not with smooth pursuit movements, the amount of overestimation is a function of the spatial frequency of the moving stimulus. In the limiting case where a single edge moves across the visual field, the Aubert-Fleischl paradox disappears (Dichgans, Wist, Diener and Brandt, 1975).

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Zusamdenfassung Es wurde der ginfluB r&nnlicher Frequenz eines horizontal bewegte:! Musters vertikaler Schwarz-WeiObalken auf der wahrgencmmenen GeDie wahrgenommene Geschwindigkeit steigt schwindigkeit unteraucht. mit zunehmender Reiemustergesehwindigkeit und riiumlicher Frequenz Der EinfluB der Sumlichen Frequenz ist unabriingfg vom linear an. zueinander; bei GrSBenverhiiltnis der Schwarz- und WeiEbalkenbreiten einem Einzelbalken wird die Geschwindigkeit entsprechend durch die Bei kolnplexen Mustern findet eine gewichteta Salkenbreite bestimmt. Die Ergebnisse sprechen fti ein nodell, Frequenzmittlung statt. das sowohl rgumliche Frequenz iiier die Messung der zeitlichen Frequenzen an einem Retinaort als such die Winkelgeschwindigkeit des Reizes beriicksichtigt.