Vi&on Rer. Vol.
16, pp. 177-180. Peqamon
Press 1976. Printed in Great Britain.
VELOCITY-TIME RECIPROCITY IN THE PERCEPTION OF MOTION: FOVEAL AND PERIPHERAL DETERMINATIONS’ CHRIS A. JOHNSON and H. W. LE~BOWITZ Department of Psychology, Pennsylvania State U~versity, University Park, PA 16802, U.S.A. (Receiued 25 Notiember 1974; in :er;ised form 17 March 1975) Abstract-Motion thresholds were determined for durations between 0*02S and 5 set in the fovea and periphery. For intermediate durations of movement between 0. I and 1-Osec. threshold is determined by a constant displacement of the stimulus. For shorter and longer durations. threshold is determined by a fixed velocity. Similar characteristics are displayed by motion detection mechanisms in the fovea and periphery. The close correspondence between resolution and motion thresholds for intermediate durations in both the fovea and the perphery is discussed.
INTRODUCTION
A large number of interrelated variables aEect the ability to discriminate motion, among which are stimulus velocity f V) and duration of exposure (T). (For a review, see Graham, 1965. Also an excellent discussion of several aspects of motion perception is availabIe in Harvey and Michon, 1974.) However, since the product of velocity and time is equal to stimulus displacement, considerable theoretical interest has been attached to the observation-that-the velocity-time product is constant for various ranges of durations (e.g. Cohen and Bonnet, 1972). This reciprocity implies that the basis for detecting motion is a constant displacement. Furthermore, since the reported value of this displacement is of the same order of magnitude as the resolution threshold, it has been suggested that resolution and motion detection are subserved by the same mechanism (Gordon, 1947). In this view, motion is detected when the excursion of the stimulus is equivalent to the minimum detectable separation between two stimuli. There is considerable evidence in the literature for velocity-time reciprocity, beginning with the results of Dimmick and Karl (1930) which suggest reciprocity at 0.5 and I.0 set, but not at durations of 2.0 and 4.0 sec. A velocity-time trade-off is also apparent in the data of Leibowitz (1955) between 0.125 and 2*0sec, and Henderson (1971) between 0.1 and I*0 sec. Recently, Cohen and Bonnet (1972) have presented evidence for “dispIacement constancy” of motion thresholds at durations between @OSand O-7 sec. Since the detection of motion encompasses a broader range of stimulus durations than have been investigated in these studies, one purpose of the present experiment is to examine velocity-time reciprocity over a wide range of durations. Secondly, because of the importance of motion percep ‘Supported by grant MH8061 from the National institute of Health. The authors wish to express their appreciation to Lewis 0. Harvey. Jr.. D. Alfred Owens and Larrv G. Kerr for assistance-in the prep~ation of the manuscript, and to Itsuo iMurase and D. Alfred Owens for serving as observers.
tion in the peripheral visual fields. and the relatively few data which exist in the literature on peripheral sensitivity, data are obtained both for fovea1 and for eccentric stimulus presentations. With data obtained over a wide range of durations and for various eccentricities in hand, it will be possible to evaluate the theoretical issues involved in the mechanisms subserving the perception of motion. METHOD Subjects The Ss were two male observers with extensive prior experience in visual psychophysical experiments. Both were right eye dominant as determined by an alignment procedure and exhibited normal 20/20 near and far visual acuity, as determined with a Titmus Vision Tester (Model OV-7M). Apparatus The S sat facing a perimeter 154-Ocm dia. the surface of which was covered with painted black flock paper (1.8% reflectance) and uniformly illuminated by two horizontal panels of incandescent tights (74.38 m-cd). A I-27 cm horizontal slit, cut along the perimeter surface at eye level. served as the stimulus presentation area for each of the stimulus eccentricities. All but the immediate stimulus presentation area of the slit opening was masked with black flock paper. The apparatus has been previously described in detail (Johnson and Leibowitz, 1974). A 20.3 cm dia cylinder, covered with black flock paper (1.8% reflectance), was positioned behind the slit opening with its long axis oriented ho~zontally. The moving stimulus was produced by a 1.27~cm-wide band of “white” plastic tape (656% reliectance) which was wrapped around the cylinder in a single helix. Rotation of the cylinder behind the slit opening produced a horizontal movement of an approximately square-shaped stimulus subtending 0.95” of visual angle. A IO-ratio gear reducer attached to a synchronous d.c. motor and controller with a micrometer dial were used to regulate both the direction and velocity of the moving stimulus. Periodic calibration of the d.c. motor-gear reducer combination was accomplished with a Strobotac. A bracket, holding the cylinder, motor, and gear reducer, was moved along a track around the outside of the perimeter to the respective stimulus locations. The duration of movement of the stimulus, which was visibie continuously, was regulated by an electronic timing system. An electric fan was employed to mask the noise and vibration produced by the d.c. motor. 177
178
C.
A. JOHMON
and H. LV. LEIBOKCTZ
Procedure
Movement thresholds were determined for each 5 at 0 (fovea). 30”. and 60” of eccentricity in the temporal visual held of the dominant (right) eye. An eye patch was worn over the left eye. The S’s head was positioned in a headand-chin rest at an observation distance of 77 cm from the perimeter surface. To avoid the interfering effects of a central fixation stimulus during peripheral determinations, a blind spot fixation method similar to that described by Teuber, Battersby and Bender (1960) was employed. The Ss were instructed to image a I .27 x 5.08 cm (0,95” x 3.80” of visual angle) white rectangular stimulus, centered at 15” eccentricity on the perimeter surface, within the blind spot. Thus, appropriate fixation resulted in the disappearance of the blind spot stimulus from the S’s visual field. Eye movements greater than approx I” were immediately apparent to the Ss by awareness of the blind spot stimulus, and trials on which eye movements were reported were disregarded. During each of the two sessions, motion thresholds were determined for each eccentricity to”, 30” and 60”) for movement durations of 0~025.0~05.0~10,0~25,0~50, 1.0.2.5 and 5,Osec. The stimulus was continuously visible. The order of presentation of the movement durations at each eccentricity was randomly determined. For one of the sessions, the testing proceeded successively from 0” to 60” of eccentricity, with the order reversed for the other session. Each session was approx 1.5 hr in length. An interleaved double staircase (Cornsweet, 1962) with variable step size was used to determine motion thresholds. Following each trial, Ss reported whether the stimulus had moved to the right. to the left, or was stationary. The 50% correct response level was selected as the threshold measure. In view of the marked improvements with practice known to occur for peripheral motion discrimination (Johnson and Leibowitz, 1974). all threshold determinations reported in this investigation
were obtained after the Ss were highly practiced and had reached a stabilized level of performance. RESULTS
The data are presented on a double logarithmic plot as the product of velocity and time as a function of time. The virtue of this format is that it facilitates theoretical analysis of the underlying motion detection mechanisms. Since the product of V and T is equal to the displacement, or distance traveled, a
horizontal line on this plot reflects the operation of ;L constant displacement at threshold. i.e. \. 1 T 7 t‘. Alternatively, a line of unit slope on this plot effectively means that time is being plotted against time, i.e. V x T = (l.O)T + C or V = C and thus the velocity required for threshold is constant. The rationale for choosing this format can be appreciated in Fig. 1, which presents the data from the fovea1 determinations. It will be noted that between approx 0.1 and I.0 sec. the data are closely described by the horizontal line reflecting the operation of a constant displacement. Over this range, the motion threshold is determined by a fixed displacement of about l-j’, in spite of changes in both velocity and time. At movement durations beyond 1.0 set, the curve changes abruptly from dependence on a constant displacement to a constant velocity, as indicated by the dose agreement between the empirical points and the theoretical curve of unit slope. In this region, a constant velocity of l.S/sec is required for threshold. Thus, increase in duration of movement beyond I.0 set does not permit a reciprocal lowering of velocity, suggesting a convenient rule for all durations longer than 0.1 sec. Under these conditions, the stimulus must move through a constant distance of approx 1.5’ within a duration of I.0 set or less. For durations of motion shorter than 0.1 sec. the transition from a constant displacement to a constant velocity is not as distinct, although the data appear to fall quite close to the constant velocity prediction. It should be recalled, however. that 0.1 set approximates the “critical duration” for intensity and time, i.e. Bloch’s Law. As duration of movement is decreased below this value, the effective luminance during the actual motion of the stimulus is reduced. Thus, for the shorter movement durations, effective luminance. time, and displacement are all varying. In spite of this, the data are closely described by a constant velocity prediction, which is approx 18’lsec. It should be noted that the data for movement durations below 0.1 set do not necessarily reflect an improvement in performance. Rather, they most likely indicate that motion
&wwnentDurotion f Seconds) Fig. 1. The velocity-time product necessary to produce threshold movement as a function of movement duration for fovea! observation. On this plot, a horizontal line indicates that the threshold is determined by a constant stimulus displacement. A line of unit slope indicates that threshold is based on a constant stimulusvelocity.
Velocity-time
obtained under such conditions are determined by factors other than a minimum displacement of the stimulus (see Discussion). The results for the two peripheral eccentricities are plotted in Fig. 2 There is a striking similarity in the shapes of the functions for the fovea1 and peripheral data at movement durations greater than O-1 sec. As would be expected, the absolute values at threshold are higher for the periphery. In the constant displacement region, the value is about 6’ for 30” of eccentricity and 9’ for 60”. For thr: constant velocity region beyond 1.0 set, it is S’lsec for both eccentricities. For movement durations shorter than 0.1 set, the data are not as clear. At 30”. the data for subject IM fall fairly close to the constant velocity prediction, but those for subject A0 are intermediate. The data for short movement durations at 60” are fairly close to the constant velocity prediction for both subjects. In accordance with previous findings (Johnson and Leibowitz, 1974). there is greater variability in the periphery than in the fovea. thresholds
DISCUSSION
The present findings indicate that for durations between 0.1 and 1.0 set, the detection of motion is determined by a constant displacement both in the fovea and in the periphery. This is consistent with previous findings (Dimmick and Karl, 1930; Leibowitz, 1955; Henderson, 1971: Cohen and Bonnet, 1972). For longer durations, a constantyelocity is required because the stimulus must move throQgh a fixed critical displacement in 1.0 set or less. Harvey and Michon’s (1974) data indicate a levelling of the velocity-duration function at about 2.0 sec. The thresholds for durations of motion below 0.1 set are more difficult to interpret, although the present data appear to be well described by the constant velocity prediction. It should be appreciated that durations below 0.1 set represent something of an experimental “artifact” as fixationai pauses under natural viewing conditions are rarely if ever this short. Since with these shorter durations both the effective luminance during movement and the stimulus excursion are decreased
:.a0 B
r ; _
300 20.0 1
I.M. .
179
reciprocity in the perception of motion
600
proportionately, the threshold is most probably determined by the acceleration characteristics of the stimuius at the beginning and termination of movement. At the onset of motion the stimulus changes from zero velocity to the constant high velocity almost instantly, undergoing the reverse process as the motion ceases. The sharp transients associated with rapid acceleration to (positive) and from (negative) high velocities may produce much lower thresholds for detecting motion (Harvey and Michon. 1974). In this respect, it should be noted that Henderson (1971), employing stimuli displayed on a cathode ray tube and visible only during the stimulus movement (zero acceleration), reported much higher thresholds for short duration-high velocity stimulus movements than those obtained in the present study. This seems to support the interpretation that for durations below 0.1 sec. motion thresholds for continuously visible stimuli (literally a “stop-go-stop” condition) are determined by the acceleration characteristics of the stimulus. Historically, the motion detection threshold value of approx l’/sec has received a rather “classical” status and has in fact become standard in human engineering practice. The correspondence between this value and the resolution threshold in the fovea has been noted. Such a correspondence suggests that motion perception, to the extent that it is determined by a constant distance travelled. may be subserved by a mechanism related to resolution properties. In this view, the moving stimulus must traverse the same retinal distance as the separation between adjacent elements in a resolution test object. We have recently obtained data on the resolution of sine wave targets as a function of eccentricity, both with and without correction of refractive error (Millodot, Johnson, Lamont and Leibowitz (1975). (Subject A0 participated in both studies.) The data indicate that acuity is degraded, on the average, by a factor of about six at 30” of eccentricity and about 10 at 60” of eccentricity under both conditions. These values correspond fairly closely with the degradation of motion perception reported in the present study as well as previous
PERIPHERY
0
0
2.5 / I 0.025
I 0.05
1 0.1
I 0.2
I 0.4
MovementDuration
I I.0
I 2.0
I 4.0
(Seconds)
Fig. 2. The velocity-time product necessary to produce threshold movement as a function of movement duration for peripheral stimulation. On this plot, a horizontal tine indicates that threshold is determined by a constant stimulus displacement. A line of unit slope indicates that threshold is tiased on a constant stimulus velocity.
investigations utilizing the same apparatus (Leibowitz, Johnson and Isabelle, 1972: Johnson
and Leibowitz. 1973).’ Whether this is a coincidence can be determined only by the introduction of additional parameters and careful determination of motion and resolution thresholds for the same observers. On the basis of the present evidence. the similarity of the resolution and motion thresholds for durations above 0.1 set suggests that the mechanisms may be related.’ Similar arguments, particu~arIy with respect to peripheral vision, have been proposed by Gordon (1947). The present findings imply distinct mechanisms for motion detection. Between O-1 and i-0 sec. a constant displacement of the order of the resolution threshold is the rule. For shorter or longer movement durations. the present resuits demonstrate an abrupt transition from a constant displacement to a constant velocity. In all cases, the shapes of the functions in the fovea and periphery are similar implying similar mechanisms. The higher values for the peripheral observations are strikingly close to the degradation observed for resolution with eccentric viewing.
‘Refractive error, which is known to affect peripheral motion thresholds (Lcibowitz et at., lQ72), was not a contributing factor in this experiment since both observers had negligible refractive error at the stimuhs eccentricities under investigation. ‘Thorson, Lange and Biederman-Thorson f 1969)report that in the periphery, apparent movement can be discerned between two flashing dots which cannot be resolved spatially. To the extent that apparent movement can be compared to real movement, their findings impiy that peripheral motion discrimination may not be dependent upon a minimum detectable separation. However the rates of apparent movement over which this effect was observed are most closely approximated by the short duration-high velocity region of motion investigated in the present study, which also departed from the “displacement constancy” rule.
REFERESCES
Cohen R. L. and Bonnet C. (1972) Xfovcmtnt drtectiun thresholds and stimulus duration. Percept. Ps~chuph~s.
12. 339-27’2. Cornsweet T. y. (1962) The staircase method in psychophysics. Am. J. Psvchoi. 73. -185-491. Dimmick’R.~ L. and Karl J.-C. (1930) The effect of the exposure time upon the R. L. of visible motion. .I. exn, Fsychol. 13. 365-369. Gordon D. A. (1947) The relation between the thresholds of form, motion and displacement in parafoveal and peripheral vision at a scotopic level of il[~minarion. .~m. J: Psvchoi. 60. 202-125. Graham C. H. (1965) Perception of movement. In Vision nnd Visual Perception (Edited by Graham C. H.). Wiley. Sew York. Harvey L. 0. and Michon J. A. (1974) Detectability of relative motion as a funetion of exposure duration. angular separation, and background, J. exp. Ps~chat, 103. 3 17-325. Henderson D. C. (1971) The relationships among time. distance, and intensity as determinants of motion discrimination. Percept. Psycfiophys. to. 313-320. Johnson C. A. and Leibowitz H. W. (I9741 Practice, refractive error. and feedback as factors influencing peripheral motion thresholds, Percept. Psyckopkvs. 15, 276-280. LeGrand Y. 11967) Form and Spaoe Vision
16, pp. 177-180. Peqamon
Press 1976. Printed in Great Britain.
VELOCITY-TIME RECIPROCITY IN THE PERCEPTION OF MOTION: FOVEAL AND PERIPHERAL DETERMINATIONS’ CHRIS A. JOHNSON and H. W. LE~BOWITZ Department of Psychology, Pennsylvania State U~versity, University Park, PA 16802, U.S.A. (Receiued 25 Notiember 1974; in :er;ised form 17 March 1975) Abstract-Motion thresholds were determined for durations between 0*02S and 5 set in the fovea and periphery. For intermediate durations of movement between 0. I and 1-Osec. threshold is determined by a constant displacement of the stimulus. For shorter and longer durations. threshold is determined by a fixed velocity. Similar characteristics are displayed by motion detection mechanisms in the fovea and periphery. The close correspondence between resolution and motion thresholds for intermediate durations in both the fovea and the perphery is discussed.
INTRODUCTION
A large number of interrelated variables aEect the ability to discriminate motion, among which are stimulus velocity f V) and duration of exposure (T). (For a review, see Graham, 1965. Also an excellent discussion of several aspects of motion perception is availabIe in Harvey and Michon, 1974.) However, since the product of velocity and time is equal to stimulus displacement, considerable theoretical interest has been attached to the observation-that-the velocity-time product is constant for various ranges of durations (e.g. Cohen and Bonnet, 1972). This reciprocity implies that the basis for detecting motion is a constant displacement. Furthermore, since the reported value of this displacement is of the same order of magnitude as the resolution threshold, it has been suggested that resolution and motion detection are subserved by the same mechanism (Gordon, 1947). In this view, motion is detected when the excursion of the stimulus is equivalent to the minimum detectable separation between two stimuli. There is considerable evidence in the literature for velocity-time reciprocity, beginning with the results of Dimmick and Karl (1930) which suggest reciprocity at 0.5 and I.0 set, but not at durations of 2.0 and 4.0 sec. A velocity-time trade-off is also apparent in the data of Leibowitz (1955) between 0.125 and 2*0sec, and Henderson (1971) between 0.1 and I*0 sec. Recently, Cohen and Bonnet (1972) have presented evidence for “dispIacement constancy” of motion thresholds at durations between @OSand O-7 sec. Since the detection of motion encompasses a broader range of stimulus durations than have been investigated in these studies, one purpose of the present experiment is to examine velocity-time reciprocity over a wide range of durations. Secondly, because of the importance of motion percep ‘Supported by grant MH8061 from the National institute of Health. The authors wish to express their appreciation to Lewis 0. Harvey. Jr.. D. Alfred Owens and Larrv G. Kerr for assistance-in the prep~ation of the manuscript, and to Itsuo iMurase and D. Alfred Owens for serving as observers.
tion in the peripheral visual fields. and the relatively few data which exist in the literature on peripheral sensitivity, data are obtained both for fovea1 and for eccentric stimulus presentations. With data obtained over a wide range of durations and for various eccentricities in hand, it will be possible to evaluate the theoretical issues involved in the mechanisms subserving the perception of motion. METHOD Subjects The Ss were two male observers with extensive prior experience in visual psychophysical experiments. Both were right eye dominant as determined by an alignment procedure and exhibited normal 20/20 near and far visual acuity, as determined with a Titmus Vision Tester (Model OV-7M). Apparatus The S sat facing a perimeter 154-Ocm dia. the surface of which was covered with painted black flock paper (1.8% reflectance) and uniformly illuminated by two horizontal panels of incandescent tights (74.38 m-cd). A I-27 cm horizontal slit, cut along the perimeter surface at eye level. served as the stimulus presentation area for each of the stimulus eccentricities. All but the immediate stimulus presentation area of the slit opening was masked with black flock paper. The apparatus has been previously described in detail (Johnson and Leibowitz, 1974). A 20.3 cm dia cylinder, covered with black flock paper (1.8% reflectance), was positioned behind the slit opening with its long axis oriented ho~zontally. The moving stimulus was produced by a 1.27~cm-wide band of “white” plastic tape (656% reliectance) which was wrapped around the cylinder in a single helix. Rotation of the cylinder behind the slit opening produced a horizontal movement of an approximately square-shaped stimulus subtending 0.95” of visual angle. A IO-ratio gear reducer attached to a synchronous d.c. motor and controller with a micrometer dial were used to regulate both the direction and velocity of the moving stimulus. Periodic calibration of the d.c. motor-gear reducer combination was accomplished with a Strobotac. A bracket, holding the cylinder, motor, and gear reducer, was moved along a track around the outside of the perimeter to the respective stimulus locations. The duration of movement of the stimulus, which was visibie continuously, was regulated by an electronic timing system. An electric fan was employed to mask the noise and vibration produced by the d.c. motor. 177
178
C.
A. JOHMON
and H. LV. LEIBOKCTZ
Procedure
Movement thresholds were determined for each 5 at 0 (fovea). 30”. and 60” of eccentricity in the temporal visual held of the dominant (right) eye. An eye patch was worn over the left eye. The S’s head was positioned in a headand-chin rest at an observation distance of 77 cm from the perimeter surface. To avoid the interfering effects of a central fixation stimulus during peripheral determinations, a blind spot fixation method similar to that described by Teuber, Battersby and Bender (1960) was employed. The Ss were instructed to image a I .27 x 5.08 cm (0,95” x 3.80” of visual angle) white rectangular stimulus, centered at 15” eccentricity on the perimeter surface, within the blind spot. Thus, appropriate fixation resulted in the disappearance of the blind spot stimulus from the S’s visual field. Eye movements greater than approx I” were immediately apparent to the Ss by awareness of the blind spot stimulus, and trials on which eye movements were reported were disregarded. During each of the two sessions, motion thresholds were determined for each eccentricity to”, 30” and 60”) for movement durations of 0~025.0~05.0~10,0~25,0~50, 1.0.2.5 and 5,Osec. The stimulus was continuously visible. The order of presentation of the movement durations at each eccentricity was randomly determined. For one of the sessions, the testing proceeded successively from 0” to 60” of eccentricity, with the order reversed for the other session. Each session was approx 1.5 hr in length. An interleaved double staircase (Cornsweet, 1962) with variable step size was used to determine motion thresholds. Following each trial, Ss reported whether the stimulus had moved to the right. to the left, or was stationary. The 50% correct response level was selected as the threshold measure. In view of the marked improvements with practice known to occur for peripheral motion discrimination (Johnson and Leibowitz, 1974). all threshold determinations reported in this investigation
were obtained after the Ss were highly practiced and had reached a stabilized level of performance. RESULTS
The data are presented on a double logarithmic plot as the product of velocity and time as a function of time. The virtue of this format is that it facilitates theoretical analysis of the underlying motion detection mechanisms. Since the product of V and T is equal to the displacement, or distance traveled, a
horizontal line on this plot reflects the operation of ;L constant displacement at threshold. i.e. \. 1 T 7 t‘. Alternatively, a line of unit slope on this plot effectively means that time is being plotted against time, i.e. V x T = (l.O)T + C or V = C and thus the velocity required for threshold is constant. The rationale for choosing this format can be appreciated in Fig. 1, which presents the data from the fovea1 determinations. It will be noted that between approx 0.1 and I.0 sec. the data are closely described by the horizontal line reflecting the operation of a constant displacement. Over this range, the motion threshold is determined by a fixed displacement of about l-j’, in spite of changes in both velocity and time. At movement durations beyond 1.0 set, the curve changes abruptly from dependence on a constant displacement to a constant velocity, as indicated by the dose agreement between the empirical points and the theoretical curve of unit slope. In this region, a constant velocity of l.S/sec is required for threshold. Thus, increase in duration of movement beyond I.0 set does not permit a reciprocal lowering of velocity, suggesting a convenient rule for all durations longer than 0.1 sec. Under these conditions, the stimulus must move through a constant distance of approx 1.5’ within a duration of I.0 set or less. For durations of motion shorter than 0.1 sec. the transition from a constant displacement to a constant velocity is not as distinct, although the data appear to fall quite close to the constant velocity prediction. It should be recalled, however. that 0.1 set approximates the “critical duration” for intensity and time, i.e. Bloch’s Law. As duration of movement is decreased below this value, the effective luminance during the actual motion of the stimulus is reduced. Thus, for the shorter movement durations, effective luminance. time, and displacement are all varying. In spite of this, the data are closely described by a constant velocity prediction, which is approx 18’lsec. It should be noted that the data for movement durations below 0.1 set do not necessarily reflect an improvement in performance. Rather, they most likely indicate that motion
&wwnentDurotion f Seconds) Fig. 1. The velocity-time product necessary to produce threshold movement as a function of movement duration for fovea! observation. On this plot, a horizontal line indicates that the threshold is determined by a constant stimulus displacement. A line of unit slope indicates that threshold is based on a constant stimulusvelocity.
Velocity-time
obtained under such conditions are determined by factors other than a minimum displacement of the stimulus (see Discussion). The results for the two peripheral eccentricities are plotted in Fig. 2 There is a striking similarity in the shapes of the functions for the fovea1 and peripheral data at movement durations greater than O-1 sec. As would be expected, the absolute values at threshold are higher for the periphery. In the constant displacement region, the value is about 6’ for 30” of eccentricity and 9’ for 60”. For thr: constant velocity region beyond 1.0 set, it is S’lsec for both eccentricities. For movement durations shorter than 0.1 set, the data are not as clear. At 30”. the data for subject IM fall fairly close to the constant velocity prediction, but those for subject A0 are intermediate. The data for short movement durations at 60” are fairly close to the constant velocity prediction for both subjects. In accordance with previous findings (Johnson and Leibowitz, 1974). there is greater variability in the periphery than in the fovea. thresholds
DISCUSSION
The present findings indicate that for durations between 0.1 and 1.0 set, the detection of motion is determined by a constant displacement both in the fovea and in the periphery. This is consistent with previous findings (Dimmick and Karl, 1930; Leibowitz, 1955; Henderson, 1971: Cohen and Bonnet, 1972). For longer durations, a constantyelocity is required because the stimulus must move throQgh a fixed critical displacement in 1.0 set or less. Harvey and Michon’s (1974) data indicate a levelling of the velocity-duration function at about 2.0 sec. The thresholds for durations of motion below 0.1 set are more difficult to interpret, although the present data appear to be well described by the constant velocity prediction. It should be appreciated that durations below 0.1 set represent something of an experimental “artifact” as fixationai pauses under natural viewing conditions are rarely if ever this short. Since with these shorter durations both the effective luminance during movement and the stimulus excursion are decreased
:.a0 B
r ; _
300 20.0 1
I.M. .
179
reciprocity in the perception of motion
600
proportionately, the threshold is most probably determined by the acceleration characteristics of the stimuius at the beginning and termination of movement. At the onset of motion the stimulus changes from zero velocity to the constant high velocity almost instantly, undergoing the reverse process as the motion ceases. The sharp transients associated with rapid acceleration to (positive) and from (negative) high velocities may produce much lower thresholds for detecting motion (Harvey and Michon. 1974). In this respect, it should be noted that Henderson (1971), employing stimuli displayed on a cathode ray tube and visible only during the stimulus movement (zero acceleration), reported much higher thresholds for short duration-high velocity stimulus movements than those obtained in the present study. This seems to support the interpretation that for durations below 0.1 sec. motion thresholds for continuously visible stimuli (literally a “stop-go-stop” condition) are determined by the acceleration characteristics of the stimulus. Historically, the motion detection threshold value of approx l’/sec has received a rather “classical” status and has in fact become standard in human engineering practice. The correspondence between this value and the resolution threshold in the fovea has been noted. Such a correspondence suggests that motion perception, to the extent that it is determined by a constant distance travelled. may be subserved by a mechanism related to resolution properties. In this view, the moving stimulus must traverse the same retinal distance as the separation between adjacent elements in a resolution test object. We have recently obtained data on the resolution of sine wave targets as a function of eccentricity, both with and without correction of refractive error (Millodot, Johnson, Lamont and Leibowitz (1975). (Subject A0 participated in both studies.) The data indicate that acuity is degraded, on the average, by a factor of about six at 30” of eccentricity and about 10 at 60” of eccentricity under both conditions. These values correspond fairly closely with the degradation of motion perception reported in the present study as well as previous
PERIPHERY
0
0
2.5 / I 0.025
I 0.05
1 0.1
I 0.2
I 0.4
MovementDuration
I I.0
I 2.0
I 4.0
(Seconds)
Fig. 2. The velocity-time product necessary to produce threshold movement as a function of movement duration for peripheral stimulation. On this plot, a horizontal tine indicates that threshold is determined by a constant stimulus displacement. A line of unit slope indicates that threshold is tiased on a constant stimulus velocity.
investigations utilizing the same apparatus (Leibowitz, Johnson and Isabelle, 1972: Johnson
and Leibowitz. 1973).’ Whether this is a coincidence can be determined only by the introduction of additional parameters and careful determination of motion and resolution thresholds for the same observers. On the basis of the present evidence. the similarity of the resolution and motion thresholds for durations above 0.1 set suggests that the mechanisms may be related.’ Similar arguments, particu~arIy with respect to peripheral vision, have been proposed by Gordon (1947). The present findings imply distinct mechanisms for motion detection. Between O-1 and i-0 sec. a constant displacement of the order of the resolution threshold is the rule. For shorter or longer movement durations. the present resuits demonstrate an abrupt transition from a constant displacement to a constant velocity. In all cases, the shapes of the functions in the fovea and periphery are similar implying similar mechanisms. The higher values for the peripheral observations are strikingly close to the degradation observed for resolution with eccentric viewing.
‘Refractive error, which is known to affect peripheral motion thresholds (Lcibowitz et at., lQ72), was not a contributing factor in this experiment since both observers had negligible refractive error at the stimuhs eccentricities under investigation. ‘Thorson, Lange and Biederman-Thorson f 1969)report that in the periphery, apparent movement can be discerned between two flashing dots which cannot be resolved spatially. To the extent that apparent movement can be compared to real movement, their findings impiy that peripheral motion discrimination may not be dependent upon a minimum detectable separation. However the rates of apparent movement over which this effect was observed are most closely approximated by the short duration-high velocity region of motion investigated in the present study, which also departed from the “displacement constancy” rule.
REFERESCES
Cohen R. L. and Bonnet C. (1972) Xfovcmtnt drtectiun thresholds and stimulus duration. Percept. Ps~chuph~s.
12. 339-27’2. Cornsweet T. y. (1962) The staircase method in psychophysics. Am. J. Psvchoi. 73. -185-491. Dimmick’R.~ L. and Karl J.-C. (1930) The effect of the exposure time upon the R. L. of visible motion. .I. exn, Fsychol. 13. 365-369. Gordon D. A. (1947) The relation between the thresholds of form, motion and displacement in parafoveal and peripheral vision at a scotopic level of il[~minarion. .~m. J: Psvchoi. 60. 202-125. Graham C. H. (1965) Perception of movement. In Vision nnd Visual Perception (Edited by Graham C. H.). Wiley. Sew York. Harvey L. 0. and Michon J. A. (1974) Detectability of relative motion as a funetion of exposure duration. angular separation, and background, J. exp. Ps~chat, 103. 3 17-325. Henderson D. C. (1971) The relationships among time. distance, and intensity as determinants of motion discrimination. Percept. Psycfiophys. to. 313-320. Johnson C. A. and Leibowitz H. W. (I9741 Practice, refractive error. and feedback as factors influencing peripheral motion thresholds, Percept. Psyckopkvs. 15, 276-280. LeGrand Y. 11967) Form and Spaoe Vision
