Motion of chromatic stimuli: First-order or second-order?

0042-6989/94$6.00+ 0.00 Copyright 0 1993Pergamon Press Ltd

Vi&m Res. Vol. 34, No. 1, pp. 49-58, 1994 Printed in Great Britain. AU rights reserved

Motion of Chromatic Second-Order?* SIMON J. CROPPER,t$

ANDREW

Stimuli: First-Order

or

M, DERR~NGTON~

Received 22 October 199.2;in revi~ed~or~ I8 March 1993

This paper measures the minimmn velocity required to discriminate the direction of motion (the lower threshold of motion-LTM) for patterns which consisted of spatial variations in luminance, ~r~a~ci~ or l~ina~ coutrast in an attempt to ~~~ between tbe ~~~~~ Mooneyselective mechanisms. The characteristics of these patterns can be defined as ~~t~rder~Fo~r stimuli ~~~na~ and chromatic gratings) or ~o~~~er~#~Fo~er stimuli (contrast gratings or “beats”). Measurements for each pattern were made at durations ranging from 0.015 to O.%see and at contrasts of 0.5 log units above detection threshold and 1.5 log units above the threshold for detecting the stationary pattern. Observers were able to discriminate the direction of motion in lank gratings and hi& contrast chromatic gratings at alI durations above 0.015 sec. Tbe dire&on of motion of beats and low contrast chromatic gratings was inviable until they bad been presented for at least 0.12 sec. This was taken to iudicate the existence of a fast-act@ and a slow-acting system dealing with the Grst- and second-order patterns respectively. When defined on this basis, the chromatic stimulus acts as a first-order (luminance) pattern at high contrasts and a second-order (beat) pattern at low contrasts. Motion

First-order

Second-order

Colour

Spatial beats

directly our ability to determine the direction of motion chromatic stimuli with both first-order (luminan~coded) stimuli and second-order (con~ast-coded or beat) stimuli. The first-order/second-order definition of Cavanagh and Mather (1989) defines the stimuli on the basis of the amount of processing needed before the pattern can be extracted, and is based on statistical principles introduced by JUlesz (1971). The critical definition is whether a correlation between two points in the pattern can be drawn directly (first-order), or whether a group of two or more points first have to be associated with each other before a correlation can be drawn with another equivalent group of points in the pattern (second-order). In this way the definition of first- and second-order can be thought of as involving one or two (or more) stages to extract the pattern and keeping the definition at this level avoids problems of making too many assumptions about the visual mechanisms involved. It is generally believed that first-order motion is anaiysed by mechanisms which extract the direction of motion of the input by spatiotemporal correlation (Reichardt, 1961; van Santen & Sperling, 1985), simultaneous analysis of the spatial and temporal gradients (Limb & Murphy, 1975; Marr & Ulhnan, 1981) or some kind of spatial and temporal filtering (Adelson & Bergen, 1985; Watson & Ahumada, 1985; Heeger, 1987). The primary inputs to all these models are sensitive to luminance changes, so these are models of first-order l~inance-coded motion only and do not explain our

INTRODUCTION Although the original distinction regarding our ability to discriminate the direction of motion in different stimuli into “short-range” and “long-range” processes (Braddick, 1974) has been superseded by the more explicit stimulus-based definition of first- and second-order (Julesz, 1971; Cavanagh & Mather, 1989), we are still left with the idea that there is a basic motion system dealing with the motion of first-order signals such as luminance edges, and a possibly more complex system dealing with second-order moving signals, such as form and texture. These could take the form of two distinct systems each using a different strategy to extract the motion, as Braddick postulated; or the dichotomy may simply be symptomatic of a more unified motion system receiving different inputs depending upon the spatial structure of the stimulus. Whatever the basis of the first-/secondorder dichotomy in motion detection, it is still not clear how we deal with a first-order chromatic stimulus when we are required to discriminate its direction of motion. For this reason, the present work seeks to compare *This work was initiallypresentedat the European Conferenceon VisualPerceptionheldin Paris, 1990. It also forms part of a Ph.D. thesis sub~tt~ to the University of Newcastle upon Tyne, England. department of Physiological Sciences, The l&&al School, Newcastle upon Tyne, NE2 4HH, England. STo whom all correspondence should be addressed at present address: Department of Ophthalmology, McGill Vision Research Centre, 687 Pine Avenue West, H4-14, Montreal, Quebec, Canada H3A 1Ai 49

SIMONJ. CROPPERand ANDREWM. DERRINGTON

50

ability to see other motion in other kinds of stimuli. We would expect an arrangement of these simple motion detectors to provide the dir~tionally-s~i~tive response rapidly, requiring the combination of only a few neurons in their construction. This is reflected in the brief spatiotemporal intervals over which we can see first-order signals move, first defined as short-range (Braddick, 1974). The movement of a second-order pattern could easily be extracted using similar strategies to those employed by any one of the above models if the input filters were sensitive to the second-order signal. We might expect it to take longer to extract a motion signal from a secondorder feature because more processing is required before that feature can be coded (Cavanagh & Mather, 1989). Derrington, Badcock and Henning (1993) showed that longer presentations are required to discriminate the direction of motion of a beat pattern (second-order) than a luminance grating (first-order), simply by measuring performance in a direction discrimination task at short and long durations of presentation. Yo and Wilson f 1992) found that the perceived direction of motion of a type II plaid changes with the duration of presentation and Wilson, Ferrera and Yo (1992) have explained this in terms of a delay in the motion processing of secondorder signals. In this paper we use the finding that motion mechanisms dealing with second-order signals cannot process brief stimuli (Derrington et al., 1993) to investigate whether chromatic stimuli are processed by such a mechanism. First, however, we establish that this time difference is a property of the motion-det~tion mechanism, rather than simply reflecting the extra processing needed to extract second-order patterns.

METHODS All stimuli in this work were made by adding one or more horizontal sinusoidal gratings, produced by the method of Schade (1956) using a one-dimensional display controller (Cambridge Research Systems VSG2/ 1) with 1Cbit metal-to-analogy converters (DACs), and displayed on a Barco CDCT6551 colour monitor running at 120 Hz frame rate and 75 kHz line rate. The mean luminance was 44.2 cd/m2 (CIE coordinates: x = 0.333, y = 0.477), and neither the mean luminance nor the mean chromatic&y of the display was altered by presentation of the stimuli. All stimuli can be described as: L(Y) =

L,,,{l + E(G,

+ G,)>

(1)

where L (y) is the luminance in cd/m2 at position y. &,is the mean luminance of the display (44.2 cd/m’). E is the temporal envelope, which was either a raised cosine function of time (t ), a Hanning window: E (t ) = O.S(cos 27Xt + 1)

(2)

- 1/2~ d t d 1/2c, and zero at other times, where c is the temporal frequency (Hz) of the envelope. Or in the case of flickered stimuli, a cosine function of time (t): E (f ) = cos 27r~.

(3)

G, and G2 are sinusoidal gratings, each of which can be described over space (y) and in time (t ) as: G,=C,*sin2rcCf,y+m,t+4).

(4)

CU is the contrast, expressed as a three-dimensional vector which specifies the chromatic and luminance properties of the waveform. J;, is the spatial frequency (c/deg), o, is the temporal drift-rate (Hz), and 4 is the spatial phase angle, As most stimuli were drifting, and the starting spatial phase of the waveform was randomized, the spatial phase angle is omitted from subsequent equations. For the simple grating stimuli, the contrast C, was set to zero. For the beat stimuli, formed by adding two gratings together of different spatial frequency (Badcock & Derrington, 198S>, C2 was set to be equal to C,. In the case of beat stimuli, equation (1) can be rewritten:

+ (% + @&)2/2)cos27c(Vi -f,)Y/2 + (0, - ~2w‘m1~~

(3

Equation (5) shows the spatiotemporal properties of the pattern in terms of the sinusoidal carrier grating and the cosinusoidal envelope (Badcock & Derrington, 1985). The spatial and temporal frequencies of the carrier grating are the mean of the spatial and temporal frequencies of the component gratings: u, +S,)/2 and (w, + 0,)/2. The cosinusoidal term in equation (5) represents the contrast envelope of the carrier which forms the beat. This term is signed but as discussed by Badcock and Derrington (1985) we are unable to distinguish between the positive and negative lobes of the envelope, so the apparent spatial frequency or “beat frequency” (Badcock & Derrington, 1985) is actually twice the spatial frequency of the cosinusoidal envelope. This gives the beat spatial and temperature frequencies which are equal to the difference between the spatial and temporal frequencies of each component: U; -f2) and (0, - a2). Thus, if we set the temporal frequency of the two components to be equal and opposite (w, = -w2) this makes the beat move and the carrier remain stationary. Carrier-motion with a stationary beat is produced by making the component temporal frequencies the same (01 = 02). The contrast (C) of the stimuli was expressed as a three-dimensional vector describing a deviation from the display’s mean luminance and chromaticity using the coordinate system of Derrington, Krauskopf and Lennie (1984). The whitepoint was chosen by setting each gun to half its maximum luminance and then altering the blue and red guns to produce a satisfactory white appearance. The proportional contribution of each gun to the whitepoint was 0.206 red, 0.678 green and

MOTION OF CHROMATIC STIMULI

Movement along the achromatic 0.116 blue. (R + G + B-“equal-energy”) axis of the space was attained simply by a proportional linear increase in the output of each gun. This maintained the hue whilst increasing the luminance, and describes a “luminance” stimulus in this work. Movement in the equiluminant plane of the colour space was achieved by keeping the total output from the guns constant but changing the relative luminance produced by each gun. This has the effect of changing the hue but maintaining the luminance. Movement along the red-green (R-G) axis, which approximates to the “constant blue” axis* of Derrington et al. (1984), was attained by modulating the red and green guns with equal and opposite signals. Subjective differences in the equiluminant plane were corrected using heterochromatic flicker photometry (see Psychophysical Procedures for a full description). All contrast thresholds used in this work are calculated and expressed in terms of cone contrasts, in order to facilitate comparisons across stimuli (Stromeyer, Cole & Kronauer, 1987; Lennie & D’Zmura, 1988). Cone contrasts were calculated using the equations of Smith and Pokorny (1975). To equate the units along each axis of colour space, the lookup tables linearizing the voltage-luminance relationship for each gun (gamma-correcting) were constructed so that movement of one table-place created the same increment in luminance on the monitor screen, whichever table was used. Because each gun has a different luminance range, each table was of a different length. The most effective phosphor is the green, the lookup table for which was chosen to be 4096 places long. The lengths of the lookup tables for the other two guns was scaled to this according to their relative luminance ranges (or e~cien~es). This meant the red gun lookup table was about 1300 places long and the blue gun table was about 800 places long. The exact length of these two tables changed very slightly each time the equipment was recalibrated. This was performed at regular intervals using a United Detector Technology Photometer 61 with a photometric filter and lumilens. The viewing distance was 3 m in all experiments which gave a screen size of 5.52 deg wide by 4.67 deg high and the observer was instructed to fixate on a small, continuously present spot in the centre of the screen, making all viewing in the central visual field. The observers were both experienced psychophysical subjects: one of whom was naive as to the aim of the experiments. They wore their prescribed optical correction and viewed the display binocularly with natural pupils and no headrestraint. Psychophysical procedures Detection thresholds. The detection threshold for each stimulus was measured using a staircase procedure

*There is a minor deviation from a true “Constant bl&

axis: mov~~nt along *s, the red-greenaxis, modulatedthe output of the the cones by about 10% of the modulation of the output of the red and green cones.

51

which altered the stimulus contrast according to the observer’s response in a temporal two-alternative forced-choice (2AFC) task. The staircase was based on a modified PEST procedure (Findlay, 1978) which adjusted contrast towards a level at which the observer scored 75% correct. On each trial the observer was presented with two intervals, separated by a pause of approx. 250 msec, each signalled by a tone throughout its duration which was at least 1 sec. Only one interval contained the stimulus, which had a drift-rate (0) of zero. The observer’s task was to indicate by means of a key press, which interval contained the stimulus. The stimulus presentation period was always centred within the observation interval and had the temporal form of a raised cosine [equation (2)]. The duration of the stimulus is expressed as the half-width of this envelope, which is the duration of a rectangular pulse with the same area. The threshold was the mean of four of these estimates: it was ensured that the standard deviation of the sample (a - 1) was co.1 log units. In the case of the beat stimuli, the non-stimulus interval contained an unmodulated grating at the same spatial frequency as the carrier grating of the beat. The contrast of this grating was randomized between the mean and the peak contrast of the carrier in the stimulus interval to avoid the presence of spurious cues in the beat-detection task. Velocity thresholds. The velocity thresholds were calculated as the minimum stimulus velocity required to discriminate correctly the direction of motion of the stimulus. These lower thresholds of motion (LTMs) were measured using the method of constant stimuli in a temporal 2AFC dir~tion-disc~mination task. The observer was presented with two intervals again, but the stimulus was present in both intervals: in one interval the stimulus moved upward, in the other it moved downward at the same rate. The observer’s task was to indicate in which interval the stimulus had moved upward. Flicker photometry. The equiluminant plane for each observer was established prior to each experiment with the chromatic stimulus to be used. The observer was presented with the chromatic grating concerned, which was cosinusoidally counter-phased at 5 HZ [equation (3)]. The grating was presented at a contrast approximately 40 times detection threshold to maximize the contrast of any luminance artifact. The observer had levers which allowed them to adjust the contrast and polarity of a luminance grating of the same spatial frequency added in phase with the chromatic grating until the perceived flicker was minimal. At this point we assumed that the luminance grating cancelled any luminance artifact in the chromatic stimulus introduced by variations in the equiluminant plane or chromatic aberration for each observer. The mean of IO of these estimates’was then used as the appropriate correction for all subsequent experiments with that stimulus and observer; the correction was checked regularly.

52

SIMON J. CROPPER and ANDREW M. DERRINGTON

Ex~riment I: contrast detection t~res~oI~ fir d@erent patterns as stimulus duration changes Derrington et al. (1993) showed that observers required a longer presentation interval to discriminate the direction of motion of contrast-coded (beat) patterns than luminance-coded patterns. There could be two possible explanations for this observation. One is that the second-order motion mechanism takes longer to work than the first-order mechanism. The other possible explanation is that the mechanism dealing with detection of the beat is causing the delay, rather than the directionally-selective mechanism providing the motion signal. To distinguish between these two possibilities we measure the ability to detect the beat at short durations of presentation, at which its direction of motion is indiscriminable (Derrington et al., 1993). If the pattern is detectable at these short durations, then the delay observed before the direction of motion can be seen must be a property of the motion-detection mechanism dealing with this second-order stimulus, since the delay would seem to occur somewhere between the processes of detection and motion-detection. The grating stimuli had a spatial frequency of 1 or 10 c/deg (luminance grating only). A spatial frequency of 1 c/deg in the chromatic grating was low enough to ensure minimal chromatic aberration in the coloured grating (Cavanagh & Anstis, 1991; Anstis & Cavanagh,

(4

0

I

0.1

Duration (seconds)

1

0 Lum grating lcpd

(b)

Lum grating lcpd

A RG grating lcpd Cl Beat 1:lOcpd V Lum grating 1Ocpd

0.01

1983) yet high enough not to lose sensitivity to the luminance grating at 0 Hz (Robson, 1966). The beat pattern was a 1 c/deg beat in a 10 c/deg carrier grating (component gratings of 9.5 and 10.5 c/deg and termed 1: 10 in this work) which ensured the beat and the carrier were far enough apart in spatial frequency to be clearly discriminable from each other. The duration of presentation of the stimuli was varied from a minimum of 0.015 set (2 frames) to 0.96 set (half the width of the raised cosine temporal envelope). Results and discussion. Figure l(a, b) plot the contrast detection thresholds for four patterns against the duration of presentation, for two observers, SJC and CL. The contrast units are expressed as the mean cone contrasts for the red and green cone-types, allowing all stimuli to be directly compared. The blue cones can be ignored at this stage because their output is constant for the red-green grating (Krauskopf, Williams & Heeley, 1982) apart from the small error described in the main methods, and it is also thought that blue cones make little or no contribution to the perception of luminance changes (MacLeod & Boynton, 1978; cf. Vos, Estevez & Walraven, 1990). In the case of the beat stimuli, the contrast is expressed in terms of the contrast of the carrier at the peaks in the contrast envelope waveform. For all stimuli there is a decrease in the threshold as the duration for which the pattern is present increases. This is as might be expected considering the effects of

RG grating lcpd 0 Beat 1:lOcpd V Lum grating IOcpd

A

c

O.oool fl 0.01

0.1

1

Duration (seconds)

FIGURE I. Contrast detection threshold plotted against the duration of presentation of the stimulus. The stimuli are luminance, chromatic or contrast gratings (beats) as explained in the text and indicated by different symbols. The beat is a 1 cjdeg beat in a 10 c/deg carrier, termed 1: 10 c/deg. Contrast is expressed as the mean cone modulation of the red and green cone types and the duration as half the width of the raised-cosine temporal envelope. Each point is the mean of four threshold estimates at a performance of 75% correct in a 24FC detection task. Standard deviations were all < 0.1 log units. (a) Observer SJC. (b) Observer CL.

53

MOTION OF CHROMATIC STIMULI

temporal integration in detection mecha~sms (Watson, 1986), and the previous ~ychophysical results regarding contrast detection thresholds at different stimulus durations (Nachmias, 1967; Breitmeyer & Ganz, 1977; Legge, 1978; Gorea & Tyler, 1986). All patterns are visible even at the shortest duration of 0.015 sec. This means that a luminance grating and a chromatic grating can be discriminated from a blank field, and that the beat can be discriminated from a grating that has the same spatial frequency as its carrier, down to a duration of 0.015 sec. This shows that the detection mechanism, dealing with each pattern is able to signal the presence of the stimulus after only a very brief presentation, even for the second-order beat stimulus. The time-course of the improvement in sensitivity is different for each type of stimulus. The improvement is most rapid for the 1 c/deg luminance grating: the observers reach a maximum sensitivity after only 0.06 sec. This is in agreement with the results of Legge (1978), who showed that for low spatial frequency gratings, detection threshold was independent of duration above 0.1 sec. The high frequency luminance grating and the beat give rise to very similar improvements in sensitivity, although somewhat slower than that observed with the 1 c/deg gratings. The improvement in sensitivity is slowest for the chromatic stimuli, which is consistent with the suggestion that chromatic detection systems have a lower temporal resolution, or longer temporal integration period, than achromatic mechanisms (Kelly, 1983; Smith, Bowen & Pokorny, 1984). The cone modulation required to detect the red-green grating is much lower than that required to detect any of the luminance stimuli, particularly at longer durations. This indicates that chromatic mechanisms show much greater ~nsiti~ty than luminance mechanisms when measured by an equivalent metric such as cone contrast. This agrees with recent work using chromatic and luminance spot stimuli (Chaparro, Stromeyer, Kronauer & Eskew, 1992). The sensitivity of individual parvocellular neurones is lower than psychophysically measured contrast sensitivity by up to a factor of 15 (Derrington et al., 1984; Derrington, 1991). This indicates that some kind of pooling of the individuai responses between units must take place to explain the psychophysical sensitivity. We might expect this pooling process to involve temporal summation of the signals, which may be the cause of the increased time taken to reach optimal sensitivity seen in these and previous results (Kelly, 1983; Smith et al., 1984). Experiment 2: the duration dependence of direction-ofmotion discrimination Here we measure the lower threshold of motion (LTM) as a function of duration for the stimuli used in Exp. 1. In the case of the “beat” stimuli, only the beat moved, the carrier remained stationary. For the “carrier” condition, the carrier moved whilst the beat remained stationary. The stimuli were set at a contrast 0.5 log units above detection threshold for the static stimulus in order that performance for the different

a loo 90 80 g

70

g z

60 50

8

40

ag

30 20 10 0 0.01

b 100 9080 2

70-

g z

6050 -

8

40-

b

30

&

t

20 10

t

Ob 0.01

, 0.1

I

I

1

10

Velocity (degrees/second) FIGURE 2. (a) Performanceagainst velocity for a 2AFC dir&ion-ofmotion di~~mination task. The stimulus was a I cjdeg luminance grating at a contrast 0.S log units above detection threshold. &ch symbol indicates a different stimulus duration. Each point is the result of 100 observations. Observer CL. (b) As (a) except the stimulus is a 1 c/deg beat in a 10 c/deg grating (f :iOc/deg).

stimuli might be compared in a direction-discrimination task. The detection threshold used for the “carrier” condition was that measured for the 10 c/deg grating alone. The observers were given a 2AFC direction discrimination task for each stimulus at each duration, using the same viewing distance and screen size as Exp. 1. The method of constant stimuli was used to collect psychometric functions for each stimulus at each duration. For each condition a range of velocities was chosen to span the performance range from 50 to 100% correct. 100 observations were made for each data point and the percentage of correct responses plotted against the velocity for each duration. Results and discussion. Two examples of the psychometric functions are shown in Fig. 2(a, b) for observer CL. These two functions are shown because they give examples of stimuli where the direction of motion can [1 cfdeg luminance grating in Fig. 2(a)] and cannot [l c/deg beat in Fig. 2(b)] be di~na~ at all durations. Each function represents the results at a single

54

SIMON J. CROPPER and ANDREW M. DERRINGTON

duration for the same stimulus, as indicated by the key. As the duration of the pattern increases, it becomes easier to see which direction it moves in, which is shown by the leftward shift of the individual functions along the abscissa (velocity axis) with increasing duration. An inability to discriminate correctly the direction of motion at the shortest durations is indicated by the flat psychometric functions in Fig. 2(b), where performance in the task does not improve with increasing velocity. As the duration of presentation increases, however, performance does improve with velocity. At high velocities and short durations, the beat becomes invisible, presumably because of the limited temporal resolution of the detection system involved. This means that, although the functions for 0.12 and 0.03 set do show an improvement in performance at higher velocities, increasing stimulus velocity reduced the visibility of the beat pattern and so did not allow a LTM to be measured. The temporal properties of the beat detection mechanism are currently under investigation. Psychometric functions, similar to those in Fig. 2, were measured for each stimulus at each duration and the lower threshold of motion (LTM) was taken as the velocity at which a performance of 75% correct was reached. The LTMs are shown for each stimulus as a function of stimulus duration in Fig. 3(a, b). The LTM expressed as a velocity (deg/sec) is plotted against the duration on logarithmic axes.

0 A 0 v 0

(a) lo F

0.01 ’ 0.01

I 0.1

Duration (seconds)

Lum grating lcpd RG grating lcpd Beat 1:locpd Lum grating locpd Carrier 1:lOcpd

4 1

The absence of a data point at a particular duration indicates that a threshold velocity could not be measured for that stimulus at that duration. The direction of motion could not be discriminated regardless of the stimulus velocity and the psychometric function was flat, as in Fig. 2(b), at short durations of presentation. The principal point to notice about Fig. 3(a, b) is that the lower threshold of motion is not measurable for all stimuli at all durations. The direction of motion of the 1 c/deg luminance grating is discriminable at all durations measured, but this is not the case for the other patterns. Referring first to the curve for the 1 c/deg luminance grating: as the duration of presentation increases from 0.0 15 set, the minimum velocity required to discriminate direction of motion decreases as we may expect and has been shown before (Boulton, 1987). The LTM is approximately proportional to duration, indicating a constant displacement sensitivity up to 0.24 set duration. Performance does not improve as the duration of presentation increases beyond 0.24 set for SJC, although CL does show some improvement at 0.96 set duration. This could be due to tracking eye movements which could be used at this kind of stimulus duration. Even though observers were instructed to fixate, it becomes hard at these long stimulus durations. Consequently, measurement of a LTM at a longer duration becomes meaningless.

0 A 0 v 0

(b) 10

0.01 1 0.01

0.1

Lum grating lcpd RG grating lcpd Beat 1:locpd Lum grating locpd Carrier 1:lOcpd

1

Duration (seconds)

FIGURE 3. Lower threshold of motion (LTM) at different stimulus durations for each stimulus. These were calculated from psychometric functions like the ones in Fig. 2 as the velocity at which a performance level of 75% correct was reached. The contrast of all patterns was 0.5 log units above detection threshold and duration is expressed as half the width of the raised-cosine temporal envelope. The patterns are specitied in the key and indicated by different symbols. The absence of a data point, as in the case of the chromatic gratings and beats at short durations, indicates that performance did not reach 75% correct in the direction discrimination task and no LTM could be measured. (a) Observer SJC. (b) Observer CL.

MOTION OF CHROMATIC

The beat and chromatic grating do not show the same pattern of results in that a LTM is unmeasurable until they have been on for longer: at least 0.12 set for both observers. This means that although the stimuli are detectable at short durations, as shown by Exp. 1, their direction of motion is indiscriminable at short durations. This is despite the fact that the observers were able to discriminate these moving stimuli from the static stimulus presented for the same duration. This is in agreement with the observation of Derrington et al. (1993) that the direction of motion of beat stimuli is indisc~minable at short durations, and shows that the first-order chromatic stimulus is behaving like a second-order (beat) stimulus in this respect. Once measurable, the LTM decreases with increasing duration and again shows an approximate function of constant displacement until maximum performance is reached, which is at a longer duration than for the luminance grating. The value of the LTM measured with beat and chromatic stimuli is greater than for a luminance grating at the same spatial frequency and duration. De Valois and Bullimore (1992) recently found a similar effect when comparing displacement sensitivity for luminance and chromatic gratings. These results are not in line with those of Lindsey and Teller (1990), who found that the contrast required to discriminate the direction of motion of a red-green (0 deg axis) grating was in excess of five times the detection threshold under slightly different stimulus conditions, most notably parafoveal stimulus presentation. At the temporal frequency and duration of presentation employed by Lindsey and Teller, which were 4.875 Hz and 0.83 set, our observers get perfect performance at three times detection threshold. Possible explanations for this difference between fovea1 and parafoveal presentation are discussed elsewhere, where a more comprehensive compa~son is carried out ~Der~ngton & Henning, 1993; Cropper & Derrington, 1993). It should be noted, however, that qualitative agreement is found when stimulus conditions are exactly replicated. The improvement in sensitivity to the direction of motion of the beat stimuli shows signs of flattening out before sensitivity to motion of the chromatic stimuli, although this is more obvious for SJC than CL. However, one cannot be sure that this difference between the beat function and the chromatic grating function indicates different underlying mechanisms rather than a difference in effectiveness as a stimulus for tracking eye movements. Our principal interest here is in the performance at short durations, and in the fact that the motion mechanism dealing with the beat and the chromatic stimuli is unable to signal the direction of motion until the patterns have been presented for more than 0.12 set, The results for the movement of the 10 c/deg carrier in the beat pattern and the 10 c/deg grating alone show a difference for the two observers, but a consistency for the two patterns for each observer. Observer CL cannot di~~minate the direction of motion of either high spatial frequency pattern at short durations. The modulated and undulated carrier gratings were included to see whether there was any effect of the beat on directionVRW--c

STIMULI

55

of-motion disc~~nation in the carrier. The consistency for each observer between the patterns indicates that there is no such effect. The results so far confirm that motion-det~to~ designed to deal with first-order signals operate more rapidly than motion-detectors designed to deal with second-order signals (Derrington et al., 1993). They also show that chromatic patterns behave as if their motion is detected by a second-order type of detector (in terms of the rate of response) despite the fact that they are first-order patterns. In the next experiment we test this result at a higher contrast.

The previous experiments show that it takes longer for observers to be able to discriminate motion in a chromatic- or contrast-defined pattern than in an equivalent luminance pattern. There could be two possible reasons for this: either there are at Ieast two motion detection processes at work, the one dealing with the luminance patterns being much faster than those dealing with the other two stimuli; or, the chromatic and contrast-dewed patterns have a much weaker input to a single motion detector, causing a less reliable response which takes longer to reach a criterion level. The experiments described below approach this question by looking at the effects of increasing input-signal strength to the motion detection systems involved. If the amplitude of the input to the motion detector from these two patterns is the limiting factor on the performance of the detector as seen in Exp. 2, the performance should improve with inputsignal strength. The observers were again given a 2AFC direction di~~mination task from which performance vs velocity curves were plotted, and then the LTM calculated, exactly as in Exp. 2. The stimuli were a 1 c/deg luminance grating (observer CL only), a 1 c/deg red-green chromatic grating and a 1 c/deg beat in a 10 c/deg carrier, termed 1: IO. These were presented at a high contrast of a maximum 1.5 log units above threshold, The actual contrast depended on the available range of the stimulus producing equipment for each stimulus, but always exceeded 1.1 log units above detection threshold. Viewing distance and all other conditions were exactly as before. desists. Figure 4(a,b) plot, for each observer, the LTM expressed in units of velocity (degjsec) against the duration of presentation of the stimulus in seconds, Open symbols indicate the results from when the stimuli were presented at low contrasts (replotted from Fig. 3), solid symbols indicate the results for the high contrast stimuli. Stimuli are as indicated in the key and, again, the absence of the data point at a particular duration indicates that no LTM could be measured for those conditions. The most important point to be seen in this figure is that when the stimuli are increased in contrast by “equivalent” amounts, observers show a much greater improvement in performance for direction-ofmotion discrimination in the chromatic grating than the

56

SIMON J. CROPPER and ANDREW M. DERRINGTON 0 L-mngratinglcpd A RG grating ~cpd cl Beat l:Xkqd A RG grating lcpd Hi C n Beat 1:lOcpd Hi C

(a) 10 r

I

0.01

0.01

Cl I

0.1

0 L.uzngratinglcpd

(b)

A Cl @ A m

10 F

0.01 ’ 0.01

Duration (seconds)

RG grating lcpd Beat 1:lOqxl Lumgrating IpdHiC RGgrating 1cpdHiC Beatl:lOcpdHiC

4

. ‘..+I 0.1

1

Duration (seconds)

FIGURE 4. LTM plotted against stimulus velocity for three low contrast and two high contrast stimuli. The open symbols indicate stimuli at 0.5 tog units above detection threshold (replotted from Fig. 3); the sofid symbols indicate stimuli presented at contrasts of a minimum of 1.1 log units, and a maximum of 1.5log units, above detection threshold (see text). Individual stimulus types as indicated in the key. The duration is expressed as half the width of the raised-cosine temporal envelope, the LTM expressed as velocity (deg/sec). The absence of a data point indicates no LTM could be measured, as before. Increasing the stimulus contrast can be seen to have a much greater effect on the chromatic stimuli than the beat stimuli. (a) Observer SJC. (b) Observer CL.

beat; there is very little improvement in performance when the contrast of the luminance grating is increased (observer CL; Boulton, 1987; Derrington & Badcock, 1985). The improvement in performance for the chromatic grating with increasing contrast is shown both in terms of the ability to discriminate direction of motion at the shortest durations and the reduction in the LTM at all durations. Performance for the high contrast chromatic grating is equivalent to, or better than, performance for the low contrast luminance grating at most durations. At these higher stimulus contrasts, the chromatic grating behaves like other first-order stimuli. The improvement in performance for the beat as contrast is increased is far less, The LTM is still unmeasurable at the shortest d~at~ons and not much reduced at longer durations.

GENERAL

DISCUSSION

There are two main points to be discussed here. The first is the fact that motion mechanisms dealing with second-order signals appear to operate more slowly, in the sense that they require longer stimulus durations than mechanisms dealing with first-order signals. The second point is that the motion of first-order chromatic gratings appears to be processed by a slow mechanism at low contrasts and by a fast mechanism at high contrasts.

“‘Slow” signals

processing

of

the

motion

of

second-order

These results, coupled with those of Derrington et al. (1993), show that there is a considerable range of short durations where we cannot discriminate the direction of motion of beats or low contrast chromatic gratings. The reason for this delay is not clear; one suggestion is that it is because a rectification or squaring process required to detect the second-order signal takes time to operate (Wilson et al., 1992). However, no delay is exhibited in a simple detection task with beats (Exp. l), and no rectification or squaring process is required to detect the chromatic grating, which also exhibits a delay in its motion processing. This strongly suggests that the delay occurs in the second-order motion-prosing system. One possible source of such a delay would be a severe low-pass temporal filter of the sort that would be necessary to prevent temporal aliasing in a system performing spatiotemporal correlations over long time delays. The mechanism that detects the beat motion could possibly receive an input signal either from a linear contrast-increment detection mechanism, or a late nonlinearity. The fact that variations in contrast have very little effect on the LTM indicates that, whatever mechanism is involved, there must either be some kind of gain control operating to decrease the predicted effect of increasing the input signal. Alternatively it is possible

MOTION OF CHROMATIC

that since the system may involve additional processing to extract the second-order signal, it doesn’t care at all about contrast as long as it is supra-threshold. This slow motion detection mechanism seems to be operating at a level close to its optimum, when the stimulus input is only 0.5 log units above contrast detection threshold. Chromatic motion mechanisms The motion of red-green gratings is analysed by mechanisms that work slowly at low contrasts and rapidly at high contrasts. Mullen and Boulton (1992) have also noted that the analysis of motion in chromatic patterns improves at higher contrasts. One could seek to account for this behaviour using already known mechanisms in two ways: the chromatic grating could provide a weaker input to the first-order motion detector, or alternatively its motion could be detected by the slow (second-order) system at low contrasts and the fast system at high contrasts. The fact that the LTMs are reduced so much with the increase in contrasts, which is not a property of the first-order mechanism [Boulton, 1987; Derrington & Badcock, 1985; Fig. 4(b)], suggests that there are at least two systems involved. The most economical suggestion would be that the motion of chromatic gratings is detected by the mechanism which analyses motion of second-order patterns when contrast is low, and by the mechanism which deals with firstorder patterns when contrast is high. However it remains a possibility that there is one (or more) motion mechanisms devoted exclusively to the analysis of chromatic patterns in motion. This contradicts the conclusions of Troscianko and Fahle (1988) who suggested that only one system was involved in the detection of motion in luminance and chromatic stimuli. Although this may be an adequate description of what happens at high chromatic contrasts (Exp. 3), it cannot explain the fact that at long durations, moving chromatic stimuli give rise to a sense of motion when the cone modulations they elicit are undetectable by the luminance system (see also Stromeyer, Eskew & Kronauer, 1990). There must be a separate, slow-acting system that senses the motion of such stimuli. The fact that it shows a comparable delay to the system that processes beats raises the possibility that the motion processing stage is similar for both kinds of stimulus.

CONCLUSIONS

The work presented here confirms that the delay in the processing of second-order motion signals (Derrington et al., 1993; Yo & Wilson, 1992; Wilson et al., 1992) is a property of the second-order motion detection system. First-order chromatic stimuli behave as if they were processed by the first-order (fast-acting) motion system at high chromatic contrasts and the second-order (slow-acting) motion system at low contrasts.

51

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Acknowledgements-This

work was financially supported by the Science and Engineering Research Council grant No. GRG 07980. SJC was supported by a SERC Image Interpretation Initiative Studentship during the work and also by Australian Research Council grant No. A79030414 during the writing of this paper. We wish to thank David Badcock and Jim May for critical reading of the manuscript.