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Velocity discrimination in chromatic gratings and beats
Vision Res. Vol. 34, No. I, pp. 4148, 1994 Printed in Great Britain. All rights reserved
Copyright
0
0042-6989/94 $6.00 + 0.00 1993 Pergamon Press Ltd
Velocity Discrimination in Chromatic Gratings and Beats* SIMON J. CROPPER? $ Received 21 December 1992; in revised form 26 May 1993
It is commonly assumed that the ability to discriminate velocity in a stimulus directly reflects the properties of the underlying directionally-selective mechanism. The results presented here show that this assumption is not always correct. Speed discrimination tasks over a range of base velocities were carried out for luminance gratings, chromatic gratings and contrast (beat) gratings of equivalent periodicity and contrasts. At low contrasts (0.5 log units above detection threshold), speed discrimination in luminance gratings was at least twice as good (when expressed as a Weber fraction), than in either chromatic gratings or beats. This is similar to the situation seen for tasks of direction discrimination using these sthnuli [e.g. Cropper and Derrington (1990) Perception, 19, A31]. When the stimulus contrasts were increased to 1.5 log tits above detection threshold, the ability to discriminate speed in both chromatic and beat stimuli improved to a performance level comparable to that shown for luminance gratings at all contrasts. ‘Ihis effect is not seen for tasks of direction discrimination when the same increase in sthnulus contrast has little effect on the lower threshold of motion (LTM) measured for beat patterns. These results indicate that the ability to discriminate velocity in a stimulus does not necessarily directly reflect the characteristics discriminate the direction of motion of that stimulus. Motion
Velocity
discrimination
Second
order
Spatial
INTRODUCTION
beats
of the ability to
Colour
lying motion-detection mechanisms the output of a motion detector is treated not only as left-right binary information but as a quantity, the magnitude of which indicates stimulus speed, and the sign its direction of motion. To extract this velocity information the system may need to compare the outputs of several directionally selective detectors (Adelson & Bergen, 1985) or to “frequency count” (Watson & Ahumada, 1985) to dissociate the effects of changing the stimulus contrast from the effects of changing the stimulus velocity. The ability to signal velocity (i.e. direction and speed of motion) has been incorporated into some popular models of motion detection (e.g. Watson & Ahumada, 1985; Adelson & Bergen, 1985; Heeger, 1987; Johnston et al., 1992) and has also been described separately, as an independent extension to directional motion detection. One such model of velocity coding in the visual system is the ratio model of Thompson (1982, 1984). In this model the speed is extracted from two overlapping, bandpass temporal filters tuned to the same direction of motion but different temporal frequency bands. The ratio of their outputs signals the contrast independent temporal frequency of the stimulus, which when correlated with the spatial sensitivity of the system can be used to give a velocity signal; the direction of motion having been previously extracted by some directionally-selective mechanism. It has been shown that we are not only very good discriminating the direction of motion of a stimulus (e.g. Braddick, 1980; Boulton, 1987) but also its speed
to discriminate the direction of motion of a stimulus and the subsequent ability to identify its speed are likely to involve common mechanisms for much of the processing involved in either task. It is feasible that both the direction of motion and the speed of a stimulus, together termed the velocity, is available to the system from the same directionally selective mechanism (e.g. Watson & Ahumada, 1985; Johnston, McOwan & Buxton, 1992). A common assumption arising from this is that the psychophysically measured characteristics of the ability to identify the velocity of a stimulus directly reflect the characteristics of the directionally-selective mechanism mediating direction discrimination in that stimulus. The results presented here indicate that this is not always the case and provide evidence for the partially separate processing of direction and speed information in some patterns. Because the ability to identify the speed of a stimulus is often assumed to reflect the properties of the underThe ability
*This work was initially presented at the Association for Research in Vision and Ophthalmology annual conference held in Sarasota, Fla in May 1992. It also forms part of a Ph.D. thesis submitted to the University of Newcastle upon Tyne, England. TDepartment of Physiological Sciences, The Medical School, Newcastle upon Tyne, NE2 4HH, England. $Present address: Department of Ophthalmology, McGill Vision Research Centre, 687 Pine Avenue West, H4-14, Montreal, Quebec, Canada H3A 1Al. 41
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SIMONJ. CROPPER
(McKee, 1981; McKee & Nakayama, 1984), at least if the stimulus is coded by luminance. When the stimulus is coded by some attribute other than luminance however, the story becomes less clear. The purpose of this paper is to study the ability to discriminate speed in patterns which are not coded by luminance but coded by modulations of either colour or contrast, which have first-order and second-order spatial properties respectively (Julesz, 1971; Cavanagh & Mather, 1989). These stimuli show different psychophysically measured properties when we are required to detect them or to discriminate their direction of motion (Cropper & Derrington, 1990, 1993a, b), which makes them potentially very useful when studying the processes involved in the extraction of their velocity. It is a common, if often subjective, observation that the perceived speed of chromatic gratings is less than that of luminance gratings of the same actual speed (Cavanagh, Tyler & Favreau, 1984; Mullen & Boulton, 1992), which indicates that there is a deficiency at some point in the coding of the velocity of chromatic stimuli. Cavanagh and Anstis (1991) suggest that this is due to a difference in the chromatic-contrast sensitivity of the two units, the ratio of whose outputs signals the velocity (Thompson, 1984). Partial support for this theory has been gained by the observation that under certain conditions, the contrast required to discriminate the direction of motion of a chromatic stimulus is greater than that required to detect the presence of the same stimulus (Cavanagh & Anstis, 1991; Derrington & Henning, 1993; Lindsey & Teller, 1990). This indicates that the directionally selective mechanism dealing with the discrimination of chromatic motion is less sensitive than a non-dir~tionally-selective mechanism dealing with simple detection of the presence of the stimulus. If this non-dire~tionaily selective mechanism replaced the temporal filter tuned to lower frequencies in the ratio model, then we could explain the observed slowing of chromatic stimuli since the denominator in the ratio calculation will be consistently larger for the same signal strength (Cavanagh & Anstis, 1991), and therefore produce a smaller output overall. Psychophysically, we would expect this slowing to shift the velocity increment discrimination function measured for chromatic stimuli toward that expected for lower base velocities than actually used. This kind of consistent shortfall in the estimation of the velocity should not, however, make the minimum detectable velocity increment larger. In some circumstances it should even make the minimum detectable increment smaller in chromatic gratings when compared with luminance gratings: if the detectible increment is an approximately linear function of base velocity (McKee, 198l), then within this range the lower perceived velocity of the chromatic grating will have a smaller velocity increment detection threshold than a luminance grating moving at the same actual speed. The perceived speed of rigidly moving amplitude modulated (AM) luminance gratings has been shown to be similar to, or slightly less than, that of luminance gratings of the same spatial frequency as the amplitude
modulation, over a range of l-5.5 deg/sec (Smith & Edgar, 1991). These patterns contain both first- and second-order motion signals, each making different predictions about the perceived speed of the moving pattern (Smith & Edgar, 1991). The measured perceived speed of the complex pattern is that which would be predicted by the second-order (contrast) cue and not the first-order ~luminan~) cue. These results suggest that the perceived speed of moving second-order signals is similar to a moving first-order signal of the same spatial frequency, and as such shows a difference in the velocity coding of the second-order (contrast) signal and a first-order chromatic signal, the perceived speed of which is significantly less than a first-order luminance signal Both the above estimates of subjective speed in complex luminance and simple chromatic gratings used relatively high contrast stimuli (in excess of 10 times detection threshold). Thus, from these observations, we should expect high contrast chromatic and second-order stimuli to both have Weber fractions expressing the ability to discriminate velocity similar to, or possibly smaller than, a low contrast luminance grating. However, when the task is one of direction discrimination, chromatic gratings and beats behave quite differently as stimulus contrast increases (Cropper & Derrington, 1990, 1993a). If the system is using the same signal to simultaneously extract the speed and direction of motion of the stimulus, then we would not necessarily expect different effects of contrast on the tasks of direction and speed discrimination (see Discussion). The work described in this paper measures the ability to discriminate the speed of different stimuli once the direction of motion of that pattern can easily be identified. The intention is to take stimuli for which we have some clear psychophysically measured differences when we are required to discriminate their direction of motion, and to investigate whether these differences remain between the stimuli when we are required to discriminate their speed. The results will assess the validity of the assumption that the characteristics of speed discrimination in a given stimulus reflect the characteristics of direction discrimination in the same stimulus. In addition to, and perhaps more importantly than this, they will also give a clearer idea of the relationship between the measures of direction and speed and how the motion system might extract them from the image. MEmODS Stimuli and equipment
The stimuli in this work were produced in exactly the same way as described in the previous paper (Cropper & Derrington, 1993a). Because the method of stimulus generation is essential to the basic argument of the paper, the details will be repeated here for clarity. The stimuli were made by adding one or more horizontal sinusoidal gratings, produced by the method of Schade (1956) using a one-dimensional display controller (Camb~dge Research Systems VSGZ/l) with 14”bit digital-to-analogue converters (DACs), and
VELOCITY DISCRIMINATION
43
grating are the mean of the spatial and temporal frequencies of the component gratings: (fi +fi)/:! and (CO,+ oZ)/2. The cosinusoidal term in equation (6) 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” L(y)=L,,(l+E(G,+G,)) (1) (Badcock & Derrington, 1985) is actually twice the where f,(y) is the luminance in cd/m2 at position y. L,,, spatial frequency of the ~osinusoidal envelope. This gives is the mean luminance of the display (44.2 cd/m2). E is the beat spatial and temporal frequencies which are the temporal envelope, which was either a raised cosine equal to the difference between the spatial and temporal function of time (I): frequencies of each component: (fi -fi) and (0, - 02). Thus, if we set the temporal frequency of the two E(t) = 0*5(cos 2Jret + 1) (2) components to be equal and opposite (0, = --ma) this - $Z< t < 4, and zero at other times where E is the makes the beat move and the carrier remain stationary. temporal frequency (Hz) of the envelope; or in the case The contrast (C ) of the stimuli was expressed as a of flickered stimuli, the envelope formed a cosine func- three-dimensional vector describing a deviation from the tion of time (t): display’s mean luminance and chromaticity using the E(t) = cos 27~. (3) coordinate system of Derrington, Krauskopf and Lennie (1984). The whitepoint was chosen by setting each gun In some cases the stimuli were both flickered and to half its maximum luminance and then altering the presented within a raised cosine temporal envelope. In blue and red guns to produce a satisfactory white this situation, for example when measuring the detection appearance. The proportional contribution of each gun threshold for stimuli flickered at a given temporal fre- to the whitepoint was 0.206 red, 0.678 green and 0.116 quency: blue. Movement along the achromatic (R + G + BE(t) = equation(2) x equation(3). (4) “equal-energy”) axis of the space was attained simply by a proportional linear increase in the output of each gun. G, and G2 (generally termed G,,) are sinusoidal gratings, This maintained the hue whilst increasing the luminance, each of which can be described over space (y) and in and describes a “luminance” stimulus in this work. time (t) as: Movement in the equiluminant plane of the colour space G,=C;sin2?r(f,y+o,t). (5) was achieved by keeping the total output from the guns constant but changing the relative luminance produced C,, is the contrast of grating n, expressed as a threedimensional vector which specifies the chromatic and by each gun. This has the effect of changing the hue but maintaining the luminance. Movement along the luminance properties of the waveform. fn is the spatial frequency (c/deg), o, is the temporal drift-rate (Hz), and red-green (R-G) axis, which approximates to the “con(b is the spatial phase angle. As most stimuli were stant blue” axis* of Derrington et al. (1984) was attained by modulating the red and green guns with equal drifting, and the starting spatial phase of the waveform and opposite signals. Subjective differences in the equiluwas randomized, the spatial phase angle is omitted from minant plane were corrected using heterochromatic subsequent equations. For the simple grating stimuli, the contrast C, was set flicker photometry. To equate the units along each axis of colour space, to zero; For the beat stimuli, formed by adding two the lookup tables linearizing the voltage-luminance regratings together of different spatial frequency (Badcock lationship for each gun (gamma-correcting) were con& Derrington, 1985), C, was set to be equal to Cl. In the case of beat stimuli, equation (1) can be structed so that movement of one table-place created the same increment in luminance on the monitor screen, rewritten: whichever table was used. Because each gun has a UY)=L,,I~ +EW[ginWf,+f,lyP different luminance range, each table was of a different length. The most effective phosphor is the green, the +&I + @-0/2) cos 27w -s,lYP lookup table for which was chosen to be 4096 places +fQ4 - ~2WNl). (6) long. The lengths of the lookup tables for the other two Equation (6) shows the spatiotemporal properties of the guns was scaled to this according to their relative pattern in terms of the sinusoidal carrier grating and the luminance ranges (or efficiencies). This meant the red cosinusoidal envelope (Badcock & Derrington, 1985). gun lookup table was about 1300 places long and the blue gun table was about 800 places long. The exact The spatial and temporal frequencies of the carrier length of these two tables changed very slightly each time the equipment was recalibrated. This was per*There is a minor deviation from a true “constant blue” axis: moveformed at regular intervals using a United Detector ment along this, the red-green axis, modulated the output of the blue cones by about 10% of the modulation of the output of the Technology Photometer 61 with a photometric filter and red and green cones. lumilens. displayed on a Barco CDCT6551 colour monitor running at 120 Hz frame rate and 75 kHz line rate. The mean l~inan~ was 44.2 cd/m2 (CIE coordinates: x = 0.333, y = 0.477) and neither the mean luminance nor the mean chromati~ty of the display was altered by presentation of the stimuli. All stimuli can be described generally as:
44
Psychophysical
SIMON J. CROPPER
methods
The contrasts of all stimuli for the speed-digrimination task were normalized to the detection threshold for that stimulus, measured under the same conditions used for the speed-discrimination task. These detection thresholds were measured using a modified PEST staircase procedure (Findlay, 1978) which varied the stimulus contrast according to the observers’ response in a temporal two-alternative forced-choice (2AFC) detection task. The stimuli were presented for a duration of 0.48 set (half the width of the raised-cosine temporal envelope) which is the same duration as subsequently used in the speed-discrimination task. When suitable, the stimuli were also flickered cosinusoidally at a temporal frequency which was equivalent to base velocity used in the speed-discrimination task. Heterochromatic flicker photometry was used to measure subjective points of minimal luminance in all chromatic stimuli prior to any measurement. The grating in question was Aickered at 5 Hz and presented at a high contrast approx. 40 times detection threshold to maximize any luminance artifact. The observer adjusted the polarity and amplitude of the luminance component in the chromatic grating until perceived flicker was minimal, at which point we assumed any luminance artifact was cancelled out by the luminance grating. The mean of 10 of these estimates was used for each chromatic stimulus condition. The minimum detectable increment in stimulus speed was measured using a temporal 2AFC speed discrimination task. The observers were presented with two intervals: in one interval, chosen at random, the stimulus was moving upward at a given (base) speed; in the other interval the stimulus also moved upwards but its speed was the base-speed with some known increment added. The observer had to say in which interval the stimulus moved faster. In this way the ~nimum detectable speed increment was measured for each stimulus under each condition. It was established prior to any speed discrimination task that the direction of motion of the stimulus was clearly discriminable (see Cropper & Derrington, 1993a) and the spatiotemporal parameters were chosen so that the stimuli were within the range of optimum performance in the task of velocity discrimination previously measured for luminance stimuli (McKee, Sivlerman & Nakayama, 1986). The stimuli were shown at base (or reference) velocities between 0.25 and 4deg/sec. The velocity increment added to these base velocities was increased in steps of 0.1 deg/sec. A maximum increment of 0.9 deg/sec was used as, in a preliminary experiment, greater increments were found to provide a spurious cue in the task by making the faster moving stimulus to appear to be at a lower contrast. The stimuli were presented for a duration of 0.48 set (half-width of the raised-cosine), and at low contrasts (detection threshold plus 0.5 log units), and high contrasts (detection threshold plus 1.5 log units), or at values between these two extremes. The three patterns were a luminance grating and an equiluminant red-green
grating, both with a spatial frequency of 1 c/deg, and a luminance beat of 1 c/deg with a 5 c/deg carrier (termed 1: 5 in the results). The spatial frequency of 1 c/deg made temporal frequency and velocity numerically equivalent throughout. All were presented at the same viewing distance of 1.25 m. The observers were the author and two naive observers. Normalization
of contrast
Contrasts for the speed-discrimination task were normalized to the detection threshold which was measured for each stimulus using the method described above. This is a standard method of normalization that was used in the work measuring the ability to discriminate the direction of motion of the different stimuli described here (Cropper & Derrington, 1993a, b) and ensures that we are using the same stimulus conditions for each task (speed discrimination and direction discrimination), in addition to facilitating comparisons across stimuli. Because there is no single, systemindependent numerical definition of contrast which can be applied to chromatic and luminance stimuli, it is both convenient and useful to choose a measure of contrast which is an indication of the individual sensitivity to each stimulus; an example of which is the contrast required to detect each stimulus. This definition has the advantage of providing a functional measure of stimulus strength and, at least to a fu-st approximation up to moderate contrasts, equating signal strengths within the system across stimuli. The work presented in this paper is concerned with the extraction of a velocity signal from stimuli coded by a modulation in luminance, colour or luminance contrast, and how this reflects upon the extraction of a signal simply indicating the direction of motion of the stimulus. In light of the recent work discussed in the Introduction (Cavanagh et al., 1984; Cavanagh & Anstis, 1991; Smith & Edgar, 1991; Cropper & Derrington, 1993a, b), if the direction and speed of a stimulus are coded in separate signals within the system then it is possible that we might see different effects of contrast on the psychophysical measures of direction discrimination and speed discrimination. If, however, the output from a single velocitysensitive mechanism were used to perform both these tasks, we would expect substantially similar effects of contrast on each psychophysical measure. Because this study is one of the effects of input signal strength on two different psychophysical tasks it is most suitable that the same contrast level be used for the two tasks (direction and speed discri~nation) and that the contrast of each stimulus type be normalized to a common measure independent of either the ability to discriminate the direction or the speed of a stimulus: the detection threshold. RESULTS Figure l(a, b) plots the Weber fraction (minimum detectable increment/base speed) against the base speed for each stimulus for two observers (SJC and CL). The
45
VELOCITY DISCRIMINATION
(4
Observer SJC
(b)
Cl Lum +0.5 0 RG +O.S A Beat +0.5 0 RG +1.5 A Beat +1.5
2.0 1.8 1.6
-0.6
Observer CL cl Lum +0.5 0 RG +0.5 A Beat +0.5 n Lum +1.5 0 RG +1.5 A Beat +1.5
2.0 1.8 1.6
0.6 0.4 0.2 0.0 Base speed (deg/aec)
Base spaed (deg/=c)
FIGURE 1. (a) Speed discrimination function for observer SJC. The Weber fraction is plotted against the base speed of the stimulus, expressed in deg/sec. Gpen symbols represent stimuli presented at a low contrast of 0.5 log units above their detection threshold, solid symbols represent the same stimuli at 1.5 log units above their detection threshold. The different stimuli are indicated in the key, the spatial frequency of each was 1 c/deg and the stimuli were presented for 0.48 set (half the width of the raised-cosine temporal envelope). All stimuli were tested at all base speeds and the absence of a symbol indicates that a Weber fraction was not measurable at that base speed: the arrows indicate the fraction was off the scale (see text). Error bars indicate the standard deviation estimated by the function fitting routine. (b) As (a) but for another observer, CL.
minimum detectable increment in speed was taken as the point on the psychometric function plotting the performance against the increment when the observer was correct 75% of the time in the speed-discrimination task described above. This threshold was calculated from the psychometric function using the method of Foster and Bischof (1991) adapted for the 2AFC discrimination procedure. The absence of a data point in these figures indicates that the observer never reached a performance of 75% correct in the task and no threshold increment was measurable in the range studied (0.1-0.9 deg/sec increment), i.e. speed discrimination was very poor under the given conditions. The stimulus referred to by each function is indicated in the key to each graph. Open symbols indicate stimuli presented at a low contrast of 0.5 log units above their detection threshold, solid symbols represent stimuli at a contrast of 1.5 log units above detection threshold. Error bars indicate the standard deviation of the threshold estimate from the curve fitting procedure. At low base speeds, the Weber fraction for all stimuli is high, indicating that performance is poor. As the base speed increases, performance improves and the curves flatten off; this is most obvious for the luminance grating. These functions show the lower portion of the classic U-shaped speed discrimination function, which as
McKee et al. (1986) note, shifts to the left at the low temporal frequencies used in this study. When comparing the stimuli presented at low contrasts (open symbols), the chromatic grating and beat stimuli show much higher Weber fractions at a given base speed than the “equivalent” luminance grating. There is no detectable increment at the lowest (and highest) base speeds for either the chromatic grating or the beat: observer CL shows particularly poor performance for the chromatic grating. This is the kind of difference between these three stimuli that we have shown for tasks of direction discrimination (Cropper & Derrington, 1990, 1993a). When the contrast of the stimulus is increased (solid symbols on the plot) the ability to discriminate speed in the chromatic and beat stimuli improves dramatically. Performance is now very similar to that for a low contrast luminance grating for both observers, with perhaps the exception of CL at a base speed of 0.75 deg/sec for the chromatic grating. This performance is however still much better than the low contrast condition when a threshold increment was not measurable. The principal point here is that although we might expect increased contrast to improve performance in chromatic speed discrimination because of the previous
46
SIMON J. CROPPER
direction disc~mination results where the lower threshold of motion (LTM) decreased with increasing stimulus contrast (Cropper & Derrington, 1993a), we would not expect this to be the case for beat stimuli because increasing stimulus contrast by an equivalent amount had little effect on the LTM measured in a direction-discrimination task for beat patterns (Cropper & Derrington, 1993a). Figure l(a, b) shows an equivalent improvement in performance for both chromatic and beat stimuli as contrast increases and therefore do not meet the expectations. Contrast has previously been shown to have little effect on performance in tasks of speed discrimination using luminance stimuli (McKee et al., 1986; Panish, 1988) as long as the presentation is sequential (Stone & Thompson, 1992), so only one observer (CL) was tested with the high contrast luminance condition. The low and high contrast functions for the luminance gratings (open and solid squares) are indeed very similar for CL which is in agreement with the previous work. We have already suggested that chromatic and beat stimuli may not be processed by the same system to mediate direction discrimination at high stimulus contrasts (Cropper & Derrington, 1993a, b): are they, however, processed by a similar system to mediate speed discrimination? Figure l(a, b) shows that the ability to discriminate speed in both chromatic gratings and beats is sensitive to stimulus contrast and suggests that a similar system may be underlying the ability to perform the task. The second experiment looks more closely at the effect of contrast on the Weber fraction for each stimulus by repeating the first experiment at different stimulus contrasts for a single base speed condition. The methods were exactly the same as in the first experiment. Figure 2(a, b) plots the Weber fraction as a function of stimulus contrast, expressed in log units above the detection threshold for that stimulus flickered at 2 Hz. The duration of presentation was 0.48 set again and the base speed chosen was 2 degjsec, within the flat portion of the curves in Fig. 1. Each figure represents the data for one observer (SJC or ME) and the two stimuli are represented by different symbols as denoted in the figure key. The horizontal line on the figure indicates the Weber fraction for a luminance grating (measured at 0.5 log units above detection threshold) which is relatively independent of contrast [McKee et al., 1986; Panish, 1988; Fig. l(b)]. Both figures show that as stimulus contrast increases, performance improves and the Weber fraction drops at an approximately equivalent rate for both stimuli. The curves begin to flatten off between 0.9 and 1.1 log units above detection threshold and at the highest contrasts, absolute performance for the chromatic and beat stimuli is very similar to that measured for low contrast luminance stimuli. DISCUSSION The results presented here measure the ability to discriminate speed in different stimuli once the direction of motion is clearly visible. These speed-discrimination
(a)
Observer SJC 0.8
l RG grating A Beat _.. ___ Lum grating
0.6
0.0
m 0.5
0.7
0.9
1.1
1.3
1.5
Contrast ahove threshold
lb)
Observer ME 0.8
l RGgrating A Beat ..___Lum grating
0.6 8 ‘G E
@I 0.4 $ P
0.2
0.0
._...._____......__-------.
I 1
I
’
I
I
0.5
0.7
0.9
8
I
1.3
1.5
,
1.1
!
Contrast above threshold FIGURE 2. (a) Plot of the Weber fraction as a function of stimulus contrast, expressed in log units above detection threshold. The base speed was 2 deg/sec, stimuli are indicated in the key and the observer was SJC. The horizontal line is the Weber fraction measured for a luminance grating at 0.5 log units above threshold. (b) As (a) except for observer ME.
results show the same difference in the processing of low contrast stimuli that were obtained in tasks of direction discrimination (Cropper & Derrington, 1993a): performance for the chromatic and beat stimuli is much worse than for the luminance grating. As contrast is increased however, speed-discrimination performance for both the
VELOCITY DISCRIMINATION
chromatic grating and the beat improves sibilantly, unlike the direction ~sc~~nation results where only performance for the chromatic grating improved to such an extent (Cropper & Derrington, 1993a). There are two aspects of these results which we must consider. Firstly, it seems that the psychophysically measured characteristics of the ability to discriminate speed in a beat (second-order) stimulus do not directly reflect the characteristics of the ability to discriminate the direction of motion in the same stimulus. Secondly, the effect of contrast is to improve performance in both speed- and dir~tion-di~~~nation tasks in chromatic stimuli, but to have no effect on performance in the same tasks for luminance stimuli. Each of these will be considered in turn.
47
extracted by different mechanisms, or available at different stages within the same mechanism. This provides a problem for models of motion perception which propose that a composite velocity signal is extracted from some second-order stimuli (e.g. Johnston et al., 1992). Speed discrimination in chromatic and luminance stimuli
The Weber fraction functions for the luminance grating and high contrast chromatic grating show very similar properties and form part of the classic U-shaped curve. The similarity between these two stimuli is in agreement with results seen for direction disc~mination tasks (Cropper & Derrington, 1993a) and suggests that similar types of system may be used in the tasks of direction and speed discrimination for these two stimuli. The modification in the ratio model of velocity coding Speed discrimination in beat stimuli (Thompson, 1984) suggested by Cavanagh and Anstis (1991) to explain the slower perceived speed of chroThe high contrast beat pattern shows a significant matic stimuli predicts results similar to those presented decrease in velocity discrimination thresholds with inhere. The fact that chromatic stimuli never elicit smaller creased contrast, an effect not seen when measuring detectable velocity increments than luminance. stimuli the lower threshold of motion (LTM) (Cropper & Derrington, 1993a) over the same contrast range. This is may be explained by a lower limit in the sensitivity of the in conflict with the results expected on the basis of the system having already been reached (for luminance ability to di~~minate the direction of motion of beat stimuli). These results, however, can also be seen to support the stimuli, which indicated that there should be little effect of contrast on speed discrimination. The results do, use of a composite velocity signal to detect motion in the however, meet the prediction made on the basis of the first-order chromatic and luminance stimuli. Contrast results of Smith and Edgar (1991) which suggested that has been shown to have a strong effect on the ability to there should not necessarily be any deficiency in the discriminate both the direction (Cropper & Derrington, velocity coding of high-contrast second-order stimuli 1993a) and speed of motion of a first-order chromatic and therefore it was necessary that performance in the stimulus, and to have virtually no effect on the same velocity discrimination task improved with increasing measures of performance in first-order luminance stimcontrast since it was very poor at low contrasts. uli. This is consistent with a mechanism signalling the We would not expect a situation where contrast has velocity of a stimulus in a composite signal, the magnilittle effect on the lower threshold of motion (LTM) but tude of which is dependent upon stimulus contrast for a strong effect on velocity ~s~~~nation. A velocitychromatic stimuli only (Cropper & Derrington, 1993a). tuned mechanism which is also partially sensitive to Thus we would expect perceived speed in chromatic contrast will change the magnitude of its output with gratings to be strongly contrast dependent, and contrast contrast and we would expect this to affect the perceived independent in luminance gratings. Although the conspeed signalled by that mechanism. However, the effect trast dependence of the perceived speed of chromatic of contrast on this output would have to be much greater gratings has not been fully assessed, Mullen and Boulton to change the sign of the signal and therefore the (1992) have recently shown that the ability to make an perceived direction of motion. This results in a contrast accurate velocity match between luminance and chrodependent perceived speed but not perceived direction matic stimuli is strongly contrast dependent. and this has been observed under some conditions In addition to this, although the perceived speed of in luminance stimuli ~ompson, 1982; Stone & luminance gratings does seem to be contrast dependent Thompson, 1992). Despite this, we would expect some under some stimulus conditions (Thomp~n, 1982; Stone effect of contrast on the minimum detectable velocity & Thompson, 1992), this seems very dependent upon the (LTM) signalled by such a system because it is likely that measurement paradigm involved. This could simply be a this particular psychophysical measure is dependent reflection of a largely contrast independent velocity upon reaching some criterion signal to noise ratio in signal for luminance stimuli whose magnitude fluctuates the output; once this criterion level has been reached, the with contrast over short periods of time only and that task of direction discrimination which only requires the fluctuation can only be identified when two stimuli of sign of the signal to be extracted, can be performed different contrasts are presented simultaneously (Stone regardless of the magnitude of the output from the & Thompson, 1992). system. Changing the signal magnitude will have a much The ratio model of Thompson (1982) was proposed to stronger effect near this criterion level, and therefore explain the apparent contrast independence of the peraffect the LTM if there is an effect on the perceived speed ceived speed of luminance stimuli. Although the prosignalled by the same mechanism. Thus it seems that the posal by Cavanagh and Anstis (1991) does explain the speed and direction of motion of a beat stimulus may be slower perceived speed of chromatic motion, there is
48
SIMON J. CROPPER
evidence to suggest that the perceived speed of chromatic stimuli is contrast dependent (Mullen & Boulton, 1992). We must consider the Iikelihood of the existence of a ratio modet of velocity coding for chromatic stimulus when it fails in its prime objective: to dissociate contrast and velocity. A full study of the perceived speed of chromatic stimuli is currently underway to look in more detail at this question.
Derrington, A. M. & Henning, G. 8. (1993). Dir~t~on-of-motion discrimjnatjon and detection of huninance and colour gratings, Vision Research, 33, 799-812. Derrington, A. M., Krauskopf, J, & Lennie, P. (1984). Chromatic mechanisms in Lateral genicuiate nucleus of macaque. Journal oj Physiology, 357, 241-265. Findlay, J. M. (1978). Estimates on probability functions: A more virulent PEST. Perception & Psychophysics, 23, 181-185. Foster, D. H. & Bischof, W. F. (1991). Thresholds from psychometric functions: Superiority of bootstrap to incremental and probit variance estimators. Psyc~a~o~~~aiBulfetin, 109, 152-t 59. Heeger, 13. J. (1987). Model for the extraction of image Bow. Journal
CONCLUSIONS
Johnston, A., Moan, P. M. & Buxton, H. (1992). A computational model of the analysis of some first-order and second-order motion patterns by simple and complex cells. Proceedings of the Roya Society of London B, 25U, 297-306. Julesz, B. (i971). Fo~~datjons of cyclopean perceptiu~. Chicago, Ill.: University of Chicago Press. Lindsey, D. T. & Teller, D. Y. (1990). Motion at isoluminance: Discrimination/detection ratios for moving isoluminant gratings.
of ihe Optieai Society of America A, 4, 1455-1471.
The aim of this study was to investigate whether a group of &early defined differences in the characteristics of the ability to disseminate the direction of motion of luminance, chromatic and beat stimuh, heid for the associated task of speed discrimination under the same stimulus conditions. The results presented here indicate that this is not always the case and imply that speed disc~mination is mediated by an additional mechanism to that which mediates direction discrimination in beat stimuli.
Adelson, E. H. & Bergen, J. R. (1985). Spatiotemporal energy models for the perception of motion. Journal of the Optical Society of America A, 2, 284-299.
Badcock, D. R. & Derrington, A. M. (1985). Detecting the displacement of periodic patterns. Vision Research, 25, 1253-1258. Boulton, J. C. (f987). Two rn~h~rns for the detection of slow motion. 3our~I of& OpticaI Socieiy of America A, 4, 1634-1642. Braddick, 0. J. (1980). Low-level and high-level processes in apparent motion. Philosaph~~al ~r~s~r~pts of the Royal Society qf London, 290, 137-151. Cavanagh, P. & An&is, S. M. (i99i). The contributions of colour to motion in normal and colour-deficient observers. Vision Research, 31, 2109-2148. Cavanagh, P. & Mather, G. (1989). Motion: The long and short of it. Spatial Vision, 4, 103-129. Cavanagh, P., Tyler, C. W. & Favreau, 0. E. (1984). Perceived velocity of moving chromatic gratings. 3ournai of the Optical Society of America A, I, 893-899.
Cropper, S. J. & Derrington, A. M. (1990). The effects of contrast and duration on the divination of motion in beats and chromatic gratings. Percept@ 19, A31. Cropper, S. J. & Derrington, A. M. (1993a). Motion of chromatic stimuli: First-order or second-order? Vision Research, 34, 49-58. Cropper, S. J. Br Derrington, A. M. (I993b). Motion of chromatic and luminance beats, Vision Research. Submitted.
Vision Research, 30, 175 1-I 762. McKee, S. P. (1981). A local mechanism for differential velocity detection. Vision Research, 21, 491-500. McKee, S. P. & Nakayama, K. (1984). The detection of motion in the
peripheral visual field. Vision Research, 24, 2532. McKee, S. P., Silverman, G. H. & Nakayama, K. (1986). Precise velocity di~~rn~~tion despite random vacations in temporal frequency and contrast. Vision Research, 26, 609419. Mullen, K. T. & Boulton, J. C. (1992). Absence of smooth motion perception in colour vision. Vision Research, 32, 483-488. Panish, S. C. (1988). Vefocity di~~~natjon at constant multiples of detection threshold. Vision Research, 28, 193-201. Schade, 0. H. (1956). Optical and photoelectric analogue of the eye. Journal of the Optical Society qf America A, 46, 721-739.
Smith, A. T. & Edgar, G. K. (1991). Perceived speed and direction of complex gratings and plaids. Journal of the Optical Society of America A, 8, 1161-1171.
Stone, L. S. 6t Thompson, P. (1992). Human speed perception is contrast dependent. Vision Research, 32, 1535-1549. Thompson, P. G. (1982). Perceived rate of movement depends on contrast. Vision Research, 22, 377-380. Thompson, P. G. (1984). The coding of velocity of movement in the human visual system. Vision Research, 24, 41-45. Watson, A. B. & Ahumada, A. J. (1985). Model of human visualmotion sensing. Journaf ej’ the Opticai Society uf America A, 2 3222341.
Acknowledgements-This
work was financially supported by the Science and Engineering Research Council grant No. GRG 07980 to Andrew M. Derrington whilst the author was supported by a SERC Image Interpretation Initiative research studentship, and also Australian Research Council grant No, A79030414. I wish to thank David Badcock and Jim May for critical reading of the unapt, Michael Cox for the fusion-~ttjng routine and Andy Smith for helpful and constructive comments.
Copyright
0
0042-6989/94 $6.00 + 0.00 1993 Pergamon Press Ltd
Velocity Discrimination in Chromatic Gratings and Beats* SIMON J. CROPPER? $ Received 21 December 1992; in revised form 26 May 1993
It is commonly assumed that the ability to discriminate velocity in a stimulus directly reflects the properties of the underlying directionally-selective mechanism. The results presented here show that this assumption is not always correct. Speed discrimination tasks over a range of base velocities were carried out for luminance gratings, chromatic gratings and contrast (beat) gratings of equivalent periodicity and contrasts. At low contrasts (0.5 log units above detection threshold), speed discrimination in luminance gratings was at least twice as good (when expressed as a Weber fraction), than in either chromatic gratings or beats. This is similar to the situation seen for tasks of direction discrimination using these sthnuli [e.g. Cropper and Derrington (1990) Perception, 19, A31]. When the stimulus contrasts were increased to 1.5 log tits above detection threshold, the ability to discriminate speed in both chromatic and beat stimuli improved to a performance level comparable to that shown for luminance gratings at all contrasts. ‘Ihis effect is not seen for tasks of direction discrimination when the same increase in sthnulus contrast has little effect on the lower threshold of motion (LTM) measured for beat patterns. These results indicate that the ability to discriminate velocity in a stimulus does not necessarily directly reflect the characteristics discriminate the direction of motion of that stimulus. Motion
Velocity
discrimination
Second
order
Spatial
INTRODUCTION
beats
of the ability to
Colour
lying motion-detection mechanisms the output of a motion detector is treated not only as left-right binary information but as a quantity, the magnitude of which indicates stimulus speed, and the sign its direction of motion. To extract this velocity information the system may need to compare the outputs of several directionally selective detectors (Adelson & Bergen, 1985) or to “frequency count” (Watson & Ahumada, 1985) to dissociate the effects of changing the stimulus contrast from the effects of changing the stimulus velocity. The ability to signal velocity (i.e. direction and speed of motion) has been incorporated into some popular models of motion detection (e.g. Watson & Ahumada, 1985; Adelson & Bergen, 1985; Heeger, 1987; Johnston et al., 1992) and has also been described separately, as an independent extension to directional motion detection. One such model of velocity coding in the visual system is the ratio model of Thompson (1982, 1984). In this model the speed is extracted from two overlapping, bandpass temporal filters tuned to the same direction of motion but different temporal frequency bands. The ratio of their outputs signals the contrast independent temporal frequency of the stimulus, which when correlated with the spatial sensitivity of the system can be used to give a velocity signal; the direction of motion having been previously extracted by some directionally-selective mechanism. It has been shown that we are not only very good discriminating the direction of motion of a stimulus (e.g. Braddick, 1980; Boulton, 1987) but also its speed
to discriminate the direction of motion of a stimulus and the subsequent ability to identify its speed are likely to involve common mechanisms for much of the processing involved in either task. It is feasible that both the direction of motion and the speed of a stimulus, together termed the velocity, is available to the system from the same directionally selective mechanism (e.g. Watson & Ahumada, 1985; Johnston, McOwan & Buxton, 1992). A common assumption arising from this is that the psychophysically measured characteristics of the ability to identify the velocity of a stimulus directly reflect the characteristics of the directionally-selective mechanism mediating direction discrimination in that stimulus. The results presented here indicate that this is not always the case and provide evidence for the partially separate processing of direction and speed information in some patterns. Because the ability to identify the speed of a stimulus is often assumed to reflect the properties of the underThe ability
*This work was initially presented at the Association for Research in Vision and Ophthalmology annual conference held in Sarasota, Fla in May 1992. It also forms part of a Ph.D. thesis submitted to the University of Newcastle upon Tyne, England. TDepartment of Physiological Sciences, The Medical School, Newcastle upon Tyne, NE2 4HH, England. $Present address: Department of Ophthalmology, McGill Vision Research Centre, 687 Pine Avenue West, H4-14, Montreal, Quebec, Canada H3A 1Al. 41
42
SIMONJ. CROPPER
(McKee, 1981; McKee & Nakayama, 1984), at least if the stimulus is coded by luminance. When the stimulus is coded by some attribute other than luminance however, the story becomes less clear. The purpose of this paper is to study the ability to discriminate speed in patterns which are not coded by luminance but coded by modulations of either colour or contrast, which have first-order and second-order spatial properties respectively (Julesz, 1971; Cavanagh & Mather, 1989). These stimuli show different psychophysically measured properties when we are required to detect them or to discriminate their direction of motion (Cropper & Derrington, 1990, 1993a, b), which makes them potentially very useful when studying the processes involved in the extraction of their velocity. It is a common, if often subjective, observation that the perceived speed of chromatic gratings is less than that of luminance gratings of the same actual speed (Cavanagh, Tyler & Favreau, 1984; Mullen & Boulton, 1992), which indicates that there is a deficiency at some point in the coding of the velocity of chromatic stimuli. Cavanagh and Anstis (1991) suggest that this is due to a difference in the chromatic-contrast sensitivity of the two units, the ratio of whose outputs signals the velocity (Thompson, 1984). Partial support for this theory has been gained by the observation that under certain conditions, the contrast required to discriminate the direction of motion of a chromatic stimulus is greater than that required to detect the presence of the same stimulus (Cavanagh & Anstis, 1991; Derrington & Henning, 1993; Lindsey & Teller, 1990). This indicates that the directionally selective mechanism dealing with the discrimination of chromatic motion is less sensitive than a non-dir~tionally-selective mechanism dealing with simple detection of the presence of the stimulus. If this non-dire~tionaily selective mechanism replaced the temporal filter tuned to lower frequencies in the ratio model, then we could explain the observed slowing of chromatic stimuli since the denominator in the ratio calculation will be consistently larger for the same signal strength (Cavanagh & Anstis, 1991), and therefore produce a smaller output overall. Psychophysically, we would expect this slowing to shift the velocity increment discrimination function measured for chromatic stimuli toward that expected for lower base velocities than actually used. This kind of consistent shortfall in the estimation of the velocity should not, however, make the minimum detectable velocity increment larger. In some circumstances it should even make the minimum detectable increment smaller in chromatic gratings when compared with luminance gratings: if the detectible increment is an approximately linear function of base velocity (McKee, 198l), then within this range the lower perceived velocity of the chromatic grating will have a smaller velocity increment detection threshold than a luminance grating moving at the same actual speed. The perceived speed of rigidly moving amplitude modulated (AM) luminance gratings has been shown to be similar to, or slightly less than, that of luminance gratings of the same spatial frequency as the amplitude
modulation, over a range of l-5.5 deg/sec (Smith & Edgar, 1991). These patterns contain both first- and second-order motion signals, each making different predictions about the perceived speed of the moving pattern (Smith & Edgar, 1991). The measured perceived speed of the complex pattern is that which would be predicted by the second-order (contrast) cue and not the first-order ~luminan~) cue. These results suggest that the perceived speed of moving second-order signals is similar to a moving first-order signal of the same spatial frequency, and as such shows a difference in the velocity coding of the second-order (contrast) signal and a first-order chromatic signal, the perceived speed of which is significantly less than a first-order luminance signal Both the above estimates of subjective speed in complex luminance and simple chromatic gratings used relatively high contrast stimuli (in excess of 10 times detection threshold). Thus, from these observations, we should expect high contrast chromatic and second-order stimuli to both have Weber fractions expressing the ability to discriminate velocity similar to, or possibly smaller than, a low contrast luminance grating. However, when the task is one of direction discrimination, chromatic gratings and beats behave quite differently as stimulus contrast increases (Cropper & Derrington, 1990, 1993a). If the system is using the same signal to simultaneously extract the speed and direction of motion of the stimulus, then we would not necessarily expect different effects of contrast on the tasks of direction and speed discrimination (see Discussion). The work described in this paper measures the ability to discriminate the speed of different stimuli once the direction of motion of that pattern can easily be identified. The intention is to take stimuli for which we have some clear psychophysically measured differences when we are required to discriminate their direction of motion, and to investigate whether these differences remain between the stimuli when we are required to discriminate their speed. The results will assess the validity of the assumption that the characteristics of speed discrimination in a given stimulus reflect the characteristics of direction discrimination in the same stimulus. In addition to, and perhaps more importantly than this, they will also give a clearer idea of the relationship between the measures of direction and speed and how the motion system might extract them from the image. MEmODS Stimuli and equipment
The stimuli in this work were produced in exactly the same way as described in the previous paper (Cropper & Derrington, 1993a). Because the method of stimulus generation is essential to the basic argument of the paper, the details will be repeated here for clarity. The stimuli were made by adding one or more horizontal sinusoidal gratings, produced by the method of Schade (1956) using a one-dimensional display controller (Camb~dge Research Systems VSGZ/l) with 14”bit digital-to-analogue converters (DACs), and
VELOCITY DISCRIMINATION
43
grating are the mean of the spatial and temporal frequencies of the component gratings: (fi +fi)/:! and (CO,+ oZ)/2. The cosinusoidal term in equation (6) 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” L(y)=L,,(l+E(G,+G,)) (1) (Badcock & Derrington, 1985) is actually twice the where f,(y) is the luminance in cd/m2 at position y. L,,, spatial frequency of the ~osinusoidal envelope. This gives is the mean luminance of the display (44.2 cd/m2). E is the beat spatial and temporal frequencies which are the temporal envelope, which was either a raised cosine equal to the difference between the spatial and temporal function of time (I): frequencies of each component: (fi -fi) and (0, - 02). Thus, if we set the temporal frequency of the two E(t) = 0*5(cos 2Jret + 1) (2) components to be equal and opposite (0, = --ma) this - $Z< t < 4, and zero at other times where E is the makes the beat move and the carrier remain stationary. temporal frequency (Hz) of the envelope; or in the case The contrast (C ) of the stimuli was expressed as a of flickered stimuli, the envelope formed a cosine func- three-dimensional vector describing a deviation from the tion of time (t): display’s mean luminance and chromaticity using the E(t) = cos 27~. (3) coordinate system of Derrington, Krauskopf and Lennie (1984). The whitepoint was chosen by setting each gun In some cases the stimuli were both flickered and to half its maximum luminance and then altering the presented within a raised cosine temporal envelope. In blue and red guns to produce a satisfactory white this situation, for example when measuring the detection appearance. The proportional contribution of each gun threshold for stimuli flickered at a given temporal fre- to the whitepoint was 0.206 red, 0.678 green and 0.116 quency: blue. Movement along the achromatic (R + G + BE(t) = equation(2) x equation(3). (4) “equal-energy”) axis of the space was attained simply by a proportional linear increase in the output of each gun. G, and G2 (generally termed G,,) are sinusoidal gratings, This maintained the hue whilst increasing the luminance, each of which can be described over space (y) and in and describes a “luminance” stimulus in this work. time (t) as: Movement in the equiluminant plane of the colour space G,=C;sin2?r(f,y+o,t). (5) was achieved by keeping the total output from the guns constant but changing the relative luminance produced C,, is the contrast of grating n, expressed as a threedimensional vector which specifies the chromatic and by each gun. This has the effect of changing the hue but maintaining the luminance. Movement along the luminance properties of the waveform. fn is the spatial frequency (c/deg), o, is the temporal drift-rate (Hz), and red-green (R-G) axis, which approximates to the “con(b is the spatial phase angle. As most stimuli were stant blue” axis* of Derrington et al. (1984) was attained by modulating the red and green guns with equal drifting, and the starting spatial phase of the waveform and opposite signals. Subjective differences in the equiluwas randomized, the spatial phase angle is omitted from minant plane were corrected using heterochromatic subsequent equations. For the simple grating stimuli, the contrast C, was set flicker photometry. To equate the units along each axis of colour space, to zero; For the beat stimuli, formed by adding two the lookup tables linearizing the voltage-luminance regratings together of different spatial frequency (Badcock lationship for each gun (gamma-correcting) were con& Derrington, 1985), C, was set to be equal to Cl. In the case of beat stimuli, equation (1) can be structed so that movement of one table-place created the same increment in luminance on the monitor screen, rewritten: whichever table was used. Because each gun has a UY)=L,,I~ +EW[ginWf,+f,lyP different luminance range, each table was of a different length. The most effective phosphor is the green, the +&I + @-0/2) cos 27w -s,lYP lookup table for which was chosen to be 4096 places +fQ4 - ~2WNl). (6) long. The lengths of the lookup tables for the other two Equation (6) shows the spatiotemporal properties of the guns was scaled to this according to their relative pattern in terms of the sinusoidal carrier grating and the luminance ranges (or efficiencies). This meant the red cosinusoidal envelope (Badcock & Derrington, 1985). gun lookup table was about 1300 places long and the blue gun table was about 800 places long. The exact The spatial and temporal frequencies of the carrier length of these two tables changed very slightly each time the equipment was recalibrated. This was per*There is a minor deviation from a true “constant blue” axis: moveformed at regular intervals using a United Detector ment along this, the red-green axis, modulated the output of the blue cones by about 10% of the modulation of the output of the Technology Photometer 61 with a photometric filter and red and green cones. lumilens. displayed on a Barco CDCT6551 colour monitor running at 120 Hz frame rate and 75 kHz line rate. The mean l~inan~ was 44.2 cd/m2 (CIE coordinates: x = 0.333, y = 0.477) and neither the mean luminance nor the mean chromati~ty of the display was altered by presentation of the stimuli. All stimuli can be described generally as:
44
Psychophysical
SIMON J. CROPPER
methods
The contrasts of all stimuli for the speed-digrimination task were normalized to the detection threshold for that stimulus, measured under the same conditions used for the speed-discrimination task. These detection thresholds were measured using a modified PEST staircase procedure (Findlay, 1978) which varied the stimulus contrast according to the observers’ response in a temporal two-alternative forced-choice (2AFC) detection task. The stimuli were presented for a duration of 0.48 set (half the width of the raised-cosine temporal envelope) which is the same duration as subsequently used in the speed-discrimination task. When suitable, the stimuli were also flickered cosinusoidally at a temporal frequency which was equivalent to base velocity used in the speed-discrimination task. Heterochromatic flicker photometry was used to measure subjective points of minimal luminance in all chromatic stimuli prior to any measurement. The grating in question was Aickered at 5 Hz and presented at a high contrast approx. 40 times detection threshold to maximize any luminance artifact. The observer adjusted the polarity and amplitude of the luminance component in the chromatic grating until perceived flicker was minimal, at which point we assumed any luminance artifact was cancelled out by the luminance grating. The mean of 10 of these estimates was used for each chromatic stimulus condition. The minimum detectable increment in stimulus speed was measured using a temporal 2AFC speed discrimination task. The observers were presented with two intervals: in one interval, chosen at random, the stimulus was moving upward at a given (base) speed; in the other interval the stimulus also moved upwards but its speed was the base-speed with some known increment added. The observer had to say in which interval the stimulus moved faster. In this way the ~nimum detectable speed increment was measured for each stimulus under each condition. It was established prior to any speed discrimination task that the direction of motion of the stimulus was clearly discriminable (see Cropper & Derrington, 1993a) and the spatiotemporal parameters were chosen so that the stimuli were within the range of optimum performance in the task of velocity discrimination previously measured for luminance stimuli (McKee, Sivlerman & Nakayama, 1986). The stimuli were shown at base (or reference) velocities between 0.25 and 4deg/sec. The velocity increment added to these base velocities was increased in steps of 0.1 deg/sec. A maximum increment of 0.9 deg/sec was used as, in a preliminary experiment, greater increments were found to provide a spurious cue in the task by making the faster moving stimulus to appear to be at a lower contrast. The stimuli were presented for a duration of 0.48 set (half-width of the raised-cosine), and at low contrasts (detection threshold plus 0.5 log units), and high contrasts (detection threshold plus 1.5 log units), or at values between these two extremes. The three patterns were a luminance grating and an equiluminant red-green
grating, both with a spatial frequency of 1 c/deg, and a luminance beat of 1 c/deg with a 5 c/deg carrier (termed 1: 5 in the results). The spatial frequency of 1 c/deg made temporal frequency and velocity numerically equivalent throughout. All were presented at the same viewing distance of 1.25 m. The observers were the author and two naive observers. Normalization
of contrast
Contrasts for the speed-discrimination task were normalized to the detection threshold which was measured for each stimulus using the method described above. This is a standard method of normalization that was used in the work measuring the ability to discriminate the direction of motion of the different stimuli described here (Cropper & Derrington, 1993a, b) and ensures that we are using the same stimulus conditions for each task (speed discrimination and direction discrimination), in addition to facilitating comparisons across stimuli. Because there is no single, systemindependent numerical definition of contrast which can be applied to chromatic and luminance stimuli, it is both convenient and useful to choose a measure of contrast which is an indication of the individual sensitivity to each stimulus; an example of which is the contrast required to detect each stimulus. This definition has the advantage of providing a functional measure of stimulus strength and, at least to a fu-st approximation up to moderate contrasts, equating signal strengths within the system across stimuli. The work presented in this paper is concerned with the extraction of a velocity signal from stimuli coded by a modulation in luminance, colour or luminance contrast, and how this reflects upon the extraction of a signal simply indicating the direction of motion of the stimulus. In light of the recent work discussed in the Introduction (Cavanagh et al., 1984; Cavanagh & Anstis, 1991; Smith & Edgar, 1991; Cropper & Derrington, 1993a, b), if the direction and speed of a stimulus are coded in separate signals within the system then it is possible that we might see different effects of contrast on the psychophysical measures of direction discrimination and speed discrimination. If, however, the output from a single velocitysensitive mechanism were used to perform both these tasks, we would expect substantially similar effects of contrast on each psychophysical measure. Because this study is one of the effects of input signal strength on two different psychophysical tasks it is most suitable that the same contrast level be used for the two tasks (direction and speed discri~nation) and that the contrast of each stimulus type be normalized to a common measure independent of either the ability to discriminate the direction or the speed of a stimulus: the detection threshold. RESULTS Figure l(a, b) plots the Weber fraction (minimum detectable increment/base speed) against the base speed for each stimulus for two observers (SJC and CL). The
45
VELOCITY DISCRIMINATION
(4
Observer SJC
(b)
Cl Lum +0.5 0 RG +O.S A Beat +0.5 0 RG +1.5 A Beat +1.5
2.0 1.8 1.6
-0.6
Observer CL cl Lum +0.5 0 RG +0.5 A Beat +0.5 n Lum +1.5 0 RG +1.5 A Beat +1.5
2.0 1.8 1.6
0.6 0.4 0.2 0.0 Base speed (deg/aec)
Base spaed (deg/=c)
FIGURE 1. (a) Speed discrimination function for observer SJC. The Weber fraction is plotted against the base speed of the stimulus, expressed in deg/sec. Gpen symbols represent stimuli presented at a low contrast of 0.5 log units above their detection threshold, solid symbols represent the same stimuli at 1.5 log units above their detection threshold. The different stimuli are indicated in the key, the spatial frequency of each was 1 c/deg and the stimuli were presented for 0.48 set (half the width of the raised-cosine temporal envelope). All stimuli were tested at all base speeds and the absence of a symbol indicates that a Weber fraction was not measurable at that base speed: the arrows indicate the fraction was off the scale (see text). Error bars indicate the standard deviation estimated by the function fitting routine. (b) As (a) but for another observer, CL.
minimum detectable increment in speed was taken as the point on the psychometric function plotting the performance against the increment when the observer was correct 75% of the time in the speed-discrimination task described above. This threshold was calculated from the psychometric function using the method of Foster and Bischof (1991) adapted for the 2AFC discrimination procedure. The absence of a data point in these figures indicates that the observer never reached a performance of 75% correct in the task and no threshold increment was measurable in the range studied (0.1-0.9 deg/sec increment), i.e. speed discrimination was very poor under the given conditions. The stimulus referred to by each function is indicated in the key to each graph. Open symbols indicate stimuli presented at a low contrast of 0.5 log units above their detection threshold, solid symbols represent stimuli at a contrast of 1.5 log units above detection threshold. Error bars indicate the standard deviation of the threshold estimate from the curve fitting procedure. At low base speeds, the Weber fraction for all stimuli is high, indicating that performance is poor. As the base speed increases, performance improves and the curves flatten off; this is most obvious for the luminance grating. These functions show the lower portion of the classic U-shaped speed discrimination function, which as
McKee et al. (1986) note, shifts to the left at the low temporal frequencies used in this study. When comparing the stimuli presented at low contrasts (open symbols), the chromatic grating and beat stimuli show much higher Weber fractions at a given base speed than the “equivalent” luminance grating. There is no detectable increment at the lowest (and highest) base speeds for either the chromatic grating or the beat: observer CL shows particularly poor performance for the chromatic grating. This is the kind of difference between these three stimuli that we have shown for tasks of direction discrimination (Cropper & Derrington, 1990, 1993a). When the contrast of the stimulus is increased (solid symbols on the plot) the ability to discriminate speed in the chromatic and beat stimuli improves dramatically. Performance is now very similar to that for a low contrast luminance grating for both observers, with perhaps the exception of CL at a base speed of 0.75 deg/sec for the chromatic grating. This performance is however still much better than the low contrast condition when a threshold increment was not measurable. The principal point here is that although we might expect increased contrast to improve performance in chromatic speed discrimination because of the previous
46
SIMON J. CROPPER
direction disc~mination results where the lower threshold of motion (LTM) decreased with increasing stimulus contrast (Cropper & Derrington, 1993a), we would not expect this to be the case for beat stimuli because increasing stimulus contrast by an equivalent amount had little effect on the LTM measured in a direction-discrimination task for beat patterns (Cropper & Derrington, 1993a). Figure l(a, b) shows an equivalent improvement in performance for both chromatic and beat stimuli as contrast increases and therefore do not meet the expectations. Contrast has previously been shown to have little effect on performance in tasks of speed discrimination using luminance stimuli (McKee et al., 1986; Panish, 1988) as long as the presentation is sequential (Stone & Thompson, 1992), so only one observer (CL) was tested with the high contrast luminance condition. The low and high contrast functions for the luminance gratings (open and solid squares) are indeed very similar for CL which is in agreement with the previous work. We have already suggested that chromatic and beat stimuli may not be processed by the same system to mediate direction discrimination at high stimulus contrasts (Cropper & Derrington, 1993a, b): are they, however, processed by a similar system to mediate speed discrimination? Figure l(a, b) shows that the ability to discriminate speed in both chromatic gratings and beats is sensitive to stimulus contrast and suggests that a similar system may be underlying the ability to perform the task. The second experiment looks more closely at the effect of contrast on the Weber fraction for each stimulus by repeating the first experiment at different stimulus contrasts for a single base speed condition. The methods were exactly the same as in the first experiment. Figure 2(a, b) plots the Weber fraction as a function of stimulus contrast, expressed in log units above the detection threshold for that stimulus flickered at 2 Hz. The duration of presentation was 0.48 set again and the base speed chosen was 2 degjsec, within the flat portion of the curves in Fig. 1. Each figure represents the data for one observer (SJC or ME) and the two stimuli are represented by different symbols as denoted in the figure key. The horizontal line on the figure indicates the Weber fraction for a luminance grating (measured at 0.5 log units above detection threshold) which is relatively independent of contrast [McKee et al., 1986; Panish, 1988; Fig. l(b)]. Both figures show that as stimulus contrast increases, performance improves and the Weber fraction drops at an approximately equivalent rate for both stimuli. The curves begin to flatten off between 0.9 and 1.1 log units above detection threshold and at the highest contrasts, absolute performance for the chromatic and beat stimuli is very similar to that measured for low contrast luminance stimuli. DISCUSSION The results presented here measure the ability to discriminate speed in different stimuli once the direction of motion is clearly visible. These speed-discrimination
(a)
Observer SJC 0.8
l RG grating A Beat _.. ___ Lum grating
0.6
0.0
m 0.5
0.7
0.9
1.1
1.3
1.5
Contrast ahove threshold
lb)
Observer ME 0.8
l RGgrating A Beat ..___Lum grating
0.6 8 ‘G E
@I 0.4 $ P
0.2
0.0
._...._____......__-------.
I 1
I
’
I
I
0.5
0.7
0.9
8
I
1.3
1.5
,
1.1
!
Contrast above threshold FIGURE 2. (a) Plot of the Weber fraction as a function of stimulus contrast, expressed in log units above detection threshold. The base speed was 2 deg/sec, stimuli are indicated in the key and the observer was SJC. The horizontal line is the Weber fraction measured for a luminance grating at 0.5 log units above threshold. (b) As (a) except for observer ME.
results show the same difference in the processing of low contrast stimuli that were obtained in tasks of direction discrimination (Cropper & Derrington, 1993a): performance for the chromatic and beat stimuli is much worse than for the luminance grating. As contrast is increased however, speed-discrimination performance for both the
VELOCITY DISCRIMINATION
chromatic grating and the beat improves sibilantly, unlike the direction ~sc~~nation results where only performance for the chromatic grating improved to such an extent (Cropper & Derrington, 1993a). There are two aspects of these results which we must consider. Firstly, it seems that the psychophysically measured characteristics of the ability to discriminate speed in a beat (second-order) stimulus do not directly reflect the characteristics of the ability to discriminate the direction of motion in the same stimulus. Secondly, the effect of contrast is to improve performance in both speed- and dir~tion-di~~~nation tasks in chromatic stimuli, but to have no effect on performance in the same tasks for luminance stimuli. Each of these will be considered in turn.
47
extracted by different mechanisms, or available at different stages within the same mechanism. This provides a problem for models of motion perception which propose that a composite velocity signal is extracted from some second-order stimuli (e.g. Johnston et al., 1992). Speed discrimination in chromatic and luminance stimuli
The Weber fraction functions for the luminance grating and high contrast chromatic grating show very similar properties and form part of the classic U-shaped curve. The similarity between these two stimuli is in agreement with results seen for direction disc~mination tasks (Cropper & Derrington, 1993a) and suggests that similar types of system may be used in the tasks of direction and speed discrimination for these two stimuli. The modification in the ratio model of velocity coding Speed discrimination in beat stimuli (Thompson, 1984) suggested by Cavanagh and Anstis (1991) to explain the slower perceived speed of chroThe high contrast beat pattern shows a significant matic stimuli predicts results similar to those presented decrease in velocity discrimination thresholds with inhere. The fact that chromatic stimuli never elicit smaller creased contrast, an effect not seen when measuring detectable velocity increments than luminance. stimuli the lower threshold of motion (LTM) (Cropper & Derrington, 1993a) over the same contrast range. This is may be explained by a lower limit in the sensitivity of the in conflict with the results expected on the basis of the system having already been reached (for luminance ability to di~~minate the direction of motion of beat stimuli). These results, however, can also be seen to support the stimuli, which indicated that there should be little effect of contrast on speed discrimination. The results do, use of a composite velocity signal to detect motion in the however, meet the prediction made on the basis of the first-order chromatic and luminance stimuli. Contrast results of Smith and Edgar (1991) which suggested that has been shown to have a strong effect on the ability to there should not necessarily be any deficiency in the discriminate both the direction (Cropper & Derrington, velocity coding of high-contrast second-order stimuli 1993a) and speed of motion of a first-order chromatic and therefore it was necessary that performance in the stimulus, and to have virtually no effect on the same velocity discrimination task improved with increasing measures of performance in first-order luminance stimcontrast since it was very poor at low contrasts. uli. This is consistent with a mechanism signalling the We would not expect a situation where contrast has velocity of a stimulus in a composite signal, the magnilittle effect on the lower threshold of motion (LTM) but tude of which is dependent upon stimulus contrast for a strong effect on velocity ~s~~~nation. A velocitychromatic stimuli only (Cropper & Derrington, 1993a). tuned mechanism which is also partially sensitive to Thus we would expect perceived speed in chromatic contrast will change the magnitude of its output with gratings to be strongly contrast dependent, and contrast contrast and we would expect this to affect the perceived independent in luminance gratings. Although the conspeed signalled by that mechanism. However, the effect trast dependence of the perceived speed of chromatic of contrast on this output would have to be much greater gratings has not been fully assessed, Mullen and Boulton to change the sign of the signal and therefore the (1992) have recently shown that the ability to make an perceived direction of motion. This results in a contrast accurate velocity match between luminance and chrodependent perceived speed but not perceived direction matic stimuli is strongly contrast dependent. and this has been observed under some conditions In addition to this, although the perceived speed of in luminance stimuli ~ompson, 1982; Stone & luminance gratings does seem to be contrast dependent Thompson, 1992). Despite this, we would expect some under some stimulus conditions (Thomp~n, 1982; Stone effect of contrast on the minimum detectable velocity & Thompson, 1992), this seems very dependent upon the (LTM) signalled by such a system because it is likely that measurement paradigm involved. This could simply be a this particular psychophysical measure is dependent reflection of a largely contrast independent velocity upon reaching some criterion signal to noise ratio in signal for luminance stimuli whose magnitude fluctuates the output; once this criterion level has been reached, the with contrast over short periods of time only and that task of direction discrimination which only requires the fluctuation can only be identified when two stimuli of sign of the signal to be extracted, can be performed different contrasts are presented simultaneously (Stone regardless of the magnitude of the output from the & Thompson, 1992). system. Changing the signal magnitude will have a much The ratio model of Thompson (1982) was proposed to stronger effect near this criterion level, and therefore explain the apparent contrast independence of the peraffect the LTM if there is an effect on the perceived speed ceived speed of luminance stimuli. Although the prosignalled by the same mechanism. Thus it seems that the posal by Cavanagh and Anstis (1991) does explain the speed and direction of motion of a beat stimulus may be slower perceived speed of chromatic motion, there is
48
SIMON J. CROPPER
evidence to suggest that the perceived speed of chromatic stimuli is contrast dependent (Mullen & Boulton, 1992). We must consider the Iikelihood of the existence of a ratio modet of velocity coding for chromatic stimulus when it fails in its prime objective: to dissociate contrast and velocity. A full study of the perceived speed of chromatic stimuli is currently underway to look in more detail at this question.
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CONCLUSIONS
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The aim of this study was to investigate whether a group of &early defined differences in the characteristics of the ability to disseminate the direction of motion of luminance, chromatic and beat stimuh, heid for the associated task of speed discrimination under the same stimulus conditions. The results presented here indicate that this is not always the case and imply that speed disc~mination is mediated by an additional mechanism to that which mediates direction discrimination in beat stimuli.
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Acknowledgements-This
work was financially supported by the Science and Engineering Research Council grant No. GRG 07980 to Andrew M. Derrington whilst the author was supported by a SERC Image Interpretation Initiative research studentship, and also Australian Research Council grant No, A79030414. I wish to thank David Badcock and Jim May for critical reading of the unapt, Michael Cox for the fusion-~ttjng routine and Andy Smith for helpful and constructive comments.