0042-6989/92 55.00 + 0.00 Copyright 0 1992 Pergamon PressLtd
Vision Res. Vol.32, No. 6, pp. 114&l 148, 1992 printed in Great Britain. Alf rights reserved
Research Note Spatial Frequency Tuning of Facilitation HARRIET
by Masks
D. SPEED,* JOHN ROSS*
Received 18 September 1991; in revised form 6 November 1991
The spatial frequency tuning of fa~ititation by masks is derived for a 2 cjdeg test grating, counte~ba~ at 8.8 Hz, from the contrasts at which masks of different spatial frequencies facilitate maximally. This tuning function has a bandwidth at half height of roughly 1.5 octaves, much broader than has been estimated previously from tuning functions determined at a constant contrast for each mask. We show also that best facilitation more than doubles sensitivity for tests of 4 c/deg and below, and that the magnitude of the facilitation effect declines at higher spatial frequencies. Facilitation
Contrast threshold
Masks Spatial frequency tuning
INTRODUCTION The function relating test threshold to the contrast of a mask that is similar to the test in spatial frequency and o~entation is typically dip~r-shard: as mask contrast increases from zero, the threshold for detecting the test first “dips” below the unmasked threshold then rises as mask contrast continues to increase. That is, the presence of a mask similar to the test can make the test grating easier to detect. The effect is commonly termed “facilitation”, though the terms “negative masking” and “the pedestal effect” have also been used. Several studies indicate that facilitation declines with difference in spatial frequency between mask and test (Tolhurst & Barfield, 1978; Legge & Foley, 1980; Swift & Smith, 1983; Georgeson & Georgeson, 1987). Only one study, that of Legge and Foley (1980) has attempted to provide a quantitative tuning estimate. They measured test threshold vs mask contrast functions for a 2 c/deg test grating using masks that varied in spatial frequency, but only up to 1 octave away from the test. To derive the tuning of facilitation, they measured facilitation due to masks of different spatial frequency at 0.4%, the contrast at which masks of the same frequency as the test facilitated maximally. The half-height bandwidth of the tuning function so derived was 0.5 octave (for wide fields), implying that facilitation is very narrowly tuned in the spatial frequency domain. A feature of Legge and Foley’s data, evident also in the data of Swift and Smith (1983) and Georgeson and Georgeson (1987), is that as test and mask diverge in spatial frequency there is a displacement of the test threshold vs mask contrast curve to the right along the
*Department of Psychology, University of Western Austrafja, Nedlands, W.A. 6009. Australia.
contrast axis: masks that differ from the test in spatial frequency, yet still facilitate detection, do so at higher contrasts than masks of the same spatial frequency as the test. In some cases, there is very little overlap of the contrast ranges within which two different masks will facilitate. In this paper we re-examine the spatial frequency tuning of facilitation over a wider range than Legge and Foley (1980). In determining tuning, we take account of the fact that threshold curves shift along the contrast axis and use, for each mask, the contrast at which it facilitates maximally. In a second experiment, we examine the size of facilitatory effects of masks similar to tests at different test spatial frequencies and the range of spatial frequencies for which facilitation is found. METHODS Both test and mask stimuli were sinusoidal gratings ~~odically reversed in contrast (squarewave modulation). The test and mask were generated on alternate frames using a raster technique described in detail elsewhere (Ross & Speed, 1991). Grating contrast, defined as L,,, - Lmln/(L,,, + Lmin),was calibrated separately for the test and mask. The display characteristics of the oscilloscope were highly linear over the range of contrasts measured (0.545%). A white cardboard screen was used to mask the display to a circular field of 16 cm dia. Mean luminance was 15 cd/m?. Threshold measurements were obtained using a version of the two-alternative forced-choice procedure, QUEST (Watson & Pelli, 1983). A trial included two intervals each of 2 set duration (separated by 500 msec), and each preceded by an audible tone. Both intervals contained the mask grating, but only one contained the test. During a trial, the contrast of the mask was fixed
1143
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RESEARCH NOTE
while that of the test was multiplied by a raised cosinusoidal temporal envelope, with a period of I.500 msec The observer’s task was to identify the interval in which the test was present by pressing one of two keys. A computer recorded the response as correct or incorrect and initiated the next trial, incrementing or decrementing test contrast depending on the previous response, Contrast threshold was defined as the contrast of the test at which an 87% correct response rate was achieved. Typically, each measurement was obtained in < 30 trials. Prior to the presentation of masks, unmasked thresholds were measured in the same way, the mask being replaced by a blank field having the same mean luminance as the gratings. The initial contrast of the test in the masking trials was reset randomly (under computer control) from one trial to the next, within A3 dB of the unmasked threshold. Some threshold measurements were obtained by method of adjustment, the decision criterion being that the subject be able to distinguish mask plus test from mask alone, not necessarily to be able to see the test itself, In Expt 1, the test was a 2 c/deg vertical grating reversed in contrast at a rate of 8.8 I-Iz. Masking gratings varied in spatial frequency within a range +2 octaves from the test frequency. A single session was devoted to one spatial frequency. The spatial frequencies chosen for the test and mask gratings did not bear exact integral relations to one another, so there was no question of aligning the two su~rirn~s~ gratings in any particular phase relationship. Within a session the mask was presented at a range of contrasts, spanning more than 2 log units (between 0.2 and 38%). the order of contrast presentation being random. The mask was also vertical but was reversed in contrast at a slightly different rate (7 Hz). In this way the observer’s task was always one of pattern discrimination even when test and mask were identical in spatial frequency and orientation. In Expt 2, the tests were vertical gratings of I2 different spatial frequencies within the range 0.13-20c/deg. The masks were identical to the test in orientation and in spatial frequency, but reversed in contrast at a different rate (at 8.8 I-12for test, 7.0 Hz for mask). As in the previous experiment, the mask was presented at a range of contrasts. spanning more than 2 log units (0.2-32%). Grating spatial frequency was varied by changing viewing distance and by changing the number of cycles of grating on the display. In Expt 1, the viewing distance varied between 114 and 456 cm. The number of cycles of the test grating and mask gratings were both varied accordingly, between 4 and 16 cycle@creen (1 cycle/cm). In Expt 2, viewing distance varied between 28.5 and 1140 cm, while the number of cycles of test and mask gratings varied together, between 4 and 16 cycles/screen. Threshold measurements were made in a semidarkened room while observers fixated a central spot on the display. All measurements were carried out in detail on one subject HS, and the results confirmed by at least one other subject.
RESULTS Figure I shows contrast thresholds for detecting a 2.0c/deg test grating when masked by gratings of various spatial frequencies, for two observers. HS (left curves) and TH (right curves). Each data point is derived from the geometric mean of 3 threshold measurements by forced-choice (HS) or method of adjustment (TH) procedure. For observer HS, we examined a total of 13 mask spatial frequencies within the range OS-8 c/deg. Figure 1 shows examples of test thresholds in the presence of 6 different mask spatial frequencies (0.5. 1, 2, 4, 6 and 8 cjdeg). Five mask frequencies were examined with observer TH, all data are shown in the figure. For clarity, the data corresponding to different mask spatial frequencies are successively displaced vertically by factors of 10 from the bottom (refer to figure caption). The ordinate for each set of data is a ratio of masked threshold to threshold for the test alone. and is plotted as a function of masker contrast. The dashed lines represent a relative threshold value of 1.0 (no masking effect). An arrow indicates the point at which a mask of the same spatial frequency as the test facilitates best. The full range of masker contrasts extended between 0.2 and 38%; here we present threshold data for the contrast range 0.2-100/o. Consider the threshold curves for subject HS. The contrast threshold for detecting the unmasked 2 c/deg vertical test grating, averaged over all sessions, is 0.45% (SE = +0.03%). In the presence of a mask of the same spatial frequency, the threshold curve is dipper-shaped. The mask lowers or elevates the threshold of the test depending on its contrast. The range of contrasts within which a 2 c(deg mask facilitates detection of the test extends over roughly 1 log unit. between 0.2 and 2%. When the mask is itself near threshold, at a contrast of 0.5%. facilitation is greatest; the threshold is slightly more than a factor of 2 lower than the unmasked threshold. Changing the spatial frequency of the mask by i octave (1 and 4 c/deg masks) pushes the entire threshold curve to the right along the contrast axis. At the contrast at which a mask of the same spatial frequency as the test facilitates maximally, I and 4 cideg masks facilita~ only slightly or not at all. It is not until the two masks are well above threshold. at around 2% contrast, that they attain maximum facilitatory strength. At spatial frequencies two octaves from the test frequency. masks no longer facilitate detection of the test and the threshold curve loses its characteristic dipper shape. The remote masks (0.5 and 8.0c/deg) leave the threshold of the test where it was, or raise it, but at no masking contrast is there any facilitation. This result was confirmed at two different viewing distances (changing the number of cycles on the screen accordingly) for both the 0.5 and 8 c/deg mask. On the right side of the figure are test threshold curves at 5 mask spatial frequencies (between 0.5 and 6cideg) measured for a second observer by method of adjustment. Although there were small individual differences in sensitivity to a
1145
RESEARCH NOTE
.C
05
c/deg
_.-.-.-.
10
c,deg
_..,
./
.
.
.'
1
100
_._*_.-0’
.,*/ MASK
60
cldeg
80
cfdeg
CONTRAST
_._._._*
------_.
I.'
(%)
FIGURE 1. Relative contrast thresholds (ratio of masked to unmasked) for detecting a 2c/deg vertical grating presented concurrently with mask gratings of various spatial frequencies, for two observers HS (lefi), obtained by forced-choice procedure, and TH (righf), by method of adjustment. The curves are successively displaced upwards by factors of 10 from the bottom. The dashed lines represent a relative threshold value of 1.0 (no masking effect), the data points should be read relative to this value. The two arrows indicate, for the respective data sets, the contrast at which a mask of the same spatial frequency as the test facilitates best. Symbol size represents approx. I SEM. The solid lines through each set of data are theoretical predictions of the model describedin Ross and Speed (1991).
2 c/deg grating, the pattern of results for both subjects was similar, despite the use of different threshold measurement procedures. The tuning curve of facilitation is shown in Fig. 2. The data points are replotted from Fig. 1, for HS (left) and TH (right), and include also, for HS, data from 7 mask spatial frequencies not shown in the figure. The ordinate is the reciprocal of relative test threshold, plotted as a function of mask spatial frequency. The two curves depict tuning functions derived via different procedures: at the point where masks of different spatial frequencies facilitate maximally (solid circles); and, at a single masker contrast (open circles) of 0.5% for HS and 1.O% for TH, the contrast which produces greatest facilitation when test and mask frequencies are equal. Curves drawn through the data are fitted by eye. For both observers, the two tuning functions are clearly different. For HS, the tuning function derived from a constant mask contrast of OS%, the method used by Legge and Foley (1980), is very narrow, having a bandwidth at half-height of approx. 0.6 octave. In comparison, the tuning func-
tion determined from masks of maximum facilitatory strength has a half-height bandwidth of roughly 1.5 octaves. The two tuning functions on the right (TH) show a similar pattern; but with so few data points no precise estimates of bandwidth can be made. In a second experiment we examined the facilitation of test thresholds by masks of the same spatial frequency as the test, at different test spatial frequencies. Test thresholds were measured as a function of mask contrast for 12 test spatial frequencies in the range 0.13-20 c/deg. Figure 3 shows examples of test threshold curves at 7 test frequencies (0.13, 0.5, 2, 6, 10, 15 and 20 c/deg). Each data point is derived from the mean of 5 threshold measurements by the method of adjustment, for observer HS. For each set of data, threshold values are displaced upwards by successive factors of 10 from the bottom. Curves drawn through the data are fitted by eye. The unmasked threshold at each spatial frequency is indicated by an arrow. All of the curves in Fig. 3 display the same qualitative features, but the position of the facilitatory dip and point of maximal facilitation shift
1146
MASK
SPATIAL
FREQUENCY
(c/dcg)
FIGURE 2. Tuning curves for facilitation derived from the contrasts where masks of different spatial frequency facilitate maximally (solid circles); and at a constant masker contrast (open circles) of 0.5% for observer HS (ieft curves) and 1.0% for TH (right curves). The data are replotted from Fig. 1 as the reciprocal of relative test threshold plotted against mask spatial frequency. For HS, the data points include threshold measurements in the presence of masks of some intermediate spatial frequencies not included in Fig. 1. Curves drawn through the data are fitted by eye. To obtain the broader tuning functions from Fig. 1, the reader should measure the amount of facilitation at each mask spatial frequency at the contrast where facilitation is maximal for that spatial frequency. To obtain the narrower tuning functions, the reader should measure the amount of facilitation at a contrast of 0.5 or 1.0% (indicated by the arrows in Fig. 1).
along the contrast axis. At 2 c/deg, the point of best facilitation is very near threshold. But at spatial frequencies more than one octave above or below 2 c/deg, it is above threshold. At the highest frequency, 20 c/leg, the displacement away from threshold is most pronounced, with masks facilitating best at a contrast of around 25%, when threshold is at 16%. Figure 4 plots contrast sensitivity (the reciprocal of contrast threshold) for test gratings of various spatial frequencies, measured either in the absence of masks or in the presence of masks of maximum facilitatory strength, as well as the ratio of the two thresholds. The thresholds are taken from the data shown in Fig. 3, and also some at intermediate test frequencies not shown in that figure. Curves drawn through the data are fitted by eye. The unmasked sensitivity curve is 0at up to about 4 c/deg, as expected (Campbell & Robson, 1968; Robson, 1966). In the presence of a mask of maximum facilitatory strength, sensitivity at all spatial frequencies is shifted upwards. In the range 0.13-4 c/deg, sensitivity is more than doubled, to a value of about 500, which represents a contrast threshold of 0.2%. The approximate constancy of the facilitated threshold in this range is confirmed by the fact that the distribution of 30 absolute contrast values at the points where masks of 4 c/deg or less facilitate best has a mean of 0.22%, and a standard deviation of 0.02%. The 30 contrast values comprise the pooled data from different subjects and from several different masking experiments (see Ross & Speed, 1991). Above 4 c/deg, where unmasked sensitivity falls away, the ratio of facilitated to unfacilitated sensitivity progressively decreases. DISCUSSION The first experiment examined the tuning of the facilitation effect with a test of 2 c/&g. Like previous
investigators (Legge & Foley, 1980; Swift & Smith, 1983; Georgeson & Georgeson, 1987) we find that as the spatial frequency of a mask shifts away from that of the test, the test threshold curve moves to the right along the contrast axis, and the contrast at which masks facilitate maximally increases. The bandwidth of the tuning function determined by choosing the contrast at which each mask is at maximum facilitatory strengths is roughly 1.5 octaves, much broader than has been estimated previously by choosing a constant contrast for each mask (Legge & Foley, 1980). Choosing different contrasts for different masks, rather than one contrast for all, is justified by a model we have recently developed (Ross & Speed, 1991) to explain a range of adaptation as well as masking effects. The curves fitted to the data points in Fig. 1 are theoretical predictions of the model. The model incorporates two distinct tuning functions. Masks reposition and reshape the transducer functions of mechanisms that respond to the test according to one very broadly tuned function, termed adaptive contrast. -Masks also stIn@&te the mechanism that detects the test according to another more narrowly tuned function, termed e&c&e contrast. The model assumes that if a mask facilitates, it-does so because the effective contrast it provides stimulates the detecting mechanism at a point where the ?Jope of its transducer function, as positioned by the adaptive contrast of the mask, is steepest. To do this the contrast of a mask that differs in spatial frequency from the test needs to be high in order for it to reach thesteepportion of the transducer function. The modeI therefore imgk that it is inappropriate to select a single contrast, as Legge and Foley (1980) did, at which to measure the relative facilitation provided by difhent n~sks. In the second experiment, we varied the spatial frequency of test gratings, keeping mask spatial frequency the same as the test. We found that at all spatial frequencies the contrast at which a mask facilitates best
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RESEARCH NOTE
.1
1
10
100
SPATIAL FREQUENCY (cnfeg)
FIGURE 4. Contrast sensitivity (reciprocal of contrast threshold) for test gratings of different spatial frequencies in the absence of masks (open circles) and in the presence of masks of maximum facilitatory strength (solid circles). The ratio of the two is shown by solid triangles. The smooth curves through the data are fitted by eye.
less. A possible explanation might be that thresholds are higher, transducer functions are more shallow and tuning is more narrow at higher spatial frequencies, where the parvo system, not the magno. operates (Kaplan & Shapley, 1986; Hawken & Parker, 1984). Masks would then need to be higher in contrast to stimulate at the steepest part of the function, where the gain (rate of change in output for contrast increment) would be less 1” -r 10 30 loo 03 i 3 0 than at lower spatial frequencies. Finally, we note that all the curves through the data MASK CONTRAST (%I points shown in Fig. 1 are theoretical curves derived FIGURE 3. Contrast thresholds for detecting vertical test gratings of from the model described by Ross and Speed (1991). 7 different spatial frequencies in the presence of masks that are Since the fits are close, the curves describing the tuning identical to the test in both orientation and spatial frequency. The test of facilitation derived from the data could have been was reversed in contrast at a rate of 8.8 Hz; the mask at a rate of 7 HZ. derived directly from the model. The empirically derived Relative thresholds as a function of mask contrast are plotted separtuning curve is different in shape from, but almost ately for each test spatial frequency. Curves are successively displaced upwards by a factor of IO from the bottom (refer to Fig. 1 caption). identical in bandwidth to the theoretical curve for the Data points are derived from the mean of 5 threshold measurements tuning of effective contrast assumed in the model. The by method of adjustment, for observer HS. Curves through each set curves differ in shape because facilitation depends on the of data are fitted by eye. Arrows indicate unmasked thresholds at each interplay of the effective and the adaptive contrast of a test spatial frequency. mask. Whether the model can be extended to explain the decrease in size of facilitation at higher spatial frequenis at or above its own threshold, A similar pattern of cies is under investigation. Preliminary results suggest results has been observed in contrast discrimination that it is necessary to assume that transducer functions thresholds (Bradley & Ohzawa, 1986). When we examine have lower slopes and that the tuning of effective absolute sensitivity to tests at the points of maximum contrast is narrower at higher spatial frequencies. It is facilitation by similar masks, we find it to be constant for intriguing to speculate whether channels at central tunall tests up to 4 c/deg in spatial frequency (see Fig. 4). ing higher than 15 c/deg need to be included to explain This is to be expected if masks reposition transducer the clear facilitation effect found at 20 c/deg. functions, and in doing so reshape them to preserve differential sensitivity, and if they facilitate because they REFERENCES stimulate at the point of maximal differential sensitivity. At spatial frequencies above 4 c/deg unfacilitated sen- Bradley, A. & Ohzawa, I. (1986). A comparison of contrast detection and discrimination. Vision Research. 26. 991-997. sitivity declines, as expected (Campbell & Robson, 1968; Robson, 1966), and so too does the improvement in Campbell, F. W. & Robson, J. G. (1968). On the application of Fourier analysis to the visibility of gratings. Journal qf Phyidogy. London, sensitivity due to facilitation. At these higher frequen197, 551-556. cies, optimal masks (of the same spatial frequency as the Georgeson, M. A. & Georgeson, J. M, (1987). Facilitation and test) behave like sub-optimal masks at lower frequencies: masking of briefly presented gratings: Time course and contrast they facilitate best at higher contrasts and they facilitate dependence. Vision Research, 27, 369-379. -7
i
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Hawken, M. J. & Parker, A. J. (1984). Contrast sensitivity and orientation selectivity in lamina IV of the striate cortex of old world monkeys. Experimental Brain Research, 54, 367-372. Kaplan, E. & Shapley, R. M. (1986). The primate retina contains two types of ganglion cells, with high and low contrast sensitivity. Proceedings of the National Academy of Science. 2755-2751. Legge, G. E. & Foley, J. M. (1980). Contrast
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83,
masking in human vision. Journal of the Optical Society of America. 70.
Ross, J. & Speed, H. D. (1991). Contrast adaptation and contrast masking in human vision. Pr0ceeding.s qf the Royal Society of London, B, 246, 61-69.
Swift, D. J. & Smith, R. A. (1983). Spatial frequency maskrng and Weber’s Law. Vision Research, 22, ___ 215-346 -._ Tolhurst, D. J. & Bartield, L. P. (1978). Interactions between spatral frequency channels. Vision Research, 18, 951-958. Watson, A. 8. & Pelli. D. G. (1983). QUEST: A bayesian adaptive psychometric method. Perception and Psychophysics, 33. 113--l 20.
1458-1471.
Robson, J. G. (1966). Spatial and temporal contrast sensitivity fimctions of the visual system. Journal of the Optical Society of America. 56. 1141-l 142.
Acknowledgement-This
NH&MRC (Australia).
report
was supported
by a grant
from
Vision Res. Vol.32, No. 6, pp. 114&l 148, 1992 printed in Great Britain. Alf rights reserved
Research Note Spatial Frequency Tuning of Facilitation HARRIET
by Masks
D. SPEED,* JOHN ROSS*
Received 18 September 1991; in revised form 6 November 1991
The spatial frequency tuning of fa~ititation by masks is derived for a 2 cjdeg test grating, counte~ba~ at 8.8 Hz, from the contrasts at which masks of different spatial frequencies facilitate maximally. This tuning function has a bandwidth at half height of roughly 1.5 octaves, much broader than has been estimated previously from tuning functions determined at a constant contrast for each mask. We show also that best facilitation more than doubles sensitivity for tests of 4 c/deg and below, and that the magnitude of the facilitation effect declines at higher spatial frequencies. Facilitation
Contrast threshold
Masks Spatial frequency tuning
INTRODUCTION The function relating test threshold to the contrast of a mask that is similar to the test in spatial frequency and o~entation is typically dip~r-shard: as mask contrast increases from zero, the threshold for detecting the test first “dips” below the unmasked threshold then rises as mask contrast continues to increase. That is, the presence of a mask similar to the test can make the test grating easier to detect. The effect is commonly termed “facilitation”, though the terms “negative masking” and “the pedestal effect” have also been used. Several studies indicate that facilitation declines with difference in spatial frequency between mask and test (Tolhurst & Barfield, 1978; Legge & Foley, 1980; Swift & Smith, 1983; Georgeson & Georgeson, 1987). Only one study, that of Legge and Foley (1980) has attempted to provide a quantitative tuning estimate. They measured test threshold vs mask contrast functions for a 2 c/deg test grating using masks that varied in spatial frequency, but only up to 1 octave away from the test. To derive the tuning of facilitation, they measured facilitation due to masks of different spatial frequency at 0.4%, the contrast at which masks of the same frequency as the test facilitated maximally. The half-height bandwidth of the tuning function so derived was 0.5 octave (for wide fields), implying that facilitation is very narrowly tuned in the spatial frequency domain. A feature of Legge and Foley’s data, evident also in the data of Swift and Smith (1983) and Georgeson and Georgeson (1987), is that as test and mask diverge in spatial frequency there is a displacement of the test threshold vs mask contrast curve to the right along the
*Department of Psychology, University of Western Austrafja, Nedlands, W.A. 6009. Australia.
contrast axis: masks that differ from the test in spatial frequency, yet still facilitate detection, do so at higher contrasts than masks of the same spatial frequency as the test. In some cases, there is very little overlap of the contrast ranges within which two different masks will facilitate. In this paper we re-examine the spatial frequency tuning of facilitation over a wider range than Legge and Foley (1980). In determining tuning, we take account of the fact that threshold curves shift along the contrast axis and use, for each mask, the contrast at which it facilitates maximally. In a second experiment, we examine the size of facilitatory effects of masks similar to tests at different test spatial frequencies and the range of spatial frequencies for which facilitation is found. METHODS Both test and mask stimuli were sinusoidal gratings ~~odically reversed in contrast (squarewave modulation). The test and mask were generated on alternate frames using a raster technique described in detail elsewhere (Ross & Speed, 1991). Grating contrast, defined as L,,, - Lmln/(L,,, + Lmin),was calibrated separately for the test and mask. The display characteristics of the oscilloscope were highly linear over the range of contrasts measured (0.545%). A white cardboard screen was used to mask the display to a circular field of 16 cm dia. Mean luminance was 15 cd/m?. Threshold measurements were obtained using a version of the two-alternative forced-choice procedure, QUEST (Watson & Pelli, 1983). A trial included two intervals each of 2 set duration (separated by 500 msec), and each preceded by an audible tone. Both intervals contained the mask grating, but only one contained the test. During a trial, the contrast of the mask was fixed
1143
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RESEARCH NOTE
while that of the test was multiplied by a raised cosinusoidal temporal envelope, with a period of I.500 msec The observer’s task was to identify the interval in which the test was present by pressing one of two keys. A computer recorded the response as correct or incorrect and initiated the next trial, incrementing or decrementing test contrast depending on the previous response, Contrast threshold was defined as the contrast of the test at which an 87% correct response rate was achieved. Typically, each measurement was obtained in < 30 trials. Prior to the presentation of masks, unmasked thresholds were measured in the same way, the mask being replaced by a blank field having the same mean luminance as the gratings. The initial contrast of the test in the masking trials was reset randomly (under computer control) from one trial to the next, within A3 dB of the unmasked threshold. Some threshold measurements were obtained by method of adjustment, the decision criterion being that the subject be able to distinguish mask plus test from mask alone, not necessarily to be able to see the test itself, In Expt 1, the test was a 2 c/deg vertical grating reversed in contrast at a rate of 8.8 I-Iz. Masking gratings varied in spatial frequency within a range +2 octaves from the test frequency. A single session was devoted to one spatial frequency. The spatial frequencies chosen for the test and mask gratings did not bear exact integral relations to one another, so there was no question of aligning the two su~rirn~s~ gratings in any particular phase relationship. Within a session the mask was presented at a range of contrasts, spanning more than 2 log units (between 0.2 and 38%). the order of contrast presentation being random. The mask was also vertical but was reversed in contrast at a slightly different rate (7 Hz). In this way the observer’s task was always one of pattern discrimination even when test and mask were identical in spatial frequency and orientation. In Expt 2, the tests were vertical gratings of I2 different spatial frequencies within the range 0.13-20c/deg. The masks were identical to the test in orientation and in spatial frequency, but reversed in contrast at a different rate (at 8.8 I-12for test, 7.0 Hz for mask). As in the previous experiment, the mask was presented at a range of contrasts. spanning more than 2 log units (0.2-32%). Grating spatial frequency was varied by changing viewing distance and by changing the number of cycles of grating on the display. In Expt 1, the viewing distance varied between 114 and 456 cm. The number of cycles of the test grating and mask gratings were both varied accordingly, between 4 and 16 cycle@creen (1 cycle/cm). In Expt 2, viewing distance varied between 28.5 and 1140 cm, while the number of cycles of test and mask gratings varied together, between 4 and 16 cycles/screen. Threshold measurements were made in a semidarkened room while observers fixated a central spot on the display. All measurements were carried out in detail on one subject HS, and the results confirmed by at least one other subject.
RESULTS Figure I shows contrast thresholds for detecting a 2.0c/deg test grating when masked by gratings of various spatial frequencies, for two observers. HS (left curves) and TH (right curves). Each data point is derived from the geometric mean of 3 threshold measurements by forced-choice (HS) or method of adjustment (TH) procedure. For observer HS, we examined a total of 13 mask spatial frequencies within the range OS-8 c/deg. Figure 1 shows examples of test thresholds in the presence of 6 different mask spatial frequencies (0.5. 1, 2, 4, 6 and 8 cjdeg). Five mask frequencies were examined with observer TH, all data are shown in the figure. For clarity, the data corresponding to different mask spatial frequencies are successively displaced vertically by factors of 10 from the bottom (refer to figure caption). The ordinate for each set of data is a ratio of masked threshold to threshold for the test alone. and is plotted as a function of masker contrast. The dashed lines represent a relative threshold value of 1.0 (no masking effect). An arrow indicates the point at which a mask of the same spatial frequency as the test facilitates best. The full range of masker contrasts extended between 0.2 and 38%; here we present threshold data for the contrast range 0.2-100/o. Consider the threshold curves for subject HS. The contrast threshold for detecting the unmasked 2 c/deg vertical test grating, averaged over all sessions, is 0.45% (SE = +0.03%). In the presence of a mask of the same spatial frequency, the threshold curve is dipper-shaped. The mask lowers or elevates the threshold of the test depending on its contrast. The range of contrasts within which a 2 c(deg mask facilitates detection of the test extends over roughly 1 log unit. between 0.2 and 2%. When the mask is itself near threshold, at a contrast of 0.5%. facilitation is greatest; the threshold is slightly more than a factor of 2 lower than the unmasked threshold. Changing the spatial frequency of the mask by i octave (1 and 4 c/deg masks) pushes the entire threshold curve to the right along the contrast axis. At the contrast at which a mask of the same spatial frequency as the test facilitates maximally, I and 4 cideg masks facilita~ only slightly or not at all. It is not until the two masks are well above threshold. at around 2% contrast, that they attain maximum facilitatory strength. At spatial frequencies two octaves from the test frequency. masks no longer facilitate detection of the test and the threshold curve loses its characteristic dipper shape. The remote masks (0.5 and 8.0c/deg) leave the threshold of the test where it was, or raise it, but at no masking contrast is there any facilitation. This result was confirmed at two different viewing distances (changing the number of cycles on the screen accordingly) for both the 0.5 and 8 c/deg mask. On the right side of the figure are test threshold curves at 5 mask spatial frequencies (between 0.5 and 6cideg) measured for a second observer by method of adjustment. Although there were small individual differences in sensitivity to a
1145
RESEARCH NOTE
.C
05
c/deg
_.-.-.-.
10
c,deg
_..,
./
.
.
.'
1
100
_._*_.-0’
.,*/ MASK
60
cldeg
80
cfdeg
CONTRAST
_._._._*
------_.
I.'
(%)
FIGURE 1. Relative contrast thresholds (ratio of masked to unmasked) for detecting a 2c/deg vertical grating presented concurrently with mask gratings of various spatial frequencies, for two observers HS (lefi), obtained by forced-choice procedure, and TH (righf), by method of adjustment. The curves are successively displaced upwards by factors of 10 from the bottom. The dashed lines represent a relative threshold value of 1.0 (no masking effect), the data points should be read relative to this value. The two arrows indicate, for the respective data sets, the contrast at which a mask of the same spatial frequency as the test facilitates best. Symbol size represents approx. I SEM. The solid lines through each set of data are theoretical predictions of the model describedin Ross and Speed (1991).
2 c/deg grating, the pattern of results for both subjects was similar, despite the use of different threshold measurement procedures. The tuning curve of facilitation is shown in Fig. 2. The data points are replotted from Fig. 1, for HS (left) and TH (right), and include also, for HS, data from 7 mask spatial frequencies not shown in the figure. The ordinate is the reciprocal of relative test threshold, plotted as a function of mask spatial frequency. The two curves depict tuning functions derived via different procedures: at the point where masks of different spatial frequencies facilitate maximally (solid circles); and, at a single masker contrast (open circles) of 0.5% for HS and 1.O% for TH, the contrast which produces greatest facilitation when test and mask frequencies are equal. Curves drawn through the data are fitted by eye. For both observers, the two tuning functions are clearly different. For HS, the tuning function derived from a constant mask contrast of OS%, the method used by Legge and Foley (1980), is very narrow, having a bandwidth at half-height of approx. 0.6 octave. In comparison, the tuning func-
tion determined from masks of maximum facilitatory strength has a half-height bandwidth of roughly 1.5 octaves. The two tuning functions on the right (TH) show a similar pattern; but with so few data points no precise estimates of bandwidth can be made. In a second experiment we examined the facilitation of test thresholds by masks of the same spatial frequency as the test, at different test spatial frequencies. Test thresholds were measured as a function of mask contrast for 12 test spatial frequencies in the range 0.13-20 c/deg. Figure 3 shows examples of test threshold curves at 7 test frequencies (0.13, 0.5, 2, 6, 10, 15 and 20 c/deg). Each data point is derived from the mean of 5 threshold measurements by the method of adjustment, for observer HS. For each set of data, threshold values are displaced upwards by successive factors of 10 from the bottom. Curves drawn through the data are fitted by eye. The unmasked threshold at each spatial frequency is indicated by an arrow. All of the curves in Fig. 3 display the same qualitative features, but the position of the facilitatory dip and point of maximal facilitation shift
1146
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SPATIAL
FREQUENCY
(c/dcg)
FIGURE 2. Tuning curves for facilitation derived from the contrasts where masks of different spatial frequency facilitate maximally (solid circles); and at a constant masker contrast (open circles) of 0.5% for observer HS (ieft curves) and 1.0% for TH (right curves). The data are replotted from Fig. 1 as the reciprocal of relative test threshold plotted against mask spatial frequency. For HS, the data points include threshold measurements in the presence of masks of some intermediate spatial frequencies not included in Fig. 1. Curves drawn through the data are fitted by eye. To obtain the broader tuning functions from Fig. 1, the reader should measure the amount of facilitation at each mask spatial frequency at the contrast where facilitation is maximal for that spatial frequency. To obtain the narrower tuning functions, the reader should measure the amount of facilitation at a contrast of 0.5 or 1.0% (indicated by the arrows in Fig. 1).
along the contrast axis. At 2 c/deg, the point of best facilitation is very near threshold. But at spatial frequencies more than one octave above or below 2 c/deg, it is above threshold. At the highest frequency, 20 c/leg, the displacement away from threshold is most pronounced, with masks facilitating best at a contrast of around 25%, when threshold is at 16%. Figure 4 plots contrast sensitivity (the reciprocal of contrast threshold) for test gratings of various spatial frequencies, measured either in the absence of masks or in the presence of masks of maximum facilitatory strength, as well as the ratio of the two thresholds. The thresholds are taken from the data shown in Fig. 3, and also some at intermediate test frequencies not shown in that figure. Curves drawn through the data are fitted by eye. The unmasked sensitivity curve is 0at up to about 4 c/deg, as expected (Campbell & Robson, 1968; Robson, 1966). In the presence of a mask of maximum facilitatory strength, sensitivity at all spatial frequencies is shifted upwards. In the range 0.13-4 c/deg, sensitivity is more than doubled, to a value of about 500, which represents a contrast threshold of 0.2%. The approximate constancy of the facilitated threshold in this range is confirmed by the fact that the distribution of 30 absolute contrast values at the points where masks of 4 c/deg or less facilitate best has a mean of 0.22%, and a standard deviation of 0.02%. The 30 contrast values comprise the pooled data from different subjects and from several different masking experiments (see Ross & Speed, 1991). Above 4 c/deg, where unmasked sensitivity falls away, the ratio of facilitated to unfacilitated sensitivity progressively decreases. DISCUSSION The first experiment examined the tuning of the facilitation effect with a test of 2 c/&g. Like previous
investigators (Legge & Foley, 1980; Swift & Smith, 1983; Georgeson & Georgeson, 1987) we find that as the spatial frequency of a mask shifts away from that of the test, the test threshold curve moves to the right along the contrast axis, and the contrast at which masks facilitate maximally increases. The bandwidth of the tuning function determined by choosing the contrast at which each mask is at maximum facilitatory strengths is roughly 1.5 octaves, much broader than has been estimated previously by choosing a constant contrast for each mask (Legge & Foley, 1980). Choosing different contrasts for different masks, rather than one contrast for all, is justified by a model we have recently developed (Ross & Speed, 1991) to explain a range of adaptation as well as masking effects. The curves fitted to the data points in Fig. 1 are theoretical predictions of the model. The model incorporates two distinct tuning functions. Masks reposition and reshape the transducer functions of mechanisms that respond to the test according to one very broadly tuned function, termed adaptive contrast. -Masks also stIn@&te the mechanism that detects the test according to another more narrowly tuned function, termed e&c&e contrast. The model assumes that if a mask facilitates, it-does so because the effective contrast it provides stimulates the detecting mechanism at a point where the ?Jope of its transducer function, as positioned by the adaptive contrast of the mask, is steepest. To do this the contrast of a mask that differs in spatial frequency from the test needs to be high in order for it to reach thesteepportion of the transducer function. The modeI therefore imgk that it is inappropriate to select a single contrast, as Legge and Foley (1980) did, at which to measure the relative facilitation provided by difhent n~sks. In the second experiment, we varied the spatial frequency of test gratings, keeping mask spatial frequency the same as the test. We found that at all spatial frequencies the contrast at which a mask facilitates best
1147
RESEARCH NOTE
.1
1
10
100
SPATIAL FREQUENCY (cnfeg)
FIGURE 4. Contrast sensitivity (reciprocal of contrast threshold) for test gratings of different spatial frequencies in the absence of masks (open circles) and in the presence of masks of maximum facilitatory strength (solid circles). The ratio of the two is shown by solid triangles. The smooth curves through the data are fitted by eye.
less. A possible explanation might be that thresholds are higher, transducer functions are more shallow and tuning is more narrow at higher spatial frequencies, where the parvo system, not the magno. operates (Kaplan & Shapley, 1986; Hawken & Parker, 1984). Masks would then need to be higher in contrast to stimulate at the steepest part of the function, where the gain (rate of change in output for contrast increment) would be less 1” -r 10 30 loo 03 i 3 0 than at lower spatial frequencies. Finally, we note that all the curves through the data MASK CONTRAST (%I points shown in Fig. 1 are theoretical curves derived FIGURE 3. Contrast thresholds for detecting vertical test gratings of from the model described by Ross and Speed (1991). 7 different spatial frequencies in the presence of masks that are Since the fits are close, the curves describing the tuning identical to the test in both orientation and spatial frequency. The test of facilitation derived from the data could have been was reversed in contrast at a rate of 8.8 Hz; the mask at a rate of 7 HZ. derived directly from the model. The empirically derived Relative thresholds as a function of mask contrast are plotted separtuning curve is different in shape from, but almost ately for each test spatial frequency. Curves are successively displaced upwards by a factor of IO from the bottom (refer to Fig. 1 caption). identical in bandwidth to the theoretical curve for the Data points are derived from the mean of 5 threshold measurements tuning of effective contrast assumed in the model. The by method of adjustment, for observer HS. Curves through each set curves differ in shape because facilitation depends on the of data are fitted by eye. Arrows indicate unmasked thresholds at each interplay of the effective and the adaptive contrast of a test spatial frequency. mask. Whether the model can be extended to explain the decrease in size of facilitation at higher spatial frequenis at or above its own threshold, A similar pattern of cies is under investigation. Preliminary results suggest results has been observed in contrast discrimination that it is necessary to assume that transducer functions thresholds (Bradley & Ohzawa, 1986). When we examine have lower slopes and that the tuning of effective absolute sensitivity to tests at the points of maximum contrast is narrower at higher spatial frequencies. It is facilitation by similar masks, we find it to be constant for intriguing to speculate whether channels at central tunall tests up to 4 c/deg in spatial frequency (see Fig. 4). ing higher than 15 c/deg need to be included to explain This is to be expected if masks reposition transducer the clear facilitation effect found at 20 c/deg. functions, and in doing so reshape them to preserve differential sensitivity, and if they facilitate because they REFERENCES stimulate at the point of maximal differential sensitivity. At spatial frequencies above 4 c/deg unfacilitated sen- Bradley, A. & Ohzawa, I. (1986). A comparison of contrast detection and discrimination. Vision Research. 26. 991-997. sitivity declines, as expected (Campbell & Robson, 1968; Robson, 1966), and so too does the improvement in Campbell, F. W. & Robson, J. G. (1968). On the application of Fourier analysis to the visibility of gratings. Journal qf Phyidogy. London, sensitivity due to facilitation. At these higher frequen197, 551-556. cies, optimal masks (of the same spatial frequency as the Georgeson, M. A. & Georgeson, J. M, (1987). Facilitation and test) behave like sub-optimal masks at lower frequencies: masking of briefly presented gratings: Time course and contrast they facilitate best at higher contrasts and they facilitate dependence. Vision Research, 27, 369-379. -7
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Hawken, M. J. & Parker, A. J. (1984). Contrast sensitivity and orientation selectivity in lamina IV of the striate cortex of old world monkeys. Experimental Brain Research, 54, 367-372. Kaplan, E. & Shapley, R. M. (1986). The primate retina contains two types of ganglion cells, with high and low contrast sensitivity. Proceedings of the National Academy of Science. 2755-2751. Legge, G. E. & Foley, J. M. (1980). Contrast
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Acknowledgement-This
NH&MRC (Australia).
report
was supported
by a grant
from
