Perceived contrast as a function of adaptation duration

OC42-6989/94 $6.00 + 0.00 Copyright 0 1993 Pergamon Press Ltd

Vision Ref. Vol. 34, No. 1, pp. 3140, 1994 Printed in Great Britain. All rights reserved

Perceived Contrast as a Function of Adaptation Duration STEPHEN

T. HAMMER,*

ROBERT J. SNOWDEN,*

ANDREW T. SMITH*

Received 7 April 1993; in revised form 27 May 1993

We measured how tbe perceived contrast of a sinusoidal grating fades as a function of time. Measurements were made for a range of temporal and spatial frequencies and eccentricities. Patterns of high temporal and low spatial frequency exhibited a greater and more rapid loss of apparent contrast (fade) than those of medium frequencies. The rate and amount of fading for a subgroup of moderate frequencies increased when presented peripherallyrather than fovealiy. Further rne~e~n~ revealed that gratings of disparate spatial frequencies, but with the same threshold sensitivity, exhibit very different fading characteristics but equal threshold elevation. We conclude that the ditferential loss of apparent contrast is not an artefact of diRering proxi~ti~ to #reshow nor can it be accounted for by differences in the adaptability of underlying spatio-temporal mechanisms at threshold. The differences in fading may thus reflect either a difference in the adaptability of underlying channels ahove threshoId or a ~e~ntial eon~i~tion of such channels to perceived contrast. Spatio-temporal frequency Adaptation

Perceived contrast

INTRODUCTION

There is substantial evidence that there are two or possibly three temporal channels in the human visual system, the lowest frequency channel being low pass and the channel(s) optimally tuned to higher frequencies being band pass (Kulikowski & Tolhurst, 1973; Mandler & Makous, 1984; Moulden, Mather & Renshaw, 1984; Anderson & Burr, 1985; Hess & Plant, 1985; Hammett & Smith, 1992; Hess & Snowden,l992). Harris et al. (1990) have suggested that differences in the time to cessation of perceived flicker at different temporal frequencies may reflect differences in the adaptability of underlying temporal channels. They found that the duration of adaptation required for subjects to report the cessation of perceived flicker in the periphery was inversely related to temporal frequency, and suggested that the higher temporal frequency channel may thus adapt faster. Indirect evidence consistent with this notion was reported by Smith and Edgar (1993) who found that the effective modelling of velocity aftereffects requires the assumption that the bandpass (higher frequency) temporal channel has greater adaptability. Differences found in the time to cessation of flicker and movement with eccentricity are suggestive of differential adaptability across the visual field as well as across temporal frequencies (Hunzellmann & Spillmann, 1984; Schieting & Spillmann, 1987). However, recent evidence (Snowden & Hess, 1992; Allen & Hess, 1992) has indicated that the sensitivity of the low-pass temporal filter decreases in the periphery. It is possible that differences in time to cessation of flicker may reflect differential changes in sensitivity rather than differential adaptability.

A strictly fixated stimulus presented in the periphery gradually fades and finally disappears (Troxler, 1804). This “Troxler effect” may be accounted for by a process of local luminance adaptation which changes sensitivity in such a way as to equalise retinal outputs (Brindley, 1960). Burbeck and Kelly (1984) have shown that the fading of stabilized images in the fovea and the formation of negative afterimages is well described by such a process. The absence of the Troxler effect for foveally presented stimuli is believed to be due to eye movements which effectively shift the retinal image and thus minimize local adaptation effects. Putative analogues of the Troxler effect have been reported for flicker (LeGrand, 1937; Monjl8c Bernsdorff, 1952; Schieting & Spillmann, 1987; Harris, Calvert & Snelgar, 1990; Hammett & Smith, 1990) and movement (Cohen, 196.5; Mackay, 1982; Hunzellman & Spillmann, 1984) whereby the perception of flicker or movement is eliminated leaving the percept of a stationary stimulus. These studies have shown that apparent flicker and motion decreases and eventually ceases for patterns presented in the periphery. Whilst the Troxler effect may be explained in terms of local adaptation to luminance the analogous effect for movement has been reported for stimuli where the mean luminance of the image over space and time is constant (Hunzellmann & Spillmann, 1984), making such an explanation untenable.

*VisionResearchUnit, School of Psychology,University of College of Cardig, P.O. Box 91, CardiffCFI 3YG, Wales.

Periphery

Wales 31

STEPHEN T. HAMMETT et al.

32

gratings decreased after adaptation in a similar way to apparent flicker and movement. Several authors (e.g. Blakemore, Muncey & Ridley, 1973; Georgeson, 1985) have reported slight reductions in the apparent contrast of test gratings after adaptation to gratings of the same contrast and spatio-temporal frequency. Georgeson (1985) found that perceived contrast decreases profoundly when the contrast of the adapting grating is greater than that of the test, but only slightly when the test and adapting patterns were of the same contrast. He suggested a simple subtractive adaptation model of these effects and proposed that his findings were commensurate with the existence of multiple contrast channels. However, Georgeson’s (1985) findings were obtained with a single spatial and temporal frequency. We measured the perceived contrast of a grating after adaptation to a grating of the same contrast at a number of temporal and spatial frequencies and eccentricities as a function of time. This was accomplished by using a modified “method of a thousand staircases” procedure (Cornsweet & Teller, 1965; Mollon & Polden, 1980). This enabled a determination of the perceived contrast of the adapting grating at various adaptation durations. Here, we report findings that indicate that, for a constant adapting contrast, the adapting effect is greater for high temporal and low spatial frequencies and for stimuli

Whilst these findings are suggestive of differential adaptability of underlying temporal mechanisms, the evidence is largely limited to differences in the time taken to cessation of perceived flicker. Direct measurements of perceived contrast as a function of time have not been reported. A further difficulty is that previous studies have employed spatially complex stimuli. Thus the limited findings so far reported do not allow firm conclusions vis h vis the adaptability of underlying spatio-temporal mechanisms. Clearly, any such differential adaptability would be of interest, both intrinsically, and also in that it may provide a useful technique for further investigation of underlying mechanisms. However, previous studies which have employed time to cessation of flicker as a dependent variable have proved prone to difficulties of interpretation. We have therefore attempted to derive evidence relating to the adaptability of underlying mechanisms by measuring perceived contrast as a function of time for a number of spatio-temporal frequencies and eccentricities. EXPERIMENT 1: PERCEIVED CONTRAST AS A FUNCTION OF TIME

We investigated whether the perceived contrast of temporally modulated (counterphased) sinusoidal

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FIGURE 1. Apparent contrast as a function of adaptation duration is shown for two subjects for 4 Hz (open circles), 8 Hz (solid circles), 16 Hz (open squares) and 24 Hz (solid squares) and three eccentricities. The spatial frequency was 0.5 c/deg.

40

PERCEIVED

CONTRAST

AND ADAPTATION

presented in the periphery than for foveally presented stimuli of moderate frequencies. Method Apparatus and stimuli. All stimuli were horizontally oriented sine-wave gratings of 0.5,2 or 8 c/deg generated electronically under computer control. The gratings were modulated over time ~counte~hased) at various temporal frequencies (4-24 Hz). They were displayed on a Hewlett-Packard 1332A oscilloscope with P4 phosphor. The mean luminance of the display was 19 cd m--2 and the frame rate was 122 Hz. The display was masked to leave two vertically-aligned circular apertures of 4 deg, their adjacent edges separated by 2 deg. The mean luminance of the masked area was approx. 3 cd m2. A small LED fixation point was located either centrally or at 10 or 20deg to the right of the centre of the display. Subjects used a chin rest at a viewing distance of 57cm. The experiment was conducted in a semidarkened room. Procedure. Contrast matches as a function of time were obtained for stimuli presented at three eccentricities (0, 10 and 20 deg) and four temporal frequencies (4, 8, 16 and 24 Hz). Contrast is defined as Michelson contrast -t Lmin where C is consuch that C = L,,, - L,,JL,,, trast, L,,, is maximum luminance and Lminis minimum luminance. On each trial a “standard” grating of 39% contrast was presented continuously for 42 set in the upper window of the display. At 6 set intervals a “test” pattern, of the same temporal frequency as the standard, was presented in the lower window for 1 sec. The onset of the first test pattern was coincident with that of the standard. Onset and offset of the gratings was abrupt and was signalled by an auditory tone. At offset of the test pattern an homogeneous field of the same mean luminance was presented. Subjects indicated which grating, standard or test, appeared to have the higher contrast by pressing a button. The contrast of the test pattern was controlled by a modified PEST procedure (Taylor & Creelman, 1967) and depended upon subjects’ previous responses. The initial contrast of the test was randomized within the range 3045%. This range was chosen on the basis of pilot results which indicated a substantial loss of perceived contrast in some conditions. A separate PEST procedure was employed for each temporal interval. The trials were separated by several minutes to allow for recovery and the procedure was repeated at least 32 times for each condition at 0.5 c/deg and 16 times for 2 and 8 c/deg stimuli. A psychometric function was obtained for each temporal interval by fitting a Weibull function (Weibull, 1951) to the data; the 50% point was taken as the contrast match. Estimates of the standard deviations of the threshold estimates, derived using a modified parametric bootstrap procedure (Foster 8c Bischoff, 1991), were typically < 5% of the match estimate. The subjects were two of the authors, STH and RJS, who both had normal vision. Stimuli were viewed binocularly with natural pupils.

DURATION

33

Results and di~c~sio~

Figures 1 and 2 show the results at 0.5 c/deg. The rate of fade for four temporal frequencies at each of three eccentricities is shown in Fig. 1. In the fovea the rate of fade appears to be strongly dependent upon temporal frequency, with lower temporal frequencies fading less and more slowly than high frequencies. This appears to be a graduated effect in the frequency range tested, i.e. there is a reasonably smooth relationship between temporal frequency and rate of fade. The results are less clear in the 20 deg condition. For one of the subjects (RJS) there appears to be no systematic effect of temporal frequency upon rate of fade, the results for the other subject show some evidence of a temporal frequency effect, but the trend is by no means as marked as is found in the fovea. A smaller data set was obtained at 10 deg. Here, the results appear to be intermediate with respect to the fovea1 and 20 deg conditions. Figure 2 shows the rate of fade for both subjects as a function of eccentricity. At all frequencies above 4 Hz, no systematic differences can be discerned. That is to say, there appears to be no difference in the rate of fade of higher frequency gratings at different eccentricities. At 4 Hz, however, the rate and amount of fading is less marked in the case of fovea1 presentation. Figures 3 and 4 shows the results for 2 c/deg stimuli. The results at this spatial frequency appear to be qualitatively similar to those obtained at 0.5 c/deg. There appears to be a gradual increase in fading with temporal frequency although the amount of fading is somewhat less profound than that found at 0.5 c/deg. Figure 4 shows the rate of fading for a 2c/deg stimulus modulated at 4 and 16 Hz for two subjects and two eccentricities. Again, the results are similar to that for 0.5 c/deg; whilst there is little fading for fovea1 presentation, fading increases markedly at 20 deg. Figure 5 shows the results for 8 c/deg gratings presented foveally. No data could be obtained eccentrically at this spatial frequency due to lack of sensitivity. The amount of fading appears to be less than that found at lower spatial frequencies, however the results are qualitatively similar in that fading appears to increase with temporal frequency. To summarize, there are three discernible trends in the data. Firstly, fading tends to increase with increases in temporal frequency. Secondly, fading decreases with increases in spatial frequency. Thirdly, fading tends to increase as eccentricity increases.

EXPERIMENT 2: CONTRAST DETECTION THRESHOLDS AND THRESHOLD ELEVATION One interpretation of the results of Expt 1 may be that the differential rate of fade reflects differences in proximity to threshold. It may be that the rate of fade across spatio-temporal frequencies is constant for a constant multiple of threshold (Harris et al., 1990; though see also Hammett & Smith, 1990) but varies with

STEPHEN T. HAMMETT et at 50

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FIGURE 2. Apparent contrast as a function of adaptation duration for fovea (open circles), 10 deg (solid (squares). The spatial frequency was 0.5 c/deg. SO

differing multiples of threshold. Since we measured fading for a constant physical contrast, such an arrangement would indeed lead to differences in perceived contrast after adaptation. In order to test this interpretation of our results we measured contrast sensitivity for a range of spatial frequencies that were temporally modulated at 8 Hz. measurement of contrast sensitivity over a range of spatial frequencies allowed us to identify patterns of the same sensitivity but different spatial frequencies and to derive estimates of the amount of fading yielded for each by reference to the results of Expt 1. If the differences in fade found in Expt 1 were an artefact of differing proximities to threshold then one would predict that spatial fr~ue~~ies to which the subjects were equally sensitive would yield similar fading characteristics. Threshold after adaptation was also measured for various frequencies in order to establish whether the degree of fading was related to the extent of threshold elevation.

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circles) and

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Method A~~~~~t~s and stimuli. All stimuli were horizontally oriented sine wave gratings modulated at 8 Hz. Stimuli were generated digitally (14~bit) by a V.S.G. Image generator fCambridge Research Systems). They were displayed on a Joyce Ekctronics C.R.T. display at a frame rate of 100 Hz. All stimuli were presented for 1 set and were temporally ramped such that they were

FIGURE 3. Apparent contrast as a function of adaptation duration at 2 cjdeg is shown for two subjects for 4 Hz (open circles), 8 HZ (solid circles), $6 Hz (open squares) and 24 Hz (solid squares). St~rnu~iwere presented foveally.

PERCEIVED

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FIGURE 4. Apparent contrast as a function of adaptation duration at 2 c/deg is shown for fovea1 (circles) and 20 deg (squares) presentation at 4 and 16 Hz.

displayed at full contrast for 0.6 sec. An auditory tone signalled the ~ginning of each stimulus presentation. Stimuli were presented in two vertically-aligned circular windows, each of which subtended 4 deg diameter. The viewing distance was 85.5 cm. As in Expt 1, the windows were separated by 2 deg and a small LED fixation point was located centrally, between the two windows. All other parameters (e.g. mean luminance, aperture size) were the same as those of Expt 1. The subjects were the same as for Expt 1. Procedure, estimates of threshold, Each trial consisted of 20 presentations of each of five interleaved spatial frequencies which ranged from 0.4 to 8.5 c/deg. The order of presentation of stimuli was randomized. The stimuli were always presented in the upper window and subjects indicated whether they had detected the stimulus (yes/no) by pressing one of two buttons. Subjects fixated the LED throughout the experiment. The contrast of the stimuli was controlled by a PEST procedure that was set to converge upon the 75% correct point and depended upon previous responses. A psychometric function was fitted to the data as in Expt 1 and the 75% point was taken as threshold. After initial estimates across a range of spatial frequencies had been derived, further threshold estimates (at least five) were taken over more limited ranges (0.4-1.0 and 7.0-8.5 c/deg) and the mean of these estimates was taken as threshold,

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FIGURE 5. Apparent contrast as a function of adaptation duration is shown for 4Hz (open circles), 8 Hz (solid circles), 16 Hz (open squares)and 24 Hz (solid squares) at 8 c/deg.

36

STEPHEN T. HAMMETT er al

In the case of estimates of threshold after adaptation, each trial consisted of 20 presentations of a single spatial frequency. Prior to the onset of the first trial an adapting pattern was presented for 1 min. After each test pattern had been presented a further 6 set “top-up” adapting pattern was presented. A blank field of the same mean luminance was presented for 100 msec prior to the onset of each test pattern. The spatial and temporal frequency of the adapting pattern was always the same as the test pattern and its contrast was constant for any one trial. A range of adapting contrasts was employed.

6.0-

Results and discussion

Adapting

Figure 6 shows thresholds for both subjects at a range of spatial frequencies modulated at 8 Hz. The threshold estimates indicate that sensitivity for subject STH is equal for patterns of 0.6 and 8 c/deg. Equal sensitivities for subject RJS are found at 0.5 and 8 c/deg. Inspection of Fig. 1 indicates that there is more fading for the 0.5 c/ deg grating at this temporal frequency. Thus the results indicate that patterns which have very similar thresholds may nevertheless fade at different rates. We therefore conclude that the differences in the rate and amount of fade found with spatial frequency are unlikely to be explicable in terms of differential proximity to threshold. Figure 7 shows threshold contrasts for 0.6 and 8 c/deg (STH) and 0.5 and 8 c/deg (RJS) after adaptation (adapting frequency equalled test frequency). The rate and amount of threshold elevation is similar for both spatial frequencies. The results indicate that the adaptability of the mechanisms most sensitive to these patterns at threshold is not straightforwardly related to the rate and amount of fading of the patterns at suprathreshold levels. These results suggest that different spatial frequencies with similar thresholds and threshold elevation characteristics may nevertheless fade at different rates when presented at suprathreshold levels. EXPERIMENT

R J S

3: CONTRAST

GAIN

The results of Expt 2 indicate that differences in fading cannot be attributed to differences in the proximity of

Adapting

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FIGURE 7. Detection thresholds for 0.6 c/deg (STH) or 0.5 c/deg (RJS) (open circles) and 8 c/deg (solid circles) are shown for a number of adapting contrasts. The spatial frequency of the adapting pattern was always the same as the test pattern. The temporal frequency was always 8 Hz.

the physical contrasts of stimuli to detection threshold. However, it may be that patterns with the same detection threshold have different perceived contrasts at suprathreshold levels. If this were the case then differences in fading may reflect differences in the proximity of perceived contrast to detection threshold. In order to examine this possibility we took our two patterns which have equal threshold sensitivity (see Expt 2) and performed contrast matches to a standard pattern, or to one another. Method

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FIGURE 6. Contrast thresholds for two subjects (circles, STH; triangles, RJS) at a range of spatial frequencies modulated at 8 Hz.

The methods were essentially the same as those of Expt 2. Perceived contrast was estimated using two procedures. In the first procedure, a standard (4c/deg, 0 Hz) was presented in the upper window and the contrast of the lower pattern [either 0,6 (0.5) c/deg, 8 Hz; or 8 c/deg, 8 Hz] was adjusted by the PEST procedure in order to produce a contrast match. A standard of intermediate spatial frequency was used in order to minimize the difficulty of the task. The second procedure was similar, except that the low spatial frequency pattern was presented in the upper window, and the high spatial frequency in the lower window in order to derive estimates of perceived contrast for the two patterns relative to one another.

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FIGURE 8. Contrast matches for 0.6 c/deg (solid circks) and 8 c/deg (STH) and 0.5 and 8 c/deg (RJS). The top panel shows matches relative to a standard satic grating of 4 cjdeg. The bottom panel shows matches made directly between 0.6 c/deg (STH) or 0.5 cfdeg (RJS) and 8 c/deg. The line of unit slope represents a veridical match.

Results

The results are shown in Fig. 8. The upper panel shows the results when matching each stimulus to the 4c/deg pattern. At low contrasts, subjects reliably needed less contrast of the low spatial frequency than the high spatial frequency in order to produce a match. At high contrasts matches were nearly veridical. The results from the direct matches (lower panel) are in agreement in showing that less contrast was needed in the low spatial frequency to match the high temporal frequency, whereas at high contrasts the match was approximately equal. Discussion These results suggest that at the adapting contrast we employed in Expt I the two patterns with equated thresholds have approximately equal apparent contrast. Hence their difference in fading cannot be due to unequal initial apparent contrast. The inequality at low contrasts suggests that when physical contrasts are equal then the low spatial frequency appears to have more contrast than the high spatial frequency.

GENERAL

DISCUSSION

It is generally agreed that there are relatively few (two or three) temporal channels in the human visual system. Estimates of the number and shape of the temporal tuning curves using a variety of methods are in agreement that the lowest frequency channel is low pass and that one or two band-pass channels exist that are tuned to higher frequencies (Kulikowski & Toihurst, 1973; Mandler & Makous, 1984; Moulden et al., 1984; Anderson & Burr, 1985; Hess & Plant, 1985; Hammett & Smith, 1992; Hess & Snowden, 1992). Apart from studies of time to cessation of perceived flicker, there is relatively little evidence bearing upon the adap~bility of these temporal mechanisms. A number of physiological studies have reported differences in the adaptabilty of neurones when stimulated at different temporal frequencies (Maddess, McCourt, Blakeslee & Cunningham, 1988; Bonds, 1991). These studies report that cortical cells in the cat are more adaptable and adapt more rapidly to high temporal frequencies. However, Lorenceau (1987) reported that while threshold elevation increases with temporal frequency it is not

38

STEPHEN T. HAMMETT et al.

dependent upon spatial frequency and concluded that his findings were not consistent with differential adaptability of sustained (low-pass) and transient (band-pass) mechanisms. The results of Expt 1 indicate that adapting to a pattern always results in some loss of apparent contrast. The rate and amount of the loss is dependent upon the spatio-temporal frequency of the pattern and its eccentricity. In the fovea, rate of fade appears to be fairly strictly related to temporal frequency for all spatial frequencies tested. Similarly there appears to be a fairly consistent increase in fading with eccentricity for all temporal frequencies tested. The degree of fading tends to decrease as spatial frequency increases. In all conditions tested here, where loss of apparent contrast was relatively large, most contrast was lost within the first 12 set of adaptation. That is to say, the rate of fade tended to decrease over time. The results of Expt 2 indicate that differences in fade cannot be ascribed to differences in proximity to threshold. This is consistent with Georgeson’s (1985) finding that, for a given adaptation duration, perceived contrast is reduced by a constant proportion (K) of adapting contrast, regardless of test contrast. Formally: C apparent = C,,, - CadaptlK where C is contrast. Georgeson measured the perceived contrast of a grating for a single spatial (3 c/deg) and temporal frequency (1 Hz drift) at various test contrasts (i.e. at various multiples of threshold) and found that perceived contrast was always reduced by around one-third of the adapting contrast. Thus both threshold elevation and loss of perceived contrast can be predicted by subtracting approximately one-third of the adapting contrast from the test contrast. The results of Expt 2 indicate that patterns of equal detection threshold exhibit equal threshold elevation. Figure 7 shows that threshold detection changes from around 1.5% before adaptation to around 5.5% after adaptation to a contrast of 40%, a shift of 4% or around one-tenth of the adapting contrast. Thus Georgeson’s model would predict that testing at 40% we would find both patterns appearing to have

around 36% contrast. Whilst the prediction of his model fits well for the pattern of 8 c/deg, the pattern of 0.6 (0.5) fades to around 20% (Figs 1 and 5). Thus our results are apparently inconsistent with a subtractive model of adaptation. At the moment the exact interpretation of our results is unclear, but several possibilities exist. Firstly, it is possible that different spatio-temporal patterns have differential adaptabilities, with temporal frequency increasing adaptability on the whole, possibly through the differential adaptability of the two temporal channels (in Georgeson’s model this would be changing the factor K). However, against this model lies the fact that detection thresholds show no change in K if threshold sensitivity is equated. Secondly, perceived contrast may be computed on the basis of the combined activity of all spatio-temporal channels. Thus such a “combined activity” model must postulate that the rate of fading of, at least some frequencies, is not related to the adaptability of the mechanisms responsible for their detection at threshold. In other words, the model implicates two forms of adaptation which operate at different contrast levels. Thirdly, there could be a single form of adaptation, but this adaptation affects detection and contrast matching tasks differently. One possible way in which this may arise is if the contribution of different temporal channels to perceived contrast is unequal or weighted. Thus the mechanism most sensitive to a given frequency at threshold may be responsible for detection but may not have a proportionate role in the determination of perceived contrast at suprathreshold levels. Our results are consistent with such an arrangement whereby perceived contrast is primarily mediated by the activity of the low-pass temporal channel. As temporal frequency increases, the sensitivity of the low-pass mechanism is reduced. Snowden (1992, 1993) has shown that the rate of threshold elevation with respect to adapting contrast increases when sensitivity is reduced, such that for a wide range of patterns threshold elevation (expressed in dB) is approximately equal for an adapting contrast of around 40%. Thus at a low temporal frequency (where sensitivity is high) threshold may move from say 2 to

1

a

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FIGURE 9. Two functions of the form R = g“(C - C,)e. The broken line depicts a lower value of p than the solid line. The functions have been normalized so as to be equal for an input contrast of 100. A particular response level (0.5) would normally correspond to a higher input contrast for a higher ~1value.

PERCEIVED CONTRAST AND ADAPTATION

6%, whereas at a high temporal frequency (where sensitivity in low) threshold may move from 8 to 24%. Taking Georgeson’s subtractive model (see above) this would mean a fade from 40 to 36 or 24% respectively. Fourthly, perceived contrast may be a very non-linear function of physical contrast. One recent formulation (Georgeson, 1991) has used the formula: R = g”.(C

-

Allen,D. & Hess, R. F. (1992). Is the visual field temporally homogeneous?Vision Research, 32, 1075-1084. Anderson,S. J. Br Burr, D. C. (1985). Spatial and temporal selectivity system.

Blakemore, C., Muncey, J. P. J. & Ridley, R. M. (1973). Stimulus specificity in the human visual system. Vision Research, 13, 1915-1931. Brindley, G. S. (1960). Physiology of the retina and visual pathway. London: Arnold. Burbeck, C. A. & Kelly, D. H. (1984). Role of local adaptation in the fading of stabilized images. Journal of rhe Optical Society of America A, 1, 216-220.

Cohen, R. L. (1965). Motion perception in the peripheral visual field. Cornsweet, T. N. & Teller, D. Y. (1965). Relation of increment thresholds to brightness and luminance. Journal of the Optical

REFERENCES

detecting

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Scandinavian Journal of Psychology, 4, 257-264.

CO)”

where R is the response of a channel, g a multiplicative gain due to “early” factors (such as optics), C the input contrast, C,, the contrast threshold, and P the exponent of a compressive transducer. It is possible that different spatio-temporal channels might have different p values. The effects of changing ,u are illustrated in Fig. 9. As p decreases the function becomes more bowed, thus apparent contrast may increase less quickly at high contrasts for small p values. If adaptation reduces response by a certain amount (dotted line) we can see that this amount of response normally corresponds to a much lower contrast for the pattern of small p value. Thus changes in the value p would predict changes in the amount of fade (if all other factors were equal). Little is currently known about the factor p at various spatio-temporal conditions. However, Legge and Foley (1980) estimate a value of around 0.4 for fovea1 vision. If this interpretation of our data is appropriate we predict that p will decrease for low spatial, high temporal frequency conditions, and as eccentricity is increased. There is some encouraging evidence that this is true for eccentric viewing (Swanson & Wilson, 1985). We find that at low contrasts the pattern of a low spatial frequency appears to have more contrast than the high spatial frequency pattern, whilst they match at high contrasts. This suggests a smaller value for p at low spatial frequencies (a more bowed function) than at high spatial frequencies and therefore supports this interpretation of the fade data. In conclusion, our results indicate that contrast fading occurs differentially across the spatio-temporal surface and visual field. Further, contrast fading is not neatly related to the adaptability of the visual system at threshold (at least for fovea1 viewing). Various possible hypotheses to explain these results are presented. Resolution of these competing hypotheses requires an accurate knowledge of how the visual system computes perceived contrast and how adaptation occurs. The possibilities outlined above are open to experimental verification and may prove fruitful in evaluating current models of contrast adaptation (e.g. Foley & Boynton, 1993; Wilson & Humanski, 1993). We are currently undertaking this task.

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Acknowledgement-S.

T. Hammett and R. J. Snowden were supported by SERC Image Interpretation grant (GR/H52375).