1744 J. Opt. Soc. Am. A/Vol. 5, No. 10/October 1988

Spatial waveform discrimination following higher-harmonicadaptation

Mark W. Greenlee and Svein Magnussen*

Neurologische Universitatsklinik mit Abteilung fur Neurophysiologie, Hansastrasse 9, 7800 Freiburg im Breisgau,Federal Republic of Germany

Received March 9, 1987; accepted June 7, 1988

Campbell and Robson [J. Physiol. (London) 197, 551 (1968)] proposed that a near-threshold square-wave gratingcan be distinguished from a sine-wave grating of the same spatial frequency and fundamental amplitude when thechannel tuned to the third-harmonic component of the square wave reaches its own threshold. To test thishypothesis, we measured waveform discrimination thresholds with two-interval forced-choice methods before andafter 4-min adaptation to a high-contrast sine-wave grating, the spatial frequency of which equaled that of thesquare wave's third harmonic. The results indicate that 3f adaptation has only a negligible effect on discriminationthresholds. In a further experiment, we adapted observers to both 3f and 5f harmonic frequencies of the square-wave test grating presented sequentially over 4 min. Although substantial threshold elevations occurred at the 3fand 5f frequencies, the elevation in waveform discrimination threshold was small. These results suggest that theindependent-channel hypothesis alone cannot account for the visibility of complex features (edges) followingharmonic adaptation.

INTRODUCTION

Campbell and Robsonl showed that, near detection thresh-old, a square-wave grating can be distinguished from a sine-wave grating of the same spatial frequency, orientation, andfundamental amplitude if the contrast of these gratings isincreased to the point where the square wave's third har-monic could be detected alone. Blakemore and Campbell 2

subsequently reported that adaptation to a grating causes anincrease in the sine-wave-square-wave discriminationthreshold, provided that the adapting frequency is threetimes higher than the test frequency (and thus equivalent tothe third-harmonic frequency of the square-wave grating).These findings and a number of subsequent reports (e.g.,Refs. 3 and 4) support the idea that a square-wave grating, orany other complex waveform, is encoded by an array ofindependent spatial channels, each tuned to one or more ofthe harmonic components in the pattern.

This picture is complicated, however, both by experi-ments suggesting interactions among channels 5- 9 and by re-cent papers questioning whether channels responding toFourier amplitude and phase spectra are sufficient to ac-count for complex grating detection and discrimination.'l0 "In a previous paper'2 we showed that the detection thresholdfor a low-frequency [0.33 cycle per degree (c/deg)] square-wave test grating was completely unaffected by adaptationto its third- (1 c/deg) and ninth- (3 c/deg) harmonic frequen-cies presented sequentially by a dual-grating adaptationtechnique. These findings suggest that a low-frequencysquare wave is detected by a mechanism locally respondingto its edges rather than by mechanisms responding indepen-dently to the Fourier components that make up the squarewave. We apply this strategy here to test the original Camp-bell-Robson' hypothesis that the channel tuned to thesquare wave's third-harmonic frequency determines thesine-wave-square-wave discrimination threshold.

METHOD

The sine-wave and square-wave gratings used in the experi-ments were presented on a high-resolution cathode ray tube(Joyce Electronics). The spatial frequency, waveform, spa-tial position, amplitude, and temporal characteristics of thegratings were produced by digital-to-analog conversion froma microprocessor. The display had a space-average lumi-nance of 60 cd/M2 , which was masked to a rectangular fieldof 100 X 15° at 114-cm viewing distance. Daily photometricmeasurements ensured a linear voltage-contrast characteris-tic of the display for the contrast range used.

Contrast thresholds were measured by using a two-inter-val forced-choice technique. A sine-wave grating was ran-domly presented in one of two intervals for 1 sec. Theintervals were defined by auditory signals. The subject hadto press one of two buttons, depending on whether hethought the grating was presented in the first or the secondinterval. A total of 40 trials per measurement was per-formed to determine the threshold. Test contrast was con-trolled by a single staircase, incrementing by 0.1 log unitfollowing an incorrect response and decrementing by 0.1 logunit after a correct response. Discrimination thresholdswere measured by using a similar two-interval forced-choicetechnique. Here, a sine-wave and a square-wave grating ofidentical spatial frequency and orientation were displayedfor 1 sec each in either of two temporal intervals. To com-pensate for the difference in the amplitude of the squarewave's fundamental, the sine-wave amplitude was multi-plied by 4/ar.' The subject's task was to signal in whichinterval the square-wave grating was presented. The abso-lute spatial phase of the test grating was varied from trial totrial to avoid fixed local cues other than waveform.

In the experiments in which we examined the effect ofadaptation at the third-harmonic frequency, subjects adapt-ed for 4 min to a stationary sine-wave grating of 0.4 contrast.

0740-3232/88/101744-05$02.00 © 1988 Optical Society of America

M. W. Greenlee and S. Magnussen

Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. A 1745

The spatial frequency of the adapting grating was 4, 8, or 16c/deg. During adaptation, subjects slowly moved their eyesalong a fixation circle of 3-deg diameter to avoid the induc-tion of retinal afterimages and to create an adaptation effectthat was random with respect to spatial phase. Before andafter this adaptation, subjects were presented sine-wavegratings, in a two-interval forced-choice procedure, and thecontrast thresholds were measured by using the same stair-case procedure over 40 trials. For the discriminationthresholds, a sine-wave and a square-wave grating were pre-sented in either interval, and the subjects had to determineon each trial in which interval the square wave was present-ed. The test frequency was one third of the adapting fre-quency. The adapting frequency was thus equal to thethird-harmonic frequency in the square-wave test grating.Each test period was 2 sec in duration and was followed by a15-sec readaptation period, during which the adapting grat-ing was again presented. The test-readapt sequence oc-curred 40 times, yielding -10 reversals of the staircase. In apreliminary experiment we found that this procedure pro-duced a steady level of adaptation throughout the test peri-od (lasting -15 min). At least 30 min was allowed betweenruns to ensure that all residual adaptation had subsided.The data shown in the figures below are based on four to fivethreshold measurements often conducted in separate re-cording sessions on different days.

In a second set of experiments, subjects adapted to twosine-wave gratings having a contrast of 0.4 and a verticalorientation but differing in spatial frequency. The firstgrating had a spatial frequency of 4.0 c/deg, and the secondgrating 6.7 c/deg. These frequencies correspond to the thirdand fifth harmonics of a 1.33-c/deg square-wave test grating.The spatial frequency of the adapting grating was changedevery second over the 4-min period. After this sequentialadaptation, the contrast threshold elevation for 1.33-, 4-,6.7-, and 9.3-c/deg sine-wave gratings was measured, as wasthe sine-wave-square-wave discrimination threshold at 1.33c/deg. In these experiments, test contrast was controlled bya staircase using a maximum-likelihood algorithm (BestPEST).' 3 The 75%-correct response level along the estimat-ed psychometric function was taken as a threshold measure-ment.

The observers were one of the authors (MWG) and twotrained subjects, JG in the first set of experiments and JO inthe second set of experiments, who were both uninformedabout the aim of the study. All observers had normal orcorrected-to-normal acuity.

RESULTS

Figure 1 illustrates predictions for the sine-wave-square-wave discrimination thresholds based on the Campbell-Robson hypothesis and includes data on the contrast thresh-old elevations caused by adaptation. Figure 1(a) shows thecontrast sensitivity function measured for MWG and thepredicted sine-wave-square-wave discrimination thresholdbased on the sensitivity at the third-harmonic frequency.According to the hypothesis, a translation by a factor of 3would be expected [dotted lines in Fig. 1(a)], since the thirdharmonic has one third of the amplitude of the fundamentalbut three times its spatial frequency.

Figure 1(b) presents the elevation in contrast threshold

caused by 4 min of adaptation to sine-wave gratings of 4(circles), 8 (squares), and 16 (triangles) c/deg for sine-wavetest gratings whose spatial frequency was within -1.5 to+1.5 octaves of the adapting frequency (indicated by ar-rows). On average, thresholds are elevated by 0.5 log unit atthe adapting frequency itself, and the adaptation effect ex-tends over a total of about 2.5 octaves. The effect thisadaptation has on the shape of the contrast sensitivity func-tion is shown in Fig. 1(c), where the continuous curve repre-sents sensitivity before adaptation and the broken curvespresent the sensitivity measured directly after adaptation toeach of the adapting frequencies (denoted again by arrows).This adaptation should also shift the sine-wave-square-wave discrimination thresholds by the same factor, and thepredicted discrimination thresholds are now shown by opensquares.

Figure 2 once again shows the contrast sensitivity function(continuous curves) and the Campbell-Robson prediction ofthe sine-wave-square-wave discrimination thresholds be-fore (dashed curves) and after (dotted curves) adaptation tothe third-harmonic frequency together with the observedresults from two subjects. The filled squares indicate thesine-wave-square-wave discrimination thresholds for 1.33,2.66, and 5.33 c/deg before adaptation, and the open squarespresent these thresholds after adaptation to the respectivethird-harmonic frequencies (4, 8, and 16 c/deg). Obviouslythere is a large discrepancy between the predicted and theobserved results. First, even in the unadapted state theCampbell-Robson model predicts only the 1.33-c/deg sine-wave-square-wave discrimination threshold accurately. Athigher spatial frequencies, the sine-wave-square-wave dis-crimination thresholds are much better than predicted.Second, adaptation to the third-harmonic frequency hasonly a negligible effect on the discrimination threshold.

The spread of adaptation to test frequencies within a ±1-octave range of the adapting grating implies that more thanthe third-harmonic frequency is affected by adaptation atthat frequency. Sensitivity at higher and lower spatial fre-quencies is also reduced. The skeptical reader might argue,however, that our third-harmonic adaptation might havefailed to affect the sine-wave-square-wave discriminationthresholds because sensitivity at even higher harmonic fre-quencies was spared. In order to counter this argument, weadapted to an even larger range of spatial frequencies, usingthe technique of sequential adaptation.' 4

In this experiment, subjects adapted for 4 min to a 0.4-contrast sine-wave grating, the spatial frequency of whichwas changed every second from 4.0 (3f) to 6.7 (5f) c/deg.Each time the spatial frequency changed, a new absolutespatial phase of the adapting grating was randomly chosen,and the subjects moved their eyes as a precaution against theforming of afterimages. Each test period was refreshed by a15-sec readaptation period during which the two adaptinggratings again were interleaved in the same manner. Wecompared the effects that this adaptation had on the sine-wave-square-wave discrimination threshold for gratings of1.33-c/deg spatial frequency as well as the effect on sine-wave detection at spatial frequencies equivalent to those ofthe square wave's first four harmonics.

The results of this experiment are shown separately forobservers MWG and JO in Table 1. The threshold valuesare based on four separate runs, each comprising 40 trials.

M. W. Greenlee and S. Magnussen

1746 J. Opt. Soc. Am. A/Vol. 5, No. 10/October 1988

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The logarithms of these mean values are shown in the table.Results for the sine-wave-square-wave discrimination taskare presented in the first column, and those for detection ofsine-wave gratings, the spatial frequency of which was equalto one of the first four harmonic frequencies of the squarewave, are shown in the next four columns. The first tworows present mean log thresholds for each subject beforeadaptation, and the next two rows show these thresholdsdirectly after 3f/5f adaptation. The next two rows give thecontrast threshold elevation in logarithmic units.

Inspection of the preadaptation and postadaptation sine-wave-square-wave discrimination thresholds (first column)confirms the results of the first experiment. Again, there isa slight increase in threshold, which is significant at the 5%level. Comparing this increase with that shown for thefundamental frequency (second column) indicates that thesizes of these threshold elevations are nearly identical. Thethird and fourth columns show that dual-grating adaptation

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Fig. 1. (a) Contrast sensitivity (left ordinate, filled circles) plot-ted as a function of the spatial frequency of a sine-wave test grating.The filled square symbols show the predicted sine-wave/square-wave discrimination thresholds based on the third-harmonic model.Note that the discrimination threshold scale (right ordinate) isplotted inversely to permit comparisons between sensitivity anddiscrimination threshold. The dotted lines show the translation bya factor of 3, as the third harmonic has a spatial frequency threetimes higher than the square wave's fundamental but one third of itsamplitude. (b) Contrast threshold elevation (in log units) shownas a function of the test spatial frequency for three adapting fre-quencies (circles, 4 c/deg; squares, 8 c/deg; triangles, 16 c/deg). Theadapting frequencies are equal to the third-harmonic frequencies ofthe square-wave test gratings used in the main experiments. Ar-rows denote the positions on the spatial frequency axis of the adapt-ing frequencies. The full bandwidth of adaptation is fairly constantat 1.2 octaves at half-height. (c) The data in (b) are replotted interms of contrast sensitivity. The dashed curve shows contrastsensitivity following adaptation to 4 c/deg, the dashed-dotted curvepresents sensitivity following adaptation to 8 c/deg, and the dashed-double-dotted curve represents sensitivity after adaptation to 16 c/deg. The open square symbols present the model prediction basedon postadaptation threshold of the third-harmonic frequency. Re-sults for MWG.

had a much larger effect on the detection thresholds for thethird- and fifth-harmonic frequencies of the square wave.We performed a multivariate analysis of variance (BMDPprogram 4V, University of California, Berkeley) to test thestatistical significance of the main effects: "subjects,""adapted versus unadapted state," and "test gratings" (sinedetection, sine-wave-square-wave discrimination). A totalof 564 observations (reversal points) was included in theanalysis. As expected, a highly significant effect was foundfor the factor "adapted versus unadapted state" [F = 468.1,degrees of freedom (df) = 1, 544, p < 0.0001] and for thefactor "test gratings" (F = 810.4, df = 4, 544, p < 0.0001).We also found a significant interaction term between thesetwo factors (F = 26.3, df = 4, 544, p < 0.001). This impliesthat the effect of adaptation significantly differed depend-ing on the spatial frequency of the test grating and on wheth-er the task was sine detection or sine-wave-square-wavediscrimination. We then compared contrast thresholds for

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Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. A 1747

the 3f (4-c/deg) test grating with the discrimination thresh-olds (1.33 c/deg) before and after adaptation. The impor-tant term here is the interaction between the factor "adapt-ed versus unadapted state" and the type of task (3f detectionversus sine-wave-square-wave discrimination). If theCampbell-Robson hypothesis were correct, then our 3f/5fadaptation should have had the same effect on these twotasks, Thus the model would predict that the interactionterm should not be significant. This interaction was, how-

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Fig. 2. Contrast sensitivity (left ordinates) and the sine-wave/square-wave discrimination thresholds (right ordinates) are shownas a function of spatial frequency. Discrimination thresholds arepresented as filled and open squares for values measured before andafter adaptation, respectively. Error bars represent one standarderror of the mean of five separate measurements. Note again thatthe discrimination threshold values are plotted inversely to permitcomparisons with sine-wave sensitivity. (a) Data from subjectMWG, (b) those for subject JG.

Table 1. Log Contrast Thresholds Before and After4-min Sequential Adaptation to Two Sine-Wave

Gratings Having Spatial Frequencies of 4 and 6.7 c/deg and a Contrast of 40%a

Sine Wave/Subject Square Wave f 3f 5f 7f

Log CTpreadaptMWG -0.176 -0.371 -0.303 0.011 0.45JO -0.146 -0.344 -0.265 -0.052 0.419

Log CTadaptMWG 0.018 -0.272 0.072 0.23 0.581JO 0.02 -0.26 0.127 0.33 0.574

Log CTelevationMWG 0.19 0.1 0.374 0.219 0.131JO 0.166 0.084 0.393 0.38 0.156

a Contrast threshold elevation (CTelev = log CTadapt - log CTpreadapt) isshown for the sine-wave/square-wave discrimination (1.33 c/deg) and sinedetection for the first four odd harmonic frequencies of the square-wavegrating. Contrast is defined here as follows: c = [(Lmax - Lmin)/(Lmax +

Lmin)] R< 100.

ever, highly significant (F = 59.6, df = 1,200, p < 0.0001),adaptation having a greater effect on 3f detection than onthe sine-wave-square-wave discrimination.

DISCUSSION

Several recent experiments are compatible with the ideathat the detection and discrimination of complex gratingsare based on the coding of the local contrast of the stimuli'sluminance profile rather than on their spatial frequency orrelative spatial phase.10 -'2 The present results and those ofan earlier study on square-wave detection thresholds follow-ing harmonic adaptation are consistent with this conclusion,which suggests the existence of mechanisms selective to localfeatures (edges) formed by several harmonic components.Somewhat surprising, but consistent with this conclusion, isthe finding that the Campbell-Robson model of sine-wave-square-wave discrimination also fails to predict the un-adapted thresholds accurately, except for 1.33 c/deg for ob-server MWG [Fig. 2(a)]. At higher spatial frequencies,thresholds are 0.2-0.3 log unit lower than that predicted bythe model.

The findings in Table 1 indicate that our sequential adap-tation procedure had a robust effect on sensitivity to sine-wave gratings having the same spatial frequency as thoseused in dual-grating adaptation. For both subjects tested,an approximate 0.4-log-unit increase in threshold at 4 c/degand a 0.4- (JO) to 0.2- (MWG) log unit increase at 6.7 c/degoccurred. Despite these threshold increases, the contrastrequired for the subjects to discriminate a square-wave froma sine-wave grating increased on average, by, only 0.17 logunit. This increase is comparable in magnitude with thatfound at the fundamental frequency for sine-wave detection(Table 1, second column), suggesting that this effect mightbe caused not by the elevations at the higher harmonic fre-quencies but rather by a general decline in sensitivity afteradaptation that is nonspecific to spatial frequency. Theanalysis of variance that we performed statistically con-firmed our observation that 3f/5f adaptation had a greatereffect on the detection of the 3f component when presentedalone than on the sine-wave-square-wave discriminationtask.

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The paper of Blakemore and Campbell2 contains a dem-onstration that adaptation to a high-contrast grating makeslow-contrast sine-wave and square-wave gratings having onethird of the adapting frequency momentarily indistinguish-able. This demonstration seems to contradict our findings,since we found little effect on the sine-wave-square-wavediscrimination thresholds after 3f adaptation. On closerexamination of their demonstration, we noted that theseauthors used a high-contrast square-wave grating as anadapting stimulus. We invite the reader to consult theirpaper and repeat the demonstration but now to blur thesquare-wave adapting grating during adaptation. Althoughthis is not equivalent to our sine-wave adaptation, blurringreduces the amplitude of the higher harmonics at the retinaand thus removes the sharp edges in the adapting grating.After such adaptation we found that the sine-wave andsquare-wave gratings could still be easily distinguished. Ittherefore appears that it is not the fundamental of theadapting grating used by Blakemore and Campbell (whichwas equivalent in frequency to the square-wave's third har-monic) but the edges in the square-wave grating that causedthe adaptation that subsequently increased the sine/square-wave discrimination threshold. This observation and ourpresent quantitative results suggest the existence of interac-tions among mechanisms that respond selectively to theedges in the square-wave grating. This type of neural cir-cuit does not appear to adapt well to single sine-wave grat-ings extending over a large region of the visual field.

What sort of mechanism is involved in the detection ordiscrimination of the square wave following adaptation tosine waves having spatial frequencies equivalent to those ofthe square wave's first two higher harmonics? One possiblehint toward answering this question can be found in therecent work by von der Heydt et al.15 They found cells inmonkey striate cortex (VI) that responded robustly to sine-wave gratings of a particular spatial frequency. However,when they presented a square-wave grating having one thirdthe spatial frequency of cell's preferred spatial frequency inthat cell's receptive field there was no response. Thus, al-though the cells selectively responded to the 3f componentalone, they failed to respond when this component was em-bedded in a square wave, suggesting inhibitory interactionsbetween neurons tuned to the different harmonics of thesquare wave.6' 7 We recently showed14 that the adaptationeffect caused by a 4-c/deg sine-wave grating can be partiallycanceled by interleaved adaptation to gratings with spatialfrequencies of 1.3 or 8-12 c/deg. We attribute such a partialcancellation of adaptation to a decline in inhibition, whichwould otherwise come from neighboring channels tuned tospatial frequencies 1.5 octaves either above or below thepreferred spatial frequency of the cell in question. Suchinhibitory interactions could be involved in the detectionand discrimination of complex patterns such as square-wavegratings. It follows that adaptation at the third-harmonicfrequency would not have the effect expected from the inde-pendent-channel hypothesis.

In summary, we have shown that adaptation to the third-and fifth-harmonic frequencies of a square-wave gratingdoes not cause the elevation in threshold for the sine-wave-square-wave discrimination task that was expected based onthe threshold elevation at the square wave's harmonic fre-quencies. This finding suggests that a simple linear filter-

ing approach to spatial waveform discrimination cannot ac-count for the human observer's ability to discriminate sine-wave from square-wave gratings after selective suppressionof sensitivity at harmonic frequencies. This result suggeststhe existence of complex interconnections between neuralmechanisms responding to local features (edges) of the reti-nal image.

ACKNOWLEDGMENTS

This research was supported by the Deutsche Forschungsge-meinschaft, SFB 325 B4. S. Magnussen received support ona sabbatical from the Alexander von Humboldt Foundation(Bonn, Federal Republic of Germany) and from the Norwe-gian Research Council for Science and the Humanities. Theauthors thank Lothar Spillmann and Michael Morgan, whocommented on this study, and J. Gerling and J. Obergfell,who served as subjects.

Some of these findings were presented at the 1985 AnnualMeeting of the Optical Society of America, October 14-18,Washington, D.C.

* Present address, Institute of Psychology, University ofOslo, Box 1094, Blindern N-0317, Oslo 3, Norway.

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2. C. Blakemore and F. W. Campbell, "On the existence of neu-rones in the human visual system selectively sensitive to theorientation and size of retinal images," J. Physiol. (London) 203,237-260 (1969).

3. N. Graham and J. Nachmias, "Detection of grating patternscontaining two spatial frequencies: a comparison of single- andmulti-channel models," Vision Res. 11, 251-259 (1971).

4. M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial frequencychannels in human vision," J. Opt. Soc. Am. 61, 1176-1186(1971).

5. D. J. Tolhurst, "Adaptation to square-wave gratings: inhibi-tion between spatial frequency channels in the human visualsystem," J. Physiol. (London) 226, 231-248 (1972).

6. J. Nachmias, R. Sansbury, A. Vassilev, and A. Weber, "Adapta-tion to square-wave gratings: in search of the elusive thirdharmonic," Vision Res. 13, 1335-1342 (1973).

7. D. J. Tolhurst and L. P. Barfield, "Interactions between spatialfrequency channels," Vision Res. 18, 951-958 (1978).

8. S. Klein and C. F. Stromeyer III, "On inhibition between spatialfrequency channels: adaptation to complex gratings," VisionRes. 20, 459-466 (1980).

9. C. F. Stromeyer III and S. Klein, "Spatial frequency channels asasymmetric (edge) mechanisms," Vision Res. 14, 1409-1420(1974).

10. D. R. Badcock, "Spatial phase or luminance profile discrimina-tion," Vision Res. 24, 613-623 (1984).

11. D. R. Badcock, "How do we discriminate relative spatial phase?"Vision Res. 24, 1847-1857 (1984).

12. M. W. Greenlee and S. Magnussen, "Higher-harmonic adapta-tion and the detection of squarewave gratings," Vision Res. 27,249-255 (1987).

13. H. R. Lieberman and A. Pentland, "Microcomputer-based esti-mate of psychophysical thresholds: the Best PEST," Res.Methods Instrum. 14, 21-25 (1982).

14. M. W. Greenlee and 8. Magnusmen, "Interactions among spatialfrequency and orientation-specific channels adapted concur-rently," Vision Res. (to be published).

15. R. von der Heydt, "Approaches to visual cortical function," Rev.Physiol. Biochem. Pharmacol. 108, 69-150 (1987).

M. W. Greenlee and S. Magnussen