J. P. Thomas and L. A. Olzak Vol. 18, No. 9 /September 2001 /J. Opt. Soc. Am. A 2197

Spatial phase sensitivity of mechanisms mediatingdiscrimination of small orientation differences

James P. Thomas

Department of Psychology, University of California, Los Angeles, Box 951563, Los Angeles, California 90095-1563

Lynn A. Olzak

Department of Psychology, Miami University of Ohio, Oxford, Ohio 45056

Received November 20, 2000; revised manuscript received March 26, 2001; accepted April 19, 2001

Experiments with spatially superimposed gratings have defined mechanisms that sum signals across spatialfrequency bands while mediating discriminations of small differences in orientation. In the present experi-ments, localized stimuli (Gaussian bars and derivatives of Gaussian bars) occupying different spatial fre-quency bands were superimposed in different phase and location relationships to assess the sensitivity of thesumming mechanisms to these differences. Masking (loss of accuracy when a second component is added asa mask) was unaffected by differences in either phase or location (15 min separation). Summation (increasein accuracy when both components vary together) occurs for all phase relationships but is reduced by spatialseparation. © 2001 Optical Society of America

OCIS codes: 330.6100, 330.6130, 330.4060, 330.5510.

1. INTRODUCTIONThe first stage of cortical processing is often modeled as amosaic of linear filters with spatially localized receptivefields and band-pass selectivity for orientation and spatialfrequency. The outputs of these filters are transformedby within-pathway nonlinearities and/or normalizationby pooled gain control processes. Investigators have suc-cessfully modeled a wide range of detection and discrimi-nation data by proposing that decision processes have di-rect access to the transformed outputs of these initialfilters.1–4 However, other visual phenomena have led in-vestigators to propose the existence of a second layer offiltering or summing mechanisms, interposed betweenthe initial filters and decision processes. Graham andSutter5 provide an excellent review of these latter propos-als. The present experiments investigate the phase sen-sitivity of one such interposed mechanism; the one thatOlzak and Thomas6–8 proposed mediates fine orientationdiscriminations.

Olzak and Thomas proposed an array of summing cir-cuits, each of which abstracts information about a par-ticular orientation by summing, over spatial frequencybands, the transformed responses of initial filters tunedto that orientation. A major feature of their proposal isthat when small differences in orientation are discrimi-nated, decision processes use only information providedby this second-order array and do not access the re-sponses of individual initial filters. The proposal is sup-ported by converging evidence from several different ex-perimental paradigms: concurrent responses,9

discrimination under stimulus uncertainty,8 and cuesummation.6,7 The present experiments use the cue-summation paradigm to explore the phase sensitivity ofthe proposed mechanism.

Small differences in orientation, as represented in the

0740-3232/2001/092197-07$15.00 ©

retinal image, play a role in many visual processes, e.g.,identifying small differences in the shapes or orientationsof objects and using linear perspective in judging dis-tances. The features whose orientations are judged areoften broadband stimuli such as edges, lines, or bars.Because the physical signatures of these features includespecific phase relationships among their components, it isof interest to know the phase selectivity of the mecha-nisms that mediate judgments about the orientations ofthe features. In the context of how features are locatedin space, differing proposals have been made concerningphase. For example, Marr and Hildreth10 proposed aphase-sensitive algorithm for edge detection, in which theretinal image is first filtered at different spatial scales orfrequency bands and then a search is made for zero cross-ings in the filtered images that are spatially coincidentacross frequency bands. At the other extreme, Morroneand Burr11 proposed that the peak generated in the spa-tial distribution of contrast energy, defined as the sum ofthe squared responses of paired sine and cosine filters, vi-sually determines the location, but not other characteris-tics, of an edge or line. Such a mechanism is phase in-sensitive. The present experiments ask whether themechanisms that mediate orientation discriminations areselective with respect to phase or whether they sum overphases as well as over spatial frequency bands. Previousexperiments did not vary the phase relationships ofstimulus components and provide no information on thisquestion.

As proposed by Olzak and Thomas,6,7 the response ofeach summing circuit is determined as follows:

Ok, j 5 (i

wk,iri, j , (1)

2001 Optical Society of America

2198 J. Opt. Soc. Am. A/Vol. 18, No. 9 /September 2001 J. P. Thomas and L. A. Olzak

where Ok, j is the response of summing circuit k to stimu-lus j, ri, j is a single number representing the transformedresponse of filter i to stimulus j, and wk,i is a weight thatdetermines the selectivity of the summing circuit with re-spect to spatial frequency, orientation, and phase rela-tionships. The value of wk,i is not task dependent; it isthis property that differentiates the action of the sum-ming circuit from the weighted sums used by decision pro-cesses. Previous research6,7 has shown that in themechanisms mediating orientation judgments, wk,i is in-sensitive to the spatial frequency of pathway i but is se-lective with respect to the latter’s orientation tuning.The main goal of the present research is to explore the se-lectivity of wk,i with respect to spatial phase.

The experiments use localized stimulus componentsthat differ in their phase spectra: a low-frequencyGaussian bar; a low-frequency quasi-edge formed by dif-ferentiating the bar; and a high-frequency quasi-edgeformed by differentiating a narrower bar. These compo-nents are paired in different combinations in order to de-termine whether the summation process is phase selec-tive or whether it occurs equally over all phaserelationships. In the experiments combinations of mask-ing and cue-summation conditions6,7 are used to evaluatethe summation process.

2. METHODA. StimuliThree stimulus components were used. (1) A positive-contrast Gaussian bar. Its luminance distribution was abivariate Gaussian with standard deviations of 20 minalong the vertical axis and 7.5 min along the horizontalaxis. (2) A wide quasi-edge, formed by taking the first de-rivative of the Gaussian bar along the horizontal axis.(3) A narrow quasi-edge, formed by taking the first deriva-tive, along the horizontal axis, of a Gaussian bar withstandard deviations of 20 min on the vertical axis and 1.5min on the horizontal axis. For simplicity, these compo-nents will be called the wide bar, the wide edge, and thenarrow edge, respectively. These components are illus-trated in Fig. 1, and their power density spectra areshown in Fig. 2. Table 1 gives contrasts of the compo-nents, defined as (maximum luminance 2 backgroundluminance)/background luminance.

The components were presented alone, in control con-ditions, or combined two at a time in four different pair-ings:

1. Same phase edges: The wide and narrow edgeswere spatially superimposed with zero crossings coinci-dent before rotation from vertical and the light areas ofboth components located to the left of the zero crossings.

2. Opposite phase edges: The wide and the narrowedges were spatially superimposed with zero crossings co-incident before rotation but with the light area to theright of the zero crossing in one component and to the leftof the zero crossing in the other component.

3. Bar-edge: The wide bar and the narrow edge werespatially superimposed with the zero crossing of the nar-row edge coincident with the peak of the wide bar beforerotation.

4. Offset edges: The wide and the narrow edges werespatially superimposed with the zero crossing of the nar-row edge located 15 min to the left of the zero crossing ofthe wide edge. The light area was to the left of the zerocrossing in both components.

The stimuli were superimposed on a 200-cd/m2 uniformcircular background, 3 deg in diameter, which was locatedin the center of a 15 3 15 deg surround of 110 cd/m2.

Fig. 1. Top row, individual stimulus components (left to right):wide bar, wide edge, and narrow bar. Bottom row, examples ofpairs superimposed in the negative cue-summation configuration(left to right): opposite phase edges, bar–edge. Marker: 0.5deg of visual angle.

Fig. 2. Power density spectra of the three stimulus components.

J. P. Thomas and L. A. Olzak Vol. 18, No. 9 /September 2001 /J. Opt. Soc. Am. A 2199

Table 1. Mean Discrimination Accuracy by Subject, Condition, and Component Pairing

A, Control B, Control A, Masked by B B, Masked by A Positive Negative

Observer LAOA 5 wide positive edge, D 5 0.7 deg, contrast 5 0.165 (163 threshold)B 5 narrow positive edge, D 5 0.7 deg, contrast 5 0.082 (73 threshold)

1.69(0.08) 1.77(0.07) 1.02(0.07) 1.23(0.15) 2.29(0.08) 1.07(0.07)A 5 wide negative edge, D 5 0.7 deg, contrast 5 0.165 (163 threshold)B 5 narrow positive edge, D 5 0.7 deg, contrast 5 0.082 (73 threshold)

1.61(0.12) 2.02(0.15) 0.78(0.10) 1.15(0.08) 2.14(0.15) 0.45(0.04)A 5 wide positive bar, D 5 0.7 deg, contrast 5 0.32 (263 threshold)B 5 narrow positive edge, D 5 0.7 deg, contrast 5 0.082 (73 threshold)

1.72(0.13) 1.95(0.08) 1.25(0.08) 1.32(0.12) 2.36(0.15) 1.25(0.05)A 5 wide positive edge, D 5 0.7 deg, contrast 5 0.165 (163 threshold)B 5 narrow positive edge, D 5 0.7 deg, contrast 5 0.082 (73 threshold), offset 15 min

2.17(0.167) 2.36(0.18) 1.65(0.13) 1.63(0.21) 2.14(0.28) 2.25(0.25)Observer JPT

A 5 wide positive edge, D 5 0.8 deg, contrast 5 0.14 (203 threshold)B 5 narrow positive edge, D 5 0.8 deg, contrast 5 0.06 (53 threshold)

2.16(0.21) 1.50(0.12) 1.01(0.11) 1.02(0.11) 2.24(0.03) 0.14(0.18)A 5 wide negative edge, D 5 0.8 deg, contrast 5 0.14 (203 threshold)B 5 narrow positive edge, D 5 0.8 deg, contrast 5 0.06 (53 threshold)

1.98(0.17) 1.76(0.09) 0.97(0.18) 0.68(0.07) 1.99(0.12) 0.66(0.23)A 5 wide positive bar, D 5 0.8 deg, contrast 5 0.20 (203 threshold)B 5 narrow positive edge, D 5 0.8 deg, contrast 5 0.06 (53 threshold)

1.54(0.04) 1.73(0.12) 1.05(0.11) 1.23(0.10) 1.91(0.13) 0.89(0.13)A 5 wide positive edge, D 5 0.8 deg, contrast 5 0.14 (203 threshold)B 5 narrow positive edge, D 5 0.8 deg, contrast 5 0.06 (53 threshold), offset 15 min

2.04(0.11) 1.83(0.13) 1.80(0.18) 1.02(0.11) 2.15(0.10) 1.65(0.11)

Each stimulus was presented for 0.5 s, with abrupt onsetand offset. The stimulus display was viewed binocularlyfrom a distance of 1.7 m.

B. ProcedureThe task of the observer was to discriminate between twostimuli that differed slightly with respect to the orienta-tion of one or both components: The component in onestimulus was rotated a fixed amount counterclockwisefrom vertical, and the corresponding component in thesecond stimulus was rotated clockwise by the sameamount. Table 1 gives the rotations used, which were de-termined by the procedure described below. Only twostimuli were used in a block of trials. One stimulus waspresented on each trial, and the observer identified whichit was. The identification response was made with a6-point rating scale in which 1 indicated high confidencethat one stimulus had been presented and 6 indicatedhigh confidence that the other stimulus had been pre-sented. Ratings were converted to d8 by application of astandard signal detection theory model assuming equal-variance Gaussian distributions.12

For each of the pairings described in Subsection 2.A,measurements were made in six different conditions, il-lustrated in Fig. 3. In the two control conditions (one foreach component), each stimulus comprised just one of thetwo components used in that pairing. In the two mask-ing conditions (one for each mask–test combination), eachstimulus comprised two components: one rotated compo-nent and one vertical component, which served as themask. In the positive-cue-summation condition, each

stimulus comprised two components, both of which wererotated counterclockwise in one stimulus and clockwise inthe second stimulus. In the negative-cue-summationcondition one stimulus comprised one component rotatedcounterclockwise and the second component rotatedclockwise. The opposite rotations were used in the sec-ond stimulus.

The contrast and rotation values for each componentand observer were determined in preliminary measure-ments under control conditions. The purpose of theseprocedures was to equate the accuracy of discrimination

Fig. 3. Illustration of the six different measurement conditions.The dark, wider rectangle represents one of the two superim-posed components in each pairing. The open, narrower rect-angle represents the second component.

2200 J. Opt. Soc. Am. A/Vol. 18, No. 9 /September 2001 J. P. Thomas and L. A. Olzak

across components, given a fixed difference in orientation.The contrast of the narrow edge was fixed at 5 (observerJPT) or 7 (observer LAO) times the detection thresholdfor that component. Using this contrast, we varied theamount of rotation across blocks of trials to estimate therotation yielding a d8 between 1.5 and 2.0. Using this ro-tation, we varied the contrasts of the wide edge and widebar across blocks of trials to estimate the contrasts yield-ing the same accuracy.

For a given pairing, measurements were made underall six conditions within a single daily session. Eachmeasurement consisted of a block of 100 trials. Measure-ments were repeated on 5 (LAO) or 6 (JPT) different days.The order in which the conditions were measured withina session was randomized over days and observers. Forobserver LAO, the repetitions for the four different pair-ings were made in four separate series of daily sessions.For observer JPT, sessions for the same phase edges andoffset edges pairings were interleaved. Sessions for theopposite-phase edges and bar–edge pairings were inter-leaved in a separate series.

Statistical significance was evaluated by a separateanalysis of variance for each observer. The four differentpairings were treated as a fixed between-groups variable,and the six different conditions were treated as a fixedwithin-group variable. Repetitions over sessions weretreated as a random variable. Each cell entry was the d8computed from the 100 trials for that particular combina-tion of condition, session, and pairing. Significant maineffects and interactions were further analyzed by plannedcomparisons. Each of the measures described in Subsec-tion 2.C was based on within-session comparisons. Itsstatistical precision was estimated from variability of thecomparisons across sessions.

C. MeasuresDiscrimination accuracy was measured by d8. For pur-poses of interpretation, the contribution of each summingcircuit to d8 is defined as follows:

dk,~AvsB !8 5 ~Ok,A 2 Ok,B!/sk 5 (i

wk,i~ r i,A 2 r i,B!/sk ,

(2)

where dk,(AvsB)8 is the accuracy component contributed bysumming circuit k for discrimination between stimuli Aand B, the overbar indicates mean value, and sk is thestandard deviation of the distribution of Ok,A . sk istaken to be constant, an assumption supported by uncer-tainty studies.8 We assume that the observer optimallycombines information from different summing circuits,yielding the resultant d8 for discrimination betweenstimuli A and B13:

d ~AvsB !8 5 H(k

@dk,~AvsB !8 #2J 0.5

. (3)

1. Masking EffectsMasking effects were determined by comparing perfor-mance in the masking condition with performance in thecorresponding control condition. An effect was computedfor each test–mask combination. For purposes of inter-pretation, it is convenient to divide the difference in the

numerator of Eq. (2) into two parts, one part reflecting thedifference in responses of pathways that respond to thelow-frequency component in stimuli A and B and one partreflecting the differences in responses of pathways thatrespond to the high-frequency component. In the mask-ing task, one part will approximate zero because its driv-ing component is the same in the two stimuli.

2. Configuration EffectsConfiguration effects were measured by comparing per-formance in the positive-cue-summation condition withperformance in the negative condition. The result of thiscomparison depends on the phase selectivity of theweighting function wi,j . If, on the one hand, the functionis independent of phase, both stimulus components willcontribute fully to the numerator on the right-hand sideof Eq. (2), regardless of their phase spectra. When bothcomponents tilt counterclockwise in one stimulus andboth tilt clockwise in the other, the sum of the differences,and thus dk,(AvsB)8 , is maximized. When the two compo-nents in each stimulus tilt in opposite directions, the sumof the differences, and thus dk,(AvsB)8 , is reduced. Thusgreater accuracy will occur in the positive condition. Onthe other hand, if the weighting function is sensitive tophase, the extent to which responses driven by the twostimulus components are summed will depend on thephase spectra of the components. When the componentshave different spectra, the configuration effect will be re-duced. In the limit, only a single stimulus componentdrives a given summing circuit, and dk,(AvsB)8 for that cir-cuit takes the same value as in the corresponding mask-ing condition. Assuming that each stimulus componentactivates a stochastically independent summing circuit,an ideal observer would combine the information from thetwo circuits, and, per Eq. (3), d8 for the discriminationwould be the Euclidean sum of the d’s in the masked con-ditions, regardless of whether the components are com-bined in the positive or negative configuration.

3. Linearity of d8 SummationLinearity of d8 summation is assessed by comparing per-formance in the positive-cue-summation condition withthe sum of performances in the two masking conditions.When the weighting function wi,j is independent of phase,the responses ri,j generated by the two stimulus compo-nents will be summed within each summing circuit re-gardless of the phase spectra of the components, and d8 inthe positive-cue-summation condition will be the linearsum of the two d’s obtained in the relevant masking con-ditions. (For the conditions of the present experiments,linearity of d8 summation holds within measurement er-ror even if the summation within summing circuits is it-self nonlinear, provided that the nonlinearity is within re-alistic bounds.7) However, if wi,j depends on phase,summation will be reduced when the components differ intheir phase spectra. In the limit, each summing circuitwill be driven by a single stimulus component, and, as in-dicated above, d8 in the positive cue condition will be theEuclidean sum of the two d’s in the masked conditions.

For each of the above comparisons, the analysis of vari-ance tested the linear differences between the d’s ob-

J. P. Thomas and L. A. Olzak Vol. 18, No. 9 /September 2001 /J. Opt. Soc. Am. A 2201

served in the conditions being compared. For ease ofinterpretation, Figs. 4–6 present these comparisons inthe form of ratios. The two forms of comparison lead tothe same conclusions in all cases.

Fig. 4. Masking ratios for the different pairings: masked d8 di-vided the corresponding control d8.

Fig. 5. Configuration ratios for the different pairings: d8 in thenegative-cue-summation condition divided by d8 in the positive-cue-summation condition.

Fig. 6. Summation ratios for the different pairings: d8 in thepositive-cue-summation condition divided by the sum of the d8values in the corresponding masking conditions.

3. RESULTSTable 1 gives accuracy measures, in the form of mean d8values, for each subject and each experimental condition.Each mean is an average of five (observer LAO) or six (ob-server JPT) daily d8 values. The standard errors (in pa-rentheses) were computed from the variation over days.In all pairings it was necessary to set the contrast of thelower-frequency component substantially higher thanthat of the higher-frequency component in order toachieve parity of performance in the control condition.When contrasts were normalized against detectionthresholds, the contrasts of the lower-frequency compo-nents were two to four times greater than the contrasts ofthe higher-frequency components.

Significant masking occurred in all stimulus pairings;i.e., judgments of the orientation of one component wereless accurate when the second component was superim-posed in the vertical orientation than when the first waspresented alone (p , 0.02 in all cases). The amount ofmasking was not affected by the substantial difference incontrast between the members of each pair. There is nosystematic trend for the higher-contrast component toproduce greater masking than the lower-contrast compo-nent.

Figure 4 shows masking effects for each of the compo-nent pairs. Masking is expressed as the ratio of accuracyin the masked condition to accuracy in the control condi-tion, averaged over both components. The profiles for thetwo subjects are alike, with a tendency for the greatestmasking to occur when wide and narrow edges are com-bined in opposite phase. However, the variation in theamount of masking across pairs reaches significance onlyfor subject JPT ( p , 0.01) and is only borderline for sub-ject LAO ( p 5 0.066).

Figure 5 shows the configuration effect, expressed asthe ratio of accuracy in the negative cue-summation con-dition to accuracy in the positive condition. As explainedabove, if the summation process is so sensitive to phasethat only a single component drives any one summing cir-cuit, a ratio of 1.0 is expected. If the summation processis insensitive to phase, a substantially smaller ratio is ex-pected. Ratios for the spatially superimposed pairs areall significantly less than 1.0 (p , 0.01 in all cases).Among these superimposed pairs, the effect of differingphase relationships is significant for JPT ( p , 0.01) butonly borderline for LAO ( p 5 0.06). Furthermore, thetwo subjects show different patterns of variation over thethree different phase relationships.

Spatial separation of the two components significantlyreduces the configuration effect (comparison of superim-posed positive edges with spatially offset positive edges,p , 0.01 both subjects). The accuracy ratio for JPT isstill significantly less than 1.0 ( p 5 0.02), indicatingsome degree of summation, while the ratio for LAOslightly exceeds 1.0 and is consistent with a total lack ofsummation.

Figure 6 shows the ratio of accuracy in the positive-cue-summation condition to the sum of accuracies in themasked conditions. To the extent that each summing cir-cuit sums the signals from both stimulus components,thisratio is expected to be 1.0.7 However, if the components

2202 J. Opt. Soc. Am. A/Vol. 18, No. 9 /September 2001 J. P. Thomas and L. A. Olzak

are processed separately in the sense that each summingcircuit is driven by only one component and informationfrom the different summing circuits is combined in accor-dance with Eq. (3), the expected ratios for the presentdata range between 0.72 and 0.73 (indicated in the figureby the horizontal bar). For both superimposed edgepairs, the ratios are significantly greater than the valuesfor separate processing (p , 0.01 for both subjects) anddo not differ significantly from the value of 1.0. At theother extreme, the ratios for the spatially separated edgesare consistent with separate processing and significantlyless than the 1.0. The ratios for the bar/edge combina-tion lie in between: They do not differ significantly from1.0, but only for LAO do they differ significantly from thevalue expected for separate processing.

4. DISCUSSIONThe wide bar and edge were presented at higher con-trasts, relative to their detection thresholds, than the nar-row edge in order to equalize discrimination performancein the control conditions. The need for higher contrastsreflects, at least in part, the broader bandwidths with re-spect to orientation of the wide components and, perhaps,of the initial filters that they activate.

Significant masking was observed for all stimuluspairs, indicating that whatever mechanism mediates themasking has a wide bandwidth in the spatial frequencydomain. This finding is consistent with results from ear-lier experiments that used grating patches for stimuli.6,7

Spatial separation of the components only slightly re-duced the magnitude of the masking effects, which sug-gests that the mechanism also has a fairly broad spatialfootprint. Although nonlinearities within the pathwaysdriven by the initial filters and within the summing cir-cuits may contribute to the observed masking, the broadspatial footprint suggests a major role for gain controlprocesses in which each response is normalized againstthe summed activity in a broad pool of heterogeneouslytuned pathways.14–17

Evaluation of the phase sensitivity of the second-ordersumming mechanisms was the main goal of the presentexperiments. Superimposing the wide and the narrowedges in the same phase and in the opposite phase pro-duced the same pattern of summation results. Therewas no consistent difference in either the magnitude ofthe observed configuration effect or the results of the d8summation test. For both subjects, the latter signifi-cantly rejected the possibility of separate processing oforientation signals from the two edge components.These results argue that the summing mechanism is in-sensitive to the phase differences produced by contrast re-versal.

Results obtained with the wide bar and narrow edgecombination are less straightforward. On the one hand,a significant configuration effect was obtained for bothsubjects, and the results of the d8 summation test wereconsistent with summation within a single mechanism.On the other hand, the results of the latter test signifi-cantly rejected separate processing only in the data ofJPT. On balance, these results support the propositionthat orientation signals from these two components were

summed but possibly not as completely as in the case ofthe edge–edge combinations.

Although the stimuli to be discriminated differed pri-marily in the orientations of their components, other fea-tures of the stimuli may have influenced the judgments,particularly in the case of the bar–edge combination.For example, the narrow edge might be perceived as di-viding the bar into two parts that, in the masking andnegative cue summation conditions, would have differentconfigurations depending on which stimulus was pre-sented. Use of such a cue would tend to reduce bothmasking and configuration effects. Because the cuewould be useful in the masking condition, but not in thepositive-cue-summation condition, it would reduce the ra-tio used in the linear summation test and bias the resultsof the test toward accepting the proposition of separateprocessing. More generally, the use of such cues wouldtend to weaken evidence of summation and, to the extentthat such cues were more salient in one pairing of compo-nents than another, lead to the appearance of some de-gree of phase sensitivity in the summation process.Thus, weaker evidence obtained with the bar–edge com-bination may reflect the use of such cues rather than a re-duced sensitivity of the summing mechanism to this com-bination of phases.

A second possible artifact is that response interferencereduces performance in negative-cue-summation condi-tions; i.e., through associations built up in other condi-tions, one component signals one type of response whilethe other component signals the opposite. To assess thispossibility, we ran controls in which observers attemptedto isolate and judge only a single component throughout agiven session using a constant relationship between per-ceived orientation and response. We found no evidence ofresponse interference. Results from concurrent responsestudies using grating stimuli also argue against an effectof response interference.9

To summarize, the evidence from these experiments in-dicates that the mechanisms that mediate fine orienta-tion discriminations sum over different phases, as well asover different spatial frequency bands. The bar–edge re-sults suggest that a small degree of selectivity might ex-ist, but this aspect of the data might also reflect the use ofcues other than perceived orientation. One conclusion tobe drawn from the lack of narrowly defined selectivity forphase is that the property of orientation is representedseparately in the visual system from the phase propertiesthat identify features as edges, lines, or bars.

ACKNOWLEDGMENTSThis work was supported by research grant EY00360from the National Eye Institute and by a grant from theUniversity of California, Los Angeles, Council on Re-search. The manuscript was prepared while J. P. Tho-mas was a Fellow of the Hanse Institute for AdvancedStudies in Delmenhorst, Germany.

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