Interactions between spatially tuned mechanisms: converging evidence

Vol. 2, No. 9/September 1985/J. Opt. Soc. Am. A 1551

Interactions between spatially tuned mechanisms:converging evidence

Lynn A. Olzak

Department of Psychology, University of California, Los Angeles, California 90024

Received January 22, 1985; accepted April 18, 1985

Detection and identification performance is measured for four pairs of sinusoidal gratings that differ in spatial-fre-quency separation. A modified two-alternative forced-choice procedure (2 X 2) is used to measure performanceon both tasks simultaneously. The results provide new evidence for the existence of interactions between tunedmechanisms that respond to widely separated frequencies. A method to compare data obtained in the 2 X 2 meth-od quantitatively with both single- and double-response rating data is developed and used to compare the currentdata with previous rating results. The magnitudes of interactions isolated by the three procedures agree closely.

INTRODUCTION

Comparisons of detection and identification performanceprovide a sensitive means of assessing the conditions underwhich two stimuli are processed by separate and independentmechanisms. This paper does three things. First, it presentsnew evidence for the existence of interactions between widelyseparated, spatially tuned mechanisms by comparing detec-tion and identification performance in a modified two-alter-native forced-choice procedure. Second, it develops a methodto compare performance based on this procedure quantita-tively with performance obtained in single-response or dou-ble-response yes/no or rating procedures. Finally, the resultsof the current experiment are quantitatively compared withresults of two previous studies based on the rating procedures.The comparison shows good agreement among the results ofthe three studies for several frequency pairs. Taken together,the results of the three studies rule out many other explana-tions for the data (see Ref. 1) and provide converging evidencefor the interaction interpretation.

BackgroundMost major models of spatial vision assume independentprocessing of frequency components that differ by more than1.0 octave. These models have been highly successful in ac-counting for performance on many tasks that involve the de-tection and identification of low-contrast stimuli: summa-tion,2 -5 adaptation, 6' 7 masking, 8-10 discriminationl' 3 andothers. When performance on these tasks is measured as afunction of spatial-frequency separation, the results clearlyindicate that stimuli that are similar in spatial frequency areprocessed by mechanisms that have overlapping ranges ofsensitivity. In each case, the effect signaling this noninde-pendence decreases as frequency separation increases, untilapparent independence of processing is observed at about 1-2octaves' separation.

When measurements are extended beyond this point ofapparent independence, models that assume independentprocessing sometimes fail. For example, both masking andadaptation results show facilitation when the adapting ormasking frequency is more than 2 octaves removed from thetest frequency, a reversal of the effect found with nearby

frequencies.1 2 "14'6 The effect is not always symmetric; whenasymmetries do occur, facilitation is greater when the testfrequency is lower than the adaptinig or masking frequency.Although the processes underlying such results are not yet wellunderstood, the involvement of inhibitory interactions be-tween responding mechanisms has been suggested.

Reversals are also found in rating detection and identifi-cation tasks performed at near-threshold levels of contrast.These results also suggest that stimuli that differ widely inspatial frequency are not processed independently. Twotypes of rating experiments will be described in some detail,as their results are used in the quantitative comparison againstthe current results. The first is a single-response rating taskused to measure both detection and identification perfor-mance. The second is a double-response rating task thatmeasures detection performance only but can be used topredict expected performance on an identification task. Thistask is referred to as the concurrent-detection task (CDT).

Single-Response Rating TasksIn these tasks, one of two stimuli can appear on a single trial.For the detection task, the screen either remains uniform(noise) or a stimulus can appear (signal). In the identificationtask, one of two signals appears on each trial, one of which isarbitrarily designated as noise for analysis purposes. De-tection and identification tasks are performed in separatesessions. Both detection and identification performance aremeasured by the area under the receiver operating charac-teristic (ROC), derived from responses on a bipolar confidencescale, where either end indicates certainty that one of the twopossible stimuli was presented.

Olzak and Thomas17 used the single-response rating taskto measure (a) the detectability of simple sinusoidal gratingsthat differed in spatial frequency, (b) the detectability of acompound grating formed by superimposing two single grat-ings, and (c) the ability to identify, or discriminate between,the two simple gratings. Gratings were paired to span a rangeof harmonically related spatial-frequency separations.

As the two simple gratings activate fewer and fewer path-ways in common by increasing the difference between them,the ability to discriminate between the two stimuli increases.The ability to detect the compound grating, on the other hand,

0740-3232/85/091551-09$02.00 © 1985 Optical Society of America

Lynn A. Olzak

1552 J. Opt. Soc. Am. A/Vol. 2, No. 9/September 1985

decreases as less and less summation occurs. When the twostimuli are processed independently, discrimination perfor-mance asymptotes at a level equal to the ability to detect thecompound stimulus. Olzak and Thomas reported equalperformance on the two tasks when the gratings differed bya factor of 2. However, when the gratings differed by morethan a factor of 2, identification performance exceeded per-formance on the compound-detection task. Such a resultcannot be explained on the basis of independent processing.It is, however, consistent with two types of interaction. Oneis an inhibitory interaction, such that the presence of onestimulus reduces the response to the other. The secondpossibility is correlation between sensory noise in the re-sponding mechanisms.

Additional analyses suggested that more than a single typeof interaction might exist. Performance on the two tasks,detection of the compound and discrimination between thecomponent gratings, was quantitatively predicted from sim-ple-grating detection levels. In the case of grating pairs thatdiffered by a factor of 3 or a factor of 4, the ability to detectthe compound was consistent with predicted levels, but theability to discriminate between the gratings was elevated.Such a result might be expected if noise between respondingmechanisms were positively correlated, but only if the corre-

-lation occurred when just a single mechanism was activated(i.e., when a simple grating was presented alone). An alter-native explanation is that with these frequency pairs, thepresence of one stimulus reduces the response to the other.Such an inhibitory interaction would make it less likely thatan observer would confuse the two stimuli.

In the case of a pair separated by a factor of 6, discrimina-tion performance was not elevated, but rather, the detect-ability of the compound was reduced below predicted values.This result might occur if noise is correlated when neither orwhen both mechanisms are activated. Alternatively, thisresult suggests that a process akin to simultaneous maskingoccurs when two extremely different gratings are simulta-neously presented.

Concurrent-Detection TaskHirsch et al. 18 and Olzak19 more closely examined the natureof interactions between spatially tuned mechanisms using theCDT procedure. In this task, the four stimuli described above(noise, a low-frequency grating, a higher-frequency grating,and a compound grating) are intermixed with equal proba-bility into a single session. On a given trial, the observermakes two detection judgments on the bipolar noise-signalscale, each referring to one of the two component gratings.Performance on each of the two detection tasks can be mea-sured by the area under the ROC for each stimulus condition,by d', or simply by comparing mean rating levels acrossstimulus conditions.

Each set of ratings is interpreted as reflecting activity in onemechanism or set of mechanisms. To the extent that pro-cessing is independent between the mechanisms, the ratingsets are also expected to be independent of each other. A lackof independence in rating sets indicates various kinds of in-teractions. Within a stimulus condition, correlation betweenthe concurrent responses over repeated trials suggests corre-lation in stochastic noise between the two mechanisms. Be-tween stimulus conditions, changes in the mean rating (orarea) to one stimulus that depend on the presence of the other

stimulus suggest direct interactions between the mechanisms.If the ratings or areas increase when the second stimulus ispresent, an excitatory influence is inferred. A suppressionof the ratings or areas suggests an inhibitory influence betweenthe mechanisms.

Hirsch et al. investigated a wide range of frequency pairs,whereas Olzak concentrated on pairs separated by more thanan octave. Despite different analysis methods and underlyingmodels, the results of the two studies were in close agreementfor the common frequency pairs. First, within a given stim-ulus condition, consistent correlation between the two con-current responses was found only in response to a uniformscreen. Thus, although noise correlation may exist, it cannotaccount for all the frequency-specific results reported by Olzakand Thomas.

Second, both studies presented evidence for interactionsamong certain responding mechanisms. Hirsch et al. re-ported a reversal in the direction of the interaction at a sep-aration of about an octave. At separations less than this, theinteraction was excitatory; at separations greater than this,the interaction was inhibitory. Olzak confirmed the presenceof the inhibitory interactions with widely separatedfrequencies and further reported two distinct patterns of in-teraction across the stimulus conditions. When frequencycomponents were separated by a factor of 4, responses corre-sponding to the lower-frequency stimulus were reduced in thepresence of the higher-frequency grating. This occurred evenwhen the low-frequency grating was not present; responsesin this case were reduced below their level to a uniform screen.Similar to the masking results, little effect was found in theopposite direction; high-frequency responses were relativelyunaffected by the presence of a lower-frequency grating. Thisasymmetry is also evident in the data of Hirsch et al. for fre-quency pairs separated by a factor of 3. At greater frequencyseparations, a different pattern was found. When the com-ponents were separated by a factor of 6, significant interac-tions occurred only when both components were simulta-neously present.

SummaryThe pattern of inhibitory interactions reported by Hirsch etal. and Olzak is in good qualitative agreement with the de-tection/discrimination results of Olzak and Thomas. In thetheory section of this paper, it is shown that the results of thetwo procedures also agree quantitatively about the patternand magnitude of the interactions. Together, these resultsstrongly suggest that interactions do occur among mechanismsthat respond to widely separated spatial frequencies.

Although the magnitude of these interactions is never es-timated to be large, their existence can create serious quan-titative errors in parameter estimates whenever models as-sume independent processing. For example, such interactionsmay affect bandwidth calculations or estimates of poolingparameters. It is therefore important to isolate and describeinteractions if they exist. On the other hand, the existenceof such interactions creates additional complexities for themodeling process. Thus the existence of such interactionsmust be conclusively demonstrated.

One objection to the evidence is that it stems from experi-ments that have used either a single or a concurrent ratingprocedure. It is possible that some type of response bias oc-curs in the concurrent rating task, at least, that mimics sensory

Lynn A. Olzak


interactions.2 0 In order to rule out this possibility, the rela-tionship between identification and detection was measuredin the current study using a different type of procedure, amodified two-alternative forced-choice task (the 2 X 2). Al-though this task, too, may be subject to response biases thatmimic interactions,20 the obtained pattern of results acrossfrequency separations cannot be explained on this basis.Instead, the current results again suggest the presence of in-teractions and show excellent quantitative agreement withthe rating results.

METHODS

Equipment and ProceduresSine-wave gratings were generated digitally by computer anddisplayed on a Tektronix 608 CRT. Appropriate triangularand ramp voltages applied to the X and Y axes formed thedisplay raster. Gratings were formed by driving the Z axiswith the computer-generated waveforms, varied around amean luminance of 74 cd/M2 . Phase was randomized withrespect to the display edge across trials. The measuredhalf-amplitude bandwidth of the display was 34 cycles perdegree (c/deg), which was more than adequate to display thehigh-frequency gratings without serious degradation. Thescreen was masked by a large surround, matched in luminanceand chromaticity to the display, to provide a 3-deg circularfield at a viewing distance of 1.5 m.

A 2 X 2 simultaneous detection-identification task was runwith four pairs of sine-wave gratings that differed in spatialfrequency. The pairs were 3-6, 3-9, 3-12, and 3-18 c/deg.Before data collection, the relative contrast of each gratingwas adjusted for each observer to yield equal detection per-formance at four different levels, ranging from approximately60 to 90% detectable. The actual (Michelson) contrast rangesfor each of the five gratings (3, 6, 9,-12, and 18 c/deg) were0.19-0.35, 0.17-0.32, 0.24-0.48, 0.58-1.08, and 0.80-1.23. Onany given day, only a single pair of gratings was used.

Each daily session consisted of 400 trials, divided into blocksof 100 trials. For half of the observers, the four contrast levelswere intermixed within each block of 100 trials (randompresentation); for the remaining observers, each contrast levelwas presented in a separate block of trials (blocked presen-tation). Random presentation was used in order to minimizeany small differences in detectability that might aid identi-fication performance. Blocked presentation was used tominimize any contrast-uncertainty effects that might exist.

Each trial was divided into two intervals of 1 sec each. Oneof the two gratings composing each pair could appear in oneof the intervals, while the other remained blank. The ob-server's task was to indicate which interval contained thegrating (the detection judgment) and to indicate which fre-quency component had been presented (the identificationjudgment). The combined choice was indicated by pressinga single switch. A minimum of four sessions were run witheach grating pair by at least two observers. Additional ses-sions and observers were run with several of the gratingpairs.

ObserversTwo observers were each run with all four grating pairs.Observer EH, a female graduate student, was a myope cor-

rected to normal vision by contact lenses. Her sessions wererun using blocked stimulus presentation. Observer DK, amale emmetrope, was run using random stimulus presenta-tion. Both were naive to the purpose of the study and werehighly practiced before data collection was started.

Three undergraduate students, naive to the purpose of thestudy, were also run in some conditions. These observers werenot well practiced and did not run in all conditions becauseof time limitations. Observer RT, a male emmetrope, ranboth the 3-6- and the 3-12-c/deg conditions with randompresentation. Observer PW, also a male emmetrope, ran inthe 3-12 and 3-18 conditions with random presentation.Observer DL, a female emmetrope, ran the 3-12 conditionwith blocked presentations. Finally, the author, a femalemyope (corrected to normal by spectacles), served as an ob-server with the 3-12-c/deg pair with blocked presentation.Thus a total of three observers ran in each of the 3-6 and 3-18conditions, and two observers ran in the 3-9 condition. In the3-12 condition, three observers ran with blocked presentationand three ran with random presentation.

RESULTS

Percent-correct detection and identification judgments weretallied independently of each other. Detection scores wereaveraged over the two intervals, and identification scores wereaveraged over the two frequency components in order tocorrect for any response preference that might exist. Eachfrequency pair was analyzed separately because of differingnumbers of observers and replications. For each frequencypair, an analysis of variance was performed. For the 3-6, 3-9,and 3-18 pairs, a three-way ANOVA was performed (ObserverX Contrast X Task). For these analyses, observers weretreated as fixed effects in order to examine interobserverdifferences, using replications as the random within-cell fac-tor. For the 3-12 pair, Presentation (random versus blocked)was included as an additional factor, with Observers nestedwithin Presentation type.

For theoretical comparisons, a linear regression was per-formed on the z transforms of the data to find the slope thatbest described the relationship between identification anddetection (the performance ratio). Regression lines wereforced through the origin in order to express the performanceratio as a single number. 21

Performance predictions for the independence case werebased on the model presented by Thomas and Gille2 2 andmodified to include uncertainty effects by Thomas et al. 13

This model predicts equal performance on detection andidentification if two sets of responding mechanisms are in-dependent. If the net response of the two is excitatory, themodel predicts that detection performance will exceed thatof identification. On the other hand, if the net response isinhibitory, the model predicts that identification performancewill be superior to detection. This model is more fully dis--cussed in the final section of this paper.

Given this model and the results of the earlier studies,qualitative performance predictions can be made for each ofthe stimulus pairs. When the frequency components areseparated by a factor of 2, independence predictions are al-most always consistent with obtained performance. Thus,for the 3-6-c/deg pair in the current study, the detection andidentification tasks should be performed equally well.

Lynn A. Olzak


1 0 0

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Fig. 1. Percent correct on the 2 X 2 identification task plotted as afunction of percent correct on the detection task. Results shown forthe 3-6-c/deg frequency pair. Top: Observer EH, blocked contrasts.Bottom: Observer DK, random contrasts.

Performance is also expected to be equal with the 3-18-c/deg pair. In both the rating detection/discrimination resultsof Olzak and Thomas17 and the concurrent detection resultsof Olzak,19 inhibitory influences occurred only when the twocomponents were simultaneously presented. In the currentstudy, component frequencies never appear simultaneously;thus the mechanisms are expected to respond as if they wereindependent.

For the 3-9- and 3-12-c/deg pairs, it is expected thatidentification performance will exceed detection. If inhibi-tory interactions do exist among mechanisms that respond tothese frequencies-and they are not just artifacts'of the ratingprocedures used in previous studies-then they should en-hance identification performance over detection performancein the current 2 X 2 forced-choice procedure.

The results obtained with each frequency pair were in goodagreement with the predictions. Figures 1-4 show the resultsfor the two main observers with each of the frequency pairs.In each figure, the percent-correct detection is plotted againstthe percent-correct identification. Each point represents dataobtained at one of the four contrast levels in a single session,and the diagonal line represents expected performance on thetasks if the gratings are processed by separate and indepen-

dent mechanisms. The figures shown here are representativeresults; the results were virtually identical for all observerswith each stimulus pair.

Analysis of Variance

TaskAs expected, the main effect of Task (detection versus iden-tification) was not significant for either the 3-6 (F 1, 10 = 0.26,p > 0.10) or the 3-18 (F 1, 19 = 0.37, p > 0.10) frequency pairs,nor did Task interact with any other factor (all p's > 0.10).Thus, for these frequency pairs, there is no evidence that theresponding mechanisms interact; the results support thepredictions based on independent processing.

Independence was not supported by the data obtained withthe intermediate frequency pairs. Identification performancewas found to be significantly better than detection perfor-mance for the 3-9 (F 1, 12 = 14.47, p < 0.01) and 3-12 (F 1, 27= 48.77, p < 0.001) frequency pairs. Task did not interactwith any other factors for the 3-9 frequency pair but did showa significant two-way interaction with Contrast (F 3, 81 = 3.67,p < 0.05) and a three-way interaction with Presentation andContrast (F 3, 81 = 3.67, p < 0.05) for the 3-12 pair. A seriesof contrasts isolated the source of these interactions at a singlepoint: The difference between detection and identification

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Lynn A. Olzak


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in performance level do not affect the main conclusions fromthe study.

The two types of presentation (random versus blocked)were used as controls in the current study, each used to min-imize the possibility that superior identification was simplya by-product of the procedure (see the section on methods).It was included as an analyzed factor only in the 3-12 condi-tion because of the limited number of observers in the re-maining conditions. Because observers were nested withinpresentation type, this effect is partially confounded withindividual differences. However, the main effect of Presen-tation did not reach significance (F 1, 27 = 3.96, p > 0.05).The more interesting interaction of Presentation type withContrast and Task has already been discussed.

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was not significant under blocked conditions at the lowestcontrast level. Under random conditions, and at all othercontrasts under blocked conditions, the simple effect of Taskwas significant (all p's < 0.05). Thus, with this one exception,the data from all observers who ran the 3-9 and 3-12 condi-tions reject the notion that these frequencies are processedindependently. Instead, the data agree with previous resultsin suggesting that inhibitory interactions do occur amongmechanisms that respond to these frequency pairs.

Other EffectsFor all frequency pairs, the main effect of Contrast was sig-nificant (all p's < 0.001). This was not a surprising result,since contrast levels were chosen to yield different levels ofperformance. A significant interaction between Contrast andObserver was found in the 3-12 and 3-18 conditions (both p's< 0.01) and approached significance in the remaining pairs(both p's < 0.10). This interaction suggests that the contrastlevels chosen for each observer did not always yield identicalperformance levels but does not detract from the main pointof these analyses. The main effect of Observer was significantonly in the 3-6 and 3-12 conditions (both p's < 0.05), but sincethis factor did not interact with Task under any stimuluscondition, it can be concluded that these individual differences

Summary and Discussion of Current ResultsThe results of the 2 X 2 procedure are in close agreement withexpectations based on previous rating studies. No differencesare found between performance on detection and identifica-tion tasks when the gratings are composed of 3-6- and 3-9-c/deg frequency components. This result is consistent withpredictions that assume independent processing of thesefrequency components. However, when the components are3-9 and 3-12 c/deg, the ability to identify the grating exceedsthe ability to detect which interval it was presented in. These

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Lynn A. Olzak


results are clearly not in agreement with predictions based onindependent processing but are consistent with expectationsbased on previous rating studies. The agreement reduces thepossibility that the conclusions based on the rating procedureswere seriously contaminated by response bias, and, conversely,increases the likelihood that a common sensory processunderlies the interactions isolated in all three sets of data.

Klein1' 20 has argued that the 2 X 2 procedure is also subjectto response bias that might mimic effects of sensory interac-tions. He has demonstrated that the 2 X 2 procedure willyield better performance on the identification task if the ob-server is able to attend to only a single mechanism and if theobserver chooses the nonattended stimulus whenever theattended stimulus is not detected. He argues that this is areasonable strategy to use in the 2 X 2 procedure when thestimuli differ considerably, because the task requires a diffi-cult four-dimensional decision space.

There are a number of reasons why this is an unlikely ex-planation for the current data. First, if such a bias occurred,one would expect it to occur in the 3-18-c/deg condition as wellas in the 3-9 and 3-12 conditions. The data do not reflectsuch an expectation. Second, although the task requires afour-dimensional decision space, it requires only that theobserver attend to two mechanisms at any given time. Thereis evidence23 24 that observers have no trouble simultaneouslymonitoring two mechanisms at separations similar to thoseused in the current study. Even if observers did adopt asingle-mechanism strategy, the long intervals (1 sec each) usedin the current study would allow time for switching attention.Thus it seems unlikely that this form of response bias is re-sponsible for the results of the current 2 X 2 study.

In the final section of this paper, the results of the currentstudy are quantitatively compared with single- and double-response rating results. Taken together, the three types ofstudies rule out many of the other explanations for these dataand converge to suggest that the results in all three cases aremost succinctly interpreted as reflecting interactions betweenresponding mechanisms.

THEORY AND DISCUSSION

Three manifestations of a single underlying model will beconsidered here. These are (a) a vector interpretation of themodel developed by Thomas and Gille22 and modified byThomas et al. 13 for the 2 X 2 procedure, (b) the Euclideandistance model presented by Olzak and Thomas' 7 for a two-alternative forced-choice (2AFC) or a single-response ratingprocedure, and (c) the Euclidean distance model presentedby Olzak'9 for the concurrent-response rating task. In thefirst two papers, the models were developed to permit aquantitative comparison between detection and identificationperformance as measured by each technique. Here, thesemeasures are transformed to the same metric in order quan-titatively to compare results obtained in the current experi-ment with those previously reported by Olzak and Thomas.17

The third paper was not directly concerned with identificationperformance but permits quantitative predictions to be madefrom estimated parameters of the response space. The tasksfor which these models were developed were briefly describedearlier in this paper.

The underlying model assumes the existence of multiple

Lynn A. Olzak

spatially tuned mechanisms that respond to a limited rangeof spatial frequencies. Each mechanism is represented by avector in an m-dimensional space that is Euclidean. Theresponse to a single stimulus is represented by a point in thespace. The output of each mechanism is assumed to be per-turbed by additive Gaussian noise, so that over repeated trialsof the same stimulus the responses of the mechanisms willform a multivariate distribution about some expected value.Performance on both detection and identification (or dis-crimination) tasks is determined by the overlap between rel-evant distributions; the greater the overlap, the poorer theperformance. The observer is assumed to make a likelihoodratio decision on each task under consideration.

Two additional simplifying assumptions are necessary.The first is that noise is uncorrelated between the mecha-nisms, and the second is that noise has unit variance in alldistributions. Then, performance on detection and identi-fication tasks is given simply by the length of the vector con-necting the expected values of the relevant distributions.

A schematic representation of the space in two dimensionsis shown in Fig. 5. The points labeled N, X, and Y representthe expected response to a uniform screen (Noise), to stimulusX, and to stimulus Y. Performance on simple detection tasksis given by the length of the vector NX (here assumed to beequal to vector NY for convenience). Performance on anidentification task is given by the length of the differencevector XY. The length of the difference vector depends bothon the detectability of the stimuli and on the degree to whichprocessing is independent, represented by the angle A. A90-deg angle indicates completely independent processing.If one assumes that angle does not change with contrast,then the ratio of the difference vector XY to the detectionvector NX is a constant. This proportion, the ratio of iden-

Fig. 5. Schematic representation of detection and identificationtasks in vector space. Each circle represents the bivariate distributionof responses that arises from repeated presentations of a uniformscreen N, stimulus X, or stimulus Y. Angle p is a measure of inde-pendence among mechanisms that respond to stimuli X and Y; when0 = 90 deg, the mechanisms are independent. Angles less than 90 degindicate excitatory interactions or overlapping sensitivity betweenthe mechanisms; angles greater than 90 deg indicate inhibitory in-teractions. The solid lines connect the centroids of each distribution,representing expected performance in response to the stimulus.Distances NX and NY represent performance in detection tasks andare assumed to be equal. Distance XY represents performance onidentification tasks. The performance ratio is the ratio of the distanceXY/NX or the ratio of identification performance to detection per-formance.


tification performance to detection performance, forms thebasis of comparison across the different procedures. How-

ever, since the different procedures use different metrics andmeasure different parameters of the space, the distances NXand XY must be defined in terms of the appropriate perfor-mance measures.

For the single-response rating task and the 2 X 2 procedure,the distances NX and XY are directly measured. In theconcurrent rating task, the (x, y) coordinates of X and Y aremeasured by a rating detection task, from which angle k canbe calculated. From this angle, the expected distance XY inthe 2 X 2 procedure can be calculated.

Detection TasksIn both the single- and concurrent-rating tasks, detectionperformance is measured by the area under the ROC. In the2 X 2 procedure, the detection task is measured by percentcorrect in a straightforward 2AFC procedure. The compar-ison of performance on the detection tasks is simplified bymeans of the theorem that percent correct in a 2AFC proce-

dure is equivalent to the area under the ROC generated in arating procedure.25 The z transform of either measure issymbolized z (D) and is related to distance NX by

NX = NY = z(D)2. (1)

Identification TasksIn the rating task, identification performance is again mea-sured by the area under the ROC (or by percent correct in a2AFC procedure). The z transform of this measure, z (I), isrelated to distance XY by

XY = z(I)-2. (2)

In the 2 X 2 procedure, identification performance is mea- 0sured by the percent correct in a classification task. The ztransform of this measure, z(C), is related to distance XY by

XY = z(C)2. (3)

In the concurrent-detection task, identification perfor- 0mance is not directly measured. E

0

Comparison of Identification with Detection PerformanceIf stimuli X and Y are processed by independent mechanisms, a.angle 4 is 90 deg, and the distance XY can be expressed interms of the detection measure

XY = NX'J_ = z(D)2.

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.

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0.96(4)

For the rating task, substituting in Eq. (2) and rearrangingleads to the prediction that when the two mechanisms areindependent,

z(I) = z(D)\/. (5)

Thus the appropriate comparison for the rating task is

XY/NX = z(I)/z(D)v'2, (6)

which yields an expected ratio of 1.0 if X and Y are indepen-dent.

For the 2 X 2 procedure, substituting in Eqs. (3) and (4) andrearranging leads to the expectation that when the twomechanisms are independent,

z (C) = z (D). (7)

Thus for the 2 X 2 task, the appropriate comparison is

XY/NX z(C)/z(D), (8)

which also yields an expected value of 1.0 if X and Y areprocessed independently.

In the concurrent-rating task, angle 0 is calculated from thedetection vectors and used to predict the expected relation-ship between identification and detection performance in the2 X 2 task. Thomas et al. 13 provide the following relationshipin Eq. (19) of their paper:

sin(0/2) = 0/(1 + 02)1/2

where 0 is the performance ratio z(C)/z(D) in the 2 X 2 pro-cedure. This can be easily rearranged to solve for the ex-pected performance ratio in the 2 X 2 procedure:

z(C)/z(D) = sin(/2)/[1 - (sin 0/2)2]1/2,

or, more simply,

z(C)/z(D) = tan(,/2). (9)

When processing of X and Y is independent, 0 = 90 deg, andagain, the performance ratio is predicted to be 1.0.

Comparisons across ProceduresData from the current experiment, the Olzak and Thomasdiscrimination data,1 7 and CDT data from Olzak' 9 and Olzakand Kramer2 6 were used to compute performance ratio met-

1.25 _ k

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c/degFig. 6. Performance ratios obtained in 2 X 2 (filled circles) andsingle-response rating (open circles) studies for four frequency pairs.Values for the performance ratio predicted from CDT results aresymbolized by filled triangles. The solid horizontal line indicates aperformance ratio of 1.0, the prediction for all tasks when the mech-anisms are independent. Points above the line indicate that identi-fication performance exceeds detection performance. The rangebetween the highest and lowest performance ratios was about 0.1 ineach case with one exception. The CDT data for the 3-12 conditionvaried over a range of about 0.2.

Lynn A. Olzak


rics as described above. CDT data were available only for the3-12- and 3-18-c/deg gratings. The average performanceratios from all studies are plotted in Fig. 6. It should be notedthat no further translations were made of the data from anystudy.

The results of the single-response rating study and of thecurrent 2 X 2 procedure show excellent quantitative agree-ment across all frequency pairs, in addition to the previouslynoted close qualitative agreement. Furthermore, the pre-dictions based on the CDT data agree fairly well where com-parison is possible. The slightly lower performance ratio (andincreased variability) found with the CDT data for the 3-12-c/deg pair can be attributed to a single observer, whoshowed quite dissimilar results from the other four data sets.The agreement is all the more remarkable because the datacome from three different studies, performed at differenttimes under somewhat different experimental conditions andwith different observers. The same pattern of results is re-peatedly obtained. The data are consistent with independentprocessing when the frequency components are 3-6 and 3-18c/deg; the performance ratio metric is close to 1.0. However,when the frequency components are 3-9 or 3-12 c/deg, theratio is consistently greater than 1.0.

Interpretation of the DataThe results of any single experiment cannot be conclusivelyinterpreted; each has its limitations. However, the closequantitative agreement among the studies suggests that acommon explanation underlies the elevated performance ratiofound with the 3-9- and 3-12-c/deg grating pairs. Responsebias is not a viable explanation for the 2 X 2 results (see thesection on results) and has never been suggested as responsiblefor the single-response rating data. The remaining candidatesfor this explanation are correlated sensory noise or inhibitoryinteractions between responding mechanisms.

Unfortunately, neither the single-response rating study northe current 2 X 2 experiment distinguishes between the pos-sible sensory interactions. The CDT experiments, however,are intended to do just that. The results reported by Hirschet al.,'8 Olzak,19 and Olzak and Kramer 26 all suggest that in-hibitory interactions occur between mechanisms separatedby factors of 3 or 4; none presents evidence for noise correla-tion that would produce elevated identification performance.Furthermore, all provide evidence that the interaction isasymmetric; the presence of a high-frequency grating reducesthe response of a mechanism tuned to a much lower frequency,but the low-frequency grating does not appear to affect re-sponses in the higher-tuned mechanism.

Klein",20 has challenged this interpretation of the CDTdata. He correctly points out that a combination of correlatedsensory noise and a particular type of correlation in decisioncriteria (response bias) can result in a reduction of themean-response level, which mimics inhibition. He furthersuggests that the asymmetry of the apparent interaction is dueto differential-response criteria for the two decisions. Itshould be noted that this argument does not refute the mainconclusion of this paper: that mechanisms that respond towidely separated frequencies interact. Rather, it implies thatcorrelated sensory noise (in combination with response bias)cannot be ruled out on the basis of CDT data alone.

The alternative interpretation of CDT data offered by Kleinis absolutely viable and must be considered any time the CDT

paradigm is used. However, it is not necessarily the mostparsimonious explanation in the case at hand. If one acceptsKlein's alternative as the explanation for the CDT results,then it is difficult quantitatively to reconcile the combinedeffects of sensory correlation and response bias with data fromthe other studies that are not subject to such response bias.If, however, one accepts the assumption that observers areable to make independent decisions about two stimuli, thenthe reduction in the low-frequency response when the high-frequency grating is presented reflects an inhibitory interac-tion that is separable and distinct from correlated sensorynoise. Without any additional assumptions, the posited in-hibitory interaction can account both qualitatively andquantitatively for all the elevated performance ratios pre-sented here.

ACKNOWLEDGMENTS

This research was supported in part by U.S. Public HealthService Research Grant EY00360 from the National Eye In-stitute to James P. Thomas. I wish to thank Dr. Thomas forhis significant contributions to this work and two reviewersfor their valuable comments. I would particularly like tothank Stanley Klein for many informative and lively discus-sions of the issues addressed in this paper. A portion of thispaper was presented at the Association for Research in Visionand Ophthalmology annual meeting, 1982.

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1. S. A. Klein, "Double-judgment psychophysics: problems andsolutions," J. Opt. Soc. Am. A 2, 1560-1585 (1985).

2. F. W. Campbell and J. G. Robson, "Application of Fourier analysisto the visibility of gratings," J. Physiol. 197, 551-566 (1968).

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

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5. A. B. Watson, "Summation of grating patches indicates manytypes of detectors at one retinal location," Vision Res. 22, 17-25(1982).

6. C. Blakemore and F. W. Campbell, "On the existence of neuronsin the human visual system selectively sensitive to the orientationand size of retinal images," J. Physiol. 203, 237-260 (1969).

7. A. Pantle and R. Sekuler, "Size detecting mechanisms in humanvision," Science 162, 1146-1148 (1968).

8. G. B. Henning, B. G. Hertz, and J. L. Hinton, "Effects of differenthypothetical detection mechanisms on the shape of spatial-fre-quency filters inferred from masking experiments," J. Opt. Soc.Am. 71, 574-581 (1981).

9. G. E. Legge and J. M. Foley, "Contrast masking in human vision,"J. Opt. Soc. Am. 70, 1458-1471 (1980).

10. C. F. Stromeyer and B. Julesz, "Spatial frequency masking invision: critical bands and spread of masking," J. Opt. Soc. Am.62, 1221-1232 (1972).

11. C. S. Furchner, J. P. Thomas, and F. W. Campbell, "Detectionand discrimination of simple and complex patterns at low spatialfrequencies," Vision Res. 17, 827-836 (1977).

12. J. Nachmias and A. Weber, "Discrimination of simple and com-plex gratings," Vision Res. 15, 217-223 (1975).

13. J. Thomas, J. Gille, and R. R. Barker, "Simultaneous detectionand identification: theory and data," J. Opt. Soc. Am. 72,1642-1651 (1982).

14. L. Barfield and D. Tolhurst, "The detection of complex gratingsby the human visual system," J. Physiol. 248, 37-38 (1975).

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15. K. K. DeValois, "Spatial frequency adaptation can enhance

contrast sensitivity," Vision Res. 17, 1057-1065 (1977).16. D. J. Tolhurst and L. P. Barfield, "Interactions between spatial

frequency channels," Vision Res. 18, 951-958 (1978).17. L. A. Olzak and J. P. Thomas, "Gratings: why frequency dis-

crimination is sometimes better than detection," J. Opt. Soc. Am.71, 64-70 (1981).

18. J. Hirsch, R. Hylton, and N. Graham, "Simultaneous recognitionof two spatial frequency components," Vision Res. 22, 365-375(1982).

19. L. A. Olzak, "Widely separated spatial frequencies: Mechanisminteractions," Vision Res. (to be published).

20. S. Klein, "Double-judgment detection and identification:problems and solutions," J. Opt. Soc. Am. A 1, 1240 (A) (1984).

21. Thomas and Gille22 found that, over 29 data sets collected usingthe 2 X 2 procedure, y intercepts calculated by normal linear re-

gression were equally distributed above and below the origin. In

addition, there was no relationship between the sign or magnitudeof y intercepts and stimulus conditions, suggesting that deviations

from the origin were simply a product of error variance. Thusforcing the regression line through the origin allows the perfor-mance ratio to be expressed as a single number without loss of

information.22. J. P. Thomas and J. Gille, "Bandwidths of orientation channels

in human vision," J. Opt. Soc. Am. 69, 652-660 (1979).

23. E. T. Davis and N. Graham, "Spatial frequency uncertainty ef-

fects in the detection of sinusoidal gratings," Vision Res. 21,705-712 (1981).

24. E. T. Davis, P. Kramer, and N. Graham, "Uncertainty aboutspatial frequency, spatial position, or contrast of visual patterns,"Percept. Psychophys. 33, 20-28 (1983).

25. D. M. Green and J. A. Swets, Signal Detection Theory and Psy-

chophysics (Kreiger, New York, 1974).

26. L. A. Olzak and P. Kramer, "Inhibition between spatially tuned

mechanisms: temporal influences," J. Opt. Soc. Am. A 1, 1290(A) (1984).

Lynn A. Olzak

* Lynn A. Olzak was born in Chicago, Illi-nois, in 1951. She received the B.A. de-

gree in psychology from the University

of California, Santa Barbara, and thePh.D. degree from the University of Cal-

ifornia, Los Angeles, in 1981. Her thesiswork on spatial interactions won the

K _ Distinguished Dissertation Award in

Psychology. During her graduate ca-

reer, she worked at the NASA-Ames Re-

search Center and in the human factorsdepartment at Hughes Aircraft Compa-

ny. She has done postdoctoral work at Stanford University. Cur-

rently, she is conducting research at UCLA and is teaching at Scripps

College in Claremont, California. Her research interests include the

development of models of spatial vision, the role of color in spatial

vision, and methodological/quantitative analysis issues related topsychophysical techniques.

Lynn A. Olzak

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Interactions between spatially tuned mechanisms: converging evidence