Visual Search for a Tilted Target: Tests of Spatial ...

T HE QUARTERLY JOURNAL OF EXPERIMENTAL PS YCHOLOGY, 1998, 51A (2), 347± 370

Visu al Search for a T ilted Target: Tests of Sp atial Un certain ty Mod els M.J. Morgan Department of Visual Science, Institute of Ophthalmology , London , U.K .

R.M. Ward Univ ersiteÂ du QueÂ bec aÁ Trois RivieÁ res, QueÂ bec, Canada

E. Castet Laboratoire de Psychophysiqu e, Univ ersiteÂ Louis Pasteur, Strasbourg, France

We report that spatial cueing of a parafoveal target in the presence of distractors enhances orientational acuity for that target. When no distractors were present, orientation thresholds were in the range 1± 48 . For long exposure times, distractors increased threshold by the amount predicted from a winner-takes-all spatial uncertainty model. For short (100- msec) exposures followed by a random dot mask, the rise in threshold with distractors was considerably greater than that predicted from spatial uncertainty. For brief exposures the effect of distractors was greater when the target and distractors were spatially crowded rather than widely spaced. Adding a tilt to the distractors in the opposite direction to the target increased thresholds still further. Cueing the target with a spatial pointer decreased the effect of distractors, even when they were crowded. We suggest that when attention cannot be appropriately focused, discrimination is carried out by a relatively coarse texture analyser, which averages over several elements, and that focused attention permits the analysis of the target over a smaller area of space.

An important question about visual cognition is whether selective attention to a target makes it easier to detect and analyse. When observers are precued to the likely spatial location of a visual target, there are some conditions under which they identify it more quickly and more accurately than when it is uncued or appears in a position different from the cue (Cheal & Lyon, 1991; Hawkins et al., 1990 ; Posner, Snyder, & Davidson, 1980). On the other hand, there are conditions under which attention to the target location has no demonstrable effect on acuity (Grindley & Townsend, 1968). Consideration of the various conditions under which cueing does or does not have a bene® cial effect

Requests for reprints should be sent to M.J. Morgan, Department of Visual Science, Institute of Ophthalmology, Bath S treet, London EC1V 9EL, U.K. T his work was supporte d by grants from the MRC and the BBS RC. We thank Nilli Lavie, University College London, for helpful suggestions, and we are grateful to John Palmer and an anonymou s referee for their help in revising the paper.

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has led to the suggestion that a major variable may be the extent to which the cue reduces the spatial uncertainty of target location (Graham, 1989; Graham, Kramer, & Haber, 1985; Palmer, 1994; Palmer, Ames, & Lindsey, 1993; Shaw, 1984; Shiu & Pashler, 1994). T hus, cueing effects are particularly likely to be found when multiple distractors are present, as in a visual search task, and when the observer does not know which of the stimuli in the visual ® eld is the true target until it has been analysed. In these circumstances, it is hardly surprising that the cue improves performance to some extent, because the distractors increase the opportunity to make errors. Suppose, for example, that the task is to decide whether an array contains the target letter `À’ ’ . If there are ten letters present, any one of them could be confused with an `À’’ and lead to a false positive response. If, on the other hand, only a single letter is present, or if the target position is precued, the opportunity for error is drastically decreased. Uncertainty reduction is a plausible explanation of cueing effects under some conditions: the question is whether it accounts entirely for the bene® cial effects of directing attention to a target location. A possible class of stimuli for examining this question are the pattern acuities for simple shapes, sometimes called ``hyperacuities’’ (Westheimer, 1979 ; Morgan, 1990). Pattern hyperacuity is an interesting case because it represents an elementary form of shape recognition where thresholds can be precisely measured by standard psychophysical techniques. Under ideal conditions, the human observer can detect shifts in the retinal position of an object that are as little as one tenth of the diameter of a foveal cone (Westheimer, 1981). T he just-noticeable difference in orientation between two lines can be as little as 0.2 8 , considerably less than the orientational bandwidth of cortical cells (De Valois, Yund, & Hepler, 1982). T he biological functions of such precise judgements is not clear, but they may represent the performance of the visual system under unrealistically optimal laboratory conditions (McKee, 1985). T he observer knows exactly where the stimulus is and what judgement is required and can devote unlimited resources to the task without time pressure. Under more natural conditions, orientational thresholds more in the region of tens of degrees may be suf® cient, but presumably will have to be obtained without focused attention, during brief glimpses of cluttered images and in competition with visual guidance of locomotion and other necessary tasks. Laboratory evidence backs up the idea that visual discriminations show a speed± accuracy trade-off. In visual search tasks, targets that are highly discriminable from the background distractors are found more quickly than those that are less discriminable (Beck, 1982; Bergen & Julesz, 1983; Wolfe, 1992). It has been demonstrated that the threshold difference of the target from the distractors for a given error rate (say, 75% correct) varies with exposure (Verghese & Nakayama, 1994). T he idea of a serial± parallel dichotomy in visual search is giving way to the view that easy and dif® cult tasks vary along a continuum (Cheal & Lyon, 1994; Duncan, 1989; Duncan & Humphreys, 1989). In an easy task, a parallel search can be carried out over many items without loss of performance, but if the encoding of each item is intrinsically noisier, processing time for a given level of acuity will rise with the number of items. If high acuity demands slower processing, then distractors might be expected to decrease acuity even more under conditions of limited exposure, by reducing the effective inspection time available for the target. T his view is challenged, however, by the ® nding

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that under certain conditions, the effects of distractors upon orientational acuity can be accounted for entirely by the effects of a simple winner-takes-all spatial uncertainty (Palmer, 1994; Palmer et al., 1993). In the winner-takes-all model of spatial uncertainty, the observer classi® es the orientation of every element in the display independently and identi® es the ``target’ ’ as the one that differs most from the ideal distractor value. (Palmer et al., 1993, give details for a 2AFC task; the equivalent model for a binary classi® cation task is given later in the present paper.) Palmer suggests that there are no advantages other than purely statistical ones in knowing the location of a target when making a decision about its orientation. T he claim is a surprising and interesting one, but it appears to con¯ ict with a different experiment by Verghese and Nakayama (1994), which compared set-size effects for different dimensions, including orientation and colour. T he effects of set size were greater for orientation than for colour, which super® cially appears to rule out spatial uncertainty as the sole explanation. T here were many differences between the sets of experiments, but the most important seems likely to have been the presence and absence of masking. Palmer and colleagues did not use masking, and thus the observer could continue processing the image for some time after its disappearance; Verghese and Nakayama, on the other hand, varied exposure duration with a post-stimulus pattern mask. It is thus unclear from existing evidence whether orientational acuity bene® ts from focused attention, over and above the effect expected from the reduction of spatial uncertainty. A further problem is that in the experiments we have just been considering, thresholds were in the region of 10 8 rather than the optimal thresholds of less than 1 8 found in the hyperacuity literature. We therefore used a version of the visual search task where the threshold without distractors was close to 1 8 . In the shortest exposure condition we used an exposure duration of 100 msec to prevent scanning eye movements. In separate experiments the exposure duration and the effect of distance between target and distractors was varied. We reasoned that a suf® ciently long exposure without cueing should allow the observer to allocate suf® cient resources to all of the elements in the display, so that the effects of spatial uncertainty could be measured without contamination from resource allocation by comparison with the brief exposure case. T he effect of cueing and precuing was examined in Experiment 3. In Experiment 4 the effects of a single distractor were measured when the target position was known, but the distractor itself was also tilted, either in the same or opposite direction to the target.

GENERAL METHOD Stimuli T he stimulus arrangement is illustrated diagrammatically in Figure 1. In Experiment 1, the target and the desired number of distractors (in the case of Figure 1 there are 7) were arranged at equal intervals around a notional circle with a diameter of 48 of visual angle, centred on a ® xation point. T he position of each of the stimuli was randomly jittered around its notional point on the circle, by randomly changing its x and y position independently on each trial from a uniform distribution of +/ 2 0.05 8 . Note that the equal spacing in Experiment 1 confounds the number of distractors with the interval between them, in contrast to the constant-spacing

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FIG. 1

A schematic representation of the stimulus array used in the experiments, with 1 tilted target (bottom left) and 7 distractors. The observer’s task is to report whethe r the target is tilted left or right of vertical. In this case there is no cue to indicate the target other than its orientation. In other experiments the target position was cued by a small spot. T he observer ® xated the central spot, and, in the brief exposure condition, the stimulus array was ¯ ashed for 100 msec, followed by a random dot mask.

condition used by Palmer (1994). In Experiment 2 we looked at the effects of spacing and number of distractors separately, by including a condition in which spacing was constant. Each of the stimuli was a ``Gabor’ ’ patch of a 4 cyc/ deg grating in cosine phase windowed by an elliptical gaussian envelope with constants s x = 0.05, s y = 0.1, and with a contrast of 100% . T he envelope allowed the central bar of the grating to be seen, ¯ anked on either side by less visible bars of the opposite contrast. (In later experiments, not reported here, we used sine-phase gratings so that there was no DC component in the windowed stimulus, but this made no difference to the ® ndings). T he orientation of the distractors was vertical. T he target (at the lower left in Figure 1) was tilted either to the left or the right of vertical. Both the grating and the envelope were tilted by the same amount. T he stimulus was followed immediately by a mask consisting of a 100% contrast binary noise pattern covering the whole viewing screen. T he stimuli were generated by a Cambridge Research Systems VSG 2/ 3 graphics card and displayed on a Barco Calibrator II CRT display 2 with a mean luminance of ~ 20cd/ m with a refresh rate of 76 Hz.

Psychophysics At the beginning of each trial, the screen was at mean luminance with a central ® xation point. T he observer initiated each trial by pressing a key. Immediately after the key press the stimulus appeared, and remained on for 100 msec. Experiment 1 also included a condition in which the stimulus array remained on until the observer pressed a key to terminate the trial. Following the 100-msec exposure the post-stimulus mask was presented for 150 msec. T he position of the target around the isoeccentric circle was randomly determined on each trial. T he observer’s task was to report the orientation (left or right of vertical) of the gabor patch that appeared most non-vertical. T here was no feedback. T he decision was indicated by selecting the appropriate one of two buttons. On each trial the orientation of the target was selected by Watt & Andrews’s Applied Probit Estimation (APE) procedure (Watt & Andrews, 1981). APE performs a probit analysis (Finney, 1971) of the psychometric function from the data collected up to the current trial and uses this to select a range of cues that will give the greatest information about the shape of the function. T he following orientation value for the target is randomly selected from that range. At the end of 64 trials, the


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session is terminated, and the ® nal analysis of the psychometric function takes place. T he standard deviation of the function, equivalent to a d9 value of unity, it taken as the measure of sensitivity. A goodness of ® t of each psychometric function to a cumulative normal was calculated, and the results were discarded if the chi-squared value was signi® cant. In all conditions at least two independent measures of the threshold were taken, and more if there appeared to be a discrepancy. Error bars in the graphs represent the standard errors of the mean of these independent observations. In Experiment 3 the error bars represent 95% con® dence intervals.

Subjects T he two main subjects were the authors MM and EC, both experienced psychophysical observers. We had no preconceived ideas of the results, and it is dif® cult if not impossible to in¯ uence the shape of psychometric functions when the stimulus sequence is under computer control and the actual stimulus present on any given trial is unknown. T he main ® ndings of Experiment 1 were con® rmed by the third author (RMW), who is also an experienced observer. In Experiment 3 (effects of cueing) three additional subjects were used, who were unaware of the predictions being tested.

Modelling T he spatial uncertainty model that we use assumes that the observer does not initially know the true position of the target on any trial (Pelli, 1986). Each stimulus in the array is internally represented as having an orientation, which is its actual orientation plus an error, due to noise. T he observer compares the internal representations without further error and bases his ® nal decision entirely on the stimulus having the greatest deviation from the vertical. Because of noise, the stimulus on which the decision is based will not necessarily be the target. T he probability of its being a distractor rises with the number of distractors (Palmer, 1994; Townsend, 1971). T he noise is assumed to be independent for the different stimuliÐ in other words, the channels for the different stimuli are independent. To calculate the effects of added distractors, we need an estimate of the noise in the orientation encoding process. We assume that this is equal for all the stimuli, including the target. T he best estimate of the noise is obtained from the case when only the target is present. We further assume that the observer’s errors depend only upon noise in the orientational encoding process, and that the noise therefore has a standard deviation equal to the standard deviation of the psychometric function. T his leads to the computational convenience of taking standard deviations of psychometric functions as the inverse measure of sensitivity. It is possible to calculate the effects of spatial uncertainty numerically, independently of the psychometric procedure, but we decided to carry out a full-scale Monte-Carlo simulation, which included the APE procedure, in case the latter had any biasing effects. It turned out that the APE procedure did not change the thresholds obtained. T he ¯ ow-diagram of the simulation is shown in Figure 2. T he critical assumptions are:

1. T he internally represented orientation of each stimulus is sampled from a gaussian noise probability density function with a mean equal to the actual orientation and a unit standard deviation. T he noise is independent for the different stimuliÐ that is, we assume fully independent channels for the different stimuli. 2. On each trial the observer compares the internally represented values of the stimuli and selects, without error, the one with the largest absolute deviation from vertical. T his is a ``winner-takes-all model’ ’ . It is possible to have other models for combinations across

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FIG. 2.


Flow diagram of the simulation used to make predictions from the spatial uncertainty model. On each trial the tilt of the target is selected by Adaptive Probit Estimation (APE). T he orientation of the target and distractors is internally represented by a noisy process that samples their orientation from a gaussian pdf with a mean equal to their actual value and unit variance. T he observer bases his orientation decision on the internally represented stimulus having the largest absolute deviation from the vertical. T he process is iterated until the experiment ends.


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stimuli. In particular, the observer could average the represented values across stimuli. We consider the spatial averaging model in Experiment 4, where the distractors had nonzero values. We also consider a late-noise model in which all the error arises after averaging of the stimulus values. T he model simulated a series of APE controlled trials and then calculated the standard deviation of the simulated psychometric function by probit analysis. T his was done with varying numbers of distractors. When no distractors were present, the simulated threshold was necessarily unity, equal to the standard deviation of the assumed underlying error distribution. For non-zero distractor numbers values greater than unity were obtained. To make ® nal numerical predictions, all values were scaled by the real observer’s threshold when no distractors were present.

EXPERIMENT 1 In the ® rst experiment we measured orientation discrimination thresholds with the number of distractors varying from 0 to 16. T he stimulus was exposed for either 100 msec or for as long as the observer required to identify the target. In the latter case, no attempt was made to hold eye ® xation. We reasoned that in the unlimited exposure condition the observer would be able to ® xate on, or at least attend to, all the stimuli in turn, so that the only effects of the distractors would be to increase spatial uncertainty. T he unlimited exposure condition, then, would give us an opportunity to test the quantitative predictions of the spatial uncertainty model and would provide a baseline from which to examine the effects of distractors in the 100-msec exposure condition.

Results and Discussion T he data are shown in Figure 3. T hresholds without distractors present were in the region of 1 8 , which compares well with results for equivalent stimuli obtained by others (reviewed by Morgan, 1990). T hresholds rose when distractors were added, both in the 100-msec exposure and the unlimited exposure conditions. When the observer had unlimited time to look at the stimulus array, the rise was very similar to that predicted by the spatial uncertainty model. But when the exposure was 100 msec, the rise in threshold due to distractors was considerably greater than that predicted by the winnertakes-all spatial uncertainty model. Figure 3 also shows (Panel a) the difference between the actual rise in threshold in the 100-msec condition and the rise predicted from spatial uncertainty alone. T he discrepancy increases with the number of stimuli. T he unlimited exposure condition allowed the observer to foveate the stimuli in turn, whereas the 100-msec exposure did not. T his difference might have been expected to produce lower overall thresholds in the unlimited exposure case, but it could not of itself account for the difference in slopes between the two conditions (Figure 3). It is of interest that the effect of presumed foveation and of exposure duration on the baseline threshold in the absence of distractors was small. For MM the thresholds in the unlimited and 100msec conditions were 0.87 8 and 1.17 8 , respectively, and for EC the ® gures were 1.19 8 and 1.41 8 . In more recent experiments we have con® rmed that high orientational acuity can be maintained at a 5 8 eccentricity, although interestingly this is not the case if only the

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FIG. 3.

Individual data for MM (a) and EC (b) in Experiment 1. Orientation discrimination threshold s (vertical axis) were measure d for target stimuli embedde d in an array of distractors (see Figure 1). Horizontal axis: number of distractors. T he error bars show standard deviations. T he solid line is a linear regression through the 100-msec data points, accounting for 99.5% (MM) and 98.2% (EC) of the variance, respectively. T he dotted curve shows the predictions of the spatial uncertainty mode l described in Figure 2 and the text. The only free parameter in this mode l is the observer’s threshold when there are no distractors present. T he prediction accounts for 91% (MM) and 90.6% (EC) of the variance in the unlimited exposure data. Panel c shows the difference between the data points in the 100-msec exposure condition and the predictions of the spatial uncertainty model. T he curves are linear regressions to the data, the equations and R values of which are shown at the top of the graph. Open circles: MM; solid squares: EC; solid circles: coincident data points for the two observers.

envelope rather than the grating and envelope of the gabor patch is tilted (Morgan & Baldassi, 1998, in prep). To see whether a different version of the spatial uncertainty model would account for the data, we assessed a spatial averaging model in which the observer takes the mean of the independently (and noisily coded) orientation values for all stimuli. In fact, this averaging model and the winner-takes-all model considered earlier are extreme versions of the more general Minkowski summation model: R = (S

b

Ri )

1/ b

1 th

where R is the response on which the decision is based, R i is the response to the i stimulus, and the exponent b is unity for the averaging model and in® nity for the winnertakes-all model (Graham, 1989, p. 169). T he different predictions of the two models are

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shown in Table 1. It will be seen from the table that the averaging model predicts a greater threshold elevation beyond n = 1 than the winner-takes-all model, but the predicted rise is still insuf® cient to account for the observed rise in threshold, for example, at n = 15, when the observed threshold is elevated by a factor of approximately 7. It follows that, as the winner-takes-all and averaging models are at opposite extremes of the continuum of Minkowski models, all versions of Minkowski summation will fail with these data. To determine the length of exposure time needed to reach the limits set by spatial uncertainty alone, we varied exposure duration with the number of distractors held constant at three. T he results are shown in Figure 4. T he data were well ® tted by power functions with slopes of 2 0.2 (MM) and 2 0.17 (EC). T he further improvements beyond 2 sec were negligible. Our results for long exposure durations con® rm those of Palmer (Palmer et al., 1993): the rise in threshold is entirely predictable from the spatial uncertainty model. For brief, post-masked exposures, however, there was a deterioration of orientational acuity due to distractors over and above that predicted from spatial uncertainty. One explanation for the discrepancy may be that we used a post-stimulus random dot mask, which prevented the direction of attention to individual stimuli after the 100-msec presentation. Another factor may be that our baseline thresholds of 1 8 were considerably lower than those of Palmer. T his may have given room for what Palmer calls ``sensory factors’ ’ to have exerted a greater in¯ uence. T he most obvious sensory factor is the greater crowding of stimuli that occurs when the number of distractors increases. It is known that orientational thresholds can be increased by nearly ¯ anking stimuli (Westheimer, 1981). To investigate the role of stimulus proximity, we carried out a second experiment in which the distance between the stimuli was independent of their number.

EXPERIMENT 2 In Experiment 1, the stimuli were spaced around the iso-eccentric circle so as to divide it into equal sectors (Figure 1). T his meant that the angle between stimuli decreased as their number was increased. For example, when there were two stimuli present, the angle between them was 180 8 ; when there were 16, the angle was 22.5 8 . T hese angular separations corresponded to linear separations of 4 8 and 0.78 8 , respectively. To control for the effects of angular separation, we repeated the 100-msec exposure condition of Experiment 1, but with the stimuli always spaced at 22.5 8 (0.78 8 of visual angle linear separation). T he absolute location of the sector containing the stimuli was randomly varied. For convenience, we refer

TABLE 1 N distractors 0 1 3 7 15

Winner-takes-all

Averaging

1.0 1.4 1.8 2.3 2.7

1.0 1.4 1.9 2.7 3.8


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FIG. 4.

T he data show how orientation discrimination threshold s (vertical axis) decreased as exposure duration (horizontal axis) increased, when 3 distractors were present (number of stimuli = 4). T he error bars show standard deviations of the mean. T he curves are linear regressions to the data, the equations and R values of which are shown at the top of the graph.

to the equal angular spacing condition of Experiment 2 as the ``crowded’ ’ condition, and the original condition of Experiment 1 as the ``spaced’ ’ condition.

Results and Discussion T he individual data from the two experiments are compared in Figure 5. T hresholds were higher for the crowded than for the spaced condition, except for n = 1 and n = 16, where the conditions were identical. T he effects of stimulus number were well ® tted by linear regression, but with a higher slope for the spaced condition than for the crowded (see equations at the top of the graphs in Figure 5). To see whether the effects of stimulus number for the spaced condition could be accounted for by crowding and spatial uncertainty alone, we subtracted the thresholds predicted from spatial uncertainty alone from those obtained in the crowded condition. T he resulting linear regressions are shown in Panel c of Figure 5. T he slopes were necessarily shallower than those before the subtraction, and in the case of EC were close to zero (0.09). T his means that for EC the effects of distractor number when crowding is constant are almost entirely explained by the effects of spatial uncertainty. For MM the slope was still positive (0.28), indicating that a further factor was involved.

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FIG. 5.

Results of Experiment 2, which compared the effects of distractors when they were equally spaced around the iso-eccentric circle (spaced condition: see Figure 1) or crowde d with a spacing equal to the n = 16 condition. Panels a and b show the individual data for EC and MM. Panel c shows the data for the crowded condition with the rise in threshold predicted from the spatial uncertainty mode l subtracted.

We infer that there are two reasons why distractors lower orientation acuityÐ crowding and stimulus uncertaintyÐ as well as a third unknown factor in the case of one subject (MM). Crowding is considered by Palmer to be a ``sensory factor’ ’ rather than an attentional one (Palmer, 1994 ; Palmer et al., 1993), which should not be affected by target cueing. In other words, if we indicate to the subject by a marker which of several stimuli is the target, this should not improve acuity any more than we expect from the reduction in spatial uncertainty. It should not decrease the effects of stimulus crowding because it does not change the distance between the stimuli. We tested this prediction in the third experiment. T he assumption that crowding is a low-level sensory effect rather than an attentional one is a common one (see, however, He, Cavanagh, & Intriligator, 1996) but this assumption has not previously been tested.

EXPERIMENT 3 T he effects of spatially cueing the target were measured in 5 subjects. Orientational thresholds were measured with 15 distractors and with a masked 100-msec exposure, as in Experiment 1. T he spatial cue was a small spot of radius 0.36 8 on the same radius as the target but at a slightly greater distance (1.8 8 ) from the centre (i.e. the separation between the centres of the cue and the gabor patch it cued was 1.8 8 ). To control for the

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possibility that the cue itself might mask the target, we also measured the effects of the cue when there were no distractors present. T he temporal properties of the cue were different for two groups of subjects. For EC, the cue was simultaneous with the target and the ® xation point remained on throughout (simultaneous cue condition). For the remaining 4 subjects the cue could ¯ ash for up to 65 msec before the target and then disappeared during the 100-msec stimulus presentation (pre-cue condition). T he ® xation spot disappeared both during the cueing interval and during stimulus presentation. Note that the total duration of precue and stimulus exposure (65 + 100 msec) was too short to allow a saccadic eye movement to a previously unknown stimulus location. We used the pre-cue condition because of pilot data indicating that it was more effective than a simultaneous cue for relatively unpracticed subjects. To see whether the pre-cue condition was indeed easier than the simultaneous, we explicitly compared the two in three subjects (MM, SB, JS).

Results and Discussion T he data are shown in Figure 6. Panel a shows the thresholds expressed in degrees. Panel b replots the data as thresholds relative to the no-distractor/ no-cue baseline. T he main ® ndings are: cueing reduced thresholds down to similar levels to those found when there was no distractors; in the no-distractor condition, the presence of the cue increased thresholds by a small and probably insigni® cant account; the rise in threshold in the no-cue/ 15 distractor condition was greater than that predicted from spatial uncertainty alone (see the horizontal arrow in Panel b), con® rming the results of our earlier experiments. An Analysis of Variance with cueing, distractors, and subjects as factors, and the 3way interaction as the error term, showed signi® cant effects of cueing, F(1, 12) = 22.78, p < .0005, distractors, F(1, 12) = 31.49; p < .0001, and of the Cueing 3 Distractors interaction, F(1, 12) = 25.33; p < .0003. T he differences between subjects approached but did not reach the 0.05 signi® cance level, F(4, 12) = 2.54; p = .095. How do these data compare with the predictions of the spatial uncertainty model, shown by the arrow in Figure 6 (Panel b)? If we scale all thresholds relative to a value of unity for the no-distractors, no-cue (0/ 2 ) condition, the mean rise in threshold due to distractors without a cue (15/ 2 ) is 6.73 (95% interval = 2.0). T his is signi® cantly greater than the rise of 2.67 predicted from the numerical simulation, which took account of the psychometric APE procedure. As before, we can therefore conclude that the distractors had an effect over and above that due to spatial uncertainty. Did cueing signi® cantly reduce the effect of distractors? T he mean relative threshold in the 15/ + condition was 1.49 (95% interval = 0.63). T his is signi® cantly less than the threshold in the 15/ 2 condition (6.73) and not signi® cantly different from the 0/ 2 baseline of 1.0. Did the cue cause any masking in the 0/ + condition? T he mean relative threshold in this condition was 1.1 (95% interval = 0.24), so we may conclude that it did not. A different way of interrogating the data is to start with the 15/ 2 condition as a baseline and to ask whether the cue reduces threshold more than would be expected from spatial uncertainty. S trictly speaking, this is not legitimate, because the 15/ 2 threshold already combines the effects of spatial uncertainty and crowding, as our previous experiments demonstrate. T he correct baseline is the 0/ 2 condition, where both spatial uncertainty


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and crowding are absent. Out of interest, however, we calculated the 15/ 2 threshold (6.73) elevation relative to the prediction of spatial uncertainty (2.67) as 2.52. T hus the cue should have reduced threshold by a factor of 2.52 if it completely removed spatial uncertainty and if the sole reason for the effect of distractors was spatial uncertainty (a dubious assumption, as we have argued). In fact, the cue reduced threshold by a factor of 4.5 (1.49

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FIG. 6.

Results of Experiment 3, which investigated the effects of cueing the target position. In Panels a and b, the conditions (horizontal axis) were: (1) no distractors, no cue; (2) no distractors, cue present; (3) 15 distractors, cue absent; (4) 15 distractors, cue present. Panel a shows the thresholds in degrees; Panel b shows the threshold s as multiples of the uncued, no- distractor thresholds. T he horizontal line with the arrow shows the relative threshold predicted by the spatial uncertainty model. T he error bars in Panels a and c represent 95% con® dence intervals. Note that cueing the target position reduces orientation discrimination threshold s (vertical axis) to a level close to that when no distractors are present. Panel c shows the comparison between the pre-cueing and simultaneous-cue condition for three of the subjects.

versus 6.73). Once again, then, we can conclude that the cue improved performance more than would be expected by reduction of spatial uncertainty. T he comparison between pre-cueing and simultaneous-cueing conditions is shown in Panel c of Figure 6. In all three subjects, the pre-cueing condition produced lower thresholds. T he effect was large in one subject ( JS) and small but probably signi® cant (note that the error bars represent 95% con® dence limits) in the other two. It may be relevant that the only subject (EC) who did not experience the pre-cue condition showed the highest relative threshold in the 15/ + cued condition (Panel b). We conclude that the spatial cue overcame, at least in large part, the effects of crowding by the distractors in addition to its effects in reducing positional uncertainty. T here may have been some remaining effect of crowding even with the cue present: this is indicated by the fact that thresholds in the cued/ distractor condition were slightly higher than in the cued/ no distractor condition in four of the ® ve subjects. Also the main effect of distractors was signi® cant in the ANOVA. However, the much larger effect is the improvement in performance in the cued versus no-cued conditions with distractors present, particularly when the cue came on slightly before the target and the ® xation point disappeared. T he question is how cueing can overcome the crowding effect.


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The Texture-processor Model of Pre-attentive Vision T he task of identifying the tilt of the target patch could be accomplished by the observer in several different ways. We suggest that switching between these different modes of analysis is the key to understanding the effects of selective attention in this task. Because the observer is instructed to report the tilt of only the target element, there is a natural tendency to assume that the decision is carried out at a processing stage where the elements of the display (target and distractors) are represented separately. But this does not have to be the case. T here is abundant evidence that texture processingÐ a fundamental mode of early visual analysisÐ is carried out by mechanisms that are sensitive to the statistical properties of regions of the display, rather than to single resolvable elements (Beck, 1982; Bergen & Adelson, 1988; Graham, Beck, & Sutter, 1992; Keeble, Kingdom, Moulden, & Morgan, 1995; Nothdurft, 1991). Keeble et al. provide evidence for a processor that analyses the mean orientation of the texture elements in a region surrounding each point in the image. Texture boundaries or discontinuities are revealed by changes in the mean value in the processed image. Applied to an image like that in Figure 1, the texture processor would deliver mean orientation values of 0 8 all around the circle except where the target was present, in which case the mean value would be different from 0 8 . To reach detection threshold, the target would have to be tilted by an amount suf® cient to raise the mean to threshold. T his will be greater than the tilt required when the target is isolated, because of the diluting effects of the distractors on the mean. T he magnitude of the dilution will increase with the proximity of the distractors (Experiment 2). We further suggest that the effect of the cue is to allow the observer to switch from a pre-attentive textural analysis to a ® ner-scale analysis that permits independent analysis of the elements comprising the display. T his idea leads to the following prediction. If, in the uncued condition, the distractors are themselves given a tilt away from the vertical, which is either less than that of the target or in the opposite direction, thresholds will be raised. T hreshold will be determined by the mean of the target and distractor orientation. For example, if the threshold for the target alone is 1 8 and the distractor has a tilt of 0.5 8 , the target will have to be tilted through 1.5 8 to reach threshold. Of course, spatial uncertainty makes qualitatively the same predictions, but they are numerically different. We attempted to distinguish quantitatively between the textural processing and spatial uncertainty models in the ® nal experiment.

EXPERIMENT 4 T he aim was to investigate the effects of a single distractor when it was tilted in either the same or the opposite direction to the target. T here was no cue to indicate which was the target. Formally, the observer’s task was to decide which stimulus had the greater absolute deviation from the vertical and to report the direction of that deviation. In practice, the target and distractor were often dif® cult to distinguish, and responses were based (subjectively) on an overall impression of the tilt of the ensemble.

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Modelling Because we are now considering a two-stage process for the task, with an early encoding stage of orientation and a subsequent averaging stage, the range of possible models becomes more complex. In particular, we have to distinguish two possible sources of noise. T he ® rst is early noise operating at the level of the orientation encoding of the single elements in the display. Early noise could be putatively identi® ed with noise in orientation-tuned units in V1 (Hubel & Wiesel, 1959). T he model of spatial uncertainty used by us so far assumes independent early noise in ® rst-stage orientational encoding. A second stage of noise could arise in the putative higher-order ® lter that collects (Morgan & Hotopf, 1989) or collates (Moulden, 1992) the output of ® rst-level ® lters over space. We call this late noise. Existing evidence suggesting that late noise may be the dominant determinant of orientation acuity is the fact that orientation acuity for two widely separated dots is similar to that for lines (see review by Morgan, 1990). It is unlikely that two widely separated dots would be encoded as ef® ciently as a line by orientationally selective V1 units, so we can infer that thresholds are limited by some later noise stage. T he models we consider are the following: 1. Spatial uncertainty (Winner-takes-all). T his is the model used above (Figure 2). T he target and distractor are independently encoded with early noise, and the decision rule is to report the sign of the deviation with the larger absolute value. 2. Spatial av eraging with early noise. T his is identical to the spatial uncertainty model (1) except that instead of winner-takes-all the average orientation is calculated over the target and the distractor. T he decision rule is to report the sign of this mean. 3. Spatial av eraging with late noise. T he orientation of the target and distractor are encoded independently with a noise-free process, and the mean is then calculated. T he mean is then subject to late noise before the decision rule is applied, the decision rule being to report the sign of the (noisy) mean. T he late noise is assumed to have the same standard deviation as the early noise and to be measured by the threshold without distractors present. T he predictions of the models are given in Table 2. T hey were derived from MonteCarlo simulations, which reproduced the exact APE psychometric procedure used in the Experiments. As before, the baseline threshold was taken to be the threshold in the nodistractors condition of Experiment 1. On each trial, the target was tilted from the vertical exactly as in the previous experiments, and the task was to report the direction of tilt (clockwise versus anticlockwise). T here was a single distractor present, with the separation of the ``crowded’ ’ condition of Experiment 2. T he target± distractor pair appeared at a random position around the isoeccentric circle, and the spatial order (target clockwise or anticlockwise to distractor) was randomized over trials. T he distractor was given a tilt that was a multiple of the target tilt: 1.0, 0.5, 0, or 2 0.5. When the gain of the distractor was 1.0, the target and distractor had the same orientation. T he distinction between them is entirely notional. When the


365

TABLE 2 G ain

Model 1

Model 2

Model 3

Data

2 0.5

2.73 1.32 0.91 0.69

2.64 1.35 0.92 0.69

4.0 2.0 1.5 1.0

6.34 3.03 1.28 0.97

+0.0 +0.5 +1.0

distractor gain was 0.5, it had half the tilt of the target, in the same direction. T he mean cue is now 0.75 that of the target, so a lowering of threshold is predicted by the texture model; and so on for the other gains.

Results and Discussion T he predictions of the models and the mean data for the two subjects are shown in Table 1. Individual data are shown graphically in Figure 7. Table 1 shows that the predictions of the Winner-takes-all and the early-noise-averaging models are virtually identical. T his is not surprising. Consider the case where the gain is 1.0. T he Winner-takes-all model predicts an improvement over baseline by a factor of sqrt(2); the early-noise-averaging model predicts that the threshold will be equal to the standard error of the mean, which is s / Ö 2, where s is the baseline threshold. T he data depart from the predictions of both early noise models in two ways. First, there is no evidence for improvement when the cue and distractor are tilted in the same direction (positive gain condition). S econd, the rise in threshold when target and distractor tilt in opposite directions is much greater than that predicted by the early noise models. S urprisingly, the late-noise averaging model does a better job. It predicts that there will be no improvement when target and distractor tilt in the same direction, and it predicts a large increase in threshold when they tilt in opposite directions. T he actual increase in the latter case is larger than that predicted, but still within the con® dence limits (Figure 7). T he implication of the late-noise averaging model is that the predominant source of noise when signals are averaged is not in the early encoding of the signals themselves, but in the subsequent converging of these signalsÐ that is, most of the noise is in the secondstage ® lter, not the ® rst. S upport for this idea in the case of orientational acuity is that orientational thresholds are quite similar for very different classes of stimuli, including separated dots, which are unlikely to be analysed by ® rst-stage orientationally tuned ® lters (see Morgan, 1990). (For further discussions of the general properties of higher-order ® lters, see Bock and Goode, 1994.) In summary, both versions of the early noise model can be clearly rejected by these data, but whether the late-noise averaging model is correct has still to be determined by further experiments with other subjects. Nevertheless, these preliminary data do suggest that some form of orientational averaging is taking place, in line with the predictions of a texture processing model.

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367

FIG. 7.

Results of Experiment 4, which investigated the effects of non-vertical distractors. T he observer’ s task, as in the previous experiment, was to report the orientation of the stimulus that was most tilted from the vertical. T he horizontal axis shows the mean of the target and distractor orientation cue, in units of the target orientation cue. When the mean was 1.0, the target and distractor had the same orientation; when it was 0.75, the distractor had half the tilt of the target, and so on. Vertical bars show 95% con® dence limits. (Except for the highest threshold for EC: see text for explanation). Panels a and b show the individual data, and the predictions of two models. T he probability summation model is the same as the spatial uncertainty model in Figure 2; the observer bases his decision on the stimulus that is internally represented as having the greater tilt from the vertical. In the mean cue model the observer is assume d to base his decision on the mean of the two stimulus values. Panel c shows the mean of the two observers’ data, with 95% con® dence limits based on their combined data.

GENERAL DISCUSSION Our ® ndings con® rm the important role that spatial uncertainty reduction can play in pattern discrimination (Palmer, 1994). In particular, we ® nd that distractors cause thresholds to rise even when the observer is allowed to inspect every element in the array in turn: the rise in threshold in these circumstances is exactly that predicted from the simplest winner-takes-all model of uncertainty reduction. On the other hand, we ® nd that uncertainty reduction is not the whole explanation of cueing effects. Our data show that directing the observer’s attention to a target amongst a set of distractors in brief, masked displays allows the observer to analyse the shape of the target with higher acuity than is the case when the observer does not know where the target is. With the opportunity to look sequentially at all the potential targets in a long exposure, there are no effects of the distractor above those predicted from spatial uncertainty.

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Similarly, with a cue to attract attention to the target, performance is almost as good as it is when there are no distractors. Without the cue to direct attention, performance deteriorates. T he improvement produced by the cue to target location is greater than that predicted from the signal-detection model of spatial uncertainty (Experiment 1). T he detrimental effects of distractors are increased when they are near to the target (Experiment 2), presumably due to crowding (He et al., 1996). T he improvement produced by the cue with the brief 100-msec exposure could not have been because the eyes moved to the target. T he exposure duration was only 100 msec, and this is too short for a saccade to occur when the target position is unpredictable, as it was in the present experiment. T he detrimental effect of the distractors upon acuity was due in large part to their spatial proximity to the target (Experiment 2), but this ``crowding’ ’ effect could be overcome by cueing the spatial position of the target (Experiment 3). To explain this effect, we suggest that cueing changes the size of the stimulus analyser that the observer brings to bear on the target. We suggest that without directed attention, the target and distractors are analysed together by a coarse-scale mechanism, probably similar to a texture analyser, as argued by Nothdurft (1991). T he analyser can crudely localize peaks of mean orientation in the image that differ from the mean surrounding orientation (Keeble et al., 1995). As evidence for this averaging mechanism, we have shown that acuity for target orientation is reduced by a distractor when attention is not cued, even if it is tilted in the same direction as the target. Acuity is predicted by the mean deviation of the target and distractor from the vertical, contrary to the predictions of probability summation (Experiment 4). We wish to make it clear that we are not arguing for an effect of attention upon the scale of spatial frequency analysis. T here is no evidence from our data that cueing switches analysis to a higher spatial frequency passband. In the now standard models of texture analysis (e.g. Malik & Peroma, 1990), texture processors consist of secondstage ® lters that collect the recti® ed output of ® rst-stage, spatial-frequency, and orientationally tuned ® lters. T he spatial range over which the second-stage ® lter operates is not necessarily related to the spatial-frequency tuning of the ® rst-stage ® lters. T he range could be large, even if the ® rst-stage ® lters were tuned to high spatial frequencies. T hus the notions of spatial range and spatial frequency should not be confused (Morgan, 1994). In summary, we argue that marking the target with a cue allows attention to be directed to it, and that this permits encoding of target shape by a stimulus analyser with a more restricted spatial range than that of the putative texture analyser. Previous work (Keeble et al., 1995) has shown that rapid texture segmentation can occur by a coarse process that involves local averaging; the present study suggests that focusing attention allows processing with a smaller spatial range, with consequent freedom of interference from distracting elements. T his hypothesis is a radical alternative to the limited-channel-capacity view of visual attention. T he reason for acuities being lower in pre-attentive vision is not that there is a limited capacity, but that the analysis is of a different kind from that in attentive vision. Indeed, the rapid statistical analysis of image properties by the pre-attentive texture analyser may have considerably greater channel capacity than the isolated-element analysis permitted by attentional mechanisms.


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