Abstract

The syndrome of unilateral spatial neglect (USN) after right-hemisphere damage is characterized by failure of salient left-sided stimuli to activate an orienting response, attract attention, and gain access to conscious awareness. The explicit failure processing left-sided visual information is not uniform, however, and patients seem to be more successful performing certain visual tasks than others. The source of this difference is still not clear. We focus on processing of visual scene statistical properties, asking whether, in computing the average size of an array of objects, USN patients give appropriate weight to objects on the left; disregard left-side objects entirely; or assign them an intermediate, lower weight, in accord with their tendency to neglect these objects. The interest in testing this question stems from a series of studies in healthy individuals that led Chong and Treisman [Chong, S. C., & Treisman, A. Statistical processing: Computing the average size in perceptual groups. Vision Research, 45, 891–900, 2005a; Chong, S. C., & Treisman, A. Attentional spread in the statistical processing of visual displays. Perception & Psychophysics, 67, 1–13, 2005b] to propose that processing of statistical properties (like the average size of visual scene elements) is carried out in parallel, with no need for serial allocation of focal attention to the different scene elements. Our results corroborate this suggestion, showing that objects in the left (“neglected”) hemispace contribute to average size computation, despite a marked imbalance in spatial distribution of attention, which leads to a reduced weight of left-side elements in the averaging computation. This finding sheds light on the nature of the impairment in USN and on basic mechanisms underlying statistical processing in vision. We confirm that statistical processing depends mainly on spread-attention mechanisms, which are largely spared in USN.

INTRODUCTION

Processing statistical properties of the visual scene—such as mean, range, and variance of the size, color, or orientation of a set of items—seems to play an important role in forming a coherent representation of the global visual scene. Ariely (2001) and Ariely and Burbeck (1995) showed that, when a set of similar objects is presented, the visual system represents the set-specific statistical properties. They used a display of circles followed by a single probe circle to be judged as larger or smaller than the circles' average size. They found that average size is perceived and maintained for immediate comparison more easily and accurately than the size of individual circles in the display.

Further exploration of the subject by Chong and Treisman (2003, 2005a, 2005b) showed that, in size comparison tasks, either in conditions of simultaneous presentation or using short ISIs, judgment of average size is more accurate than judgment of the size of a randomly selected member of the set. Furthermore, using brief exposure durations, they ensured that participants had no time to compute the average by serial assessment of individual objects, summation, and division of the sum by the number of objects.

Perception of statistical properties is not limited to average size of elements. For example, Alvarez and Oliva (2008, 2009) found that observers perceive what they call “ensemble statistics,” including summary location or orientation, even in unattended scene elements. Furthermore, Haberman and Whitney (2007) found that mean emotion and gender are also rapidly perceived for a group of face images. Taken together, these results suggest that perception of statistical properties is a basic, rather than a derived, visual function.

Chong and Treisman (2003, 2005a, 2005b) proposed that size average perception is a parallel, preattentive process. Classical studies by Treisman and colleagues defined and compared visual skills using rapid spread attention (classically called “preattentive” perception) and slower perception using serial focused attention. The first leads to the famous feature search “pop-out” phenomenon, where RT is independent of set size or number of items to be searched. In contrast, the latter is found when searching for a target defined by the conjunction of two features or by a small feature difference, and search time here is linearly related to set size (Treisman, 2006; Treisman & Gelade, 1980; see also Wolfe & Robertson, 2012).

Unilateral spatial neglect (USN) is a common neurological disorder caused by unilateral brain damage, usually in the right hemisphere, characterized by a failure to perceive and explore stimuli on the contralesional side (i.e., usually on the left; Kerkhoff, 2001; Mesulam, 1999; Heilman, Watson, & Valenstein, 1993). USN is attributed to the inability of focusing attention, preventing left-side inputs from reaching conscious awareness, and eliciting orienting behavior (Kinsbourne, 1993; Posner, Walker, Friedrich, & Rafal, 1987; see Driver & Vuilleumier, 2001, for a review).

A common finding among patients with USN is the phenomenon of extinction, in which patients disregard a contralesional stimulus in conditions of simultaneous bilateral stimulation, although the same stimulus may be detected and reported when presented in isolation. Recent studies found a double dissociation between neglect and extinction, suggesting that these two conditions may reflect separate dysfunctions (Umarova et al., 2011; Vossel et al., 2011; Pavlovskaya, Soroker, & Bonneh, 2007; Bonneh, Pavlovskaya, Ring, & Soroker, 2004; Karnath, Himmelbach, & Küker, 2003; for a review, see de Haan, Karnath, & Driver, 2012).

Not all tasks require focused attention. In fact, many tasks may be accomplished so rapidly that there is insufficient time for serially focusing attention to the variety of local scene attributes. As discussed above, feature search pop-out is one such example. Reverse hierarchy theory suggested an anatomical–physiological separation between spread versus focused attention mechanisms (Ahissar, Nahum, Nelken, & Hochstein, 2009; Hershler & Hochstein, 2005, 2006; Hochstein & Ahissar, 2002; see also Pavlovskaya & Hochstein, 2011; Ishizu, Ayabe, & Kojima, 2009; Juan, Campana, & Walsh, 2004; Di Russo, Martinez, & Hillyard, 2003; Pascual-Leone & Walsh, 2001; for Reverse Hierarchy Theory of perceptual learning see Ahissar & Hochstein, 1997, 2000, 2004).

If USN indeed impairs mainly focused attention mechanisms and related perception of local features (Pavlovskaya, Ring, Groswasser, & Hochstein, 2002), we might expect USN to spare perception of global statistical properties. Indeed, we previously found that USN patients have a much greater deficit for conjunction search, which depends on serial focused attention, than for feature search, which requires only spread attention—when studied using laterally presented search arrays (Bonneh et al., 2008; Pavlovskaya et al., 2002; see also Van Vleet & Robertson, 2009; List et al., 2008; Eglin, Robertson, & Knight, 1989; Robertson, Lamb, & Knight, 1988). Similarly, Yamanashi Leib, Landau, Baek, Chong, and Robertson (2012) found that, when USN patients performed a search task, there was some implicit averaging of size information in the left hemifield, which actually interfered with performance. Furthermore, these patients found it harder to disregard left-side elements when searching on the right. Taken together, these findings are consistent with neglect syndrome affecting mainly focused attention.

In the current study, we aim to elucidate further the question of processing asymmetry in USN, using the task of average size computation as a probe. Specifically, we ask whether right-hemisphere-damaged participants with USN, in whom allocation of focused attention to left-sided stimuli is markedly impaired, include objects on the left in a size averaging task. Such a result would support the preattentive account of statistical processing (Chong & Treisman, 2003, 2005a, 2005b). In contrast, total disregard of the contribution of left-side objects to the group average would be expected if the task is performed by serial, attention-demanding weighting mechanisms, which are deficient in USN patients. We use a variety of experimental conditions related to the complex nature of the neglect phenomenon, including the division between neglect and extinction. Preliminary reports of parts of this study were presented at international conferences (Pavlovskaya, Bonneh, Soroker, & Hochstein, 2010, 2011).

METHODS

Participants

Twelve right-hemisphere-damaged stroke patients with left-sided neglect, hospitalized at the Loewenstein Hospital (Raanana, Israel) for rehabilitation, were recruited for the study. There were three women and nine men at an age range of 53–74 years and an educational level of 7–19 years of formal schooling. Inclusion criteria were (1) first event of ischemic or hemorrhagic stroke affecting the right cerebral hemisphere, (2) negative neurological or psychiatric past history, (3) stable clinical and metabolic state, and (4) left-sided USN revealed in at least one of the following diagnostic tests: the Behavioral Inattention Test (Wilson, Cockburn, & Halligan, 1987), line bisection, Mesulam–Weintraub Cancellation Test (Weintraub & Mesulam, 1988), or the computerized Starry Night Test (SNT; Deouell, Sacher, & Soroker, 2005). Performance scores for these tests are shown in Table 1. Exclusion criteria were (a) hemianopia or quadrantanopia on confrontation test and (b) difficulty comprehending the instructions or completing the task. All patients were right handed, except D. T., who was left handed yet portrayed a typical left-side neglect profile. Nine patients exhibited extinction of left-sided visual stimuli in conditions of bilateral simultaneous stimulation (the three who did not show extinction in the confrontation test were S. G., P. S., and U. B. H.). Experimental testing commenced 3–27 weeks after the onset of stroke during inpatient rehabilitation (see Table 1 for demographic, clinical, and lesion details).

Table 1. 

Demographic, Clinical, and Lesion Data of the USN Patients

PatientAge (y)/SexYears of EducationLesion Type and LocationNeglect Tests
D. T.a 74/M I: T-P junction area, Ins, CP, IHWM BIT: 125, SC: 19–26 
MWCT: 12–19 
LB: 26.5 ± 7.3 
SNT: RT L > R 
S. G. 73/M 10 I (watershed, paramedian): F, P, O BIT: 105; SC: 0–23 
A. A. 66/M 12 H: CP, IHWM, F, P BIT: 105, SC: 8–13 
MWCT: 2–22 
LB: 18.4 ± 9.3 
SNT: RT L > R 
B. S. 53/F 13 H: T, P, O BIT: 134, SC: 24–27 
S. M. 60/M 19 I: F, T, P, Ins, CP, IHWM BIT: 129, SC: 22–25 
MWCT: 23–30 
LB: 3.5 ± 4.7 
SNT: RT L > R 
VISSTA C: 0.75–1.0, F: 0.82–0.95 
M. I. 63/M 12 I: T, P, Ins, CP, IHWM BIT: 128, SC: 23–27 
VISSTA-C: 0.72–0.97 
P. S. 62/F 12 I: F, T, P, Ins, CP, IHWM BIT: 111, SC: 22–27 
J. J. 59/M I: F, P, T, O, Ins, CP, IHWM BIT: 126, SC: 18–26 
C. S. 56/F 20 I: T, P, CP, IHWM BIT: 123, SC: 25–24 
V. P. 58/M 19 I: T, P, F, Ins, CP, IHWM BIT: 111, SC: 35 
Y. B. D. 62/M 12 I: F, P, CP, IHWM BIT: 122, SC: 23–27 
MWCT: 18–30 
SNT: RT L > R 
U. B. H. 67/M 16 I: Ins, CP, IHWM, F BIT: 133, SC: 24–27 
Mean (62.7) (13.3)   
PatientAge (y)/SexYears of EducationLesion Type and LocationNeglect Tests
D. T.a 74/M I: T-P junction area, Ins, CP, IHWM BIT: 125, SC: 19–26 
MWCT: 12–19 
LB: 26.5 ± 7.3 
SNT: RT L > R 
S. G. 73/M 10 I (watershed, paramedian): F, P, O BIT: 105; SC: 0–23 
A. A. 66/M 12 H: CP, IHWM, F, P BIT: 105, SC: 8–13 
MWCT: 2–22 
LB: 18.4 ± 9.3 
SNT: RT L > R 
B. S. 53/F 13 H: T, P, O BIT: 134, SC: 24–27 
S. M. 60/M 19 I: F, T, P, Ins, CP, IHWM BIT: 129, SC: 22–25 
MWCT: 23–30 
LB: 3.5 ± 4.7 
SNT: RT L > R 
VISSTA C: 0.75–1.0, F: 0.82–0.95 
M. I. 63/M 12 I: T, P, Ins, CP, IHWM BIT: 128, SC: 23–27 
VISSTA-C: 0.72–0.97 
P. S. 62/F 12 I: F, T, P, Ins, CP, IHWM BIT: 111, SC: 22–27 
J. J. 59/M I: F, P, T, O, Ins, CP, IHWM BIT: 126, SC: 18–26 
C. S. 56/F 20 I: T, P, CP, IHWM BIT: 123, SC: 25–24 
V. P. 58/M 19 I: T, P, F, Ins, CP, IHWM BIT: 111, SC: 35 
Y. B. D. 62/M 12 I: F, P, CP, IHWM BIT: 122, SC: 23–27 
MWCT: 18–30 
SNT: RT L > R 
U. B. H. 67/M 16 I: Ins, CP, IHWM, F BIT: 133, SC: 24–27 
Mean (62.7) (13.3)   

M = male, F = female; Edu. = education, years of formal schooling; I = ischemic stroke; H = hemorrhagic stroke; I (H) = ischemic infarction with hemorrhagic transformation; Regions: CP = capsular-putaminal; IHWM = intra-hemispheric white matter; Ins = Insula; F = frontal; T = temporal; P = parietal; O = occipital; BIT = Behavioral Inattention Test (Wilson, Cockburn, & Halligan, 1987; cut-off for normality = 130; maximal score = 146; the values shown are of test results obtained shortly before the experimental testing); MWCT = Mesulam-Weintraub Cancellation Test (Weintraub & Mesulam, 1988; L-R values = number of target stimuli (out of 30 on each side) detected on the left/right sides of the page; LB = line bisection, rightward mean signed displacement in mm (± standard deviation) of the subjective midpoint from the objective midpoint in lines of 180 mm; SNT = computerized Starry Night Test (Deouell, Sacher, & Soroker, 2005); RT = reaction time; All the patients who were tested in the feature-search module of the SNT (D. T., A. A., S. M., and Y. B. D.) showed significantly longer reaction time for target stimuli in the 3 contralesional columns compared to 3 ipsilesional columns (t test, p < .05).

aPatient D. T. was left handed; all others were right handed. All patients had preserved visual fields in confrontation test; yet all except S. G., P. S., and U. B. H. showed extinction of the left-sided stimulus in bilateral simultaneous stimulation conditions.

Ten healthy control participants (eight women, two men) were recruited from family members of the patients and acquaintances of the experimenters; age range was 24–65 years, and educational level was 11–22 years. All control participants were right handed, with normal or corrected-to-normal vision and no prior neurological or psychiatric problems. The study was approved by the ethics (Helsinki) committee at the Loewenstein Rehabilitation Center, Raanana, Israel, and all participants, patients, and controls gave their informed consent to participate.

Apparatus

Stimuli were displayed on a 19-in. color CRT monitor controlled by dedicated OpenGL-based (Austin, TX) software running on a Windows PC. The video format was true color (RGB), 100-Hz refresh rate, with a 1024 × 768 pixel resolution occupying a 14° × 11° area. Luminance values were gamma corrected, and the mean luminance was ∼30 cd/m2. Sitting distance was 0.7 m, and experiments were administered in near darkness. For patients, the experimenter initiated the trials, and responses were given orally and recorded by the experimenter.

Quantitative Assessment of Lateralized Inattention and the Added Effect of Extinction

We assessed contrast detection threshold on each side, in unilateral and simultaneous bilateral stimulation conditions, as done in our earlier USN studies (e.g., Pavlovskaya et al., 2007). First, we computed a measure of lateralized inattention by testing contrast detection threshold for right and left visual stimuli, considering the magnitude of left/right threshold difference as a quantitative measure of uneven distribution of attention. We used single even-symmetric 5-cycle/deg Gabor patches presented at 2.5°–3.5° eccentricity on either side of fixation. Trials were initiated by the experimenter and consisted of a single presentation interval of 250 msec, in which the patch appeared in half of the trials, and the observer was asked to reply yes/no to indicate presence or absence of the patch. Left- and right-side presentations were randomly interleaved, and an adaptive 3-up–1-down staircase procedure was applied to the contrast on each side independently, determining threshold as the average of eight contrast reversals. Second, we quantified the effect of extinction (deterioration of detection rate in one side when another stimulus is shown concomitantly on the other side) by presenting two Gabor patches simultaneously on the left and right sides, using a fixed contrast chosen to be somewhat above the left-side threshold contrast. Trials of unilateral-right, unilateral-left, simultaneous bilateral, and no stimulation were randomly interleaved with equal probability. Patients reported presence or absence of a stimulus on each side of a central fixation point (left/right/both/neither responses). The magnitude of left-side extinction was calculated by comparing left-side stimulus detection under bilateral and left unilateral conditions. Earlier studies using this task showed that healthy individuals have a similar contrast detection threshold on both sides, although they might show some right-side extinction (Pavlovskaya, Ring, Groswasser, Keren, & Hochstein, 2001).

Patients tested in the current study showed significantly higher detection thresholds in the left hemifield, as demonstrated in Figure 1A (see also Figure 1B, comparing red and blue bars), consistent with their asymmetric performance in traditional USN tasks (Table 1). They also revealed left-side extinction, as reflected in reduced rate of correct responses on the left in conditions of bilateral simultaneous stimulation, as seen in Figure 1B (compare pink with red bars).

Figure 1. 

Average data for 12 USN patients. (A) Contrast detection thresholds in left and right hemifields (LHF and RHF, respectively) showing significant disadvantage on the left (t test, p < .001). (B) Detection rates in unilateral presentation (red and blue bars for left and right sides, respectively) and simultaneous bilateral presentation (pink and light blue bars for left and right sides, respectively). The effect of extinction is noted by significant degradation of detection rate on the left comparing bilateral with unilateral presentation conditions (t test, p < .01).

Figure 1. 

Average data for 12 USN patients. (A) Contrast detection thresholds in left and right hemifields (LHF and RHF, respectively) showing significant disadvantage on the left (t test, p < .001). (B) Detection rates in unilateral presentation (red and blue bars for left and right sides, respectively) and simultaneous bilateral presentation (pink and light blue bars for left and right sides, respectively). The effect of extinction is noted by significant degradation of detection rate on the left comparing bilateral with unilateral presentation conditions (t test, p < .01).

Stimuli and Procedure

The experimental set-up is demonstrated schematically in the final figure (Figure 9) of this article.

Experiment 1: Average Size Computation in Lateralized Arrays

This experiment tests the ability to judge average size of an array of circles presented on one side of the vertical meridian. Participants were asked to fixate a central cross. After keypress initiation of the trial by the observer, a single reference circle appeared at fixation for 500 msec with a diameter of 1.1° (0.7° for the second paradigm; see below). The screen was then blanked for 1300 msec, followed by brief presentation for 250 msec of a lateral (left or right) array of 12 nonoverlapping circles, randomly positioned within a 6° × 6° region, with an average circle diameter A that was either larger or smaller than the reference circle by eight different delta values (including subpixel differences): 0.25, 0.5, 0.75, 1.5, 2.5, 4, 7, and 10 pixels (equivalent to about 0.01–0.30° or about 1–25%). Individual circle diameters in the array were randomly selected from a uniform distribution in the range of A ± 37% (i.e., A ± ∼0.4°), with final adjustment to obtain the desired average, A. The task was to judge which was larger—the reference circle or the array average. Trials with variable differences between the average group size and the constant reference circle, different delta values, were randomly interleaved to produce a psychometric curve. Eccentricity was 6° from fixation to the middle of the array of circles. Figure 2 describes the trial sequence in this experiment.

Figure 2. 

Trial sequence in average computation using lateralized arrays (Experiment 1). After trial initiation by the observer, a single reference circle at fixation appeared for 500 msec, then a blank screen for 1300 msec, followed by a lateral (left or right) array of 12 nonoverlapping circles, randomly positioned in a 6° × 6° region, with an average size that was either larger or smaller than the reference circle. The task was to judge whether the average size of the lateralized array is larger or smaller than the constant reference.

Figure 2. 

Trial sequence in average computation using lateralized arrays (Experiment 1). After trial initiation by the observer, a single reference circle at fixation appeared for 500 msec, then a blank screen for 1300 msec, followed by a lateral (left or right) array of 12 nonoverlapping circles, randomly positioned in a 6° × 6° region, with an average size that was either larger or smaller than the reference circle. The task was to judge whether the average size of the lateralized array is larger or smaller than the constant reference.

Experiment 2: Size Judgment for a Single Lateralized Object

This experiment tests the ability to judge the size of a single circle presented on one side of the vertical meridian. The paradigm was identical to Experiment 1 except that the number of circles in the lateral array was reduced to one.

Experiment 3a: Average Size Computation in a Bilateral Array with Concordant Delta Directions

This experiment tests the ability to compute the average size of an array of circles presented simultaneously on both sides of the vertical meridian. Here, the array of circles was a combination of two lateral arrays similar to those used in Experiment 1, except that they appeared simultaneously and were positioned adjacent to one another. The average size of the left and right arrays could be either “identical” (“both” condition) or “different” (“left” and “right” conditions, for left delta bigger than right delta and right delta bigger than left delta, respectively). Examples are shown in Figure 3, top and center, respectively. The two different conditions were used to assess the relative impact of the circles on each side on the computed average of the bilateral array. In the different conditions, the delta from the reference on one side was one quarter of the delta on the other side (i.e., both sides provided information about the group average, but one side had a larger delta, i.e., a larger difference from the constant reference than the other side).

Figure 3. 

Sample stimuli used in average size computation in bilateral arrays. Top: Average size on both sides of the array equally smaller than the reference circle (as seen in Figure 2). Center: Concordant delta (Experiment 3a): Mean sizes on two sides of the array are smaller than the reference, but difference from the reference is greater for left-side circles than for those on the right. Bottom: Discordant delta (Experiment 3b): Mean size of circles on right side of the array is smaller than the reference, whereas mean size of left-side circles is larger than the reference. Actual mean sizes and which side had larger delta varied from trial to trial (see text).

Figure 3. 

Sample stimuli used in average size computation in bilateral arrays. Top: Average size on both sides of the array equally smaller than the reference circle (as seen in Figure 2). Center: Concordant delta (Experiment 3a): Mean sizes on two sides of the array are smaller than the reference, but difference from the reference is greater for left-side circles than for those on the right. Bottom: Discordant delta (Experiment 3b): Mean size of circles on right side of the array is smaller than the reference, whereas mean size of left-side circles is larger than the reference. Actual mean sizes and which side had larger delta varied from trial to trial (see text).

Observers could get the correct answer by attending to the left or right side, although performance would be superior if they attended only to the side with the larger average-to-reference delta. Of course, participants could not know in advance which side had the larger delta, so they could not prepare to attend to only one side. Performance is expected to be poorer than for the easier “both” condition, where the deltas on both sides are the same, that is, have the larger difference from the reference.

For example, a delta of 4 pixels means that, in the “both” condition, the average size of the circles in the cloud was either 4 pixels larger (or 4 pixels smaller) than the reference. In the “right” condition, it was 4 pixels larger (or smaller) on the right side, but only 1 pixel larger (or smaller) on the left side, and in the “left” condition, the deltas were reversed. In all cases, the size differences on the two sides were in the same direction—that is, either both larger or both smaller than the reference. Our expectation was that USN patients, if they totally neglect left-side elements, would show large performance deficits for the “left” condition, where they would depend on the one-quarter-sized delta present on the right side, and that they may be better than controls for the “right” condition, where they would not be confused by the smaller delta on the left side.

Experiment 3b: Average Size Computation in a Bilateral Array with Discordant Delta Directions

This experiment is similar to the preceding one except that, in the “different” (right or left) conditions, when the average size of the circles on one side is bigger than the reference circle, that is, positive delta values, the average size of the circles on the other side is smaller than the reference, that is, negative delta. As in Experiment 3a, the delta value (difference of average size from the reference) on one side was one quarter of the delta on the other side, but, whereas in 3a, the two delta values were concordant (both positive or both negative), in 3b, they were discordant (one delta positive and one negative, i.e., the left and right means were one larger and one smaller than the reference, as demonstrated in Figure 3, bottom row). Experiment 3b is more sensitive than Experiment 3a to possible effects of processing asymmetry, because of the increased lateral asymmetry in average stimulus size in this task.

For example, a delta of +4 pixels means that, in the “both” condition, the average size of the circles in the cloud was 4 pixels larger than the reference. In the “right” condition, it was 4 pixels larger on the right side but 1 pixel smaller on the left side, and in the “left” condition, the deltas were reversed. Thus, in both the “right” and “left” cases, the size differences on the two sides went in opposite directions compared with the reference. Therefore, if the observer attended to only one side, he or she would have responded correctly when attending to the side with the larger delta and incorrectly if attending to the side with the smaller delta. Again, because participants could not know on which side the larger delta would appear, we would expect controls to spread their attention to both sides and show poorer performance in the “left” or “right” case compared with the “both” case. This performance would also be poorer for Experiment 3b than for Experiment 3a. If USN patients totally neglect left-side elements, our expectation would be that, for Experiment 3b, these patients would not only show a large performance deficit for the “left” condition, where they would depend on the one-quarter-sized delta present on the right side but also get most trials wrong, because the right side has a delta in the opposite direction. On the other hand, in this paradigm, too, they might be better than controls for the “right” condition, where they would not be confused by the opposite direction, albeit smaller delta on the left side.

To demonstrate, in Experiment 3b, for the “left” condition, when the left array mean is larger than the reference and the right array mean is smaller than the reference, then, if USN patients were to totally neglect elements on their left side, we would expect them to err and report a mean that is somewhat smaller (rather than very much larger) than the reference. Furthermore, in the “right” condition, we would expect no difference between the results of Experiments 3a and 3b, again, if they totally neglect elements on their left side.

Data Analysis

Our experiments had of necessity a complex design, because they had four noncoextensive factors: group (patients, controls), experiment (single, unilateral, bilateral), paradigm (concordant, discordant), and side (left, right, both), as between- and within-subject variables, respectively. The single and unilateral experiments were of course only on one side, either left or right and not both. In our special case, the bilateral cloud could be the same on both sides, and so called, “both,” or it could have a larger mean-to-reference delta on one side, and so called, “left” or “right,” accordingly. These contingencies are shown in Figure 4. We therefore computed two ANOVAs: The first (Figure 4, blue dotted lines) has main factors Group (patients, controls) × Experiment (single, unilateral, bilateral) × Side (right, left). Here, we average over concordant and discordant paradigms for the bilateral experiment and leave out the data for the both-sides condition. The second ANOVA deals only with the bilateral experiment (Figure 4, red continuous lines) and has main factors Group (patients, controls) × Paradigm (concordant, discordant) × Side (right, left, both). Post hoc t tests were performed to reveal further statistical trends. Data for the delta range of 1.5–10 pixels were used for these tests.

Figure 4. 

Experimental design had four main factors: Group, Experiment, Paradigm, and Side. The figure shows how these were distributed, because not all contingencies are possible for each factor value. Blue dotted lines are division for the first ANOVA; red lines are for the second ANOVA (see text).

Figure 4. 

Experimental design had four main factors: Group, Experiment, Paradigm, and Side. The figure shows how these were distributed, because not all contingencies are possible for each factor value. Blue dotted lines are division for the first ANOVA; red lines are for the second ANOVA (see text).

RESULTS

Comparing Performance for Left and Right Sides

We find that patients had significantly reduced performance for left-side presentation, compared with right-side presentation, in all tasks. Controls, on the other hand, showed similar performance for either side. The patient deficit was stronger when they determined the average of a unilateral array than when judging size of a single circle and still stronger for averaging left-side circles in cases of extinction, that is, when there were also circles presented on the right.

For the first ANOVA, we found a main effect for Side (F(1, 20) = 24, p < .001) stemming from lower accuracy on the left side compared with the right side (means [M] are Mleft = 0.809, SD = 0.0848; Mright = 0.870, SD = 0.047). We also found a main effect of Group (F(1, 20) = 9.381, p < .01) stemming from better performance for controls compared with patients (Mcontrols = 0.975, SD = 0.049; Mpatients = 0.810, SD = 0.049).

The most important result is the interaction between Side and Group (F(1, 40) = 18.36, p < .001). This interaction suggests that the difference in performance between left and right is greater in patients than in controls. In fact, it is significant for the patients and not for the controls (patients: Mleft = 0.757 [SD = 0.072], Mright = 0.863 [SD = 0.041], Mleft–right difference = 0.106 [SD = 0.063], SE = 0.018, t = 5.784, df = 11, p < .001; controls: Mleft = 0.871 [SD = 0.050], Mright = 0.879 [SD = 0.054], Mleft–right difference = 0.007 [SD = 0.037], SE = 0.011, t = 0.657, df = 9, p = .527). This comparison is shown in the bar graphs of the inset to Figure 5.

Figure 5. 

Interaction between side and group. The first ANOVA showed main effects for both Side and Group and an interaction between them such that performance was poorer for left side in patients but not for controls, as seen in inset. Bar graphs in main figure show effect of presentation side for USN patients for each experiment. Performance is shown for each experiment (single circle, unilateral array, and bilateral array) and for each group of participants (USN patients and controls). Note the consistently poorer performance for left side compared with right side for patients but not for controls. This is most striking for bilateral arrays where extinction effects are present. Overall, performance is superior for unilateral compared with bilateral arrays (when considering both paradigms and disregarding the “both” condition). Legends in this and following figures show color code for patients; similar textured colors apply for controls: blue or bluish for left side, red or pinkish for right side, and green or textured green for both.

Figure 5. 

Interaction between side and group. The first ANOVA showed main effects for both Side and Group and an interaction between them such that performance was poorer for left side in patients but not for controls, as seen in inset. Bar graphs in main figure show effect of presentation side for USN patients for each experiment. Performance is shown for each experiment (single circle, unilateral array, and bilateral array) and for each group of participants (USN patients and controls). Note the consistently poorer performance for left side compared with right side for patients but not for controls. This is most striking for bilateral arrays where extinction effects are present. Overall, performance is superior for unilateral compared with bilateral arrays (when considering both paradigms and disregarding the “both” condition). Legends in this and following figures show color code for patients; similar textured colors apply for controls: blue or bluish for left side, red or pinkish for right side, and green or textured green for both.

As shown in the main part of Figure 5, post hoc t tests show that the side difference for patients is significant in each of the three conditions: single (Mleft = 0.87, Mright = 0.93, Mdifference = 0.06, SE = 0.01, t = 5.112, p < .001), unilateral (Mleft = 0.81, Mright = 0.87, Mdifference = 0.05, SE = 0.02, t = 1.931, p < .05), and bilateral (Mleft = 0.59, Mright = 0.80, Mdifference = 0.02, SE = 0.03, t = 6.144, p < .001). For controls, the differences were not significant.

Even more significant are the differences between patients and controls in the bilateral array task, when considering separately the concordant and discordant deltas, as described in the following sections, based on the second ANOVA.

Comparing Performance for Left and Right Sides with Bilateral Presentation

We now look at performance with bilateral presentations, with different reference-to-array average deltas on the two sides, or with identical deltas, called the “both” condition. When the deltas are different, performance would be enhanced by concentrating on the side with the larger delta (“right” or “left” conditions). We expect superior performance for the “both” condition, where the larger delta is present on both sides.

We find that controls indeed perform equally in the “right” and “left” conditions and better in the “both” condition, where they can integrate information from the two sides. Patients show deficient performance in the “left” condition compared with either the “right” or “both” condition, but their performance is significantly worse for the “right” condition compared with the “both” condition (which differ in the left-side delta), indicating that left-side circles do contribute to the average.

For the second ANOVA, including the “both” condition, all three main effects were significant as were their interactions. There is a main effect of Paradigm (F(1, 18) = 6.69, p < .02) with concordant performance better than discordant performance (Mconcordant = 0.813, SD = 0.0775; Mdiscordant = 0.748, SD = 0.069). This is expected because, in the discordant case, the delta is in opposite directions for the two sides. There is a main effect of Group (F(1, 18) = 9.207, p < .01) with controls performing better than patients (Mcontrol = 0.825, SD = 0.069; Mpatients = 0.749, SD = 0.073), again, as expected.

There is also a main effect of Side (F(2, 36) = 84.416, p < .001; Mleft = 0.669, SD = 0.151; Mright = 0.798, SD = 0.077; Mboth = 0.883, SD = 0.053). Because there are three values for Side, we performed pair comparisons to determine the source of this main effect. Furthermore, there is a significant Side × Group interaction (F(2, 36) = 17, p < .001), so we performed the pair comparisons for each group separately, as follows, as demonstrated in the top of Figure 6.

Figure 6. 

Results for healthy controls (left) and USN patients (right) in the different conditions of Experiment 3 with bilateral arrays. Top: Results averaging data for the two paradigms. For the “left” and “right” conditions, the mean reference delta was one quarter as large on the second side, leading to poorer performance than in the “both” condition. This performance reduction was about equal on the two sides for the controls but was much larger for the left side for USN patients. Nevertheless, performance for patients, too, was somewhat poorer for right side compared with both sides, suggesting that they, too, use the left side in conjunction with the right side to improve performance. Center and bottom: Results with data separated for the concordant (center) and discordant (bottom) paradigms, respectively. Introducing discordant deltas (bottom) exaggerates the trends seen with concordant deltas (center). Performance in the “left” and “right” conditions is considerably poorer compared with the “both” condition even in controls. Patients have especially poor performance in the “left” condition, which is actually below 50% in the discordant condition, meaning that, when the averages on the two sides are in opposite directions compared with the reference circle, patients depend more on the smaller right-side average delta than on the larger left-side average delta. Nevertheless, the smaller (and incorrectly signed) delta on the left side still affects performance, and it is poorer in the “right” condition than in the “both” condition.

Figure 6. 

Results for healthy controls (left) and USN patients (right) in the different conditions of Experiment 3 with bilateral arrays. Top: Results averaging data for the two paradigms. For the “left” and “right” conditions, the mean reference delta was one quarter as large on the second side, leading to poorer performance than in the “both” condition. This performance reduction was about equal on the two sides for the controls but was much larger for the left side for USN patients. Nevertheless, performance for patients, too, was somewhat poorer for right side compared with both sides, suggesting that they, too, use the left side in conjunction with the right side to improve performance. Center and bottom: Results with data separated for the concordant (center) and discordant (bottom) paradigms, respectively. Introducing discordant deltas (bottom) exaggerates the trends seen with concordant deltas (center). Performance in the “left” and “right” conditions is considerably poorer compared with the “both” condition even in controls. Patients have especially poor performance in the “left” condition, which is actually below 50% in the discordant condition, meaning that, when the averages on the two sides are in opposite directions compared with the reference circle, patients depend more on the smaller right-side average delta than on the larger left-side average delta. Nevertheless, the smaller (and incorrectly signed) delta on the left side still affects performance, and it is poorer in the “right” condition than in the “both” condition.

Performing pair comparisons for the controls, we find no significant difference between left- and right-side performance (Mleft = 0.765, SD = 0.10; Mright = 0.796, SD = 0.094; t = 1.074, p = .3), suggesting they are about as good on either side. On the other hand, there was a significant difference between the “left” and “both” conditions (Mboth = 0.915, SD = 0.042; t = 6.202, p < .001) as well as between the “right” and “both” conditions (t = 5.583, p < .001), suggesting they integrate information over the two sides when available to improve performance.

Pair comparisons for the patients are very different. They have a side effect with left-side performance being significantly poorer than right-side performance (Mleft = 0.589, SD = 0.143; Mright = 0.801, SD = 0.066; t = 6.144, p < .001) and, similarly, a large benefit of both over left alone (Mboth = 0.858, SD = 0.05; t = 7.682, p < .001). Importantly, there is also a significant (although smaller) difference between right alone and both (t = 2.914, p < .01), suggesting that, nevertheless, the left side adds information beyond the right-alone condition.

The [both – right side] difference in the patient group (Mboth–right = 0.057, SD = 0.068) is significantly smaller than in the control group (Mboth–right = 0.119, SD = 0.067; F(1, 18) = 4.6, p < .05), indicating that, although the left side adds to the right side for the “both” condition in patients, as well, its contribution is smaller than in the control group.

We expect a greater difference between left or right performance compared with the “both” condition for the discordant condition, where the deltas are in opposite directions, than the concordant condition, where they are in the same direction. This was indeed found. The difference between the “both” condition compared with the “left” or “right” conditions for all participants was significantly larger in the discordant condition (Mdiscordant = 0.197, SD = 0.047) than in the concordant condition (Mconcordant = 0.110, SD = 0.058; t(20) = 3.729, p < .001). We now analyze the results for concordant and discordant deltas separately.

Average Size Computation in a Bilateral Array with Concordant Delta Directions (Figure 6, Center)

Healthy controls performed better when the average sizes of the circles on the two sides were equal. The difference in accuracy between the identical or “both” (91.63 ± 0.05%) and the two “different” (i.e., left or right, 82.0 ± 6.0%) conditions was significant (F(1, 9) = 104.85, p < .001). Performance in the “left” condition (80.7 ± 7.9%) did not differ significantly from the “right” condition (83.4 ± 9.1%; F(1, 9) = 0.54, p = .48).

USN patients' average rate of correct responses was 86.7 ± 6.1%, 67.3 ± 11.6%, and 81.6 ± 8.3% for the “both,” “left,” and “right” conditions, respectively. Paired t tests showed significant differences between “both” and “left” (t(6) = 5.811, p < .001) and “left” and “right” (t(6) = 4.204, p < .01) conditions. The latter comparison indicates a disadvantage for the “left” condition, not found in controls (compare leftmost bars in left and right parts of Figure 6, center). Importantly, performance on the “right” condition is slightly worse than in the “both” condition (t(6) = 1.61, p = .08), which means that, in the “both” condition, patients did take the left side into account. This result is even stronger for the second discordant paradigm, as follows.

Average Computation in a Bilateral Array with Discordant Delta Directions (Figure 6, Bottom)

Again, healthy controls performed better when the average sizes of the circles on the two sides were equal. Controls' correct-response rate was 91.3 ± 3.6%, 72.25 ± 10.7%, and 75.75 ± 8.27%, for “both,” “left,” and “right” conditions, respectively. Paired t tests showed significant differences between “both” and “left” (p < .001) and “both” and “right” (p < .001) conditions. The difference between left and right was not significant (p = .21).

USN patients' average rate of correct response was 84.7 ± 2.8% for the “both” condition (similar to their performance in the concordant experiment, as expected because, for the “both” condition, the two experiments are equivalent). Their performance was 47.1 ± 7.37% and 78.0 ± 2.5% for the “left” and “right” conditions, respectively (somewhat poorer than in the concordant experiment). Paired t tests showed significant differences between “both” and “left” (p < .001), “both” and “right” (t(4) = 3.186, p < .01), and “left” and “right” conditions (p < .001).

We conclude that USN patients make a weighted average across sides, giving only partial weight to the left side, perhaps because of extinction.

Performance as a Function of Delta

Figures 7 and 8 demonstrate performance for controls and patients in the different conditions as a function of the delta difference between the average circle size and the reference circle. In general, as delta increases, performance improves. The interesting part of these graphs is for delta greater than 1 (greater than 0 in log units), where performance begins to be greater than 0.5, chance level (the data used in the above ANOVAs). A few points should be noted, as follows.

Figure 7. 

Performance as a function of delta: lateralized display. The rate of correct response is shown as a function of delta (the difference between the average size of the lateralized circles and the size of the central reference circle, in log units; see text). Performance is shown for average size computation in unilateral (“left” or “right”) arrays of circles (top) or for a single lateralized circle (bottom). For the realm of significant performance, (log delta > 0), USN patients show a disadvantage on the left, whereas healthy controls perform equally on the two sides. Note that performance rises linearly with log delta.

Figure 7. 

Performance as a function of delta: lateralized display. The rate of correct response is shown as a function of delta (the difference between the average size of the lateralized circles and the size of the central reference circle, in log units; see text). Performance is shown for average size computation in unilateral (“left” or “right”) arrays of circles (top) or for a single lateralized circle (bottom). For the realm of significant performance, (log delta > 0), USN patients show a disadvantage on the left, whereas healthy controls perform equally on the two sides. Note that performance rises linearly with log delta.

Figure 8. 

Performance as a function of delta: bilateral arrays. Average size computation in bilateral arrays with concordant delta direction on the two sides (top) or with discordant delta directions (bottom). In both participant groups, performance is better when the average size of the circles on one side is the same as on the other side (the “both” condition) relative to trials where the average size is different on the two sides (“right” and “left” conditions). The magnitude of the difference in performance between “both” and “right” (or “left”) conditions reflects the weight given to right-sided (or left-sided) circles in the computation of the group average. It can be seen that, whereas, for controls, the “both”–“right” and “both”–“left” differences are equal, for USN patients, the latter difference is much bigger, reflecting a relatively smaller weight given to left circles in comparison with the right circles. However, it is evident that left-side circles contribute to the average computation even in the USN group. As in Figure 8, the trend seen for concordant deltas is more explicit for discordant deltas with a notable disadvantage for “left” compared with “right” in the USN group but not in healthy controls. Note that, for patients and the “left” condition, for discordant deltas, that is, when the deltas on the two sides are in opposite directions, increasing delta augments the contribution of the second side, which for these patients is the dominant right side. This leads to poorer and poorer performance, seen as judging most arrays as in the direction of the smaller right-side delta rather than in the direction of the larger left-side delta. This is the only case of performance below 50% and the only case of performance decreasing rather than increasing with increasing delta.

Figure 8. 

Performance as a function of delta: bilateral arrays. Average size computation in bilateral arrays with concordant delta direction on the two sides (top) or with discordant delta directions (bottom). In both participant groups, performance is better when the average size of the circles on one side is the same as on the other side (the “both” condition) relative to trials where the average size is different on the two sides (“right” and “left” conditions). The magnitude of the difference in performance between “both” and “right” (or “left”) conditions reflects the weight given to right-sided (or left-sided) circles in the computation of the group average. It can be seen that, whereas, for controls, the “both”–“right” and “both”–“left” differences are equal, for USN patients, the latter difference is much bigger, reflecting a relatively smaller weight given to left circles in comparison with the right circles. However, it is evident that left-side circles contribute to the average computation even in the USN group. As in Figure 8, the trend seen for concordant deltas is more explicit for discordant deltas with a notable disadvantage for “left” compared with “right” in the USN group but not in healthy controls. Note that, for patients and the “left” condition, for discordant deltas, that is, when the deltas on the two sides are in opposite directions, increasing delta augments the contribution of the second side, which for these patients is the dominant right side. This leads to poorer and poorer performance, seen as judging most arrays as in the direction of the smaller right-side delta rather than in the direction of the larger left-side delta. This is the only case of performance below 50% and the only case of performance decreasing rather than increasing with increasing delta.

Performance for left and right is identical for controls and clearly poorer for left than for right in patients in all cases. Performance with bilateral arrays (Figure 8) is better for both than for either right or left, for the concordant and especially for the discordant paradigm, and for controls as well as for patients. Furthermore, performance for USN patients is somewhat similar in the “both” and “right” conditions. This reflects the limited contribution of the left-side circles to performance. At the same time, it is especially informative that patient performance for the “both” condition is still superior to that for the “right” condition, indicating that patients do use their left-side field as well. It is also indicative that, for the left side in the discordant condition, performance actually drops with increasing delta; this is the only case of a decrease in performance with increasing delta. This oddity derives from more and more interference from the right side in this confusing discordant condition.

Analysis of the Left-side Deficit in Estimating Statistical Properties

If neglect is such that patients do not take into account elements in their left visual fields at all, we should have found large differences between performance for the “left” and “right” conditions, with performance for the “right” condition being the same as that for the “both” condition and performance for the “left” condition being much worse (a shift to the right of the curve by a Factor 4 in element difference). Furthermore, there should not have been a difference between the two cases of concordant versus discordant conditions. The intermediate findings we found indicate an intermediate situation, with USN patients including elements from their left visual fields in mean size computation, but giving lesser weight to these elements.

Average Computation in a Bilateral Array with Concordant versus Discordant Delta Directions

For both paradigms, in the “left” and “right” conditions, the two sides have different deltas, with one quarter of the delta on one side. What could be the strategies used by the observers to perform this task? The simplest strategy would be to compute the total average across both sides. This would yield worse performance in the “left” and “right” conditions compared with the “both” condition, as the average in the lateral mix would be (1 + 0.25)/2 * size difference, which means ∼0.63 of the difference in the “both” condition, and should be reflected in a proportional shift in performance. An alternative strategy would be to compare both sides independently and use the one with the higher confidence. Note that one could not simply base the decision on the side with the larger average, as the difference could be both positive and negative.

As can be seen in Figures 7 and 8, the data lie along a straight line when plotting performance versus log delta (i.e., size difference between reference and average circle sizes on a log scale). These lines are nearly parallel in most cases, so that the effect of the changes in conditions—patients versus controls, left versus right side, and right or left versus both sides—can be seen in a shift of the lines, for example, at performance equal to 0.75 correct. When the lines are not parallel, this is seen in their different slopes. The intercepts and slopes for the data of Figures 7 and 8 are shown in Table 2, together with the resulting shift at fraction correct 0.75.

Table 2. 

Average Computation in a Bilateral Array with Concordant and Discordant Delta Directions on Both Sides When Delta = 1 Pixel

Right–Left DeltaConditionIntercept: Fraction Correct Delta = 1 PixelSlope (Log Units)Shift (Log Units/Pixels) at 0.75 Correct
ControlsPatientsControlsPatientsControlsPatients
Concordant Both 0.68 0.68 0.32 0.26 0.22/1.7 0.34/2.2 
Right 0.62 0.62 0.29 0.26 0.49/3.1 0.50/3.2 
Left 0.61 0.52 0.27 0.22 0.49/3.1 1.05/11.2 
Discordant Both 0.68 0.62 0.32 0.32 0.22/1.7 0.34/2.2 
Right 0.58 0.59 0.23 0.26 0.77/5.9 0.61/4.1 
Left 0.58 0.53 0.21 −0.07 0.77/5.9 −3.10/1300 
Right–Left DeltaConditionIntercept: Fraction Correct Delta = 1 PixelSlope (Log Units)Shift (Log Units/Pixels) at 0.75 Correct
ControlsPatientsControlsPatientsControlsPatients
Concordant Both 0.68 0.68 0.32 0.26 0.22/1.7 0.34/2.2 
Right 0.62 0.62 0.29 0.26 0.49/3.1 0.50/3.2 
Left 0.61 0.52 0.27 0.22 0.49/3.1 1.05/11.2 
Discordant Both 0.68 0.62 0.32 0.32 0.22/1.7 0.34/2.2 
Right 0.58 0.59 0.23 0.26 0.77/5.9 0.61/4.1 
Left 0.58 0.53 0.21 −0.07 0.77/5.9 −3.10/1300 

What shifts are expected? If controls average across the two sides, we expect the best performance for the “both” condition and a decrement for the “left” and “right” conditions (i.e., a larger shift), which should be the same for either side. Furthermore, this shift should be larger for the discordant condition, where the second side delta is in the “wrong” direction. This is exactly what is found in Table 2 for the controls.

For USN patients, there are three possibilities: If neglect has no effect, the data for patients should be the same as for controls, with, for example, the same shifts for the “left” and “right” conditions and equal differences between “both” and either “left” or “right.” This is clearly not the case. If patients do not take into account elements in their left visual fields at all, we should find large differences between performance for “left” and “right” conditions, with performance for the “right” condition being the same as that for the “both” condition and performance for the “left” condition being much worse—with a shift rightward by a Factor 4 in delta. Furthermore, as mentioned, there should be no difference between the concordant and discordant conditions. Data in Table 2 do not go so far. The third possibility, which is supported by the data of Table 2, is an intermediate effect: USN patients do indeed take into account elements on their left side in mean size computation, but giving lesser weight to these elements. Because patient performance is compromised even in the lateralized condition (with a single element or a cloud), giving lesser weight to the less certain left-side percept is actually advantageous.

Further insight is gained from the bilateral array experiments with concordant (Experiment 3a) and discordant (Experiment 3b) deltas (Figures 6, center; Figure 8, top; and Figures 6 and 8, bottom, respectively). Although, in the “both” condition, participants could in principle get the correct answer by attending constantly to one side only, such a strategy would yield a significant cost in the left, contralateral different condition and significant benefit in the “right”, ipsilateral “different” condition. This is because the three conditions were presented in random order on different trials, and participants did not know before trial initiation which was going to be the side with the larger average-to-reference delta value (which in itself would indicate the correct answer). Thus, the disadvantage shown by healthy controls in both different conditions relative to the “both” condition points to employment of a processing mechanism that averages objects on the two sides. Moreover, performance similarity in the two different conditions suggests employment of similar processing strategies for the two sides (both the intercept and slope of the line describing rate of correct response as a function of delta size do not show significant differences between the two different conditions).

The USN patients manifested a different pattern. First of all, the difference between “left” and “both” conditions was much more conspicuous than in healthy controls (especially in Experiment 3b, when they had to compute the average in arrays with discordant delta directions on the two sides; Figures 6 and 8, bottom). Second, the difference between “right” and “both” conditions was somewhat smaller than in healthy controls; yet, the advantage of the “both” condition was maintained in the USN group even in relation to the “right” condition. Note that, in Experiment 3b, performance accuracy in the “left” condition dropped to an average of 47% (compared with 67% in Experiment 3a, when delta direction on the two sides was concordant). This finding may reflect the increased likelihood to err in “left” discordant compared with “left” concordant conditions because of the increased impact of extinction in the former. Yet, the significant superiority of performance in the “both” condition compared with the “right” condition shows that, even in the latter condition, USN patients took into account at least part of the left-sided circles when they computed the average size (Figures 6 and 8).

DISCUSSION

The patients who participated in this study demonstrated (a) left-side neglect in standard diagnostic tests (Table 1), (b) asymmetric distribution of attention making contrast detection threshold on the left much higher than on the right (Figure 1A), and (c) marked tendency for left-sided stimuli to undergo extinction in conditions of bilateral simultaneous stimulation (Figure 1B). These patients' performance in perception of the average size of a lateralized array of circles was worse on the left side relative to the right side (accuracy: 81% vs. 87% on left vs. right arrays, respectively, compared with bilateral average of 90% in the control group; Figure 5). The same pattern was found in their size judgment of a single lateralized circle (accuracy: 87% and 93% for left and right presentations, respectively, compared with a bilateral average of 95% in the control group; Figure 5). Left-side disadvantage in these two tests was small but significant and contrasted with healthy controls, who scored equally on the two sides. Note that the deficit in judgment of a single circle suggests that the difficulty in estimating the average of the lateralized cloud is not only in the computational function of averaging itself but also may derive at least partially from an uncertainty in perceiving each circle's size. One would expect uncertainty to be diminished when averaging many circles, but if anything, the left-side deficit only gets worse.

Close examination of the lateral asymmetry shown by the USN patients when tested with a lateralized single circle or array of circles reveals that the line describing the rate of correct response as a function of delta size (Figure 7) has indeed a higher intercept on the left (the intercept is the calculated rate of correct responses when delta size is 1 pixel), but the slope is the same for the two sides. Such a result would be unlikely if the patients used a different processing strategy on the neglected and nonneglected sides (e.g., parallel processing using spread attention on the former and serial processing using focused attention on the latter). This finding suggests that the USN patients, despite their one-sided brain damage, employed in these two tasks similar processing strategies for the right and left hemispaces, with somewhat diminished efficiency on the left.

The essential question is what happens with USN patients in the bilateral array task, demonstrated schematically in Figure 9. The left-side deficit is more robust for bilateral arrays where right-field circles compete with left-field circles for patients' attention, and the extinction phenomenon is present. For bilateral arrays, there is much worse performance for the “left” compared with the “right” condition, with performance on the “right” condition approaching that for the “both” condition. Still, patients clearly include left-side circles in their estimate, leading to the remaining difference between performance in the “right” and “both” conditions. These circles receive lower weight in patients' averaging, reflecting extinction. The strong dependence on average-to-reference delta and the dramatic difference between the concordant and discordant conditions confirm inclusion of left-side circles in patients' average computation. Inclusion of left side circles confirms the reduced deficit for spread-attention compared to focused-attention tasks, consistent with Reverse Hierarchy Theory suggestions differentiating the anatomical site of these processes (Hochstein & Ahissar, 2002).

Figure 9. 

Schematic drawing of the experimental set-up.

Figure 9. 

Schematic drawing of the experimental set-up.

USN patients manifest asymmetric performance also in other tasks using spread attention and parallel processing. For example, they show prolonged RT and reduced hit rate on the left in “pop-out” conditions of visual search (Pavlovskaya et al., 2002), as used in the computerized SNT (Deouell et al., 2005). Thus, the small asymmetry shown in average size computation cannot be taken as a disproof of the parallel processing conjecture of average computation (Chong & Treisman, 2003, 2005a, 2005b).

Yamanashi Leib et al. (2012) studied four patients with mild chronic left-side neglect. After presentation of a target circle, the task was to search for a circle of the same size, when presented in a cloud of various-sized circles, all on one side of the display. This was a study of extinction effects because there were always distractors (triangles) on the other side. Hit rate was 50% on the left, compared with 70% on the right, confirming extinction. Most interestingly, when the target was absent, false alarm rate was greater when mean circle size equaled the target size, but only for left-side clouds, implying that patients implicitly computed mean size in their neglect field. Left-side distractor triangle size also affected search on the right side, supporting this conclusion. We now confirm and extend their findings. Whereas they found signs of implicit extraction of mean size summary in the neglect field, we directly tested, and found, explicit mean size computation in the neglect field. We demonstrate directly that this is mainly the effect of extinction, by testing mean size computation with and without presence of arrays in the right hemifield. Importantly, we measure the extent of the effect by varying the difference between the mean and the reference (delta). Finally, we introduced the novel discordant test, with mean circle size larger than the reference on one side and smaller on the other, and thereby measure competition between the two sides. This allows us to determine that left-side mean computation contributes only a fraction of the weight of right-side computation.

As mentioned in the Introduction, there is a growing body of evidence that the neglect or extinction deficit is less profound when considering global effects perceived without focused attention. Statistical properties (Yamanashi Leib et al., 2012, and the current study), cross-midline effects (Brooks, Wong, & Robertson, 2005), grouping effects (Pavlovskaya, Sagi, Soroker, & Ring, 1997), and feature search (Pavlovskaya et al., 2002) are all perceived with less deficit than are focused-attention-specific properties. These findings support the conclusion that information about crowds and single objects might be quite independent (Alvarez & Oliva, 2008, 2009; Haberman & Whitney, 2007; Chong & Treisman, 2003, 2005a, 2005b; Ariely, 2001; Ariely & Burbeck, 1995). Further work is needed to expand the list of global perception features that can be perceived without focused attention and might be spared in neglect syndrome.

Conclusions

There are three important implications of the current results, in terms of understanding rapid perception in general and the neglect syndrome deficit in particular:

  • (1) 

    Evidence that USN patients with spatial attention disorders are able nevertheless to extract (to some degree) statistical properties of the visual scene suggests that this process is a parallel preattentive or spread attention process (Chong & Treisman, 2003, 2005a, 2005b; Hochstein & Ahissar, 2002).

  • (2) 

    Given the accumulating empirical evidence that points to a processing mechanism based on spread attention in computation of statistical properties of visual scenes, the ability of USN patients to evaluate statistical properties on the neglected side implies that USN affects primarily focused attention processes. Posterior right-hemisphere damage causing USN does not abolish the patients' ability to retrieve and use visual information from the contralesional side, as evidenced here by the left-side contribution to the computation of the average size. Statistical property perception is relatively more preserved, because it is based on processing using spread attention. Given that mechanisms for top–down allocation of attention seem to reside in more dorsal and less frequently damaged frontoparietal regions on both hemispheres, the failure revealed in left-sided perceptual processing based on focused or intrinsic bottom–up attention can be explained in terms of interhemispheric and intrahemispheric disconnection between different components of the attention system (Corbetta & Shulman, 2011; Corbetta, Kincade, Lewis, Snyder, & Sapir, 2005). This would be in accord with Corbetta's theory, derived from independent empirical evidence.

  • (3) 

    Because USN patients succeed somewhat in both unilateral and bilateral cloud tasks, we can conclude that both neglect and extinction are primarily deficits in focused attention mechanisms or perhaps in the interface between spread and focused attention. At the same time, we found a difference in the degree of deficit for these tasks, with unilateral tasks more spared than bilateral tasks. This suggests that extinction rather than neglect itself was the major aspect of the USN syndrome that led to the deficits found.

Acknowledgments

We thank Anne Treisman and Lynn Robertson for extensive discussions concerning this study. We thank Ariel Goldstein for performing statistical analyses and Anna Nesterov for assistance with graphics.

Reprint requests should be sent to Marina Pavlovskaya, Department of Neurophysiology, Loewenstein Rehabilitation Hospital, 278 Ahuza Str., Raanana, Israel 43100, or via e-mail: marina@netvision.net.il.

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