Neuropsycholo`ia\ Vol[ 25\ No[ 4\ pp[ 358Ð364\ 0887Þ 0887 Elsevier Science Ltd[ All rights reserved\ Pergamon Printed in Great Britain

9917Ð2821:87 ,08[99¦9[99PII] S9917Ð2821"86#99020Ð9

Note

Visuospatial neglect in normal subjects] alteredspatial representations induced by a perceptual

illusion

JAMES FLEMING� and MARLENE BEHRMANN$

� Department of Neuroscience\ University of Pittsburgh\ Pittsburgh\ Pennsylvania\ 04159\ U[S[A[^ $ Department of Psychology\Carnegie Mellon University\ Pittsburgh\ Pennsylvania\ U[S[A[

"Received 17 May 0886^ accepted 14 Au`ust 0886#

Abstract*Previous studies have suggested that the representation of space is distorted in patients with hemispatial neglect[ Toexamine the nature of the altered spatial representation\ we developed an analog of neglect in normal subjects using bisections ofthe Judd visual illusion "e[g[\ ³**г# whose direction "facing left:right:both# and _n angle "03>:34>:65># were orthogonally varied[Subjects made bisection errors that deviated signi_cantly in a direction opposite to that in which the _ns pointed\ and these deviationsdecreased as _n angle increased[ We replicated these _ndings in a second task in which subjects were given the midpoint and placedthe two _ns at the ends of an imaginary shaft "e[g[\ ³ = ³\ note] dot � true center#[ These _ndings suggest that the geometricproperties of the display have a strong in~uence on the representation of space\ and thus may be used to induce a distorted perceptionof space analogous to that observed in patients with visuospatial neglect[ Þ 0887 Elsevier Science Ltd[ All rights reserved[

Key Words] neglect\ perceptual illusion\ spatial representation[

Introduction

The search for the relation between space of the {physi!cal world|\ i[e[ the world which exists apart from thatmentally instantiated by organisms\ and {psychologicalspace|\ i[e[ space represented by neurons or ensembles ofneurons\ has persisted for many years ð0Ł[ Though thelink between neural processing and spatial representationremains poorly understood\ important insights into themechanisms underlying spatial representation have beenobtained from patients with a visuospatial de_citacquired following brain damage[ Patients with left hemi!spatial neglect "typically after lesions to the right parietalregion# may fail to respond to or report information onthe contralesional side of space "see Bisiach and Vallarð1Ł for an overview#[ In an attempt to understand themechanisms responsible for spatial coding\ recent studieshave been concerned with establishing the nature of thespatial map derived by these patients and the cor!

� Address for correspondence^ tel[] "301#157!3026^ fax]"301#513!8087^ e!mail] j~emingÝandrew[cmu[edu

358

respondence between these perturbed internal spatial rep!resentations and veridical physical space[

One potentially useful method for studying the spatialanisometry in neglect is to induce {neglect| in normalsubjects and to use this analog to analyze the resultingspatial topography[ Several recent studies have shed lighton the ~exibility of spatial and attentional processing"see\ for example\ ð2Ð4Ł# by unleashing or exaggerating theattentional biases of normal subjects or by manipulatingtheir spatial representations[ In line with these studies\we induce neglect!like performance in normal subjects byusing visual illusions to alter their perception of spatialextent\ and then we examine their subsequent behavior[

A study by Mattingley and colleagues ð5Ł\ though notexplicitly directed at inducing neglect!like performance\had subjects bisect the Judd visual illusion\ a variant ofthe Mu�llerÐLyer illusion[ They demonstrated that theperception of spatial extents can be manipulated so as toinduce neglect!like bisection errors "ð5Ł] see also ð6Ł^ seeFig[ 0#^ speci_cally\ on both the unilateral!_n and bilat!eral!_n Judd illusions\ normal subjects and neglect pat!ients made bisections that were displaced away from the

J[ Fleming and M[ Behrmann:Neglect by perceptual illusion369

Fig[ 0[ The results from Mattingley et al[ ð08Ł using Judd _gures having _n length � 2[4 cm\ shaft length � 04 cm\ and _n angles of39>[ Notice the marked bisection errors generated by normal subjects on both Leftward and Rightward _gures[ The shafts of the

Judd _gures and the control line are aligned[

objective midline\ and shifted towards the outward!projecting _n and away from the inward!projecting _n[Relative to a no!_ns control line\ normal subjects mademean errors of approximately 7[7) and −4[1) on Right!ward "_ns going to the right# and Leftward Judd _gures\respectively[

Mattingley and colleagues proposed that the bisectionerrors arise from a perceptual compromise ð5\ 7\ 8Ł betweencon~icting cues derived from the horizontal extent of theshaft and from the horizontal extent of the entire _gure[They argued that\ for the inward!projecting _n on theleft side of a Rightward Judd _gure as in Fig[ 0\ theleft endpoint of the shaft is "mis#perceived as beginningslightly to the right of its true position[ Hence\ bisectionmarks are displaced to the right of the actual midpoint[Similarly\ an outward!projecting _n on the right side ofthe Rightward _gure causes the shaft to be "mis#perceivedso that it extends further to the right\ thereby leading torightward bisection displacements[ The same perceptualcompromises hold for Leftward _gures[

While a perceptual compromise interpretation mayprovide a general description of the illusory e}ects\ per!haps a more _ne!grained explanation is that the _nsinduce a distorted representation of the spatial extent ofthe shaft^ inward _ns distort the shaft\ pushing the mid!line to the opposite side whereas outward _ns pull themidline towards themselves[ Indeed\ several studies usingvariants of the Mu�llerÐLyer illusion have demonstratedsuch distortion e}ects "see Greene and Nelson ð09Ł for abrief review#[ Importantly\ a perceptual distortion ofspace resulting in a deviation from the midline in a linebisection task is considered to be one of the de_ningcharacteristics of hemispatial neglect ð00Ł[ Given thatsuch a distortion is also considered to give rise to bisectionerrors in normal subjects on visual illusions\ in this paper\we use the bisection of the Judd _gure as an analog ofneglect and explore the altered visuospatial rep!resentations induced in normal subjects[

Our study has three main parts]

0[ We initially replicate the basic _nding of Mattingleyet al[ ð5Ł to con_rm that the Judd _gure gives rise tothe reported robust displacements in line bisection andthat these displacements vary with the direction of the_gure[ Whereas shaft length is known to play somerole in determining bisection errors "albeit small inMattingley et al[ ð5Ł and large in Greene and Nelsonð09Ł#\ numerous studies have consistently dem!onstrated that the _ns play a substantial role in dis!torting perceived length and distance "see Greene andNelson ð09Ł for a brief overview#[ More speci_cally\the magnitude of the _n angle\ formed by the _n andshaft\ in~uences the distortion[ Although\ the exactrelation between _n angle and nature of the distortionfunction\ whether monotonic "see for example\ ð01\02Ł# or curvilinear "such as ð03\ 04Ł#\ is still contro!versial[ Given the consistent e}ect of _n angle\ weexamine the in~uence of the magnitude of the _nangles on bisection deviation by measuring subjects|bisection performance using displays with small "03>#\intermediate "34># and large "65># _n angles[

1[ Because we do not know what particular aspects ofthe illusion are critical for inducing the errors\ weanalyze systematically the in~uence of various geo!metric properties of the display on the bisection error[More speci_cally\ we evaluate the individual con!tribution of the three components of the _n anglegeometry\ the W "length of the _n#\ X "portion of theshaft that underlies the _n#\ and Y "vertical dimensionof the _n angle# components "see Fig[ 1#\ by holdingone of the single components "W\ X\ or Y# constantat a pre!speci_ed measurement while allowing theother two components to vary with _n angle[ If thebisection error varies when a given component is heldconstant\ then that _n component cannot be totallyresponsible for producing the errors[

J[ Fleming and M[ Behrmann:Neglect by perceptual illusion 360

Fig[ 1[ An example of a bilateral!_n Judd _gure[ The geometric components of a _n angle are shown[ "W# is the length of the _n\"X# is the length of the portion of the shaft that underlies the _n\ and "Y# is the height of the top of the _n to the shaft[

2[ We verify our results using an alternative techniquedeveloped by Bisiach and colleagues in order to dem!onstrate disordered spatial representations in patientswith visuospatial neglect ð05\ 06Ł[ In this procedure\subjects are given only the midpoint of a virtual shaftand are required to place the _ns at the correspondingend!points[ We predict that even in the absence of theshaft\ the end!point _ns would induce a deviationof the subjective midpoint biased by the angle anddirection of the _ns[

Our claim\ then\ is that irrespective of the technique"line bisection\ end!point _n placement#\ simply varyingthe angle and direction of the _ns will give rise to pre!dictable changes in the severity of the distorted perceptionof the shaft[ The rightward distortions with Rightward_gures may mimic left!sided neglect\ and leftward dis!tortions with Leftward _gures may mimic the less com!mon right!sided neglect ð07Ł[ Thus\ line bisection on Juddillusion displays may potentially provide insight into thenature of the spatial representational anisometry inneglect[

Method

Subjects

Three groups of ten\ right!handed subjects were recruited\one for each of the W!\ X!\ and Y!display versions of theexperiment[ The subjects were undergraduate and graduate stu!dents\ as well as friends of varying educational backgrounds[Subjects had no signi_cant medical\ neurological\ or psychiatrichistory and had normal or corrected!to!normal vision[ The "W#group consisted of 4 males and 4 females with mean age of 13[1yrs "S[D[ � 2[57#\ the "X# group consisted of 2 females and 6males with a mean age of 19[8 yrs "S[D[ � 1[40#\ and the "Y#group consisted of 4 females and 4 males with a mean age of11[8 yrs "S[D[ � 2[64#[

Materials and procedures

Geometric dimensions known to be robust in eliciting anillusion ð04Ł were used as a guide in selecting the geometric

components of the Judd _gures[ Because the distortion e}ectsare robust at a length of 04 cm "see Fig[ 1\ ð5Ł#\ all displays hadshafts that were 04 cm long and 9[914 cm wide[ Fins were also9[914 cm wide\ and _n angles were identical above and belowthe shaft[ The displays were presented in black ink on 7 0:1×03in[ white paper[ The shaft was positioned parallel to the hori!zontal edge of the paper and displaced vertically 0[4 cm and 1[3cm to the right of a center position on the page[ This was doneto prevent subjects from using the corners of the page to guidethe transection towards a shaft with its midpoint at the centerof the page[

Fin angle and direction were both manipulated within!subject whereas the geometric properties of the _n angle "W\ X\and Y# were manipulated between!subject "see Fig[ 2#[ The _nangle varied from 03>\ 34> and 65>$ and the _ns opened outeither Ri`htwards "³**г#\ Leftwards "×**Ð×#\ or Both"׳**Ð׳#[ This last display is a control condition in which thecon_gural properties should elicit both rightward and leftwardperceptual distortions that potentially cancel out one anotherand result in accurate bisections[ This produces a total of nineconditions[

The dimensions for the between!subject factor of geometriccomponents "W\ X\ and Y# were as follows "see Appendix 0 forfurther details#]

"a# W!displays] the "W# component or _n length was held con!stant at 6[4 cm in length\ i[e[ 49) as long as the shaft length"04 cm#\ while the X and Y components varied with _nangle "see Fig[ 2\ Panel A#^

"b# X!displays] the "X# component or horizontal portion of theshaft covered by the _n was held constant at 2[0 cm whilethe W and Y components varied with _n angle[ This Xdimension was chosen so that all stimuli would _t on the 70:1×03 in[ paper "see Fig[ 2\ Panel B#^ and

"c# Y!displays] the "Y# component or height was held constantwhile W and X components varied with _n angle[ The Ydimension "Y � 0[74 cm# was equal to that at the 03> _nangle conditions of the W!display\ and was chosen to avoidcrossing of the _ns in the control conditions[ Thus\ the03> _n angle conditions were identical to the 03> _n angle

$ The 03> control conditions in the W! and Y!display versionshave a narrow space between the inward tips of the _ns[ Toprevent subjects from using this space to guide bisection of theshaft\ either to the top left\ inward!projecting _n or the bottomright\ inward!_n was 6[54 cm long instead of 6[4 cm[ Theseconditions were presented randomly and caused the narrowspace to be displaced such that it did not overlie the true centerof the shaft[

J[ Fleming and M[ Behrmann:Neglect by perceptual illusion361

Fig[ 2[ Test and control Judd _gures^ "A# W!displays\ "B# X!displays and "C# Y!displays are illustrated[ The _n angle mag!nitudes are noted to the left of the stimuli\ and the directionthat the _ns open is noted above the stimuli[ Note that whilethe _n dimensions "W\ X\ Y# vary between experiments\ thesame magnitude of _n angles and shaft length are used in each

experiment[

conditions of the W!displays\ but the 34> and 65> displaysdi}ered "see Fig[ 2\ Panel C#[

Subjects were seated at a table and a sheet of paper containinga Judd display was presented aligned with the sagittal mid!plane of the body and positioned parallel to the edge of thetable[ The distance between the display and the body was variedso that subjects were comfortable while performing the task[Subjects were instructed to evaluate the horizontal extent of theshaft of the _gure\ to _nd the midpoint of the shaft\ and to placea transection mark through the perceived midpoint[ Carefulobservation ensured that subjects performed the task correctlyand that they did not use their hands or other instruments todetermine the midpoint of the shaft[ Ten trials were presentedin each of the nine conditions in randomized order[ Displayswere presented for an unlimited duration until transection[

The displacement of the transection mark from the truecenter of the shaft was measured to within 9[94 cm for eachdisplay\ divided by 04 cm "shaft length# and multiplied by 099to yield a percent bisection error[ As is the convention\ errorsto the right of the midpoint were denoted with a positive valueand those to the left with a negative value[ The main analysis

involved a repeated!measures analysis of variance "ANOVA#with direction "Both\ Rightward\ Leftward# and _n angle "03>\34>\ 65># as within!subject factors\ geometric component display"W\ X\ Y# as a between!subjects factor and percent bisectionerror as the dependent measure[ To understand the relativecontributions of direction and component display and theirinteractions with angle\ we also performed post!hoc testing ateach level of the factor of interest[ Pairwise comparisons weredone using Tukey HSD tests and a correction procedure tomaintain family!wise at 9[94[

Results

The main analysis designed to examine the e}ects ofdirection and angle\ as well as the contribution of eachgeometric component of the _n angle\ revealed a sig!ni_cant three!way interaction between _n angle\ direc!tion\ and component display ðF"7\097#�4[46\P³ 9[990Ł[ The mean bisection errors as a function of_n angle and direction are shown in Fig[ 3 separately forthe three component displays[ As in Mattingley et al[ ð5Ł\we observed a signi_cant di}erence in the direction of theerror depending on the direction of the _ns\ðF"1\3#�139[69\ P³ 9[90Ł^ relative to the control con!ditions averaged over all angles and component displays"mean ) error "MPE#�9[42#\ there were greater left!ward errors with Leftward _gures "MPE�−2[18# andgreater rightward errors with Rightward _gures"MPE�2[73#[%

A comparison of our 34> conditions with the 39> con!ditions of Mattingley et al[ showed no di}erences betweenthe bisection errors on Leftward stimuli "Mattingley etal[|s MPE�−4[07^ our MPE�−3[64#[& There was\however\ a signi_cant di}erence between out Rightwardcondition and that of Mattingley et al[ "Mattingley etal[|s MPE�7[68^ our MPE�3[08#[ This di}erence maypossibly be attributed to the di}erence in age betweenthe control groups in these studies "Mattingley et al[age�50[0\ S[D[�05[1\ our subjects age�13[1\S[D[�2[57#[ A comparison of errors obtained by us witha group of elderly control subjects "not presented here#to those of Mattingley et al[ revealed equivalent perform!ance across groups for both theRightward ðF"0\01#�1[18\P× 9[94Ł and Leftward ðF"0\01#�9[88\ P× 9[94Łconditions[

To examine the extent of the bisection error as a func!tion of both _n angle and direction\ we performed threerepeated measures ANOVAs at each level of the between!subject factor of the component displays "W\ X\ Y#[ Allthree ANOVAs revealed signi_cant e}ects of direction

% An analysis using the absolute values of bisection errorsrevealed that the errors on Leftward stimuli were not stat!istically di}erent in magnitude from the errors on the cor!responding Rightward stimuli ðF"0\16# � 9[710\ P×9[94Ł[

& Planned comparisons involved uncorrected separate vari!ance t!tests[ The errors from the 39> conditions involved inthese comparisons are shown in Fig[ 2\ p[ 310 of Mattingley etal[ ð5Ł[

J[ Fleming and M[ Behrmann:Neglect by perceptual illusion 362

Fig[ 3[ The mean ) bisection errors and standard error bars as a function of _n angle for test and control _gures are shown[ Positivepoints on the Y!axis indicate rightward bisection errors\ negative points indicate leftward errors[ Sample displays are included for

reference[ "A# W!display experiment\ "B# X!display\ "C# Y!display[

ðW] F"1\07#�79[76\ P³ 9[990^ X] F"1\07#�36[32\P³ 9[990^ Y] F"1\07#�067[89\ P³ 9[990Ł as well asdirection by angle ðW] F"3\25#�15[29\ P³ 9[990^ X]F"3\25#�08[31\ P³ 9[990^ Y] F"3\25#�57[42\P³ 9[990Ł[ As is evident from Fig[ 3\ for both the W! andthe Y!display experiments\ the errors with all Rightwardconditions di}ered signi_cantly from each other anddecreased monotonically as the _n angle increased\ andsimilarly all Leftward conditions di}ered from each otherwith the same pattern[ For the X!display experiment\only the Rightward "03> vs 34># and Leftward "03> vs34># comparisons were not signi_cantly di}erent fromeach other\ although the trend is in the correct directionfor both[

In order to determine the relative contribution of eachcomponent display and _n angle to the bisection error foreach of the three component displays\ separate ANOVAswere performed at each level of direction[ We considerthe control condition before moving on to the analysis ofthe Leftward and Rightward trials[ In the control "Both#condition\ the _rst important post!hoc _nding is thaterrors did not vary with _n angle ðF"1\16#�9[04\P× 9[94Ł or with component display ðF"1\16#�0[38\P× 9[94Ł\ indicating the suitability of the control con!ditions[ As expected\ the interaction of angle by com!ponent display was not signi_cant ðF"1\3#�9[79\P× 9[94Ł[ Furthermore\ for all three componentdisplays\ most of the errors\ with the exception of the 03>W!displays "MPE�9[39#\ 34> X!display "MPE�0[02#\and 03> Y!displays "MPE�9[49#\ did not di}er fromzero\ indicating the stability of the control condition[

Interestingly\ there were no di}erences in the extent ofthe error across the three component displays for trialsin the Rightward condition ðF"1\74#�0[39\ P× 9[94Ł\indicating that the magnitude of the _n angle\ irrespectiveof the dimensions of its geometric components\ is respon!sible for the errors on Rightward _gures[ However\ therewas a main e}ect of angle ðF"1\74#�39[75\ P³ 9[990]

Rightward\ averaged over component display] 03>MPE�5[13^ 34> MPE�2[64^ 65> MPE�0[44Ł\ con!_rming the previous _ndings of bisection errors varyingwith _n angle ð01\ 02Ł[

In contrast\ errors for trials in the Leftward conditiondid vary with component display\ as re~ected in theANOVA with the within!subject factor of angle andbetween!subject factor of component displayðF"1\16#�5[07\ P³ 9[90^ component display errorsaveraged over angle] W MPE�−3[76^ XMPE�−0[71^ Y MPE�−2[06Ł[ As expected from theabove\ there was a main e}ect of angle "Leftward 03>MPE�−4[48^ 34> MPE�−2[22^ 65> MPE�−9[83#\as well as an interaction of angle by component displayðF"1\3#�7[35\ P³ 9[94Ł for Leftward stimuli[ This inter!action is likely to be the underlying cause of the three!wayinteraction of direction by angle by component displaymentioned above[ Therefore\ we set out to determinewhich speci_c pairwise di}erences account for this angleby component display interaction[ Importantly\ pairwisecomparisons revealed that for the Leftward direction theonly signi_cant di}erence was between the W! and X!displays at 03> "W MPE�−6[30^ X MPE�−2[91#[

Because this single di}erence between component dis!play versions appears to have no obvious theoretical sig!ni_cance\ we suggest that the major _nding is that themagnitude and pattern of the bisection errors do notdi}er among the three component versions of the experi!ment[ In fact\ as seen from the displays in Fig[ 2\ thedimensions giving rise to a given _n angle are quitedi}erent across the three component displays\ and yetnearly the same bisection errors were generated by that_n angle regardless of whether W!\ X!\ or Y!componentwas held constant[ Consistent with this\ there was nomain e}ect of component display "W!\ X!\ or Y!display#ðF"1\16#�1[97\ P× 9[94Ł as re~ected in the main three!way ANOVA[

To verify that the results from the Judd bisection task

J[ Fleming and M[ Behrmann:Neglect by perceptual illusion363

are due to a distorted representation of space\ we utilizeda second procedure\ the end!point placement task\developed by Bisiach et al[ to demonstrate that neglectpatients have a distorted representation of space ð05\ 06Ł[Another group of 09 healthy right!handed subjects whomet the previously de_ned inclusion criteria participatedin this task[ Subjects _rst bisected 04 cm long lines with!out _ns[ They were then presented with trials containinga single dot on a page and were required to positionleft! and right!sided _ns having the same dimensions\ _nangles\ and directions as those of the W!display experi!ment at the end!points of a virtual shaft of 04 cm inlength[ An ANOVA comparing the line bisection pro!cedure involving the W!displays and the end!point _nplacement procedure\ and again with _n angle and direc!tion as within!subject factors\ revealed no di}erencebetween procedures ðF"0\07#�0[92\ P× 9[94Ł[ Fur!thermore\ there were no signi_cant two! or three!wayinteractions involving this factor of procedure[ There washowever\ as expected\ a main e}ect of directionðF"1\25#�095[93\ P³ 9[990Ł as well as an interaction ofdirection by angle ðF"3\61#�31[17\ P³ 9[990Ł[

Discussion and Conclusion

The goal of this study was to develop and study ananalog of visuospatial neglect in normal subjects using avisual illusion that distorts horizontal spatial extent[ The_rst important _nding was that\ as in Mattingley et al[ð5Ł\ the Judd _gures successfully induced a displacementof the subjective midline relative to the control conditionand the direction of the error varied with the direction ofthe _ns[ In the control conditions\ bisection was approxi!mately equivalent to the objective midpoint of the shaft^the presence of inward and outward _ns on each endof the shaft likely cancelled out inward! and outward!directed distortion e}ects[ In contrast\ when only a singleinward _n appears on one end of the shaft and an out!ward _n on the other\ bisection errors are systematicallybiased away from the inward _n and towards the outward_n[ These bisection errors may thus re~ect a distortedperception of the horizontal extent of the shaft^ theinward!projecting _ns may induce an inward!directeddistortion of the space encompassing the shaft\ and theoutward!projecting _ns may induce an outward!directeddistortion[

Interestingly\ the extent of this bias is contingent uponthe angle of the _n[ As the _n angle increased\ the bisec!tion error declined monotonically[ These _ndings areconsistent with many psychophysical studies usingMu�llerÐLyer variants indicating that the degree of per!ceived distortion decreases monotonically with increasing_n angle "for example\ ð01\ 02Ł#[ The analysis of the geo!metric components of the _n angle suggests that the mag!nitude of the _n angle itself rather than any singlegeometric component is responsible for the distorted rep!resentation of the subjective midpoint[ The central result\

then\ is that the nature and extent of the bisection errorvaries signi_cantly as a function of _n angle magnitudeand direction\ irrespective of the particular geometricdimensions comprising the _n angle[ Furthermore\ thesemodulations of bisection error by the direction and angleof the _ns were veri_ed with the end!point _n placementtask\ thereby demonstrating the robustness and e.cacyof the distortion e}ects[

The results cannot be fully accounted for by the prin!ciple of perceptual compromise as suggested by Day ð7\8Ł and Mattingley et al[ ð5Ł[ Mattingley et al[ argued thatwith an outward!projecting _n\ the extent of the shaft isperceived as a compromise between its true magnitudeand that of the entire _gure\ thereby leading to bisectiondeviations toward the outward!projecting _n[ In the caseof an inward!projecting _n\ the end!point of the shaftnearest the _n is perceived as being shifted away fromthe vertex of the _n angle\ and the subjective midpoint isthus also shifted because the shaft has shifted[ This thenleads to bisection errors[ However\ in the X!displayexperiment a perceptual compromise between the lengthof the shaft and that of the overall _gure cannot explainthe observed modulation of bisection error[ For bothinward! and outward!projecting _ns in this experiment\the "X# component of the _n angle was held constant[Thus\ the overall length of each _gure and the length ofthe shaft did not change across conditions as the _n anglevaried from 03>\ 34>\ and 65> "see Fig[ 2\ Panel B#[ If aperceptual compromise is responsible for bisection error\then this compromise should have been of the same mag!nitude for all test conditions\ yielding identical resultswith all _n angles[ This was obviously not the case[

This paper has shown that several tasks involving ananalysis of the horizontal space of the Judd _gure maybe used to distort the representation of space in normalsubjects[ While these distorted representations yieldeddeviations of subjective midpoint that are relatively small"up to 6)#\ these errors are robust across subjects andare systematically a}ected by the geometric properties ofthe display[ Moreover\ these distortions may serve as agood analog of neglect as they mirror the same behavioralpatterns seen with neglect patients on similar tasks[ Eva!luating how the representation of space is distorted innormal subjects bisecting the Judd illusion may thereforeyield a greater understanding of the disordered mediumof space in neglect[ Moreover\ once this analog is furtherexplored and understood\ it may be used further to shedlight on the relation between the space of the {physicalworld| and {psychological space|[

Acknowled`ements*The research reported in this paper wassupported by a graduate fellowship from the Center for theNeural Basis of Cognition and by grant MH43135!90 from theNational Institute of Mental Health to MB[ We thank JimNelson for his help with data collection and Jason Mattingleyfor providing us with his normal subject bisection error data[We also thank Edoardo Bisiach\ Jason Mattingley and ananonymous reviewer for their helpful comments[

J[ Fleming and M[ Behrmann:Neglect by perceptual illusion 364

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07[ Mennemeier\ M[\ Vezey\ E[\ Chatterjee\ A[\ Rapcsak\Z[\ and Heilman\ K[\ Contributions of the left andright cerebral hemispheres to line bisection[ Neu!ropsycholo`ia\ 0886\ 24"4#\ 692Ð604[

Appendix

Dimensions of the W\ X and Y components "in cm# of the _nangles

Experiment Fin angle "># W X Y

W!display 03 6[4 6[24 0[7434 6[4 4[24 4[2765 6[4 0[84 6[2

X!display 03 2[1 2[0 9[7434 3[4 2[0 2[165 02[9 2[0 01[5

Y!display 03 6[4 6[24 0[7434 1[51 0[74 0[7465 1[96 9[49 0[74