Eccentric grouping by proximity in multistable dot lattices

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1 Aville online t Vision Reserh 8 (8) Eentri grouping y proximity in multistle ot ltties Lizzy Bleumers *, Peter De Gref, Krl Verfillie, John Wgemns Lortory of Experimentl Psyhology, Deprtment of Psyhology, Fulty of Psyhology n Eutionl Sienes, K.U. Leuven, Tiensestrt, B- Leuven, Belgium Reeive 8 Deemer ; reeive in revise form Otoer 7 Astrt The Pure Distne Lw preits grouping y proximity in ot ltties tht n e orgnise in four wys y grouping ots long prllel lines. It speifies quntittive reltionship etween the reltive proility of pereiving n orgnistion n the reltive istne etween the groupe ots. The urrent stuy ws set up to investigte whether this priniple hols oth for entrlly n for eentrilly isplye ot ltties. To this en, ot ltties were isplye either in entrl vision, or to the right of fixtion with their losest orer t or. We foun tht the Pure Distne Lw equtely preite grouping of entrlly isplye ot ltties ut i not pture the eentri t well, even when the eentri ot ltties were sle. Speifilly, etter fit ws otine when we inlue the possiility in the moel tht in some trils prtiipnts oul not report n orgnistion n onsequently respone rnomly. A plusile interprettion for the ourrene of rnom responses in the eentri onitions is tht uner these irumstnes n ttention shift is require from the lous of fixtion towrs the ot lttie, whih osionlly fils to tke ple. When grouping oul e reporte, sle n eentriity ppere to intert. The effet of the reltive interot istnes on the pereptul orgnistion of the ot ltties ws estimte to e stronger in peripherl vision thn in entrl vision t the two lrgest sles, ut this ifferene isppere when the smllest sle ws pplie. Ó 7 Elsevier Lt. All rights reserve. Keywors: Centrl vision; Peripherl vision; Grouping; Proximity; Gestlt. Introution The legy of erly Gestlt psyhologists remins of onsierle vlue to vision sientists n visul neurosientists toy (Rok & Plmer, 9; Spillmnn, 999; Westheimer, 999). One prtiulrly importnt Gestlt ontriution is the efinition of grouping priniples governing pereptul orgnistion. A group of reserhers hs tken up the hllenge of speifying these priniples quntittively so tht onrete preitions n e erive from them (e.g., Kuovy, Holome, & Wgemns, 998; Quinln & Wilton, 998). Among these priniples, the Pure Distne Lw (Clessens & Wgemns, ; Kuovy & Wgemns, 99; Kuovy et l., 998) hs een propose s n ojetive quntifition of the Gestlt lw * Corresponing uthor. Fx: E-mil ress: Lizzy.Bleumers@juii.nl (L. Bleumers). of proximity, whih sttes tht units tht re lose together ten to e groupe together. The moel hs een shown to preit grouping y proximity in ot ltties, lss of multistle ot ltties tht n e orgnise in four wys (,, n ; see Fig. A n B) s olletion of prllel lines (Kuovy, 99). Centrl to the moel esription of the Pure Distne Lw is the ssumption tht the proility of mking prtiulr orgnistion epens purely on the istne etween the ots tht re groupe together ( v ) reltive to the shortest possile interot istne ( ) in the ot lttie. The ext funtion is given in Eq. (). The moel prmeter expresses the strength of this reltionship. The higher this vlue, the more grouping will epen on the reltive interot istne. Note tht in this eqution n throughout the rtile n orgnistion is inite y olfe letter (e.g., ) n the orresponing interot istne is inite y the mrkers (e.g., ). -989/$ - see front mtter Ó 7 Elsevier Lt. All rights reserve. oi:./j.visres.7..

2 L. Bleumers et l. / Vision Reserh 8 (8) 79 9 γ Fig.. (A) Illustrtion of ot lttie. Note tht there re four possile orgnistions in the ot lttie on the left, eh illustrte on the right y line initing the orienttion of the grouping. Orgnistions n ten to e seen more frequently. (B) Bsi prllelogrm of ot lttie. The si prllelogrm hrterises the ot lttie n is etermine y the length of two vetors n, tht orrespon to the sies of the prllelogrm, n the ngle esrie y the two vetors (). Vetors n orrespon to the shortest n the seon shortest interot istne. The - n -vetors orrespon to the igonls of the se prllelogrm. In the se of retngulr ot ltties, the si prllelogrm is retngle. The four vetors inite the four possile orgnistions of ot lttie (pte from Kuovy et l., 998). fðvþ ¼ pðvþ jvj pðþ ¼ e jj The reltionship expresse in Eq. () is exponentil. A liner eqution is more onvenient for moelling n isplying the results. Suh n eqution is otine y tking the nturl logrithm of f(v) in the ove formul. The result is lle the logit vlue of pereiving orgnistion v (see Eq. ()). ln pðvþ pðþ ¼ jvj jj It is ssume tht the four possile orgnistions of the ot ltties (,, n ) re exhustive n mutully exlusive, whih is expresse in the following eqution: pðþþpðþþpðþþpðþ ¼ From Eqs. () n (), we n erive the preite proilities for eh orgnistion: ðþ ðþ ðþ pðþ ¼ pðþ ¼ pðþ ¼ pðþ ¼ jj jj þ e jj jj þ e jj jj þ e þ e e þ e jj jj jj jj jj jj þ e jj jj þ e e jj jj þ e e jj jj þ e þ e jj jj jj jj jj jj þ e jj jj jj jj þ e jj jj The Pure Distne Lw hs een teste n onfirme for lrge ot ltties (perture rius of. ) shown entrlly. This mens tht oth entrl n peripherl informtion ws ville. In the urrent stuy we exmine grouping of ot ltties either shown entrlly or t eentri lotions. We investigte whether the moel still hols in the ltter onitions in whih only peripherl informtion is ville. Peripherl visul input is unersmple n unerrepresente reltive to entrl vision, ue to ntomil ifferenes lrey pprent t the retinl level n ontinuing up the visul pthwys (Wilson, Levi, Mffei, Rovmo, &

3 L. Bleumers et l. / Vision Reserh 8 (8) DeVlois, 9). Given the unerrepresenttion of peripherl vision, one might expet visul performne to e egre for peripherl stimuli. However, this ppers to epen on the visul funtion uner srutiny n the properties of the isplye stimuli. In the literture, t lest three tegories of visul funtions n e istinguishe se on how peripherl performne ompres to entrl performne (Anstis, 998; Poirier & Gurnsey, ): () visul funtions tht re egre in the periphery ut for whih peripherl performne n e rought to the level of entrl vision y pplying single sling ftor to the stimuli, for exmple, ontrst sensitivity n Vernier uity (Kelly, 98; Levi, Klein, & Aitseomo, 98); () visul funtions tht re lso egre in the periphery, ut nnot e rought to the level of entrl vision y oneimensionl sling, e.g., urve ontour integrtion (Hess & Dkin, 999; Nugent, Keswni, Woos, & Peli, ) n lssifition lerning (Jüttner & Rentshler, ); n () visul funtions tht improve when stimuli re shown t lotion wy from fixtion, e.g., segmenttion of ertin types of textures (Morikw, ). To our knowlege, grouping y proximity hs not een ompre etween entrl n peripherl vision, s we hve one in the present stuy. It is importnt to note tht the outome of pplying the Pure Distne Lw to ot lttie grouping t ifferent eentriities nnot e frme in terms of inferiority or superiority of eentri vision s in the previous prgrph. This is euse there is no right or wrong nswer when grouping the ot ltties. Rther, the purpose of this stuy is to speify whether the Pure Distne Lw hols for grouping y proximity of eentrilly isplye ot ltties n, if it oes, whether the epeneny on istne rtios esrie y it (i.e., ), is eqully strong in entrl n eentri vision. Poor moel fit oul inite tht the ot ltties nee to e sle in eentri vision to hieve grouping ehviour tht is omprle to tht in entrl vision. This woul imply tht not only reltive ut lso solute interot istnes hve to e tken into ount in omprehensive explntion of ot lttie orgnistion. If the poor moel fit is not remeie y sling, however, it woul e initive of ifferene etween the proesses unerlying grouping of the ot ltties in entrl versus eentri vision. In this se, the moel woul hve to e moifie or reple. If the moel oes fit the t, ut the results suggest lrger or smller vlues t more eentri ot lttie positions, then grouping y proximity woul either e more or less influene y hnge in istne rtios in eentri vision thn in entrl vision. Asie from our min fous on the tenility of the Pure Distne Lw ross multiple eentriities, two itionl issues were resse tht re relevnt to the moel uner investigtion. First, in orer to isply the ltties within onfine eentri regions, ot ltties were shown through smller perture thn in previous ot lttie experiments (Kuovy & Wgemns, 99; Kuovy et l., 998). Therefore, we neee to verify whether this reution of perture size i not signifintly ffet how prtiipnts groupe the isply. The Pure Distne moel oes not ontin speifi preitions out the role of perture size (Kuovy et l., 998). However, reution of perture size might use lol ftors to gin importne tht woul otherwise e irrelevnt (e.g., the position of the ots t the orer of the perture). Seon, the originl Pure Distne moel ssumes tht wht prtiipnts pereive is only influene y the reltive interot istnes n tht wht prtiipnts sy they pereive urtely reflets wht they sw. These ssumptions re violte when, respetively, pereptul is or response is is present. To exmine pereptul is, we teste whether prtiipnts were more inline to pereive n orgnistion long speifi orienttion. For instne, prtiipnts might pereive the ot ltties more esily s oriente horizontlly or vertilly, regrless of the lttie struture. To exmine response is, we teste whether prtiipnts preferre ertin response option positions over others when seleting them in the response isply.. Generl metho.. Prtiipnts In totl, 7 volunteers ( women n men, etween n yers ol [men: 9. yers]) gve their informe onsent to tke prt in this stuy. All prtiipnts h norml or orrete-to-norml vision... Stimuli n pprtus All stimuli in the urrent stuy were retngulr ot ltties, onsisting of white ots in grey, irulr perture. In these ltties, the istne vetors initing the - n -orgnistion re orthogonl to eh other ( = ) n the orresponing interot istnes, n, re shorter thn n. We mnipulte the / rtios:,.8,.7 n. (i.e., spet rtios). This uses the / n / rtios to hnge oringly; the orresponing vlues were.,.7,. n.. Stimuli were isplye t viewing istne of m with sptil resolution of y 78 pixels n refresh rte of 8 Hz. The luminne ontrst of the white ots on the grey perture ws pproximtely % i:e:; L ots Lperture L ots. þlperture Both stimulus isply n response registrtion were hnle y n Intel Pentium. Right eye movements were registere with the SR Reserh Eyelink II he-mounte eye trker t smpling rte of Hz (pupil-only) n with gze position error smller thn.. This enle fixtion ontrol n eye movement ontrolle response seletion. He movement ws restrite y hin-rest... Proeure A shemti overview of single tril is ville in Fig.. Prtiipnts were instrute to fix their gze on ot entre on the sreen n then initite the tril y pressing the spe r. A ot lttie ws then shown entrlly or t speifi eentriity for ms (see Setion. for etils onerning the presenttion onitions). During stimulus presenttion, re fixtion ot ws visile on the sreen. If the prtiipnt lost fixtion (i.e., his or her gze move outsie entrl retngle of y ) while the lttie ws shown, the tril ws skippe n repete one t the en of the session. Trils tht were skippe seon time were lssifie s never omplete. After the ot lttie isppere, response sreen ws isplye with four options orresponing to the four lterntive orgnistions of the ot lttie. Eh orgnistion ws represente y line initing its orienttion within smll perture. The positions of

4 8 L. Bleumers et l. / Vision Reserh 8 (8) 79 9 Response sreen Lttie ms Until fixtion Fig.. Shemti representtion of the proeure. the response options were rnomly hosen from four fixe positions (left, right, top n ottom) to ontrol for response is. Prtiipnts selete response option y looking t it. Using the eye trker signl, the fixte option ws then highlighte utomtilly n prtiipnts onfirme the seletion y pressing utton. The orienttion of the orgnistion orresponing to the shortest interot istne ws vrie; the ounter-lokwise ngle of the -vetor reltive to the horizontl line ws either,,,, or (eh ourring eqully frequently). This wy, orienttion is oul e ssesse. In the extreme se of prtiipnts exhiiting n orienttion is to suh egree tht they lwys opte for n orgnistion lose to the preferre orienttion, fitting the Pure Distne Lw woul rightly revel tht there ws no reltionship etween the pereive orgnistion n the reltive interot istnes (i.e., woul e zero). The experimentl esign ws within-sujet n trils were loke per presenttion onition to filitte optiml ttention llotion towrs the ot lttie. Two experiments were rrie out. Prtiipnts omplete four loks in four sessions in eh of these experiments n lok orer ws vrie ross sujets [in totl trils = (presenttion onitions = sessions) (spet rtios) (orienttions) (repetitions)]. The first experiment ws initite with rief prtie session with ot ltties ifferent from the ones use in this experiment to fmilirise prtiipnts with the proeure. Eh lok ws preee y lirtion phse n interrupte for short rek in the mile fter whih lirtion ws repete. Smll evitions from initil lirtion (e.g., euse of heset slippge) were orrete for uring the session, s rift orretion ws performe t the strt of eh tril... Experiments n Two experiments were onute with the sme group of prtiipnts. In Experiment, we use unsle stimuli: we kept fixe t 7 pixels (. ) n vrie (n therey qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lso n, whih n e erive using Pythgors theorem: jj þjj ). We hose so tht i+ / i ws fixe. Dot rius ws set to pixels (. ). Dot ltties h n perture rius of n ppere t one of three positions: entre on fixtion or to the right of fixtion with the losest ege of the perture either t or eentriity (entre positions t 9 n. ). An itionl entrl presenttion onition ws inlue with n perture rius of.. This rius ws use in previous ot lttie experiments (Kuovy & Wgemns, 99; Kuovy et l., 998) n it ws e to exmine the effet of reuing perture size. Thus, there were four presenttion onitions ( lrge smll smll smll). Stimuli in Experiment were isplye on Sony Trinitron GDM-F ( m viewle re) monitor with L ots = 7 /m n L perture =.8 /m. As will e isusse in more etil elow, the fit of the Pure Distne moel to the t for the eentri onitions ws poor. To etermine whether this oul e expline y lk of stimulus sling, we onute seon experiment. In Experiment, the shortest interot istne,, ws hnge to e either hlf or twie the shortest interot istne use in Experiment. The originl reltive interot istnes were mintine. Aperture rius (i.e., the rius of the smll perture) n ot size were sle oringly so tht the numer of visile ots ws hel onstnt. Dot ltties were positione either entrlly or t. This yiele gin four presenttion onitions ( hlf oule hlf oule). Stimuli in Experiment were isplye on n Iiym HMDT A ( m viewle re) monitor with L ots = 7. /m n L perture =. /m... Dt nlysis For moel fitting, the t of the seven prtiipnts were poole. The Pure Distne Lw n extene versions of it were fitte to the t vi mximum likelihoo estimtion of their prmeters. The min moel prmeter to e estimte ws, whih inites, s expline previously, the extent to whih the pereive orgnistion epene on the orresponing reltive interot istne. The reltive fit of the moels ws evlute using the likelihoo rtio sttisti whih ompres the likelihoo of the t given se moel with how likely the t re given n extene version of tht moel (LR = (L extene moel L se moel ), egrees of freeom: f = f extene moel f se moel ). Gooness-of-fit tests were se on the Person hi-squre sttisti (Chisq): X n X i¼ v¼;;; ðy iv m i p i ðvþþ ; f ¼ ðk Þn q m i p i ðvþ

5 L. Bleumers et l. / Vision Reserh 8 (8) in whih n is the totl numer of tril types (i.e., the numer of omintions of the experimentl ftors), Y iv is the numer of times n orgnistion v ws hosen for tril type i, m i is the numer of oservtions for tril type i, p i (v) is the preite proility of pereiving orgnistion v in tht type of tril, k is the numer of possile orgnistions (i.e., ) n finlly q is the numer of prmeters to e estimte in the moel. In ition to fitting the Pure Distne moel to the t, we pplie n nlysis of vrine to the proportion of skippe n never omplete trils. We lso resse potentil intr-iniviul ises y performing hi-squre tests on the istriution of responses ross response option positions n ross orienttions of the - n -vetor in the ltties. For ll nlyses, the ritil p-vlue ws set t... Results.. Centrl n eentri ot lttie grouping: Fitting the Pure Distne Lw... Response istriutions per presenttion onition In Fig. A D we present the rw t of Experiment : the perentges of trils in whih eh possile orgnistion ws hosen, long with the perentge of trils tht were never omplete. The t re plotte ginst the rtio of the seon shortest n the shortest interot istne (istne rtio / ). Rell tht when / inreses, / n / lso inrese oringly. Eh grph orrespons with prtiulr presenttion onition: lrge, smll, smll, smll. First, some generl oservtions n e me. When / ws equl to, orgnistions n were hosen out eqully often. When the istne rtio / inrese, prtiipnts were more likely to hoose the orgnistion tht orrespons to the shortest interot istne (orgnistion ). At the sme time, oservers eme less likely to hoose the orgnistion tht orrespons with the seon shortest interot istne (orgnistion ). While oth - n -responses were prevlent throughout the experiment, orgnistions n were rrely hosen. These finings re onsistent with the Pure Distne Lw tht sttes tht the reltive interot istnes etermine grouping. Compring the rw t ross the ifferent grphs, we fin tht, in the eentri onitions, the ivergene of - n -responses s funtion of istne rtio ws greter thn in the entrl onitions, prtiulrly in the onition. This seems to inite tht for the eentri ltties, oservers re highly sensitive to the struture of the lttie % trils lrge smll n istne rtio / % trils istne rtio / n % trils 7 smll 9 n % trils 7 smll 9 n istne rtio / istne rtio / Fig.. Perentge of trils in whih either the -, -, - or-orgnistion ws selete or tht were never omplete (n) s funtion of istne rtio /. Eh grph orrespons with ifferent presenttion onition of Experiment (A: lrge, B: smll, C: smll, D: smll).

6 8 L. Bleumers et l. / Vision Reserh 8 (8) 79 9 in terms of the reltive istnes etween the ots. At the sme time, however, the - n -responses ppere to e istne-inepenent n were somewht more frequent in the fr eentri onition thn in the entrl onitions. This suggests the evelopment of two qulittively ifferent response popultions in the fr eentri onition. Finlly, we oserve tht prtiipnts h more iffiulty mintining fixtion when the ot ltties were ple eentrilly, s eviene y higher perentges of never omplete trils. These iffiulties were most pronoune in the eentriity onition.... Moelling grouping of entrlly isplye ot ltties The Pure Distne Lw ws first fitte to the grouping t for the entrlly isplye ltties, oth for lrge n for smll pertures, to investigte whether grouping uner these viewing onitions ws equtely moelle y the Pure Distne Lw. Furthermore, to test whether the reution of perture size signifintly influene grouping ehviour, the min moel prmeter,, ws either hel fixe (moel FIX) or ws llowe to vry etween perture sizes (moel VAR). The preitive vliity of these two moels ws then ompre. Our nlyses onfirm tht the Pure Distne Lw provies signifint ontriution to the preition of the proilities for hoosing eh orgnistion, oth in se of FIX, LR(f = ) =, p <. n in se of VAR, LR(f = ) =, p <.. On the whole, prtiipnts grouping ehviour ws moelle quite well y the Pure Distne Lw. The Person hi-squre gooness-of-fit tests inite n exellent fit for the lrge ot ltties, Chisq(f = ) =., p =.9. However, preitions were less urte when the ot ltties were smll, Chisq(f = ) =., p =.. The egree to whih grouping ws influene y hnges of the istne rtios i not iffer signifintly etween the two perture onitions, LR(f = ) =.8, p =.87. FIX estimte to e.. VAR estimte to e. n., respetively, for the lrge n smll pertures. Thus, espite the poorer fit in the smll perture onition, similr estimtes of were otine for oth perture sizes. Therefore, the t were poole ross the two entrl onitions, efore proeeing to moel n ompre performne t the ifferent ot lttie positions (entrl, n ).... Moelling grouping of ot ltties t ifferent visul positions without sling After pooling the t for the lrge n smll entrlly isplye ot ltties, we fitte the Pure Distne Lw to To etermine whether moel ontriute to preiting the proilities for hoosing eh orgnistion, the likelihoo of the t given eh moel ws ompre with the likelihoo of the t given moel without the prmeter. To voi onfusion: lthough the Person hi-squre test is ommonly referre to s gooness-of-fit test, lower p-vlue inites tht the fit of the moel is reltively worse. the t t the three possile ot lttie positions (entrl, n ). Agin, ws either hel fixe (Moel FIX) or oul vry (Moel VAR), ut now etween ot lttie positions. It ws first investigte whether these moel versions yiele n equte preition of the prtiipnts hoies t the ifferent ot lttie positions (entrl, or ). Both FIX n VAR signifintly preite the proilities of hoosing eh orgnistion, respetively, LR(f = ) = 8, p <. n LR(f = ) = 87, p <.. The qulity of the moel fit epene on the position t whih the ot lttie ws isplye. While the t in the entrl onition were fitte well y oth moels, moel fit ws reltively poor in the eentri onitions, prtiulrly in the onition (see Tle for fit sttistis). This is illustrte in Fig. A C. These grphs show the oserve logits n the logits preite y the moels for pereiving the -orgnistion t eh of the three ot lttie positions. These figures show tht the preitions of the Pure Distne Lw evite from the oserve t. Speifilly, for eentri ltties n espeilly in the onition, the proility of pereiving the -orgnistion ereses muh more rpily s funtion of spet rtio thn the Pure Distne Lw preits, s n e seen from the ft tht oserve - logits lie well elow the lines preite y FIX n VAR. Furthermore, this erese is lerly non-liner. Despite the reltively poor fit in the eentri onitions oth for FIX n VAR, the t were etter ounte for when ws llowe to vry ross the ifferent ot lttie positions, LR(f = ) =., p <.. estimtes otine with VAR for the entrl, n onition were, respetively:.,.8 n.8 (FIX yiele n estimte of.9). In view of the poor moel fit for the eentri onitions, it seems unwise, however, to interpret the eentri estimtes s relile inition tht ot grouping is less epenent on the reltive interot istnes in the most eentri onition. The Pure Distne Lw oes not ssign ny speifi importne to solute interot istnes. Tht is why we kept the solute interot istnes onstnt ross ll ot lttie positions in Experiment. However, this ftor my nevertheless hve ontriute to the oserve entrl eentri ifferene. Consequently, sling the ot ltties ppropritely t eentri lotions my use eentri grouping to eome similr to grouping of the entrlly isplye ot ltties. In Experiment, we therefore either hlve or Tle Person hi-squre sttistis for FIX (A) n VAR (B) Position Chisq f p A ALL. <. B poole 8.7. smll.. smll.8 <. ALL. <.

7 L. Bleumers et l. / Vision Reserh 8 (8) logit () logit () logit () entrl istne rtio / oserve preite FIX preite VAR preite MOD istne rtio / oserve preite FIX preite VAR preite MOD istne rtio / oserve preite FIX preite VAR preite MOD Fig.. Oserve n preite logits of pereiving the -orgnistion s funtion of the orresponing istne rtio for eh ot lttie position (A: entrl, B:, C: ). In moel FIX, ws hel fixe ross lttie positions. In moel VAR, oul vry ross lttie positions. Moel MOD resulte from ing prmeter to VAR whih represents the perentge of rnom response trils t eh ot lttie position. oule the solute interot istnes in the lttie reltive to those use in the first experiment. Aperture rius n ot size were ltere oringly. As inite erlier, ot ltties were presente only entrlly or t eentriity in Experiment... Explining the entrl eentri ifferene: Role of sling... Response istriutions per sle presenttion onition The response istriutions per presenttion onition of Experiment re isplye in Fig. A D. Visul inspetion of the t shows four min results. First, fewer trils were lost in Experiment, whih is likely to e ue to the prtiipnts experiene with the proeure. Seon, when ompring the results of the entrl onitions ( oule n hlf) with the entrl t t the originl sle (i.e., smll, see Fig. B), it eomes pprent tht vrying the istne rtios h smller effet on the response istriution in the hlf onition. However, ouling the interot istnes le to results tht resemle the entrl t t the originl sle. Compring the results of the peripherl onitions ( oule n hlf) with the originl onition (see Fig. D), we oserve similr pttern: the strong ivergene of - n -responses foun for the originl sle is fr less pronoune in the hlf onition, while it is lerly present in the oule onition. Thir, moving the ot ltties to the periphery proue stronger ivergene etween the perentges of - n -responses t eh sle. Finlly, ompring the oule onition with the smll onition of Experiment revels tht entrl peripherl ifferene is still present, even when the eentri ot ltties re oule in size. Speifilly, the peripherl ltties still eliite more - n -responses n the rtios of - to -responses still evelope more quikly s funtion of istne rtio. When the eentri ot ltties re hlve in size, however, the only pprent ifferene with the smll onition is the lrger numer of - n -responses.... Moelling grouping of ot ltties t ifferent visul positions After inspeting the t, we exmine nlytilly whether pplying one of the hosen sling vlues to the eentri ot ltties le to peripherl grouping ehviour tht resemle entrl grouping ehviour t the originl sle (i.e., smll onition). To this en, we took the following steps, whih re omprle to the nlyti steps tken in Experiment. First, we fitte the Pure Distne Lw to the smll onition of Experiment n speifi eentriity onition while holing fixe ross these two onitions (moel FIX). This ws one three times, eh time with ifferent sle for the eentri onition (i.e., oule, hlf or originl; FIX DOUBLE, FIX HALF, FIX ORIGINAL). We then repete the fitting proeure, ut now llowing seprte estimtes for eh presenttion onition uner srutiny (moel VAR). After oing so, we evlute for the three pirs, eh ontining the entrl onition of Experiment n peripherl onition, whether preitions were signifintly improve when ws llowe to vry ross these two onitions. FIX ORIGINAL yiele n estimte of., while FIX DOUBLE n FIX HALF yiele estimtes of.7 n., respetively. From VAR we otine n estimte. for the entrl onition t the originl sle n estimtes of.8,. n. for, respetively, the originl, oule n hlf onitions. Fit vlues for oth moels n e foun in Tle. Juging y the smll p-vlues, sling the eentri stimuli oes not le to goo moel fit for either of the two moels. Nevertheless, the t re ommote signifintly etter y VAR for the three pirs of onitions [originl: LR(f = ) = 7, p <.; oule: LR(f = ) =

8 8 L. Bleumers et l. / Vision Reserh 8 (8) 79 9 % trils 7 9 oule 8 n % trils 9 9 oule 8 8 n.8.7. istne rtio / istne rtio / % trils hlf 9 9 n % trils hlf istne rtio / istne rtio / n Fig.. Perentge of trils in whih either the -, -, - or-orgnistion ws selete or tht were never omplete (n) s funtion of istne rtio /. Eh grph orrespons with ifferent presenttion onition of Experiment (A: oule, B: oule, C: hlf, D: hlf). 9, p <.; hlf: LR(f = ) =, p <.]. Due to the poor moel fit, gin, ution is wrrnte when trying to interpret the estimtes. However, we n onlue tht ifferene etween entrl n peripherl t remins present for the sling ftors we use... Explining the entrl eentri ifferene: Rnom responses Apprently, the sling oes not eliminte the entrl peripherl ifferene we oserve in Experiment. Within eh sle, eentri grouping exhiits stronger effet of the istne rtios in the ot lttie s expresse y n overll stronger erese of -responses s funtion of istne rtio. At the sme time, oservers show stronger teneny in the periphery to give - n -responses, initive of grouping tht is less epenent on reltive istnes. Together, these oservtions seem to suggest the existene of two seprte response popultions. We therefore hypothesize tht the eentri t my e etter pture y moifie version of the Pure Distne Lw: Moel MOD. Speifilly, in MOD, the possiility ws implemente tht prtiipnts my not e le to mke n expliit grouping jugment on numer of trils n, in tht se, respon rnomly ( rnom ). In the remining trils, the ot ltties re ssume to e groupe oring to the Pure Distne moel ( PureDist ). Thus, there re two irumstnes in whih orgnistion v is ssume to e selete s response, seeing v n seleting v y hne, n the finl proility of hoosing v is the sum of the proilities of these two events. Suppose R j inites the proility of mking rnom response t ot lttie position j (thus: R j ). We n then erive mthemtilly whih proilities re to e expete for eh orgnistion t tht position: p j ðvþ¼p j ðvjrnomþp j ðrnomþþp j ðvjpuredistþp j ðpuredistþ e j jvj jj p j ðvþ¼:r j þ þ e jj j jj þ e j jj jj ð R j Þ þ e jj j jj ðþ

9 L. Bleumers et l. / Vision Reserh 8 (8) Tle Person hi-squre sttistis for FIX (A) n VAR (B) s pplie to three pirs of onitions ( smll n oule; smll n hlf; smll n smll) to evlute the role of sle in the entrl peripherl ifferene Conitions Chisq f p A smll + oule (FIX DOUBLE) 9.9 <. smll + hlf (FIX HALF).7. smll + smll (FIX ORIGINAL).9 <. B VAR DOUBLE smll.. oule 9. <. ALL 9.7 <. VAR HALF smll.. hlf 7.8 <. ALL 87.9 <. VAR ORIGINAL smll.. smll.8 <. ALL.9 <. For lrifition, oring to Eq. (), MOD ssumes there re two groups of omplete trils, eh with speifi response istriution. One group ontins those trils in whih prtiipnts oul not report n orgnistion n selete response rnomly. This proportion of trils is preite y R j, n the response istriution orresponing with this group is uniform: the four possile responses re preite to e given eqully often (i.e., with proility of.). The other group ontins those trils in whih n orgnistion oul e reporte. This proportion of trils is represente in the moel y R j. The ssoite response istriution is ssume to e preite y the Pure Distne Lw. Note tht y llowing R j to iffer from zero, non-liner reltionship eomes possile etween the logits n the orresponing istne rtios. As note erlier, filure of the previous moels in the eentri onitions ws prtly ue to non-linerity in the t. MOD ws first pplie to the t of Experiment n mximum likelihoo estimtes were otine of j n R j per ot lttie position. MOD signifintly ontriute to the preition of the proilities for eh orgnistion, LR(f = ) = 878, p <.. Logits preite y the moel for pereiving the -orgnistion re plotte in Fig. A C longsie the preitions of the previous moels. MOD fits the t etter thn the moel in whih oul lso vry ross ot lttie positions ut in whih R j is ssume to e zero (i.e., VAR in Setion..). This is onfirme y the likelihoo rtio test, LR(f = ) =, p <.. The lower Person hi-squre sttistis re in line with the improve fit Tle (Tle ). The grphs illustrte tht moel fit is mrkely improve in the onition, in whih logit() is pture etter. Improvements were lso oserve in the onition, resulting in n eptle moel fit. Given the improve fit, it eomes of interest to onsier the prmeter estimtes n their implitions. The estimte of n the estimte of the proportion of rnom response trils oth inrese when the ot ltties re positione more eentrilly, whih n e seen in Tle. Note, tht the onfiene intervls of these estimtes for eh ot lttie position o not overlp, lthough the onfiene intervl for the estimte of is reltively ro t the lrgest eentriity. Apprently, prtiipnts ten to give rnom responses more often s ltties re ple further in eentri vision. However, when they re le to report pereive orgnistion, it is influene more strongly y the istne rtios in the ot lttie. This explins why in the rw t in Fig., -responses re still frequent in the onition even though greter perentge of rnom response trils in this onition woul seem to imply tht - n -responses shoul eome more likely, while oth - n -responses shoul eome less likely. However, oring to our moel, moving the ot ltties to the periphery oes not only le to n inrese in the proportion of rnom responses (expresse y R), ut lso to n inrese in the egree to whih response proilities epen on the reltive istne rtios (expresse y ) for those trils in whih n orgnistion oul effetively e reporte. It is the omintion of these two hnges tht shpes the finl response istriution. We ontinue our nlyses y fitting version of MOD to the sle onitions of Experiment. Our primry gol ws now to investigte whether it ws still useful to tke up prmeter R j in the moel one the peripherl stimuli were sle. This requires omprison of VAR n MOD, pplie to the pirs of onitions esrie in Setion... MOD fits the t etter for ll pirs of onitions [originl: LR() =, p <.; oule: LR() = 99, p <.; hlf: LR() =, p =.]. Fit vlues n e inspete in Tle. The outome of the ove moel omprison implies tht even when the eentri ot ltties re sle, the t re ommote signifintly etter y ssuming tht prtiipnts rnomly selete response in some trils uring the eentri grouping tsk. In Tle, MOD estimtes n onfiene intervls re presente for ll sle onitions. These estimtes, together with those from Tle, enle us to ompre the estimtes for eh of the sle eentri onitions with those for the smll onition of Experiment. Aoring to the estimtes, oservers me rnom Tle Person hi-squre gooness-of-fit tests for MOD per ot lttie position Position Chisq f p poole 8.7. smll.. smll.. ALL..

10 88 L. Bleumers et l. / Vision Reserh 8 (8) 79 9 Tle Estimtes of n R n orresponing onfiene limits per ot lttie position of Experiment Conition Prmeter Estimte CL lower CL upper poole... R. Lower ounry smll R..7. smll 7... R.8.. smll... R Aitionlly, the estimtes for the smll onition re inlue. responses in eh of the onitions, while they i not in the smll onition. The reltionship etween the istne rtios n the response proilities ws stronger for the oule eentri ot ltties thn for the smll entrl ot ltties. When the solute interot istnes were hlve, however, this reltionship ws estimte to e eqully strong in entrl n peripherl vision. The estimtes in Tles n lso mke it possile to evlute the effet of ot lttie position, while keeping sle (n perture rius) onstnt n vie vers. First, moving the ot lttie to the periphery les to n estimte proportion of rnom responses ifferent from zero t eh sle. It inreses the estimte of in se of the originl n the oule sle, ut oes not hve signifint effet on this prmeter in se of the hlve sle. Seon, when keeping ot lttie position onstnt, we n onlue tht sling of the entrl ot ltties oes not ffet the proportion of trils in whih rnom responses were me; this proportion is still estimte to e. It oes hve smll ut signifint effet on ; this estimte is signifintly higher in the oule onition thn in the hlf onition. Sling the eentri ot ltties hnges oth estimtes of R n. Tle Person hi-squre gooness-of-fit tests for MOD s pplie to the three pirs of onitions ( smll n oule; smll n hlf; smll n smll) to evlute the role of sle in the entrl peripherl ifferene Conition Chisq f p Doule smll..8 oule 8.8. ALL 8.9 <. Hlf smll..8 hlf ALL 9.9. Originl smll..8 smll.. ALL. <. Tle Estimtes of n R n orresponing onfiene limits per sle onition of Experiment Conition Prmeter Estimte CL lower CL upper oule...7 R. Lower ounry hlf...9 R. Lower ounry oule R..7. hlf... R.7.9. We n onlue tht oth ot lttie eentriity n sle n influene the egree to whih grouping ehviour epens on the reltive interot istne () n the proportion of rnom response trils (R). Furthermore, these ftors intert in oing so... Aitionl ontrols In the following setions, three itionl issues re resse. We evlute whether the proportions of skippe n never omplete trils were omprle ross onitions, we investigte whether prtiipnts were inline to pereive ertin orienttions more often, n we teste whether they exhiite preferene for speifi response option in the response sreen. The reporte nlyses pertin to the t of Experiment.... Skippe n never omplete trils To ssess the reltive reliility of the prmeters estimte for entrl n peripherl ot ltties uner the Pure Distne moel, repete-mesures ANOVA ws pplie to the perentge of skippe trils. Position, s well s spet rtio n orienttion of the -vetor of the ot ltties were entere s explntory vriles, ut neither signifint min nor intertion effets were oserve. The sme ANOVA ws performe on the perentge of trils tht were never omplete (i.e., skippe twie), n gin the position of the ot lttie h no effet: while sujets foun it hrest to mintin fixtion when the lttie ws in the ner periphery (8.% unomplete trils in the onition), the perentge of unomplete trils in this onition ws not signifintly higher thn in the entrl (%) or the onition (.7%).... Orienttion is Prtiipnts in this stuy oul e influene y orienttion is, hene the ontrol of showing ot ltties in ifferent orienttions. To fin out whether suh is ws tully present, we selete those trils in whih prtiipnts respone tht they h pereive either orgnistion or, n we etermine the orienttion of the istne vetor orresponing to tht orgnistion. A lk of orienttion is woul e expresse y the ft tht eh

11 L. Bleumers et l. / Vision Reserh 8 (8) of the possile orienttions ( y steps of ) ws hosen n equl numer of times. Chi-squre tests emonstrte the presene of orienttion is mong prtiipnts (Tle 7). When the ot ltties were isplye entrlly, ll prtiipnts were sujet to orienttion is, showing n overll preferene for the vertil orienttion. However, s n e seen in Tle 7, the mount of orienttion is iffere ross ot lttie positions. For eentrilly isplye ot ltties, orienttion is ws less strong n in some ses even sent. This teneny for reue orienttion is for more eentri ot ltties ws sttistilly onfirme y hi-squre tests for the inepenene of ot lttie position n orienttion is (Tle 8). From these t we n onlue tht the hosen orgnistion is not etermine y lttie struture lone. There is orienttion is present n this oinies with reue sensitivity to hnge in spet rtio (i.e., lower vlue), given tht the orienttion of eh orgnistion is vrie ross the entire possile rnge.... Response is We evlute whether prtiipnts h preferene for hoosing response option t speifi position (either top, ottom, left or right position). For instne, in the eentri onitions preferene might exist for the response option t the right sie s the stimulus ws lso ple to the right of fixtion. Therefore, we performe hi-squre tests for eh prtiipnt to hek whether ll response options were selete n equl numer of times, oth for entrlly n eentrilly ple ot ltties. When the ot ltties were ple entrlly, responses were istriute pproximtely uniformly ross the ifferent response option positions for eh prtiipnt. For the ot ltties, similr pttern emerge. Two prtiipnts i show some is, leit not signifintly. When the ot ltties were shown t, there ws only one prtiipnt for whom the frequeny vrition ross response option positions ws signifintly lrge; Chisq(f = ) = 8.7, p <.. This prtiipnt inee tene to selet the right response option more often. Suh response preferene is ssoite with lower vlue. Tle 8 Result of hi-squre tests for inepenene of ot lttie position n orienttion is Prtiipnt Chisq f p PDG 7. <. RG.9 <. GK.. GVB. <. AK.9 <. EA 9.88 <. MD.9 <.. Disussion The Pure Distne Lw ws previously shown to suessfully preit grouping y proximity of entrlly isplye ot ltties. In the urrent stuy, its preitive vliity ws evlute t three ifferent lotions in the visul fiel. We investigte whether grouping y proximity of ot ltties shown t eentri lotions ws ifferent, quntittively or qulittively, from grouping of entrlly isplye ltties. Speifilly, retngulr ot ltties were shown entrlly, or to the right of fixtion with the losest orer t or t eentriity. The spet rtio of the ot ltties (i.e., rtio of the seon shortest to the shortest interot istne) ws vrie n we registere its effet on prtiipnts grouping ehviour. In generl, we foun tht grouping of the ot ltties ws ffete y hnges in the reltive interot istnes (i.e., rtios of the interot istnes to the shortest interot istne) oth for entrlly n eentrilly isplye ot ltties. This epeneny ws well esrie y the Pure Distne Lw for the entrl ot ltties, repliting erlier results, regrless of perture size. When the ot ltties were isplye t eentri lotions, however, the moel i not equtely preit the proilities of hoosing eh orgnistion, even when the strength of the efine reltionship etween the proilities for pereiving eh orgnistion n the orresponing reltive interot istne ws llowe to vry ross ot lttie positions. The ifferene etween the preitions n the tul t ws prtiulrly lrge in the onition. Tle 7 Orienttion is for eh prtiipnt t the three possile ot lttie positions, quntifie y hi-squre test sttistis n orresponing p-vlues Prtiipnt Centrl Chisq f p Chisq f p Chisq f p PDG 9. <..9 <..9 <. RG.7 < GK 8. < GVB.9 <..... AK 88. <. 79. <. 7.8 <. EA 8.8 <..9 <...7 MD 88. <..88 <..8.9 A signifint hi-squre vlue inites tht some orienttions were hosen signifintly more often thn others.

12 L. Bleumers et l. / Vision Reserh 8 (8) 79 9 To investigte whether this poor moel fit ws ue to lk of sling, grouping ws teste in numer of itionl onitions. In these onitions, the shortest solute interot istne ws either hlf or twie the vlue use in the originl experiment. Aperture size n ot size were lso juste n the reltive interot istnes remine the sme. Dot ltties were now shown either entrlly or t eentriity. We foun tht sling oes ffet grouping ehviour, t oth ot lttie positions, ut we still oserve ifferene etween the entrl n peripherl response t for the sling vlues we pplie. Eentri t oul not e moelle ppropritely y the Pure Distne Lw. The ft tht the poor moel fit ws not remeie y sling inite tht there ws nother use for the ifferene etween the grouping results for the entrl n peripherl ot ltties. Our ount for this ifferene is se on the presene of two ontrsting oservtions regring the proportions with whih the ifferent lttie orgnistions were selete y the viewers. On the one hn, the ivergene of - n -responses ws stronger in the periphery. On the other hn, prtiipnts lso selete - n -responses more often in the periphery. This suggeste the existene of two response popultions in the peripherl onitions: one epenent on istne rtios n one resistnt to it. We hypothesize tht prtiipnts respone rnomly on some of the trils, leing to the ltter response popultion. Therefore, we onstrute n teste moifie version of the originl Pure Distne Lw moel, inorporting the possiility tht on numer of trils prtiipnts oul not report n orgnistion of the isplye lttie n selete response rnomly. On the remining trils, their response pttern ws ssume to orrespon with the preitions me y the Pure Distne Lw. The moifie moel ommote the t rther well, oth in the entrl n eentri onitions. Aoring to this moel, grouping responses n e ounte for y ssuming tht when the ot ltties were in entrl view, prtiipnts never respone rnomly, ut lwys reporte their perept whih ws governe y the Pure Distne Lw. When the ot ltties were isplye eentrilly, the perentge of rnom response trils ws estimte to inrese s the ltties were move further into eentri vision. However, when responses were not rnom ut were se on wht ws pereive, the reltionship etween grouping ehviour n the reltive interot istnes in the ot lttie (expresse y the moel prmeter ) eme stronger with eentriity. Sling of the ot ltties showe tht this eentri strengthening epene on the sle tht ws pplie. It remine present when ouling the sle t eentriity (i.e., rius ), while hlving the sle (i.e., rius ) t this eentriity me the epeneny of grouping on the istne rtios omprle to tht foun for entrl vision. Likewise, the moel outome suggeste the effet of sling epene on the eentriity of the ot ltties. Sling ws estimte to hve no effet on rnom response proility for entrl ltties. For the eentri ot ltties, however, rnom response proility ws estimte to e highest for ltties with rius n relily lower for ltties with rius n ltties with rius. Finlly, sling entrl ltties reue the impt of the Pure Distne Lw (i.e., ) when ltties were reue in size, while sling eentri ltties reue, oth when ltties were lrger ( rius) or smller ( rius) thn the initil rius use in Experiment. Sine our moel inites tht oth the proportion of rnom responses n the strength of the reltionship etween the istne rtios n the proilities for pereiving eh orgnistion were influene intertively y ot lttie eentriity n size, we nee to explin why this pttern of intertion ourre. With regr to the rnom responses, we propose tht ot lttie eentriity n size my hve ffete the ttentionl ynmis in our tsk resulting in onitions where ttention ws not suessfully llote to peripherl ot lttie, leving prtiipnts unle to report the orgnistion of the lttie n foring them to respon rnomly. Inee, there is eviene tht ttention is require to expliitly report grouping (Moore & Egeth, 997). Whether or not peripherl ot lttie is properly ttene in our present tsk, will epen on the ury n spee with whih overt ttention n e isengge from the entrl fixtion point n re-llote to the peripherl lttie. Two types of ttention shifts oul our in the present prigm: fst, involuntry shifts in response to the suen pperne of peripherl ot lttie t n ntiipte lotion, n slow voluntry shifts proue y the tsk requirement to overtly mintin entrl fixtion while overtly proessing the peripherl ot lttie (Nkym & Mkeen, 989). Fst, exogenously triggere ttention shifts were most prominent for ot ltties t, s inite y the greter prevlene of involuntry reflexive ses leing to tril ortion in tht onition (Fisher & Breitmeyer, 987; Mkeen & Nkym, 99). Of ll peripherl onitions, tht onition ws lso estimte to hve the lowest proportion of rnom responses, supporting our hypothesis of link etween filures to shift ttention n rnom responses. Slow, enogenously ontrolle ttention shifts hve een rgue to shre mny sptio temporl properties with voluntry ses (e.g., Kowler, Anerson, Dosher, & Blser, 99; Shll, ; Shneier, 99; Theeuwes, Goijn, & Prtt, ). It hs een emonstrte tht si ltenies inrese n tht si ury ereses when the eentriity n size of se trgets inreses (Bell, Everling, & Munoz, ; Ploner, Ostenorf, & Dik, ). Uner the ssumption tht similr properties re shre y voluntry ttention shifts, we n expet more filures to properly tten to lrger n more eentri ltties. Agin, this higher

13 L. Bleumers et l. / Vision Reserh 8 (8) Estimte rnom response proportion i not linerly inrese s funtion of peripherl lttie size, ut eentriity effets on ttention shifting hve een shown to moulte trget size effets in non-liner fshion, s ws emonstrte erlier for ses (Dik, Ostenorf, Krft, & Ploner, ). likelihoo of ttentionl lpses orreltes with higher estimtes of rnom response frequenies. Hving ounte for eentriity n sle effets on the frequeny of rnom responses, the question rises wht use to e higher in eentri onitions, thn in the entrl onitions, for the lrger sles (i.e., originl n oule)? In the literture, we only foun one other stuy whih expliitly resse Gestlt grouping in the periphery (Sill, ). In this stuy, it ws foun tht oservers effiieny in letter ientifition tsk ws more strongly etermine y goo ontinution of the omponents shping the letters in the periphery (i.e., Gor elements) thn in entrl vision. As suh, they lso oserve tht Gestlt grouping seems to ply greter role in the periphery. Yet, the question remins why proximity-epenent grouping in our stuy ws stronger in peripherl vision. One possiility is tht the higher vlues re ue to the less pronoune n sometimes even sent orienttion is when the ot ltties re presente eentrilly. However, it is unler how orienttion is n grouping y proximity intert to etermine the pereive orgnistion (see lso Clessens & Wgemns, in preprtion). Speifilly, the weker orienttion is oul e the result, rther thn the use of stronger grouping y proximity in the periphery. A more promising explntion of the stronger proximity-epenent grouping for peripherl ltties tkes into ount tht eentriity interte with sle in etermining the mgnitue of. Speifilly, for the smllest ltties there ws no relile ifferene in for entrl n eentri ltties, n for the most eentri ltties n inrese in sle i not lwys proue n inrese of. One wy to ount for these intertions is to ssume tht proximity-epenent grouping requires prtiulr sptil resolution n tht the omintion of ot lttie sle, retinl lotion of the lttie, n sene/presene of ttention to tht lotion n proue mth or mismth etween require n pplie resolution. This ount ws previously propose y Yeshurun n Crrso (998) to explin why texture segregtion performne peke t ifferent retinl eentriities epening on the ext omintion of texture sle n presene/sene of fouse ttention. Future reserh shoul serve to further lrify n test our finings. The moels isusse in this rtile provie mens to preit n test the omine effets of sle n eentriity. This my then gin le to n extene n improve quntittive funtion pturing pereptul grouping responses t ifferent sles n eentriities. Another line of investigtion shoul fous on the role of ttention. By using sptil pre-ueing of ot lttie position, we shoul e le to systemtilly influene the vlue of the n R prmeters in our moel. Furthermore, if ttention is inee n importnt ftor in this expliit grouping tsk, it eomes worthwhile hllenge to esign n impliit grouping tsk from whih mesure n e erive of the strength of the reltionship etween grouping n the reltive interot istnes. Suh n estimte oul then e iretly ompre with the estimtes of the urrent stuy. Finlly, it woul e useful to hve n externl riterion to ientify single trils s rnom response trils in orer to vlite our mximum likelihoo estimtes of the perentge of rnom response trils. In summry, the urrent stuy ws onute to iretly ompre grouping of ot ltties in entrl n eentri vision. Speifilly, we set out to evlute the preitive vliity of the Pure Distne Lw for grouping of ot ltties t ifferent positions in the visul fiel. The Pure Distne Lw neee to e pte to ommote the t in the eentri onitions, even when sling ws pplie. Sle oes mtter, however: sle n eentriity vritions intertively influene grouping of multistle ot ltties. When the ot ltties re ple further wy from fixtion, the results suggest tht grouping eomes more strongly etermine y the inherent struture of the ot ltties, provie tht the sle is lrge enough. Furthermore, eentri grouping y proximity requires tht ttention is properly irete towrs the ot lttie. When the ot ltties re ple eentrilly, ttentionl lpses our n the frequeny of rnom, proximity-inepenent grouping responses inreses. Aknowlegments This reserh ws supporte y grnts from the Fun for Sientifi Reserh-Flners (G.9.) to J.W. n from the Reserh Fun of the K.U. Leuven (GOA /) to Géry Yewlle, K.V. n J.W. We thnk Peter Clessens for llowing us to use his progrm for generting ot ltties n for giving us vie on this mtter. We lso thnk Mrten Demeyer n Hns Op e Beek for omments on previous rft. Likewise, we re grteful for the vlule omments me y oth the Eitor n the two Reviewers, whih helpe us to improve this mnusript. Referenes Anstis, S. (998). Pituring peripherl uity. Pereption, 7, Bell, A. H., Everling, S., & Munoz, D. (). Influene of stimulus eentriity n iretion on hrteristis of pro- n ntises in non-humn primtes. Journl of Neurophysiology, 8, 9. Clessens, P. M., & Wgemns, J. (). Pereptul grouping in Gor ltties: Proximity n lignment. Pereption & Psyhophysis, 7(8), 9. Clessens, P. M., & Wgemns, J. (in preprtion). A Byesin frmework for ue integrtion in multistle grouping: Proximity, ollinerity n orienttion priors in zig-zg ltties.