What constitutes an efficient reference frame for vision?

Transcription

1 Wht constitutes n efficient reference frme for vision? Duje Tdin, Joseph S. Lppin, Rndolph Blke nd Emily D. Grossmn Vnderilt Vision Reserch Center, 30 Wilson Hll, Vnderilt University, 2 st Avenue South, Nshville, Tennessee 37203, USA Correspondence should e ddressed to D.T. (duje.tdin@vnderilt.edu) Pulished online: 3 Septemer 2002, doi:0.038/nn94 Vision requires reference frme. To wht extent does this reference frme depend on the structure of the visul input, rther thn just on retinl lndmrks? This question is prticulrly relevnt to the perception of dynmic scenes, when keeping trck of externl motion reltive to the retin is difficult. We tested humn sujects ility to discriminte the motion nd temporl coherence of chnging elements tht were emedded in glol ptterns nd whose perceptul orgniztion ws mnipulted in wy tht cused only minor chnges to the retinl imge. Coherence discrimintions were lwys etter when locl elements were perceived to e orgnized s glol moving form thn when they were perceived to e unorgnized, individully moving entities. Our results indicte tht perceived form influences the neurl representtion of its component fetures, nd from this, we propose new method for studying perceptul orgniztion. According to the lws of physics, the position nd motion of n oject cn only e defined reltive to some reference frme. Neurl representtions of visul position nd motion must ide y the sme principles s physicl motion, ut wht is the nture of the reference frme in which the visul system ttins efficient representtion of position nd motion? The nervous system receives visul informtion in retinocentric coordintes; then this informtion is trnsformed into hed-centered coordintes for stle perception during eye movements nd into ody-centered reference frme to link perception nd ction 3. Depending on the reference frme, neurl representtions of motion cn e more or less ccurte (veridicl with respect to the physicl world) nd more or less efficient (computtionlly complex). Anlogously, plnetry motions re oth more ccurte nd more efficient when represented in heliocentric, rther thn geocentric, reference frme. Retinl coordintes, long with eye-position correction, re often ssumed to e the primry reference frme for neurl representtions of position nd motion. The sptil lyout of photoreceptors in the retin is replicted throughout the ntomicl hierrchy of visul res s retinotopiclly orgnized mps 4. This retinotopic orgniztion preserves the originl retinl coordintes, which could serve s the reference frme for encoding the motion nd position of ojects. In the humn visul system, however, the motion of n oject on the retin does not necessrily imply tht the oject itself is moving, ecuse our eyes re lso usully moving. An ccurte retinlly sed representtion would require precise nd continuously updted extr-retinl compenstion for chnges in eye nd hed position. Vision is known to exploit informtion in extr-retinl reference signls to compenste for displcements of the retinl imge 5 8, ut the ccurcy of this compenstion is detle 9. Even if the extr-retinl compenstion for chnges in eye position is precise, the motions of visul forms nd their component fetures often remin complex; this is prolem for oth eye-centered nd hed-centered representtions. The visul world is dynmic. Sptilly seprte moving fetures, such s the rms nd legs of n niml, often elong to the sme visul form nd my even hve different trjectories. Individul spots on leoprd s skin will hve diverse motion trjectories, which my e very different from the motion of the glol form (the whole leoprd). The motion of ech spot in the retinl reference frme is rther complex nd mounts to the vector sum of the oserver s motion (eye nd ody), leoprd motion nd spot motion. In contrst, if the motion of spot is visully represented reltive to the leoprd s form, its motion ecomes simpler. Such representtion my result in more ccurte perception of visul reltionships mong locl moving fetures (spots), nd culminte in more efficient perception of the glol moving form (leoprd). The motion nd position of feture my e encoded nd represented in reltion to other sttionry or moving ojects 0 2, therey simplifying tht feture s visul representtion. By definition, this reference frme is non-retinl; it is dynmic nd must e continuously updted y new visul input. To wht extent do visul reference frmes depend on the structure of visul input, not just locl retinl coordintes? Cn vision ypss or supplement the computtionl difficulties ssocited with retinl reference frme y encoding position nd motion reltive to perceived forms? This question is especilly relevnt for perceiving dynmic scenes nd for ctively exploring one s environment when the reference frmes defined y visul input move reltive to the retin. To determine whether visul informtion is encoded more efficiently when form informtion is ville, we mnipulted the recognizility of motion-defined form while minimizing chnges in the retinl imge. We modified two well-known protocols: iologicl motion ( iomotion ) 3 nd trnslting pentgon seen through n perture msk (dpted from ref. 4). These were chosen ecuse simple mnipultions up/down inversion of iomotion nd msking of pentgon 00 nture neuroscience volume 5 no 0 octoer 2002

2 trnsform these perceptully structured moving forms into conglomertions of unorgnized elements. Humn form in motion is redily perceived from point-light nimtions composed of only 2 points on mjor joints of the ody 3. If the point-light nimtion is inverted, humn form is no longer perceived lthough the nimtion retins its originl sptiotemporl structure 5,6. In msked pentgon displys, the sides of pentgon re seen through five tht occlude its vertices, while the pentgon is trnslting long circulr pth. As consequence of the perture prolem 7,8, the motions of individul line segments re inherently miguous, ut oservers integrte the motion signls cross line segments nd rigidly trnslting form is redily perceived 4. If the re invisile, oservers perceive only the motions of individul line segments with no pprent glol structure. Both point-light wlker (PLW) nd msked pentgon (MP) nimtions were modified for this study. PLW nimtions were mended y plcing smll Gor ptches on the mjor joints of humn wlker (Fig. ). Oservers discriminted motion coherence of Gor ptches tht oscillted (Fig. ) either coherently in phse or with some phse difference. These Gor ptches were plced on either upright or inverted PLWs. In nlogous experiments, oservers judged the coherence of counterphsing lck/white disks nd rottionlly oscillting windmills (Fig. c). In MP nimtions, the pentgon ws presented ehind five nd trnslted long circulr pth. Ech pentgon side ws defined y n oscillting grting oriented prllel to the side (Fig. 2). Oservers discriminted motion coherence of the five grtings. In seprte conditions, the pentgon were either visile (coherent form perceived, Fig. 2) or invisile (no form perceived, Fig. 2). In ll experiments, glol form (or its sence) ws, in principle, irrelevnt for the coherence discrimintion tsk. We mnipulted the slience of motion-defined form in PLW nd MP nimtions while mking only miniml chnges reltive to the retinl reference frme. Crucilly, context ws lwys irrelevnt for performing the tsks. If reltive positions nd motions of individul elements in perceptully structured displys (upright PLW nd MP with visile ) re more efficiently encoded ecuse of the vilility of form informtion, perception of sptiotemporl reltionships mong individul elements should e fcilitted. We found tht cross ll displys nd tsks, coherence discrimintions were more c Fig.. Point-light wlker nimtions. () Six frmes illustrting the 60-frme point-light wlker (PLW) nimtion defined y Gor ptches. Animtion durtion ws.4 s. Ech frme in isoltion ppers s rndom pttern of Gor ptches, ut when the nimtion is set into motion, humn form is redily perceived. Sequentilly shifting the gze from frme to frme my give wek impression of iologicl motion. In ctul experiments, however, oservers did not visully pursue the PLW, ut fixted t the fixtion cross in the center of the screen. () Eight frmes showing full cycle of 2-Hz oscilltory motion of the grting within the Gor ptch tht defines the shoulder of the PLW. The first frme corresponds to the outlined region in pnel (). Arrows indicte motion direction nd speed of the grting. Note tht the position of the entire Gor ptch chnges from frme to frme. The mgnitude of this position chnge depends on the Gor loction, with the wrist Gors undergoing the lrgest position chnges. (c) First frmes from iologicl motion nimtions defined y counterphsing lck/white disks (left) nd rottionlly oscillting windmills (right, illustrting the inverted condition). ccurte when the stimulus ws perceptully structured, defining glol moving form. RESULTS Biologicl motion In series of conditions, we estimted oservers ility to discriminte perceptul coherence of vrious dynmic elements tht defined either upright or inverted PLW nimtions (Methods nd Fig. ). For ll tsks nd ll oservers, perceptul coherence judgments were more ccurte (thresholds 6% lower) when the locl fetures (Gors, disks or windmills) defined n upright PLW (Fig. 3 e). The criticl difference etween the two conditions ws tht well-orgnized glol form is perceived in the upright, ut not the inverted, PLW condition 5,6. Fig. 2. Trnslting pentgon nimtions. () A trnslting pentgon ws presented ehind five (dshed outline is for illustrtion only). The pentgon trnslted clockwise long the circulr pth (s illustrted y the schemtic in the ottom right corner). The circle inside the pentgon represents the pth tken. The rrow on the circle mrks the current position long the pth nd the direction of trnsltion. The motion of the pentgon results in the ck nd forth motion of the line segments within. Arrows mrk the loctions where the line segments would shift s the pentgon moves from the 3 o clock to the 6 o clock position. Note tht direction nd speed vry mong different line segments, s depicted y the vrile lengths of the rrows. When the were visile (s shown), oservers perceived trnslting pentgon shpe. Independent of the pentgon trnsltion, five grtings oscillted either coherently or incoherently within the limits of pentgon sides. () Sme disply except tht the luminnce of the perture msk is the sme s the ckground, rendering the invisile. In this condition, oservers sw only ck nd forth motion of the line segments, with no glol form informtion. nture neuroscience volume 5 no 0 octoer

3 Oservers mde perceptul coherence judgments out chnging locl fetures tht were moving long complex trjectories produced y the PLW nimtions. (Imgine compring severl similr ojects while your friend is juggling them.) In the inverted PLW condition, feture trjectories pper glolly unstructured. In upright PLW conditions, the motions of locl fetures re prt of the recognizle glol form moving cross the screen. If these motions re represented reltive to the moving humn form, trjectories of locl fetures pper relted to ech other in perceptully meningful wy. Evidently, the presence of glol moving form fcilittes performnce y providing reference frme in which perceptul coherence judgments re esier. Inversion preserves reltive, ut not solute, position nd motion of locl elements comprising PLW nimtions (Fig. c). To verify tht our results were indeed due to differences in perceived form, we crried out nother version of the initil experiment: oservers discriminted motion coherence of oscillting Gor ptches emedded in sttionry ptterns tht were selected from PLW nimtions. On ech tril, Gor ptch positions were ssigned on the sis of single frme tht ws rndomly selected from upright or inverted PLW nimtion sequences (for exmple, the third frme from Fig. ). In these displys, the differences in solute positions of locl elements comprising upright nd inverted PLWs re retined, ut there is no difference in perceived form oth upright nd inverted displys look like rndomly positioned oscillting Gor ptches. Other methods were the sme s efore. Differences in solute position did not ffect performnce (Fig. 3f). We set up control experiment to ddress the possiility tht the presence of iologicl form my increse ttentionl enggement 9,20 ecuse upright PLW nimtions re rguly more interesting thn inverted PLWs. This could conceivly result in etter performnce. In the control study, oservers simply detected the rottion of windmills emedded in either upright or inverted PLW nimtions. Windmills were either sttionry or oscillted t 2.4 Hz. The threshold mplitude of oscilltion ws estimted for inverted PLW nd upright PLW conditions. Other methods were the sme s efore. Unlike the previous tsks, this detection tsk did not require ny perceptul comprisons mong multiple fetures. Scrutiny of just one feture (for exmple, windmill plced on the hip of PLW) would suffice. Therefore, the reference frme provided y the upright PLW ws less importnt, ut ny ttentionl enefits of iologicl motion should hve remined. There ws no difference, however, etween upright nd inverted PLW conditions (Fig. 4). Biologicl motion ws used in this study to mnipulte the slience of perceived form while minimizing chnges in the retinl imge. Next, we used very different visul displys to investigte whether this result generlizes to other motion-defined forms. Gor Blck & white disks c Threshold phse rnge CF Gor B & W Windmills MG d e f Gor indmills Windmills Sttionry PLWs Upright Inverted CF MG Gor Fig. 3. Results from PLW experiments. ( c) Psychometric functions for upright nd inverted PLW conditions for oserver oscillting Gor ptches (), counterphsing lck/white disks (), nd rottionlly oscillting windmills (c). Verticl error rs show s.e.m. for ech dt point. Horizontl error rs (plced on the 82% point on the psychometric functions) show 95% confidence intervls round threshold estimtes. (d, e) Phse rnge thresholds (82% correct) for two other oservers. Thresholds lrger thn indicte tht oservers ccurcy ws elow the 82% criterion t the mximum possile phse rnge (360 ). Error rs show 95% confidence intervls round threshold estimtes. (f) Phse rnge thresholds for oscillting Gor ptches emedded in sttionry PLW displys for two oservers. Note the reduced rnge of the y-xis, indicting tht the thresholds were significntly lower when the Gor ptches were emedded in sttionry pttern. Error rs follow the sme convention s (d) nd (e). Msked pentgon Results with PLWs were extended y estimting oservers ility to perceive motion coherence of five oscillting grtings, ech locted t side of trnslting pentgon. The pentgon ws presented ehind either visile or invisile (Methods nd Fig. 2). In similr displys (typiclly dimond), the visiility of determines whether or not rigid form is perceived 4. We used pentgon shpe insted of dimond ecuse the opposing prllel sides of dimond re lwys pirwise-rigid. When viewed through, the sides of trnslting pentgon (nd ny other geometric shpe without prllel sides) never move rigidly, therey potentilly enhncing the perceived disorgniztion when re invisile. Motion coherence judgments were much etter when the were visile nd rigid glol form ws perceived (Fig. 5 nd ). At the phse rnge where performnce in the condition with visile ws lmost perfect, performnce with invisile ws ner chnce. This result corresponded with perceptul shift: when the were visile, oservers reported seeing rigid form trnslting ehind the perture msk, nd when the were invisile, they sw disorgnized motions of five line segments moving ck nd forth. The differences in mgnitude of the oserved effects in PLW (Fig. 3 e) nd MP (Fig. 5 nd ) experiments my e due, in prt, to the differences in the extent to which perceptul orgniztion ws mnipulted in ech experiment. In MP nimtions, the contrst ws etween rigid moving oject (pentgon) nd five disorgnized line segments moving non-rigidly. In PLW nimtions, the contrst ws etween non-rigid ut perceptully well-orgnized humn wlker nd n eqully non-rigid ut perceptully disorgnized inverted wlker. The inverted PLW ws not Threshold phse rnge 02 nture neuroscience volume 5 no 0 octoer 2002

4 Oscilltion mplitude (rcmin) perceived s recognizle form, ut it ws fr from eing completely rndom. Some of its locl components re pirwise-rigid (for exmple, nkle nd knee elements), providing some structure. One oserver descried inverted PLWs s four grvity-defying pendulums. The presence of some structure in inverted PLWs my e responsile for the lrger effect seen with MP nimtions. Although we ttempted to minimize chnges in the retinl reference frme for these experiments, retinl imges for the two conditions were not identicl. Sheer presence of the lrge perture msk in one condition might conceivly fcilitte performnce. To ddress this possiility, we repeted the experiment with displys in which the pentgon ws sttionry (the rdius of trnsltion ws zero). In these displys, conditions with nd without visile do not differ in how structured or disorgnized they ppered. The presence of the perture msk did not ffect performnce (Fig. 5c nd d), nd thus cnnot explin the results tht we ttriuted to the visiility of form. DISCUSSION We developed novel stimuli to mnipulte the slience of the form-defined frme of reference while minimizing chnges of the retinl imge. Our results strongly indicte tht when perceptully orgnized reference frme is ville, the reltionships mong moving fetures re represented more ccurtely. The specific mechnisms underlying this process re not yet evident, ut, intuitively, the vilility of form my llow for more efficient encoding of reltive position nd motion. Perceptully orgnized form provides well-structured reference frme which my promote perceptully meningful representtion of the incoming visul input. This is nlogous to elortion effects in humn memory: mteril is etter rememered when it is encoded in meningful context 2. The present finding is consistent with other psychophysicl results showing tht motion perception often depends on the visul context For exmple, the motion ftereffect is mrkedly reduced if the motion is presented lone, in the sence of ny externl reference frme 22, nd enhnced if the ckground is moving in the opposite direction from the dpted motion 26. The presence of form tht might serve s reference frme in such experiments is confounded, however, y sustntil chnges in the retinl imge (for exmple, the presence of conspicuous ckground versus lnk ckground). The unique dvntge of our pproch is tht it minimizes this confound nd llows us Fig. 5. Results from MP experiments. Psychometric functions for visile nd invisile perture conditions in motion coherence tsk for oservers DT nd EG in the trnslting (, ) nd sttionry (c, d) pentgon experiments. Note the reduced rnge of the x-xis in (c) nd (d), indicting tht when the pentgon ws sttionry, motion coherence thresholds were significntly reduced. Verticl nd horizontl error rs follow the sme convention s Fig. 3. CF MG Threshold oscilltion mplitude (rcmin) Fig. 4. Results from the motion detection tsk. () Psychometric functions for upright nd inverted PLW conditions for oserver. () Oscilltion mplitude thresholds (82% correct) for two other oservers. Verticl nd horizontl error rs follow the sme convention s Fig. 3. to drw conclusions out the effects of form lone on visul motion representtions. We used two clsses of displys whose perceptul orgniztion is well-studied nd esily mnipulted. In prctice, perceptul orgniztion of moving ptterns is difficult prolem. Our finding tht motion coherence thresholds re reduced when the visul context is perceptully well-orgnized moving pttern (such s upright PLW) provides generl method for ssessing the strength of perceptul orgniztion. Specificlly, if n experimentl mnipultion of the moving pttern results in reduction of the coherence thresholds, it my e possile to conclude tht perceptul orgniztion of the moving pttern hs improved. The oservtion tht lrger effects were mesured with MP nimtions whose perceptul orgniztion differed more profoundly etween conditions suggests tht this method is sensitive to the grded disruption of perceptul orgniztion. We found tht the vilility of motion-defined form oosts performnce in low-level visul tsks. This requires tht form informtion must e ville t or efore the neurl stge(s) where motion coherence nd temporl coherence re processed. Evidence indictes tht middle temporl visul re (MT or V5) is the neurl locus of motion coherence perception 29,30, wheres perception of temporl coherence is generlly thought to e n erlier step in visul processing 3. The present results imply tht the neurl representtion in such erly visul res is influenced y the vilility of form. Results from recent psychophysicl nd physiologicl 35 studies re consistent with n erly influence of form in vision. Our results introduce potentilly importnt function of this erly influence: to provide frme of reference for more ccurte representtion of the visul input. Collectively, our results indicte tht form hs n erly influence in visul processing, resulting in more ccurte representtion of its component fetures. Our finding does not c DT DT Trnslting pentgon Sttionry pentgon d Visile Invisile Visile Invisile EG EG nture neuroscience volume 5 no 0 octoer

5 imply tht the visul system ignores the retinl reference frme. Indeed, retinl representtion with extr-retinl compenstion is crucil for estimtion of heding nd visully guided movement 6. Evidently, when form-defined reference frme is ville, vision is cple of exploiting the dditionl enefits it provides. These enefits my e gretest while viewing dynmic scenes (s in our displys) or during ctive explortion of the environment. In such cses, keeping trck of motions nd positions reltive to the retin is difficult, nd potentil gins from representing t lest some of the fetures reltive to visul forms re the gretest. Similr ides of multiple representtions hve een dvnced to descrie how the nervous system trnsforms sensory input into representtion used y the motor system,36,37. The two clsses of displys tht we used here re remrkle exmples of form-from-motion. Motion, however, is just one of severl wys in which form cn e defined y the visul system. Luminnce, color, texture nd stereo cues lso contriute significntly to our perception of form 38. We hve focused on moving forms ecuse they re more difficult to represent within the retinl reference frme. Representing sttionry ojects within retinl coordintes is computtionlly simpler (prticulrly in sence of eye movements), nd thus potentil enefits of form-defined reference frmes my e less importnt. Indeed, our control experiments with sttionry ptterns show highest performnce, with thresholds out hlf of those for trnslting pentgon seen through visile (compre Fig. 5 nd with Fig. 5c nd d). It is ltogether possile tht the present results will generlize to other types of form cues, ut we speculte tht the effects my e smller thn those otined with motion-defined form. Humn vision hs evolved into flexile neurl system tht mkes use of diverse sources of informtion. One of these sources is the structure of the visul stimulus itself 0, which my e exploited y the nervous system to otin n ccurte nd efficient representtion of the visul environment. The results presented here show tht the visul system tkes dvntge of the structure of its input to more efficiently represent reltive positions nd motions. METHODS Stimulus ptterns were creted with the Psychophysics Toolox 39,40 on n Apple Mcintosh G4 computer (Cuppertino, Cliforni). Ptterns were displyed on linerized monitor t 85 Hz. Viewing ws inoculr nd conducted in photopic mient illumintion (4.8 cd/m 2 ). Bckground luminnce ws 6 cd/m 2. Thresholds were estimted y the method of constnt stimuli. A session comprised 200 trils, with five conveniently chosen stimulus levels. Three or four sessions were run for ech condition nd 82% thresholds were estimted y fitting Weiull distriution 4 to the dt. Confidence intervls (95%) round threshold estimtes were determined using ootstrp procedure 42,43. Trils were self-pced, nd feedck ws provided for correct responses. Three nïve, pid nd well-prcticed oservers prticipted in the PLW experiments. Two uthors were oservers for the MP experiments. All experiments complied with Vnderilt University Institutionl Review Bord procedures, nd ll oservers gve informed consent. Biologicl motion. Biologicl motion displys were creted y plcing ten Gor ptches (σ = 5 rcmin; 4 cycles/, 92% contrst) on the mjor joints of humn point-light wlker (Fig. ). Ech Gor ptch consisted of moving sine grting windowed y sttionry Gussin envelope. All Gor ptches hd the sme orienttion, which ws rndomly selected on ech tril. Gor ptches (grtings therein) oscillted sinusoidlly (2 Hz, mplitude 80, strting sptil phse rndomized), either coherently or with some phse difference. The oserver s tsk ws to report if the Gor ptches oscillted coherently or incoherently. The tsk difficulty ws controlled y djusting the rnge of possile phses from which in incoherent trils the oscilltion phse for ech Gor ws rndomly selected. When the phse rnge is sufficiently nrrow, incoherently oscillting Gor ptches pper to move coherently. Before thresholds could e estimted, phse rnge vlues were trnsformed to correct for the fct tht the verge phse difference etween Gor ptches increses non-linerly for phse rnges etween 80 nd 360 (see Supplementry Methods nd Supplementry Fig. online). As Gor ptches were plced on the joints of PLW, the position of ech Gor ptch chnged every 70 ms ( 4 Hz). This chnge of position ws independent of the 2-Hz Gor ptch oscilltion (smpled t 42.5 Hz) nd irrelevnt for the tsk. Ech tril lsted.4 s, during which the PLW wlked for 2 (.4 /s). The PLW strted t eccentricity on either side of fixtion nd wlked through the fove. At this speed, the PLW ( 3.8 tll) ppered to wlk nturlly. Trils of inverted PLWs were intermixed with upright PLW trils. In inverted PLW trils, oservers generlly perceived disorgnized motion of independent fetures without ny glol structure, consistent with previous oservtions 5,6. During the nlysis, the trils with upright nd inverted PLWs were seprted nd psychometric function ws estimted for ech condition. In n nlogous experiment, lck/white disks (rdius 8 rcmin) were plced on the joints of inverted nd upright PLWs (Fig. c). On the first frme, the top nd ottom hlves of ech disk were either lck nd white or white nd lck, rndomly ssigned. The polrity of the disks ws reversed t 2 Hz, either coherently or incoherently. In coherent trils, ll disks switched polrity synchronously (with the first switch occurring within the first 500 ms), wheres in incoherent trils, the switching occurred within certin phse rnge. The oservers tsk ws to mke judgments out the temporl coherence 3,44 of counterphsing lck/white disks. In the third experiment, oservers discriminted the perceptul coherence of rottionlly oscillting windmills (rdil grtings) emedded in PLW nimtions (Fig. c). Windmills (rdius 9 rcmin, 92% contrst) rotted sinusoidlly (2.4 Hz, mplitude 80, strting sptil phse rndomized) either coherently or incoherently with oscilltion phses rndomly selected from rnge of phse lgs. The rottion direction of ech windmill ws rndomly ssigned every tril, so windmills prcticlly never rotted in the sme direction. In coherent trils, windmills switched direction synchronously, ut lso hd identicl ngulr speed t ny point in time (ut not identicl velocity, s oscilltion directions were rndom). Msked pentgon. In MP displys (Fig. 2), n outline of n equilterl pentgon (side length 40 rcmin, side width 40 rcmin) ws presented ehind five rectngulr. The pentgon trnslted long circulr pth (rdius 6 rcmin, 2.4 rev/s) for 470 ms. Apertures were fixed in loction nd plced so tht pentgon vertices were lwys occluded. The foreground of the perture msk hd luminnce tht ws either identicl to the ckground, rendering the invisile (Fig. 2), or.5 cd/m 2 lighter thn the ckground, resulting in visile (Fig. 2). Ech pentgon side ws defined y sine grting (3.5 cycles/, 46% contrst) oriented prllel to the side. Within the limits of the pentgon orders, grtings oscillted sinusoidlly either coherently or incoherently with some phse difference (2.Hz, mplitude 80, strting sptil phse rndomized). These oscilltions were independent of the line segment motion resulting from pentgon trnsltion. As efore, tsk difficulty ws controlled y djusting the phse rnge from which oscilltion phses were selected in incoherent trils. In single tril, incoherent nd coherent displys were presented in seprte temporl intervls nd oservers identified the intervl in which the five grtings oscillted coherently (temporl 2AFC tsk with n interstimulus intervl of 470 ms). Trils with visile nd invisile were intermixed, nd fter the experiment, psychometric function ws estimted for ech condition seprtely. 04 nture neuroscience volume 5 no 0 octoer 2002

6 Note: Supplementry informtion is ville on the Nture Neuroscience wesite. Acknowledgments This work ws supported y EY07760 to R.B., P30-EY0826 nd T32-EY0735. We thnk C. Freid, M. Gumin nd B. Froelke for help with dt collection, nd M. Shiffrr nd G. Logn for helpful suggestions. Competing interests sttement The uthors declre tht they hve no competing finncil interests. RECEIVED 8 APRIL; ACCEPTED 6 AUGUST Boussoud, D. & Bremmer, F. Gze effects in the cererl cortex: reference frmes for spce coding nd ction. Exp. Brin Res. 28, (999). 2. Buneo, C. A., Jrvis, M. R., Btist, A. P. & Andersen, R. A. Direct visuomotor trnsformtions for reching. Nture 46, (2002). 3. Soechting, J. F. & Flnders, M. Moving in three-dimensionl spce: frmes of reference, vectors, nd coordinte systems. Annu. Rev. Neurosci. 5, 67 9 (992). 4. Fellemn, D. J. & Vn Essen, D. C. Distriuted hierrchicl processing in the primte cererl cortex. Cere. Cortex, 47 (99). 5. Brdley, D. C., Mxwell, M., Andersen, R. A., Bnks, M. S. & Shenoy, K. V. Mechnisms of heding perception in primte visul cortex. Science 273, (996). 6. Crowell, J. A., Bnks, M. S., Shenoy, K. V. & Andersen, R. A. Visul selfmotion perception during hed turns. Nt. Neurosci., (998). 7. Hrmeier, T., Thier, P., Repnow, M. & Petersen, D. Flse perception of motion in ptient who cnnot compenste for eye movements. Nture 389, (997). 8. Hrmeier, T., Bunjes, F., Lindner, A., Berret, E. & Thier, P. Optimizing visul motion perception during eye movements. Neuron 32, (200). 9. Turno, K. A. & Heidenreich, S. M. Eye movements ffect the perceived speed of visul motion. Vision Res. 39, (999). 0. Gison, J. J. The Perception of the Visul World (Houghton Mifflin, Boston, 950).. Johnsson, G. in Perceiving Events nd Ojects (eds. Jnsson, G., Bergstrom, S. S. & Epstein, W.) (Lwrence Erlum, Hillsdle, New Jersey, 994). 2. Wde, N. J. & Swnston, M. T. A generl model for the perception of spce nd motion. Perception 25, (996). 3. Johnsson, G. Visul perception of iologicl motion nd model for its nlysis. Percept. Psychophys. 4, 20 2 (973). 4. Lorenceu, J. & Shiffrr, M. The influence of termintors on motion integrtion cross spce. Vision Res. 32, (992). 5. Fox, R. & McDniel, C. The perception of iologicl motion y humn infnts. Science 28, (982). 6. Pvlov, M. & Sokolov, A. Orienttion specificity in iologicl motion perception. Percept. Psychophys. 62, (2000). 7. Mrr, D. & Ullmn, S. Directionl selectivity nd its use in erly visul processing. Proc. R. Soc. Lond. B Biol. Sci. 2, (98). 8. Morgn, M. J., Findly, J. M. & Wtt, R. J. Aperture viewing: review nd synthesis. Q. J. Exp. Psychol. 34A, (982). 9. Cvngh, P., Linc, A. T. & Thornton, I. M. Attention-sed visul routines: sprites. Cognition 80, (200). 20. Vin, L. M., Solomon, J., Chowdhury, S., Sinh, P. & Belliveu, J. W. Functionl neurontomy of iologicl motion perception in humns. Proc. Ntl. Acd. Sci. USA 98, (200). 2. Crik, F. I. M. & Tulving, E. Depth of processing nd the retention of words in episodic memory. J. Exp. Psychol. Gen. 04, (975). 22. Dy, R. H. & Strelow, E. Reduction or disppernce of visul fter effect of movement in the sence of ptterned surround. Nture 230, (97). 23. Lppin, J. S. & Crft, W. D. Foundtions of sptil vision: from retinl imges to perceived shpes. Psychol. Rev. 07, 6 38 (2000). 24. Lppin, J. S., Donnelly, M. P. & Kojim, H. Coherence of erly motion signls. Vision Res. 4, (200). 25. Legge, G. E. & Cmpell, F. W. Displcement detection in humn vision. Vision Res. 2, (98). 26. Murkmi, I. & Shimojo, S. Modultion of motion ftereffect y surround motion nd its dependence on stimulus size nd eccentricity. Vision Res. 35, (995). 27. Nkym, K. & Tyler, C. W. Reltive motion induced etween sttionry lines. Vision Res. 8, (978). 28. Nwrot, M. & Sekuler, R. Assimiltion nd contrst in motion perception: explortions in coopertivity. Vision Res. 30, (990). 29. Newsome, W. T., Britten, K. H. & Movshon, J. A. Neuronl correltes of perceptul decision. Nture 34, (989). 30. Shdlen, M. N., Britten, K. H., Newsome, W. T. & Movshon, J. A. A computtionl nlysis of the reltionship etween neuronl nd ehviorl responses to visul motion. J. Neurosci. 6, (996). 3. Lee, S. -H. & Blke, R. Visul form creted solely from temporl structure. Science 284, (999). 32. Croner, L. J. & Alright, T. D. Imge segmenttion enhnces discrimintion of motion in visul noise. Vision Res. 37, (997). 33. Lorenceu, J. & Alis, S. Form constrints in motion inding. Nt. Neurosci. 4, (200). 34. Verghese, P. & Stone, L. S. Perceived visul speed constrined y imge segmenttion. Nture 38, 6 63 (996). 35. Croner, L. J. & Alright, T. D. Segmenttion y color influences responses of motion-sensitive neurons in the corticl middle temporl visul re. J. Neurosci. 9, (999). 36. Bttgli-Myer, A. et l. Erly coding of reching in the prieto-occipitl cortex. J. Neurophysiol. 83, (2000). 37. Snyder, L. H. Coordinte trnsformtions for eye nd rm movements in the rin. Curr. Opin. Neuroiol. 0, (2000). 38. Regn, D. M. Humn Perception of Ojects (Sinuer, Sunderlnd, Msschusetts, 2000). 39. Brinrd, D. H. The psychophysics toolox. Spt. Vis. 0, (997). 40. Pelli, D. G. The Video Toolox softwre for visul psychophysics: trnsforming numers into movies. Spt. Vis. 0, (997). 4. Quick, R. F. Jr. A vector-mgnitude model of contrst detection. Kyernetik 6, (974). 42. Wichmnn, F. A. & Hill, N. J. The psychometric function: I. Fitting, smpling, nd goodness of fit. Percept. Psychophys. 63, (200). 43. Wichmnn, F. A. & Hill, N. J. The psychometric function: II. Bootstrp-sed confidence intervls nd smpling. Percept. Psychophys. 63, (200). 44. Blke, R. & Yng, Y. Sptil nd temporl coherence in perceptul inding. Proc. Ntl. Acd. Sci. USA 94, (997). nture neuroscience volume 5 no 0 octoer