Visual mvement perceptin: A cmparisn f abslute and relative mvement discriminatin R. A. KlNCHLA Princetn University, Princetn, New Jersey 08540 It is prpsed that there are tw types f visual mvement perceptin, abslute and relative. The frmer ccurs when an bject is seen t mve in an therwise hmgeneus (r at least lcally hmgeneus) visual field. Relative judgments ccur when ne bject is seen t mve with respect t anther, i.e., the separatin between them is seen t change. Quantitative mdels fr bth prcesses are develped, and an experiment reprted fr which the mdels seem apprpriate. The results appear relevant t a thery f size f length perceptin as well as t the general perceptual issue f abslute and relativejudgments. Earlier papers by this authr and his clleagues (e.g., Kinchla & Smyzer, 1967; Kinchla & Allan, 1969, 1970) deal primarily with abslute mvement perceptin: seeing an bject mve in an therwise hmgeneus visual field (Ganzfeld). This paper relates that perceptual prcess t anther, termed relative mvement perceptin: seeing ne bject mve relative t the psitin f anther bject in yur visual field. This distinctin between abslute and relative mvement perceptin is illustrated by the prblem f judging the mvement f a small clud seen directly verhead in an therwise clear blue sky. If its mvement were difficult t discern, a natural strategy wuld be t mve next t sme bject like a building s that the clud appeared clse t the tp f the building. Mvement f the clud, riginally imperceptable, is ften quite apparent when seen in relatin t the fixed reference pint prvided by the tp f the building. The fact that tw types f mvement perceptin are invlved is suggested by the illusin f "induced mvement" (Dunker, 1929) ccasinally prduced in this situatin: mvement f the clud "induces" an illusin that the building is mving ("falling frward r backwards") rather than the clud. Nte that ne crrectly perceives a change in separatin between clud and building (relative mvement) but errneusly attributes it t (abslute) mvement f the building. A highly simplified frm f the preceding perceptual situatin was emplyed in the experiment reprted in this paper. Rather than judging the mvement f a clud in a clear blue sky, Os were asked t judge the mvement f a single pint f light seen in the dark. Anther pint f light, rather than a 'The authr is indebted t Charles Cllyer fr his assistance in cnducting the experiment reprted in this paper. rftp, was then intrduced at varius distances frm the test light in rder t assess the effect f a reference pint n the Os' judgments. Befre cnsidering the experiment, it will be useful t develp a mre precise terminlgy with which t discuss visual mvement perceptin, and t cnsider sme simple theretical mdels fr the abslute and relative frms f this prcess. MOVEMENT DISCRIMINATION TASKS Perhaps the mst elementary experimental situatin ne culd emply t study abslute mvement perceptin is t ask an 0 t judge the mvement f a single pint f light presented in the dark. Tw types f stimulus patterns ne might emply are illustrated in Fig. I. Illuminatins f small pints f light in an therwise dark rm are specified in time and space crdinates. Time in secnds is represented n the abscissa, while the rdinate dentes Lateral Psitin L in degrees f visual angle. Psitin 0 (L = 0) crrespnds t sme arbitrary pint in frnt f an 0, and the ther psitins are specified by their hrizntal angular displacement frm Psitin 0, psitive t the right and negative t the left. All pints are assumed t be at an equal distance frm the O. Tw clsely related types f mvement patterns are illustrated: a discrete pattern, dented by the slid lines, and a cntinuus pattern, dented by a brken line. The cntinuus pattern cnsists f a pint f light cntinuusly illuminated frm Time 0 until Time t, mving hrizntally at a cnstant angular velcity f v deg/sec, The light cmes n at Psitin 0 and ges ff at Psitin m, s that the angular velcity, v, is simply m divided by t. The discrete pattern cnsists f successive illuminatins f tw statinary pints f light; the first light is at Psitin 0 and the secnd at Psitin m, with a t-scc perid f darknessbetween the successive illuminatins. Thus bth the discrete and cntinuus mvement patterns in Fig. I can be defined in terms f m and 1. The expsure time, e, f the lights in the discrete pattern des nt seem t be an imprtant cnsideratin, s lng as it is sufficient t make the tw statinary lights visible. The displacement, m, will be referred t as the "mvement f a pattern," with a "statinary" pattern simply ne which has n mvement (m = 0). Mvement discriminatin willbe defined as an O's ability t discriminate mvement patterns slely n the basis f mvement. Thus, mvement discriminatin is required t distinguish any pair f mvement patterns, Si and Sj, which are identical except fr their respective m values, m, and mj' If Sj and Sj differ in any ther respect, it is difficult t determine whether the 0 is really basing his discriminatin n the m values r n this ther dimensin. Fr example, if Si and Sj differ in respect t t, the 0 might simply make a tempral discriminatin. It shuld be emphasized that discriminating a discrete pattern frm a cntinuus pattern is nt mvement discriminatin. The familiar phi illusin is nt an errr in mvement discriminatin (the tw successively illuminated lights actually are in different psitins); rather, it is a failure t discriminate between discrete and cntinuus mvement. Thus, "mvement perceptin" as emplyed here will simply dente the perceptin f a change in psitin. The subsequent theretical arguments are meant t apply t either discrete r cntinuus mvement patterns, althugh nly discrete patterns were emplyed in the experiment reprted in this paper. In either case, the theretical arguments can be develped mst simply in terms f a simple frm f mvement discriminatin: distinguishing a statinary pint f light frm ne that mves t the right. These tw stimulus patterns will be dented, 5 m.:e II> Q...J - e, 0 T: time Fig. I. An illustrative Sj discrete (slid lines) and cntinuus (brken line) mvement stimulus pattern. Perceptin & Psychphysics, 1971, Vl. 9 (2A) Cpyright 197/, Psychnmic Jurnals. II/c.. Austill, Tl.xas 165
am '';: 'iii 0..J ' T: time Fig. 2. An illustrative Sj discrete (slid lines) and cntinuus (brken line) mvement pattern with a reference light at Psitin r. respectively, by S and S" where the mvement f the statinary pattern, m, equals zer and the mvement f the SI pattern, m., is greater than zer; i.e., the secnd light is displaced t the right rn, deg. The discriminatin task cnsists f a series f trials, with either S, r S presented with equal prbability n each trial. Fllwing each presentatin f a pattern the 0 must indicate either that S, was presented, an RI respnse, r that S was presented, an R respnse. In rder t perceive the mvement defined by ne f the patterns (discrete r cntinuus) in Fig. 1, the 0 must recgnize that the psitin f the light at Time t is different frm the psitin f the light at Time 0 In this sense his perceptual prblem is ne f visual psitin memry. A mdel f perceptual memry (Kinchla & Smyzer, 1967) riginally emplyed t represent an O's memry fr auditry amplitude, has been successfully develped as a mdel fr discriminatins invlving patterns f the type illustrated in Fig. I (Kinchla & Allen, 1969). Hwever, cnsider the type f visual psitin memry that might be emplyed t perceive the mvement f the pattern illustrated in Fig. 2. Here a reference light at Psitin r is added t the patterns illustrated in Fig. I. Ina discrete pattern, this reference light is illuminated in synchrny with the tw successively illuminated statinary pints, while in the cntinuus case, the reference pint is illuminated cntinuusly frm Time 0 t Time t. If the 0 were t ignre the reference pint, his perceptual prblem wuld be the same as befre, he must "remember" the abslute lcatin f Psitin 0 until Time t in rder t ntice the mvement, m. Hwever, the 0 might simply "remember" the relative psitin f the tw lights at Time 0 (the distance between Psitin 0 and Psitin r) and cmpare this memry with the separatin between the lights at Time t (the distance between Psitin m and Psitin r). If his memry fr relative psitin were mre efficient than his memry fr abslute psitin, he wuld be mre accurate in discr iminating mvement when the reference light was present. A MODEL FOR ABSOLUTE MOVEMENT PERCEPTION The mdel fr abslute mvement perceptin (Kinchla & Allan, 1969) may be summarized as fllws. Let Sj be a stimulus pattern f the srt illustrated in Fig. I, with Parameters m, and t. Each presentatin f Sj prduces sme value xa f a hypthetical variable XA, where XA equals the actual mvement f the pattern (mj) plus a Gaussian randm variable, N A. This "nise" variable has an expected value f zer and a variance defined as fllws: The cnstants A and 1TA can be interpreted as measures f the "nise" in different phases f the perceptual prcess, Specifically, 21TA dentes the ttal input nise accrued in generating internal representatins f the initial and terminal psitins f the light, while epa t is the memry nise accrued in maintaining a memry f the initial psitin during the ti sec befre the terminal psitin is defined (i.e., memry nise is directly prprtinal t 1. The expected value and variance f X will be related t the stimulus parameters as fllws: and. t'1l.c L 0.. (2) Var (X l Sj) =Var (NA I Sj) = At + 21TA. (3) If the theretical distributin f XA given S, IS similar t that given S, the 0 will have difficulty deciding whether certain x values were evked by S, r S. It is assumed that he reprts S, (makes an RI respnse) nly if XA exceeds his respnse criterin fr abslute mvement, ~A' This leads t the familiar statistical decisin prblem illustrated in Fig. 3, which shws hypthetical distributins f X fr S, and S and an arbitrary respnse criterin, ~. The areas t the right f ~ under each curve crrespnd t the prbability f an RI respnse given that stimulus pattern, i.e., t peri lsi)' and peri I S). While the mdel is similar t the psychphysical thery f signal detectin described by Green and Swets (1966), it has a unique time-dependent feature whereby the "verlap" between the tw distributins in Fig. 3 increases durine the t secnd stimulus perid. Specifically, if we express the distance between the means f the tw distributins in units f the standard deviatin f X, we can define a di scriminability measure fr abslute mvement, DA' analgus t the d' measure f Green and Swets: E(X lsi) - E(X I S) DA=------ [Var (X I S)J Vz Fig. 3. Hypthetical distributins f X A (r XR) given S and 8, with an arbitrary respnse criterin. (4) An imprtant prperty f DA is that it can be estimated directly frm an, O's perfrmance. Specifically, if peri lsi) dentes the prprtin f R, respnses the.1-----'--------- (3 m, X: Subjective impressin f mvement Stimulus pattern 166 Perceptin & Psychphsycis, 1971, Vl. 9 (2A)
kzi' made t an Si pattern (i =0, I), and Zj dentes that value f a nrmal deviate exceeded with a prbability equal t P(RI I Sj), then the difference between ~ and ZI is an estimate f VA, dented DA: It has been shwn (Kinchla & Allan, 1969) that in mst applicatins f this mdel the input nise (21fA in Eq. 3) is negligible relative t the memry nise (rf>a tj in Eq.3). While there may be situatins in which input nise culd be an imprtant cmpnent (e.g., if the 0 were seated n a vibratingplatfrm), the general mdel can usually be defined in a ne-parameter frm (1fA =0) s that Eq. 4 becmes (6) with IPA equal t abut 1.8 sq deg/sec fr a typicalo. A MODEL FOR RELATIVE MOVEMENT PERCEPTION It is prpsed here that an 0 may als "input" and "remember" the separatin between tw lights, althugh the efficiency f this prcess is inversely related t the size f the separatin. In ther wrds, it is prpsed that a mdel fr relative judgments can be defined in a manner analgus t that fr abslute judgments, except that the nise in bth the input and memry prcesses will be prprtinal t the separatin between the tw lights, i.e., a type f Weber assumptin. Specifically, let Sj be a pattern f the srt illustrated in Fig. 2 and assume that each presentatin f Si evkes a value XR f a hypthetical variable XR, where XR equals the actual mvement f the pattern (m.) plus a Gaussian randm variable, NR. This nise variable has an expected value f zer and a variance defined as fllws: (7) Nte that quantity (IPR t + 1fR)r can be interpreted as the nise accrued when the initial separatin between the tw ligh ts (r) is input and remembered until Time t. Whereas the quantity 1fR(r- ITIi) is simply the nise accrued when the terminal separatin between the tw lights (r-- rn, is input at Time t. The expected value and variance f XR will be defined as fllws: E(XR I S0 =m, + E(N) The preceding assumptins imply that =m; relative mvement judgments will be (8) superir t abslute judgments nly if the "nise" in the frmer prcess, and Var (XR I S), is less than that in the Var(XR I Sj) =Var(NI Sj) latter, Var (XA); specifically, DR in Eq. 12 is greater than DA in Eq. 6 nly if =(.:PR t +1fR)r + 1fR (r - mj), (qlr t + 21fR)r is less than IPA t. It is als clear frm Eq. 12 that DR diminishes as r increases. Thus, if r e is a value f r such (9) that CPA t equals (CPR t + 21fR)r e, r Assuming that an 0 reprts relative mvement (reprts SI) nly when xr excee ds sme criterin fr relative mvement, I3R, his decisin prblem is essentially the same as that encuntered in abslute judgments (and illustrated in Fig. 3). The mdel is slightly mre cmplicated since,by Eq. 9, while Thus while Var (X A I S) equals Var (X A i s.), Var(XR I S) exceeds Var (XR I Sd by the amunt ml1fr' A discriminability measure fr relative judgments, DR, can be defined in a manner analgus t DA ( q. 4): where =-------- ( 12) Hwever, because Var (XR I S) des nt equal Var(XR I SI), ur estimate f DR differs slightly frm that in the abslute mdel (Eq. 5): b R =Z '0 (II) (13) [Var (XR I SdP'2 k =--------. (14) [Var (XR I S») y, It shuld be nted that k is apprximately ne if the quantity 1fRml is small with respect t the quantity CPR tr + 21fR r (see Eq. II). When k is clse t ne, an estimate f DR can be.btained in the same fashin as DA in Eq. 5, i.e., (16) then an 0 might make relative judgments nly when r is less than r e If r is greater than r e, he can d better if he ignres the reference light and simply makes an abslute judgment. This argument suggests that the discriminability f patterns like thse in Fig. 1b shuld initially diminish as r is increased (by Eq. 12) until discriminatin is equal t that attained withut a reference light (Eq.4); perfrmance shuld then be unaffected by further increments in r. (One might als assume that NA and NR are at least partially independent and that the 0 culd use bth XA and XR in each judgment. While mdels f this srt are interesting, the simpler assumptin that either XA r XR is used willbe emplyed in the present analysis.) AN EXPERIMENT The fllwing experiment was designed t assess the rle f a reference light in mvement perceptin. Three Os perfrmed a discrete mvement discriminatin task invlving tw stimuluspatterns, S and SI, with m equal t 0 deg and m, equal t.13 deg. Smetimes a reference light was presented, as in Fig. 2, with r equalling I, 3, 5, 10, 15, r 20 deg, while ther times there was n referencelight, as in Fig. I. In all cases, the interval t was either.5 r 2 sec. (These particular values were chsen n the basis f preliminary testing with ther Os.) The pssible cmbinatins f these factrs defined 14 experimental cnditins. Prcedure Each 0 was tested daily fr 35 days. The first seven sessins were cnsidered practice, with each f the 14 cnditins in effect during ne-half f a particular sessin. A single cnditin was in effect thrughut each f the remaining 28 sessins, such that tw sessins were run under each f the 14 cnditins. The particular sequence f cnditins was delennined randmly fr each O. Perceptin & Psychphysics, 1971. Vl. 9 (2A) 167
Table I Values f hr I ISI!, Dented PI' f(r I j S), Dented P, and Pc' fr Each Observer Under Each Experimental Cnditin. The n-reference-light abslute-judgment cnditin is dented by r = A. t 01 02 03 (Secnds) PI f Pc PI P Pc PI P Pc.5 1 Deg.74.27.74.72.14.79.63.29.67.5 3 Deg.63.32.66.47.15.66.63.46.58.5 5 Deg.56.33.62.61.31.65.63.47.58.5 10 Deg.52.38.57.61.39.61.56.38.59.5 15 Deg.64.45.60.41.21.60.57 Al.58.5 20 Deg.46.25.60.57.35.61.51.39.56.5 A.38.21.58.67.45.61.47.32.58 2 I Deg.61.34.64.47.16.66.63.42.60 2 3 Deg.59 AD.60.43.23.60.61.50.56 2 5 Deg.48.34.57.42.27.58.51.46.52 2 10 Deg.47.35.56.62.47.58.50.46.52 2 15 Deg.47.37.55.40.30.55.46.36.55 2 20 Deg.40.30.55 048.35.56.46.38.54 2 A.41.31.55.54.43.56.38.32.53 A daily testing sessin was divided int five successive blcks f 100 trials, with a l-min rest perid in the dark between blcks. Each trial began with a clearly audible l-sec-duratin 500 Hz warning tne, filwed immediately by the stimulus pattern. The 0 then had 2 sec in which t indicate his respnse (pressing ne f tw buttns) befre the start f the next trial. Bth SI. and S patterns ccurred equally ften in a randmly determined sequence within each blck f trials. The stimulus lights were tungsten filament "indicatr" lamps[dialcn. 39) with a flat circular surface f white pal glass. They were equated phtmetrically and interchanged several times during the experiment. They were lcated 4.1 m in frnt f the 0 where they subtended.033 deg f visual angle. The lights were clearly visible at abut 4 ml, althugh nt bright enugh t reveal any ther detailsin the therwise dark testing rm. Each illuminatin f a light was fr 100 msec (et and e2 in Figs. 1 and 2). Results The first 100 trials duringeach f the 28 data sessins were treated as "warmup" r practice trials, s that each 0 prduced 800 trials f data (400 fr each stimulus) under each f the 14 experimental cnditins. His perfrmance under each cnditin will be summarized by the prprtin f R I. respnses t each stimulus, P(RI!Sd 'and P(RI I S). It is als interesting t cnsider the prprtin f "crrect" respnses dented by Pc, where A cnventinal chi-square analysis is sufficient t reveal a statisticallysignificant (p <.01) effect f bth t and r n each a's perfrmance. The general nature f these effects is apparent in Fig. 4, where the Pc values frm Table 1 are presented graphically. The Pc values btained with a reference light are indicated by data pints, while brken lines indicate the Pc values attained withut a reference light. Values fr the t =.5 sec and t = 2 sec cnditins are presented n separate graphs. While Pc was generally larger fr the shrter t value, the reference light appeared t imprve perfrmance nly when r was small. When r waslarger than 8 r 10 deg, perfrmance with the reference light was essentially the same as perfrmance withut it. ThereticalAnalysis The data btained withut a reference light can be interpreted in terms f the mdel fr abslute mvement perceptin with an estimate f DA defined by Eq. 5. A similar estimate f discriminability will be emplyed in analyzing the data - f8 c.2-5 OBSERVER ONE. :r\ t '5sc. l t ~ Q, '8~ btained with a reference light (Eq, 15). This prcedure seems apprpriate fr tw reasns: First, the as may have made abslute judgments even when the reference light was presented, and secnd, it will be shwn that Eq, 15 seems an apprpriate apprximatin (k in Eq. 16 is apprximately ne) even when the 0 appears t have made a relative judgment. (The reader wh wishes t apply the mdel withut making this assumptinis referred t the sectin in Green & Swets, 1968, which discusses the "unequal variance" pdel f signal detectin.) Since DA and DR are bth defined as the difference between Z and ZI (Eqs. 5 and 15), the discriminability measure will simply be dented by D. This measure, fr each 0 in each experimental cnditin, is presented numerically in Table 2 and graphically in Fig. 5. First f all, cnsider the values f 0 btained withut a reference light. These measures are presented in the bttm rw (labeled "A" fr abslute) in Table 2, and as slid data pints at the far right f each graph in Fig. S. Previus wrk (e.g., Kinchla & Allan, 1969) has shwn that abslute judgments f this kind are cnsistent with the ne-parameter frm f the abslute mvement perceptin mdel. Accrdingly, an estimate f A was btained fr each a by selecting that value f A whichminimized the sum f squared deviatins between the values f 0 he attained withut a reference light, with t =.5 sec and t =2 sec, and thse defined by Eq. 6. These cba valueswere.120,.132, and.180 sq deg/sec fr Os 1, 2, and 3, respectively. The theretical values f D fr each <f;a value are indicated by hrizntal brken lines n each graph in Fig. 5; the upper line indicates the predicted D fr t =.5 sec and the lwer line fr t = 2 sec. It is clear that the superir discriminability withut a DeSERVER TWO OBSERVER THIlEE e.5sc l 1-5 lee 6~~6r~6t~ f, I! I! t t!,! I! l,.tjl...l.'-l, _-'-_L-_ t s 2 sec. ::,,- =--<>-- "'-"--'-'.-J-'_-'-_J...-_ 0/ 3 5 10 15 20,St 1-2... 8L:,2SOC. ~ ~.6~.6 _ T, ",!, 0135/0/520 01 3 5 10 15 20 These prprtins fr each a under each experimental cnditin are presented numerically in Table 1, with each prprtin based n 400 trials f data. r: prximity f reference light in degreesvisual angle Fig. 4. Values f Pc fr each 0 under each experimental cnditin bth with (data pints) and withut (brken lines) a referencelight. 168 Perceptin& Psychphysics, 1971, Vl. 9 (2A)
OBSERvER' OBSERVER 2 OBSERVER 3 "R' 004 >. - ep '20 A :0 0 15 R' ()12 15 c: 10,0 E 0 ~ 0 III "0.'-.5 0 0+..-...-.--_---_ R= 009 15 R 021 "R' 001 11 007 R epa '32 ~ ~.t 5 10 A epa' 1SO '~n:." -- _-0-_ '.2 +-----...l.--_, 3 5 10 15 20 A 0' 3 5 '0 20 A 0' 3 5 10 20.. r: prximity f reference light in degrees visual angle Fig. S. Estimated (data pints) and theretical values f DA and DR fr each 0 in each experimental cnditin. reference light at the larger (2 sec) t value is generally cnsistent with the abslute judgment mdel. Furthermre, the values f A are similar t thse btained in earlier studies f abslute-mvement perceptin.. The fact that a reference light imprved perfrmance nly when r was small is as apparent in Fig. 5 as it was in Fi~. 3. The chief advantage f cnsidering D rather than Pc is that the frmer is theretically independent f respnse bias (~), whereas Pc is nt. Hwever, Eq. 12 specifies the theretical relatin between m, t, and r (the independent variables) and b (the dependent variable) nly when the 0 was making a relative judgment. Itwas prpsed earlier in this paper that an 0 makes relative judgments nly when they are superir t abslute judgments, i.e., when DR> DA. Thus, the relative judgment mdel wuld apply nly in thse experimental cnditins where the 0 did better than culd be attribu ted t the abslute judgment prcess. While mre elabrate strategies fr identifying these cnditins culd be derived. the fllwing simple prcedure seemed suitable fr purpses f this paper: It was assumed that an 0 utilized relative judgments at all r Table 2 Values f D fr Each 0 in Each Experimental Cnditin Based n the Data in Table t and Eq.5 01 02 03 ---- t=.5 t= 2.0 t=.5 t= 2.0 t=.:5 t= 2.0 t 1.18.68 1.67.94.88.53 3.77.46.96.58 40.28 5.57.34.76.40.39.24 10.49.29.53.34.47.24 15.48.25.58.28.40.25 20.57.28.55.29.42.22 A.52.26.54.26.40.20 values lwer than the smallest r cnditin fr which b was smaller than that predicted by the abslute judgment mdel. Fr example, fr 0 I this included the r =1, 3, and 5 deg cnditins when t =.5 sec, and the r =1, 3, 5, and 10 deg cnditins when t =2 sec. Estimates f R and 7TR were then btained which minimized the sum f squared discrepancies between the D values fr thse seven cnditins and thse defined by Eq. 12. Estimates fr the ther tw Os were calculated in a similar fashin. The values f R fr Os I, 2, and 3, respectively, were.012,.009, and.021, while the crrespnding values f iii{ were.004,.001, and.007. The theretical values f DI{ defined by these estimates and Eq. 12 are shwn by the cntinuus curves n each graph in Fig. 5. T be cnsistent with the earlier arguments the data pints shuld lie n the slid curve s lng as it is abve the brken line and n the brken line therwise. It is clear frm inspectin f Fig. 5 that the theretical arguments prvide a plausible interpretatin f the data. Discriminability (0) seems cnsistent with the relative judgment prcess s lng as DI{ > DA' and cnsistent with the abslute judgment prcess when DR < D A. Fr example, cnsider the t =.5 cnditins fr 1. The relative judgment curve (slid line) drps belw the abslute judgment curve (brken line) at r = 4.3 deg (rc in Eq. lh). The i) values fr r < 4.3 deg arc cnsistent with the relative judgment curve, whereas the ther 6 values are generally cnsistent with the abslute judgment mdel (i.e.. cnsistent with perfrmance when n reference light was presented). Similar features can be seen in the data btained when t =2 sec. and in the data frm the ther tw Os. In each case, the data suggest a shift frm relative t abslute judgments when r exceeds r c ; rc- Eq. 16, is indicated by the pint at which the theretical discriminability functins fr abslute and relative judgments intersect in Fig. 5. Nte that a psitive relatin between rc and t fllws frm Eq. 16 when A ><PR, and A exceeded R fr all three Os. Thus the results suggest that the minimal prximity f reference light required t prduce relative judgments is psitively related tv t. Hwever, Eq. 16 implies that r c appraches a limiting value equal t cjja/</jr as t becmes very large. The largest limiting value f r c is suggested by the perfrmance f 0 2, whse theretical parameter estimates indicate a limit f 14.3 deg. Thus, even if t was much larger, all f the Os wuld be expected t have reverted t abslute judgments when the reference light was mre than abut 15 deg frm the test light. It shuld be emphasized that the preceding analysis is nt presented as an extensive empirical test f the relative judgment mdel. The mdel is applied here in a highly tentative fashin, bth t illustrate its applicatin and t prvide an explicit quantitative framewrk in which t discuss the data. Nevertheless, the tw mdels seem t prvide a reasnable interpretatin f the experimental results. DISCUSSION The experimental evidence appears cnsistent with a tw-prcess view f visual mvement perceptin. Os seem t make abslute judgments nt nly when an bject is seen in an therwise ttally hmgeneus visual field (Ganzfeld). but als when the field is nly lcally devid f reference pints (a "lcal Ganzfeld"). The minimal prximity f a reference pint Perceptin & Psychphysics, 1971, Vl. 9 (2A) 169
c ~ b ;;:.~ Q....J -e, 0 (0) T: time T: time Fig. 6. Alternatives t the type f stimulus patterns shwn in Fig. 2 which might als prduce relative judgments. which will prduce relative judgments is, apparently, never much mre than IS deg, althugh the pint must be even clser if the stimulus is nly briefly bserved (t < 2 f 3 sec). This minimal prximity, r c, is specified by Eq, 16. Furthermre, while the present experiment utilized discrete mvement patterns, the cnclusins shuld als apply t fixed-velcity cntinuus mvement since r c is independent f m; i.e., if an bject were mvingcntinuusly at a fixed velcity, v (equal t rn/t), the value f r e shuld depend nly n the perid f bservatin, 1. While the present analysis suggests that an a uses either abslute r relative judgments, it is pssible that he can utilize bth at the same time, and it wuld be premature t cnclude that the tw types f judgmental prcesses are mutually exclusive simply n the basis f the data presented here. Hwever, the simple mutually exclusive assumptin des seem t prvide a reasnably satisfactry interpretatin f these data. The phenmenn f induced mvement is a natural cnsequence f the tw theretical prcesses. If tw bjects are sufficiently clse, ne might clearly discern relative mvement while having little basis fr an abslute judgment. This wuld be the case whenever DR was large while D A was very small, fr example in the r = I deg cnditin in the present experiment. Hwever, here the as knew that the right-hand light in each display was always in the same psitin (Psitin r). Thus they culd always interpret a perceptin f relative mvement as indicating a displacement f the light n the left. If an a did nt knw which f the tw lights might be displaced, he culd be quite accurate in discriminating a change in the separatin between the tw lights (relative mvement) while essentially having t guess which light had actually been displaced (abslute mvement). Experiments f this srt have been c (b) b ~'[/ -e, 0 cnducted in this labratry and are in preparatin fr publicatin. While a detailed develpment f this wrk will nt be attempted here, it indicates that the clarity f relative mvement increases as the tw lights are brught clser tgether, almst independently f the O's ability t discern which light has actually mved. Hw relative mvement is interpreted in the absence f an unambiguus reference pint is particularly interesting. In general, it seems as if an a simply adpts ne pint as his reference and interprets all mvement in respect t it. Fr example, a cmmn prcedure fr demnstrating the illusin f induced mvement is t prject a small spt f light n a large screen. If the screen is surreptitiusly mved while the spt remains stabile, an a will ften reprt that it was the spt that mved; i.e., he crrectly perceives the relative mvement f the spt with respect t the screen, but mistakenly interprets this as mvement f the spt. This suggests that an a tends t chse the larger f tw bjects as a reference pint. Cnjectures f this srt wuld seem amenable t an experimental analysis based n the theretical apprach develped in this paper. Finally, it shuld be nted that there are sme bvius alternatives t the types f stimulus patterns represented in Fig. 2. Fr example, suppse the reference pint was presented nly during the perid frm Time t Time t, as shwn in Fig. 6a. An a culd either make a relative judgment by cmparing the separatin defined at Time 0, c - a, t that defined at Time t, c ~ b, r make an abslute judgment by cmparing the psitin defined prir t Time 0, a, with that defined after Time t, b. Similarly, mvement defined as in Fig. 6b culd. als prduce either an abslute r relative judgment. In any case, the theretical mdels seem apprpriate even if patterns f the type shwn in Fig. 6 (rather than Fig. 2) had been emplyed in the experiment. The stimulus parameters wuld still be m, t, and r, and there is n bvius reasn t suppse the theretical ( and 1T) parameters wuld differ. Thus, in the absence f further data, it seems reasnable t suppse that ur general cnclusins apply t mvement patterns f this srt as well. LENGTHPERCEPTION One culd interpret the preceding experiment as invlving judgments f length: The as were asked t cmpare a separatin ("length") presented at Time a with ne presented t sec later. Thus, the theretical arguments shuld als be relevant t a thery f length (r "size," r "distance") perceptin. Fr example, suppse a "length" was specified by a black line presented fr e sec in an therwise hmgeneus white visual field (Ganzfeld). If this line were remved and fllwed t sec later by an e-sec presentatin f a secnd line, an a culd be asked t decide whether the secnd line was the same length as the first r shrter. If the riginalline subtended r deg f visual angle while the secnd subtended r - m deg, the a's ability t perceive the m-deg change in length shuld be the same as his ability t perceive the m-deg displacement illustrated in Fig. 2. Nte that this argument assumes that the psitin f the secnd line is identical except fr the m-deg shrtening f ne end f the line. If the a knew which end f the line might be shrtened, he culd either cmpare the riginal and terminal psitins f that end f the line (an abslute judgment) r cmpare the ttal length f the line at Time at its length at Time t (a relative judgment). If he did nt knw which end f the line might be shrtened, he wuld have the same prblem as an 0 in the induced-mvement experiment described in the preceding sectin. He might perceive a shrtening f the line withut knwing which end had actually been abbreviated. Of curse, there are even mre cmplicated prcedures where bth ends f the line are abbreviated t prduce the ttal m deg f shrtening, r where the line is presented within a visual field cntaining alternative reference pints (such as the edge f a screen). In any case, the imprtance f such cnsideratins is suggested by the preceding experiment. With adequately cntrlled experimental cnditins, it shuld be pssible t interpret certain "length" judgments using the tw mdels presented in this paper. THE GENERAL ISSUE OF ABSOLUTE AND RELATIVE JUDGMENTS The theretical arguments develped here als seem relevant t the perceptin f ther-than-visual-psitin stimuli. Fur 170 Perceptin s. Psychphysics, 1971, Vl. 9 (2A)
example, suppse the stimulus dimensin, L, in Fig. 6a dented the amplitude f a pure tne. If the a were asked t cmpare Amplitudes a and b, his judgments might be mre r less independent f c, suggesting all abslute judgment prcess, r critically dependent n c, suggesting a relative judgment prcess. In ther wrds, an a might cmpare b with his "memry" f a at Time t (as specified by the abslute judgment mdel); r he might cmpare the difference, "shift in amplitude," defined at Time t, c - b, with his memry f the difference defined earlier at Time 0, c - a (as specified in the relative judgment mdel). In fact, the abslute mdel was riginally applied t an auditry amplitude task (Kinchla & Srnyzer, 1968), in which a and b (Fig. 6a) were clearly audible j,ooo-hz tnes and c was "silence" (zer amplitude). Cnditins in which the relative judgment mdel might be applicable wuld be thse in which c was just barely discriminable frm b, and where t was quite large, e.g., t > 5 sec. While n data explicitly bearing n this issue seem t be available in the literature, phenmena f this srt have been demnstrated in this authr's labratry and are the bject f current experimentatin. An a's ability t discriminate tw clearly audible, but barely discriminable, tnes presented 5 sec apart against a backgrund fsilence is markedly imprved if the backgrund amplitude is made similar t, but clearly discriminable frm, the ther tw tnes. It seems clear that discriminatin imprves because the a cmpares the difference between the first tne and the backgrund with the difference between the secnd tne and the backgrund. Nte that it seems t be the similarity ("prximity") f the backgrund r reference level t the ther tw amplitudes that is critical, just as it is in the case f relative mvement perceptin. It is easy t devise similar examples f this phenmenn invlving ther stimulus dimensins, e.g., brightness, hue, pitch, spatial psitin f a tactile stimulus, etc. In any case, the bject here is simply t suggest the mre general implicatins f the present analysis f visual mvement perceptin. If tw stimulus values seem t be cmpared independently f their relatin t any ther "reference" value, ne culd describe the prcess as an abslute judgment, if the cmparisn seems t depend n the difference between each f the tw stimulus values and sme ther "reference" value, the prcess culd be termed a relative judgment. The tw mdels presented here are ne way f representing a distinctin f this srt. REFERENCES DUNKER, K. Uber induzierte Bewegung (ein Beitrag zur Therie p t i s c h Whrgenmmener). Psychlgische Frschung, 1929, 12, 180-259. GREEN, D. M., & SWETS, J. A. Signal detectin thery and psychphysics. New Yrk: Wiley, 1966. KINCHLA. R. A., & ALLAN, L. G. A thery f visual mvement perceptin. Psychlgical Review. 1969,76,537 558. KINCHLA, R. A., & ALLAN, L. G. Visual mvement perceptin: A cmparisn f sensitivity t vertical and hrizntal mvement. Perceptin & Psychphysics, 1970, 8,399-405. KINCHLA, R. A., & SMYZER, F. A. A diffusin mdel f perceptual memry. Perceptin & Psychphysics, 1967, 2, 219-229. (Accepted lrpublicatin July 6, 1970.) Perceptin & Psychphysics, \97\, Vl. 9 (2A) 171