Pereption & Psyhophysis 2000,62 (7),13211331 Late influenes on pereptual grouping: Illusory figures STEPHENE. PALMER and ROLFNELSON University ofcalifornia, Berkeley, California Two experiments demonstrate that grouping an be strongly influened by the presene of figures defined by illusory ontours. Retangular arrays were onstruted in whih a entral olumn of figures ould group either with those on one side, on the basis of pereption of figures defined by illusory ontours, or with those on the otherside, on the basis of physially present induing elements. In all displays, subjets grouped aording to the illusory figures signifiantly more often than for ontrol displays that ontained the same induing elements, but rearranged so that illusory ontours were degraded or eliminated. A seond experiment showed that in objetively defined grouping tasks, subjets grouped faster by illusory figures than by induing elements. These results indiate that grouping an our after illusory ontours have been pereived. In 1923, Max Wertheimer alled attention to one ofthe fundamental problems of visual pereption: How does the visual system organize the omplex array oflight striking the retina into the oherent spatial array of objets that we experiene when we view the world? Although he did not by any means solve this omplex and diffiult problem, whih persists to this day, he did make substantial inroads by identifying a number of stimulusdriven priniples ofgrouping. These are the wellknown "laws" ofpereptual grouping (e.g., proximity, similarity, good ontinuation, and ommon fate) that are disussed in virtually all introdutory textbooks. Other priniples of grouping have sine been added to this list, inluding ommon region (Palmer, 1992), element onnetedness (Palmer & Rok, 1994b), and synhrony (Palmer & Levitin, 2000), but Wertheimer's original artile has been the preeminent statement ofboth the problem and the nature of its solution for most of this entury. Reently, there has been interest in understanding how the mehanisms responsible for grouping fit within modern information proessing theories ofvision. Central to this task has been the attempt to speify where grouping operates along the temporal flow of visual proessing (e.g., Palmer, 1999; Palmer & Rok, 1994a, 1994b). Following Wertheimer's disussion, the standard assumption appears to have been that grouping proesses operate fairly early in visual proessing, within what would now be alled a 2D, imagebased representation. For example, Mart's (1982) influential theory ofvision plaed at least The preparation of this artile was supported by Grant 1RO 1 MH46141 from the National Institute of Mental Health to S.E.P. We thank Steven Yantis, Thomas Sanoki, and two anonymous reviewers for their helpful omments on an earlier draft of this artile. Correspondene should be addressed to S. E. Palmer, Psyhology Department, University of California, Berkeley, CA 947201650 (email: palmer@ogsi.berkeley.edu). some grouping operations right after the "raw primal sketh." He proposed that grouping proesses organized the edges, lines, blobs, and terminators ofthe raw primal sketh into the more global elements of the "full primal sketh." Beause both primal skethes are 2D imagebased representations that preede onstrution ofhigher level surfaebased and/or objetbased representations, grouping operates before the pereptionofdepth and olusion relations in Marr's theory. Other theorists who have addressed the issue of when grouping ours also plae it early, typially proposing that it ours before the operation of seletive attention (e.g., Kahneman & Henik, 1981; Neisser, 1967; Treisman, 1986). The rationale for this laim is that attention must selet among a set of unified objets or elements and that grouping is needed to arrive at suh objets or elements. Palmer and Rok (1994a, 1994b) hallenged the "earlyonly" view that all grouping ours at an early (i.e., 2D, preonstany) stage ofproessing. First, they ited Rok and Brosgole's (1964) demonstration that grouping an be strongly influened by binoularly pereived depth. In a dark room, subjets were shown flat retangular arrays ofluminous beads that were loser together vertially than horizontally when they were presented in the frontal plane. Under these onditions, all subjets saw them grouped vertially rather than horizontally beause of proximity. Then subjets saw the same arrays slanted in depth (i.e., rotated around a vertial axis) so that horizontal distanes were foreshortened. Subjets still reported seeing vertial olumns ofbeads, even when their retinal projetions were loser together horizontally than vertially. This result ourred only when subjets saw the displays with both eyes open, however, so that they pereived the array in stereosopi depth. With only one eye open, subjets saw the beads group horizontally at preisely the slant at whih the projeted distanes were smaller horizontally than vertially. Rok and Brosgole 1321 Copyright 2000 Psyhonomi Soiety, In.
1322 PALMER AND NELSON therefore onluded that the final pereption ofgrouping must take plae after depth pereption based on binoular disparity. A seond telling result ame from an experiment by Rok, Nijhawan, Palmer, and Tudor (1992), who addressed the analogous issue in the domain of ahromati olor pereption. They asked whether the important fator in grouping by olor similarity is the retinally measured luminanes of elements or their phenomenally pereived lightnesses after lightness onstany has been ahieved. As illustrated in Figure I, they used a ast shadow to deouple image luminane and pereived lightness. The ritial display was arefully onstruted so that the squares in the entral olumn ofthe array were idential in physial refletane to the squares on one side (i.e., they were made ofpaper that was the same shade of gray), but were seen under a shadow ast by an opaque vertial strip hanging nearby, so that their retinal luminane was idential to that of the darker squares on the other side. The results showed that grouping followed the preditions of the late (postonstany) grouping hypothesis: Similarity grouping was governed by the pereived lightnesses of the squares rather than by their retinal luminanes. The same result was obtained when the entral squares were displayed behind a transluent strip ofpiasti instead of in a ast shadow. Control onditions effetively ruled out an alternative explanation that retinalluminane ratios were responsible for the obtained results. More reently, Palmer, Neff, and Bek (1996) showed that grouping by shape similarity is affeted by olusion relations and visual ompletion phenomena. Using the same type ofdisplays as Rok et al. (1992), these investigators onstruted displays in whih halfirles in the entral olumn are generally pereived as whole irles partly oluded by a vertial strip, as shown in Figure 2. An early view ofgrouping predits that the entral elements will still be seen to group with the halfirles on the left beause both have the retinal shape ofa halfirle. A late view of grouping predits that they will group with the full irles on the right beause they are pereived as ompleted behind the oluding strip. The results showed a robust tendeny for the entral olumn of oluded figures to group with the full irles, indiating that grouping is strongly influened by similarity ofompleted shape rather than retinal shape. The purpose ofthe present study is to extend this line of inquiry about the lous of grouping by determining whether it is ompleted before or after the pereption of illusory figures, suh as the wellknown Kanisza triangle. Although the explanation of illusory figuresthat is, figures defined at least in part by zeroontrast ontours rather than real onesis ontroversial, one possibility is that they arise when the visual system enounters evidene that one surfae oludesanotherin plaes where there is no ontrast in luminane between the oluding surfae and the oluded one behind it (Rok & Anson, 1979). In the ase of the Kanisza triangle, people pereive the edges ofa white triangle not only where it partly oludes the three blak induing irles (via highontrast edges), but also where it oludes the white bakground between the blak irles (via zeroontrast edges). By this aount, the pereption ofillusory figures must arise at a level ofthe visual system after the spatial integrationof depth edges defined by olusion. (The interested reader is referred to Lesher, 1995, and Spillmann & Dresp, 1995, for reviews of the extensive literature on illusory ontours.) EXPERIMENT 1 SUbjetive Grouping Reports Refletane Mathed Luminane Mathed Figure I. The ritial display in an experiment on grouping and lightness onstany by Rok, Nijhawan, Palmer, and Tudor (1992). Subjets report seeing the middle olumn group to the left with refletanemathed figures rather than to the right with luminanemathed regions. (See text for further details.) The initial study employed the same type of subjetive grouping paradigm as Rok et al. (1992) and Palmer et al. (1996). In this ase, the entral olumn ofthe array should be grouped with the elements on one side if grouping is based on the pereption ofillusory ontours and figures, and on the other side ifit is based on the pereption of the ontours of the induing elements. Figure 3 illustrates the experimental stimuli. In eah ase, the entral olumn of the display an be grouped either to the left (with similar shapes defined by illusory ontours) or to the right (with similar shapes defined by the physial ontours of the induing elements). Two of the stimuli ontain edgeindued illusory ontours (Figures 3A and 3B) and the other two ontain lineindued illusory ontours (Figures 3C and 3D). Method Subjets. Twentyeight undergraduates from the University of California, Berkeley partiipated in the study. These students re
GROUPING BY ILLUSORY FIGURES 1323 Figure 2. The ritial display in an experiment on grouping and amodal ompletion by Palmer, Neff, and Bek (1996). Subjets report seeing the partly oluded middle olumn of retinal halfirles group to the right with the retinally omplete full irles rather than to the left with the retinally omplete halfirles. (See text for further details.) eived ourse redit for one ofseveral psyhology ourses. All were naive with respet to the experimental hypothesis, and all had normal or orretedtonormal vision. Materials. Stimuli were displayed on a l7in. AppleVision monitor via a Maintosh Power PC 7500. Subjets sat approximately 2 ft from the monitor. Stimuli were displayed via PsySop, a presentation programming language (Cohen, MaWhinney, Flatt, & Provost, 1993). Subjets first indiated their hoie ofgrouping by pressing one of two buttons on a button box. They then rated the strength of this grouping by entering a number (I = weak; 3 = strong) on the omputer keyboard. Stimuli and Proedure. The figures within eah display were arranged in retangular arrays. The subjets' primary task was always to deide whether the middle olumn of figures grouped to the left or to the right. The four experimental types ofarrays are shown in Figure 3. Eah figure within an array is onstruted ofphysially defined induing elements onfigured to produe lear pereptions of illusory figures. For example, in Figure 3A, the illusory figures are retangles (analogous to Kanisza triangles) that arise from onfigurations ofinduing elements onsisting ofnothed bakground ovals. The experimental arrays were onstruted so that grouping based on the illusory figures always onflited with that based on the induing elements; that is, if the illusory figures biased grouping to the left, the induing elements biased grouping to the right, or vie versa. In Figure 3A, for instane, the illusory retangles should bias grouping toward the left, whereas the orientation of the induing ovals should bias grouping toward the right. We did not expet that illusory ontours would be the sole influene on grouping performane, beause strong similarities among the induing elements are also present in all displays. To assess whether illusory ontours affet grouping, we onstruted ontrol displays that ontained the same induing elements, but differently arranged so that they eliminated or weakened the distintive illusory ontours. In Figures 4A and 48, the positions ofthe orner induing elements have been altered to weaken or destroy the pereption of illusory figures while leaving all of the induing elements otherwise intat. Although it is perhaps more diffiult to verify in Figures 4C and 4D without lose srutiny, these are likewise spa tially rearrangedversions offigures 3C and 3D that weaken the distintiveness of the illusory ontours. The rationale in both ases is that the influene ofillusory ontours on grouping an be measured by omparing the results of these ontrol stimuli in Figure 4 with the orresponding experimental displays in Figure 3. If grouping is influened by illusory ontours, subjets should be more likely to group the entral olumn with the same illusory figures (i.e., to the left) in Figure 3 than in Figure 4. The stimuli shown in Figures 5 and 6 were used as filler items to measure the strength of unambiguous grouping in similar stimuli based only on expliit, physially present ontours. In the ontouronly onditions (Figure 5), the illusory figures offigure 3 were made expliit and the induing elements were eliminated. In the elementonly onditions (Figure 6), arrays onsistingofjust the (ompleted) induing elements in Figure 3 were presented. Weassumed that in the absene of onflit, grouping would always our in the unambiguous diretion, but we wanted to hek this for stimuli similar to those in the experimental and ontrol onditions. These unambiguous stimuli also ensured that subjets would be attending to both global figures and induing elements on some trials during the experiment. In eah display, square brakets were positioned above and below the entral olumn indiating the olumn whose grouping subjets were to report. Subjets indiated the diretion ofgrouping (left or right) by pressing the orresponding button on a box that was labeled "left grouping" above the left button and "right grouping" above the right button. They were instruted to press a button as soon as they saw the entral olumn group one way or the other. Subjets were then to indiate the strength ofthe grouping they reported by pressing a numbered button (I = weak; 2 = medium; 3 = strong). If the subjet felt that he/she had aidentally pressed the wrong button on the button box, he/she ould press the "error key," whih nulled the response and aused the same trial to be retaken later. All stimuli remained on the monitor until a strength rating had been entered. After subjets had been read the instrutions, they were given eight pratie trials with stimuli unrelated to the ritial stimuli to familiarize them with the proedure and to give them an idea ofhow the rating sale was to be used. Eah subjet was reorded for 64 trials onsisting of four repliations for eah ondition shown in Figures 36. Results and Disussion The results for the baseline onditions (ontours only and elements only) were as expeted, with 99% overall grouping in the predited diretion. These data indiate that attention was paid to the task and that subjets reliably grouped with physiallypresentontours for the unambiguous stimuli we used. The results for the ambiguous experimental and ontrol trials were sored in two ways. First, we alulated the perentage oftrials on whih subjets reported grouping of the entral olumn with the illusory ontours (or its weakened analogue in the ontrol ondition) versus the induing elements. Seond, we alulated the average signed rating by soring the ratings onsistent with the illusory figures as positive numbers and those onsistent with the induing elements as negative numbers. Both methods gave essentially the same results. The perentages of trials on whih subjets reported grouping with the illusory ontours (or its weakened analogue in the ontrol ondition) versus the induing elements are shown below the experimental and ontrol stimuli in Figures 3 and 4. The ritial omparison is that
1324 PALMER AND NELSON f1f1.,., tjljt...... f1f1.., ljljt... 4..... f1f1..,... tjtj 4... flf1..,..., tjtj......t4..... 99% A 1% Jt.) 'I._.;.a.:tJt.) 'I._.;.a..:.:tJt.) 'I._.;.a 63% B 37% e 81% 19% 73% D 27% Figure 3. The ambiguous ritial displays used in Experiment 1. A and 8 show the ritial edgeindued illusory figures display, and C and D show the ritial lineindued illusory figures display. Numbers below eah display to the left and right indiate the perentage of trials on whih subjets reported that the entral olumn grouped with the olumns on its left and right side, respetively. between the perentage grouped in the diretion predited by similarity of illusory figures (i.e., to the left in Figure 3) versus the orresponding "srambled"versions in the ontrol onditions (i.e., to the left in Figure 4). In every ase, the perentage ofgrouping responses in the diretion biased by the illusory ontours was signifiantly greater than the orresponding perentage in the ontrol ondition [t(27) = 9.63,5.16, 10.24, and 13.00, for the retangles, frames, irles, and squares in Figures 3 and 4, respetively; p <.001 in eah ase]. Indeed, in all four ases, the pattern ofgrouping reversed for the ritial onditions: The majority of responses favored the similar illusory figures in the experimental onditions, but favored the similar induing elements in the ontrol onditions. These data thus indiate that illusory ontours strongly influene pereived grouping. The same pattern was found for the rating data [t(27) = 11.36,5.56, 11.70, and 13.27, for the retangles, frames, irles, and squares in Figures 3 and 4, respetively; p <.00 I in eah ase]. The results thus strongly support the hypothesis that grouping is influened by illusory figures. Indeed, illusory figures appear to dominate subjetive grouping reports with our experimental task and stimuli. The key finding is that removing or weakening the illusory ontours of the displays in Figure 3 deisively reversed the pattern of responses.
GROUPING BY ILLUSORY FIGURES 1325,t,t... I:I,.: 1,11,1... _.. L;.:,t,t... 1,11,1..._.. 1:1,.e,t,t... L;.: 1,11,1... _..,t,t... I:t,...:. 1,11,1... _.. L;.:4! 43% A 57% 25% B 75% 1 ff ff,, ' B /# /#,, f ff ff, 1 ff,, B f 1 'l#, 8% 92% 4% 96% C Figure 4. The ambiguous ontrol displays used in Experiment 1. The induing elements in Figure 3 have been rearranged (see text) to weaken or eliminate the pereption of illusory figures. Numbers below eah display to the left and right indiate the perentage of trials on whih subjets reported that the entral olumn grouped with the olumns on its left and right side, respetively. D EXPERIMENT 2 Speeded Performane ofgrouping Experiment 1 shows that illusory figures an dominate grouping in a subjetive report paradigm in whih there is no orret answer and subjets are able to view the figures for as long as they want. In Experiment 2, we asked whether this dominane would also be found for objetive measures in a speeded performane task. In Experiment 2, subjets had to perform two different, objetively defined grouping tasks, one based on illusory figures and the other based on induing elements. In the figuredireted bloks ofthe experiment, subjets were required to indiate whether the entral olumn grouped with the left or right side of the display speifially with respet to the illusory figures present, independent of the nature of the induing elements. In the elementdireted bloks, they were required to indiate the diretion ofgrouping with respet to the induing elements, independent ofthe illusory figures. We measured how quikly and aurately they were able to perform these two tasks. If subjets perform faster when they group aording to the illusory figures than when they group aording to the induing elements, then it is reasonable to onlude that the illusory figures dominate pereived organization even under speeded performane onditions.
1326 PALMER AND NELSON 99% A 1% 888CDCD 888CDCD 888CDCD 888CDCD 888CDCD 99% 1% 100% 98% B D 0% 2% Figure 5. The unambiguous figural displays used in Experiment 1. These displays show just the global figures from Figure 3 without the induing elements. Numbers below eah display to the left and right indiate the perentage of trials on whih subjets reported that the entral olumn grouped with the olumns on its left and right side, respetively. As a onverging operation, we also studied the effets ofinterferene between illusory figures and induing elements in this task. In Experiment 1, grouping by illusory figures always onflited with grouping by induing elements, but these fators an also be onsistentwith eah other. In Experiment 2, we inluded both onsistent and inonsistent onditions, as shown in Figure 7A and 7B, respetively, for just the retangle stimuli. In the elementdireted trials, the subjets' task was to indiate the grouping of the entral olumn aording to the nature ofthe induing elements; in the figuredireted trials, theirtask was to do so aording to the nature of the illusory figure. Ifillusory figures truly dominate grouping, then onsisteny should not matter in the figuredireted trials, but onsistent onditions should be faster than inonsistent ones in the elementdireted trials. We also inluded orrespondingdisplays in whih the figural ontours were physially present rather than illusory (Figures 7C and 7D) to determine how muh, ifat all, the absene ofphysial ontours matters for performane in these tasks. These ontours were added by inluding a thin blak line over the full extent ofall illusory ontours in every display. Method Subjets. Twentyfive undergraduates from the University of California, Berkeley partiipated in the study for partial ourse redit in one of several psyhology ourses. All were naive with respet to the experimental hypothesis, and all had normal or orretedtonormal vision. Materials. The omputer and assoiated equipment were the same as in Experiment 1. Stimuli and Proedure. Thirtytwo stimulus arrays were onstruted by the orthogonal ombination of the following four fators: the four stimulus types (Figures 3A3D), the status ofthe figural ontours (illusory or expliit), the side toward whih the figure grouped (left or right), and the side toward whih the induing elements grouped (left or right). Eah stimulus array was presented in two kinds of trials. In elementdireted trials, subjets were instruted to deter
100% A 0% 98% 2% GROUPING BY ILLUSORY FIGURES 1327......".............. 99% B 1% 97% o 3% Figure 6. The unambiguous element displays used in Experiment 1. These displays show just the induing elements from Figure 3 without any illusory figures. Numbers below eah display to the left and right indiate the perentage of trials on whih subjets reported that the entral olumn grouped with the olumns on its left and right side, respetively. mine the side toward whih the entral olumn grouped aording to similarity of the induing elements. In figuredireted trials, subjets were instruted to determine the side toward whih the entral olumn grouped aording to similarity of the illusory figures or the orresponding expliit figures in the ase ofexpliit ontour stimuli. The displays were presented in groups ofeight bloks, one figuredireted and one elementdireted blok for eah ofthe four stimulus types. In the figuredireted bloks, the nature ofthe illusory ontour was explained with the aid of an expliit piture. In these figural bloks, subjets were instruted always to group aording to the illusory or expliit figural ontours and to ignore the induing elements. In the elementdireted bloks, subjets were instruted always to group aording to the induing elements and to ignore the illusory or expliit figures. Subjets were instruted to make their responses as quikly as possible while keeping their error rate reasonably low. (Feedbak was given by sounding a buzzer when subjets made an inorret response.) Sine orret and inorret responses were well defined for eah trial, errortrials were disarded and retaken later in the experiment. Only response times on orret trials were analyzed. Eah subjet was presented with a total of320 trials in a sixway fatorial design: 5 repetitions X 4 stimulus types (Figures 3A3D) X 2 figural types (illusory or expliit) X 2 relations between figures and induers (onfliting or onsistent) X 2 grouping tasks (elementdireted or figuredireted) X 2 responses (left or right). Results and Disussion The data from 3 subjets were disarded beause their error rates were greater than 10% and/or their response times were more than 3 SD above the group mean. The average error rate for the remaining 22 subjets was 3.4%.
1328 PALMER AND NELSON CJ) Q) I.. 0) u, C" O CJ) :::J Consistent...f'fl '''4.4.'''lJlJ...f'f' 4... 4...4...lJlJ...rlf'..... 4.4..."JtJ...,f'rl...lJlJ A Inonsistent fa., fa.,...,...........t.."'''''''' fa., fa.,..... 4.... fa., (/II".......4...t....,.,..... 'fiij4.'"... B CJ) :::J 0) u:::... :2 0 x W tjootltl 00000 tjoodtl OOOOD Figure 7. Examples of the stimulus displays used in Experiment 2. Global figures were defined either by illusory or expliit ontours and defined a grouping struture that was either onsistent or inonsistent with the loal induing elements. The example shown orresponds to Figure 3A in Experiment 1, but orresponding versions of Figures 38, 3C, and 3D were also used. The average times for orretresponses ofthese subjets were omputed and analyzed statistially. The primary data of interest are plotted in Figure 8, averaged over subjets, repetitions, responses, and stimuli within the edge and lineindued types. Subjets performed the figuredireted task (irles) faster than the elementdireted task (squares) [t(1,21) = 8.26,p<.001]. This was true for both the edge and lineindued figures [t(21) = 7.96, 6.43,ps <.001, respetively] and for both expliit figures (solid lines) and illusory figures (dashed lines) [t(2l) = 8.62, 8.63,ps <.001, respetively]. These fats are onsistent with the hypothesis that grouping by figures was pereptually more salient than grouping by elements, even when the figures were illusory rather than real. The data also show that subjets responded faster overall to the displays in whih the figural and element groupings were onsistent than when they were inonsistent [t(21) = 7.05,p <.001]. However, this differene was muh greater when subjets were performing the element task [t(21) = 7.62, 5.73,ps <.001, for edge and lineindued stimuli, respetively] than when they were performing the figural task [t(21) = 3.15,3.91,p <.01]. This pattern of results is also onsistent with the hypothesis that grouping by figures was pereptuallymore salient than grouping by elements, beause onfliting figural grouping slowed performane in the element grouping task, but onfliting element grouping did not slow performane in the figural grouping task nearly as muh [t(21) = 5.38, 2.10,ps <.001,.05, for edge and
GROUPING BY ILLUSORY FIGURES 1329. A. EDGEINDUCED FIGURES j Q) 1200 w E,. ', :.:::I!!t Element 1100.' direted Q) E 1000 i= C " ' Q) 900 w 0 800 direted 0 w Q) a: 700.==.e Figure Consistent Confliting o Q) w E Q) E i= Q) w o0 W Q) a: 1400 1300 1200 1100 1000 900 800 700 B. LINEINDUCED FIGURES e _e 00 Figuredireted Elementdireted Illusory Figures Expliit Figures Consistent Consisteny Condition Confliting Figure 8. The results of Experiment 2. Response times to report the required grouping of the entral olumn of displays in figuredireted and elementdireted tasks are plotted for global figures defined by expliit and illusory ontours under onditions in whih their grouping is onsistent with or onflits with that based on the induing elements. lineindued figures, respetively]. Interestingly, this pattern held regardless ofwhether the ontours ofthe figures were illusory or expliit, even though expliit ontours were responded to overall slightly faster than illusory ones [t(21) = 3.88,p <.01). The qualitative pattern ofresults desribed above held for both edge and lineinduedstimulustypes, as shown in Figure 8, although the magnitude of the different effets varied somewhat between them. The main differene seems to be that the edgeindued stimuli showed a smaller differene between figure and elements tasks than the lineindued stimuli did [t(21) = 3.66,p <.01). This differene may be due to the relatively lower visibility ofthe induing line elements in the lineindued stimuli than the induing edges in the edgeindued stimuli. It may also be due to the relative disriminability ofthe differenes between the figures and induing elements, as we will suggest in the General Disussion. These findings are largely onsistent with the hypothesis that grouping by illusory figures dominates grouping by induing elements in these stimuli. First, grouping based on illusoryfigures was muh faster than that based
1330 PALMER AND NELSON "', tttt r 4 4.. "', ttttr 4.4.. ttttr 4.4 "&,.. ttttr 4.4 "',.. "', ttttr 4.4.. Figure 9. An example in whih grouping by induing elements dominates grouping by illusory figures. This display is qualitatively the same as Figure 3A exept that the differene in aspet ratios of the induing elements has been inreased, whereas that of the illusory retangles has been dereased. on induing elements for both edge and lineindued displays. Seond, there was more interferene from inonsistent figural grouping when subjets were direted to group aording to the induing elements than there was from inonsistent element grouping when subjets were direted to group aording to illusory figures. This pattern learly shows that grouping by illusory figures was stronger than grouping by induing elements in these stimulus displays. Another result ofinterest is that, at least for the edgeindued figures, there was virtually no differene in response times between the expliit and the illusory figures. This finding suggests that pereptual grouping is based on a representation that is largely indifferent to whether pereived ontours are expliit or illusory, at least for ertain types of displays. GENERAL DISCUSSION The results of both experiments support the onlusion that grouping is strongly influenedby illusory ontours. Indeed, illusory figures appear to dominate both subjetive grouping reports (Experiment 1) and speeded performane measures (Experiment 2), at least with our experimental stimuli and tasks. We do not laim that this dominane is present in all suh displays beause it learly depends on the relative disriminability of the differenes between the illusory figures versus those between the induing elements. Figure 9 shows an example ofa display that is qualitatively the same as that in Figure 3A, yet illustrates that induing elements an sometimes dominate illusory figures in grouping. The reversed dominane results from reduing the differene in the aspet ratios between the two shapes ofillusory retangles in Figure 3A and inreasing the differene in aspet ratios between the two shapes of induing elements. This makes the orientational differenes between the induing elements more pronouned than those between the illusory figures. The result is that grouping is now dominated by the induing elements rather than by the illusory ontours. Does the existene of displays like the one in Figure 9 invalidate the onlusion drawn from the present data that grouping an our after the pereption of illusory ontours? We argue that it does not, for at least two reasons. First, we do not laim to have shown that grouping annot our before the pereption ofillusory ontours, but only that it an (and does) our afterward in at least some ases. This onlusion is required by the existene of any displays in whih grouping by illusory figures dominates that by induing elements. Figure 3 shows four suh displays, as unequivoally indiated by the results of Experiments 1 and 2. Seond, we ontend that the dominane of grouping aording to the induing elements in Figure 9 does not neessarily support the preillusoryontours hypothesis that pereption ofgrouping in these ases is based on a representation of the stimulus before illusory ontours have been proessed. Rather, it is equally ompatible with the hypothesis that grouping ours after illusory ontours are pereived. Ifthe "late" representation on whih grouping operates inludes both the illusory figures and the ompleted elements that they partly over, the ambiguity between elementbased and illusoryfigurebased grouping might arise simply from ompetition between the onfliting organizations for the illusory figures and the ompleted elements they over. No grouping prior to the onstrution of illusory ontours and figures needs to be assumed. The results of Experiment 2 appear to support the postillusoryfigures hypothesis that grouping in all our displays ours after the pereption ofillusory ontours. The argument goes like this. The alternative to the postillusoryfigures aount just desribed is one in whih grouping by elements is based on a preillusoryfigures representation and grouping by figures is based on a postillusoryfigures representation. But this hypothesis predits that grouping by induing elements should be faster than grouping by illusory figures beause the preillusoryontours representation must logially ome first. The results of Experiment 2 show that this is not true: Grouping by illusory figures is faster. It therefore seems likely that grouping by both illusory figures and induing elements ours after surfaes and olusion relations have been represented, at least for these displays. Some readers may objet to our haraterization of representations that inlude illusory ontours as "late," partiularlyin light ofthe findings by von der Heydt and Peterhans (1989; Peterhans & von der Heydt, 1989) that ells in area V2 ofmonkey ortex respond to the presene ofillusory ontours. Our distintion is logial ratherthan
GROUPING BY ILLUSORY FIGURES 1331 physiologial, however, and does not make ontat with anatomial loation. We laim only that grouping is "late" with respet to the proesses that support pereption of illusory ontours and illusory figures, wherever they may our in the visual nervous system. Ifthey our in V2, then at least some proessing in V2 is "late" by our definition, even ifv2 seems relatively "early" by anatomial riteria. In defense ofour view, we note the following two possibilities that bear on the "lateness" ofvon der Heydt and Peterhans's interpretation of their results: (1) Proessing ofillusory ontours and figures may begin in V2, but may not be ompleted until some later stage of proessing is reahed, and (2) ells in V2 may respond to illusory ontours in part due to feedbak from higher visual areas that inlude a great deal offurther proessing. In either ase, finding ells responsive to illusory ontours in V2 does not indiate that pereption ofillusory ontours orresponds to the initial ativation ofsuh ells, and this is the only interpretation under whih a good ase an be made for an "early" view ofillusory ontour pereption. The results of the present experiments are thus onsistent with the findings of Palmer et al. (1996), Rok et al. (1992), and Rok and Brosgole (1964) that grouping does not operate exlusively on an early, 2D, imagebased representation, but also on some later representation that inludes pereived threedimensional spae, lightness onstany, ompleted shape, and illusory ontours. This onlusion does not warrant the stronger inferene that grouping ours only after these surfaebased representations have been onstruted. It is quite possible that grouping ours throughout visual proessing as a bootstrapping proess, being ontinually revised as more sophistiated and veridial representations evolve within the visual system. Imagebased representations (e.g., Marr's, 1982, primal skethes) may be organized by some very basi set ofpriniples, suh as uniform onnetedness (Palmer & Rok, 1994b) and 2D versions of grouping fators like proximity, good ontinuation, similarity, and ommon fate. These rude organizations may then assist the onstrution of a representation of surfaes oriented in depth (e.g., Marr & Nishihara's, 1978, 2.5D sketh or Barrow & Tennenbaum's, 1978, intrinsi images) that enorporate the various onstanies, depth relations, and figural ompletions. The result then may require signifiant revisions in organization, espeially when the newly derived intrinsi properties ofthe surfaes ditate alternative groupings. This new organization an then be used in onstruting higher level representations of3d volumes and/or objet ategories, whih may in turn produe further reorganizations. 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