Research Methods PSYC 512
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Available online at www5ciencedirectcom scENcEDnecT Vision Research 44 2004 2505 2513 Vision Research wwwelseviercomlocatevisres Effect of background motion on the perceived shape of a 3D object Huiying Zhong Myron L Braunstein Department of Cognitive Sciences University of California Irvine CA 92697 5100 USA Received 28 October 2003 received in revised form 5 May 2004 Abstract The effect of the speed of a background surface on the judged shape of a moving object was investigated in four experiments Observers judged the magnitude of a concave dihedral angle translating or rotating against a planar background Judged angle mag nitude decreased indicating an increase in perceived depth with increasing background speed until the background speed reached the speed of the front edge of the angle Judged angle magnitude then increased with background speed until the difference between the background and front edge speed was large A model that was previously proposed to account for angle magnitude judgments from translations and rotations is extended to displays with a moving background 2004 Elsevier Ltd All rights reserved Keywords Three dimensional Motion parallax Structure from motion Shape 1 Introduction The human visual system can construct a 3D inter pretation of a scene from 2D retinal images using motion information Rogers and Graham 1979 dem onstrated that object shape and relative depth can be recovered from the motion parallax produced by per spective views of horizontal translations generated either by selfmotion or object motion Wallach and O Connell 1953 showed that 3D shape can be recov ered from shadow projections of objects rotated in depth They called this the kinetic depth effect and it is often referred to as quotstructurefrommotion Ull man 1979 Although retrieving 3D information from motion in 2D images is an illposed problem our visual system seems to be able to resolve the ambiguities by applying constraints For example according to the rigidity principle motion in a 2D image is interpreted as the projection of rigid motion in 3D whenever possi ble Ullman 1979 For a recent review of motion par Corresponding author E mail address mlbraunsorionoacuciedu ML Braunstein 0042 6989l see front matter 2004 Elsevier Ltd All rights reserved doi101016jvisres200405012 allax and structurefrommotion see Howard amp Rogers 2002 Most of the previous research on the recovery of ob ject shape from motion parallax and structurefrom motion has focused on the recovery of the 3D structure of isolated objects or surfaces In a typical 3D scene however there may be several moving objects and inter actions between the motions of these objects and sur faces may affect the judged shape of an object in the scene This is expected because the perceived 2D speed of a surface is affected by the speed of a surrounding sur face For example Duncker 1929 Loomis and Nakay ama 1973 and Tynan and Sekuler 1975 found effects of a moving surround on perceived target speed and Whitney and Cavanagh 2002 found effects of a moving surround on perceived target location Norman Nor man Todd and Lindsey 1996 using a 2D display with a circular disk as a target and a surrounding annu lus as the background found that the perceived target speed was a Ushaped function of the background speed The visual processing of the 2D speeds in an im age that form the basis for the perception of 3D shape from motion parallax or structurefrommotion may be affected by background speed in a similar manner 2506 H Zhang ML Braunstein Vision Research 44 2004 2505 2513 The object that we used to study the effect of back ground speed on judgments of 3D shape was a dihedral angle This object was selected because a number of pre vious studies eg Braunstein amp Andersen 1981 Braun stein Liter amp Tittle 1993 Liter amp Braunstein 1998 Todd amp Norman 1995 2003 Todd amp Perotti 1999 have examined the effects of the relative velocities within the dihedral angle on judgments of its shape The dihe dral angle consisted of two planar facets slanted in depth Fig 1 The intersection of the two planar facets is the dihedral edge In a convex dihedral angle the dihedral edge is the edge closest to the observer In a concave angle the dihedral edge is farthest from the observer In the present experiments the simulated dihedral angle was concave for perspective projections orthographic projections will be discussed later The two edges clos est to the observer will be referred to as the front edges The magnitude of the dihedral angle is determined by measuring the interior angle between the two slanted planes The formula for computing the magnitude of a dihe dral angle from image parameters depends on the type of motion and projection When a dihedral angle is translating under perspective projection the angle mag Front Edge Dihcdral Edge Front Edge Background Angle 5quot Background Fig 1 A schematic dihedral angle top panel and a horizontal dihedral angle as displayed bottom panel The dashed lines in the bottom panel which show the positions of the front edges did not appear in the display The dihedral edge was midway between the front edges The arrows to the right of the display indicate the relative dot speeds for a display with a 1 s background speed a 25 s front edge speed and a 2 s dihedral edge speed nitude t is a function of the ratio of the maximum to minimum velocities and the visual angle measured from the upper front edge to the lower front edge Braunstein et al 1993 1 ac t 2tan 1ltr 1tan 1 where r is the ratio of the maximum to minimum veloc ity for a concave angle and at is the visual angle For a dihedral angle rotating under orthographic projection the angle magnitude r is a function of the difference between the maximum and minimum velocities and the angle through which the dihedral angle has rotated Braunstein et al 1993 7 1 hsin6 miztan 2d lt2 where h is the projected height of the dihedral angle in the image 6 is the rotation angle and d is the difference between the maximum and minimum velocities Judg ments of angle magnitude by human observers seem to be related to these geometrical derivations The judged angle magnitude decreased with an increase in the velo city ratio for a dihedral angle shown translating under perspective projection For an angle shown rotating under orthographic projection however judged angle magnitude was a function of the difference between the velocities Braunstein et al 1993 The perceived magnitude of the dihedral angle is usu ally overestimated the depth is underestimated when the angle translates under perspective projection and underestimated the depth is overestimated when the angle rotates under orthographic projection Braunstein et al 1993 Braunstein et al 1993 proposed a com promise hypothesis to account for these results The compromise hypothesis states that both perceived translation and perceived rotation contribute to the angle size judgments whether the angle is actually trans lating or rotating he purpose of the present study was to determine the relationship between the velocity of a background plane and the judged shape of a dihedral angle We also examined whether the compromise hypothesis could be modi ed to account for the effect of a background plane There are four principal experiments described in this paper In the rst experiment the stimulus was a horizontal dihedral angle translating horizontally against a background that was either stationary or was translating horizontally in the same direction as the angle In the second experiment the angle and the back ground both translated horizontally but in opposite directions In the third experiment the dihedral angle was vertical and both the angle and background trans lated vertically In the fourth experiment a horizontal dihedral angle was rotated back and forth with the H Zhang ML Braurtstein Visiart Research 44 2004 2505 2513 2507 background translating horizontally in phase with the rotation In a control experiment a horizontal dihedral angle translated horizontally with no background pre sent 2 General methods 21 Stimuli The stimuli were computergenerated random dot patterns simulating horizontally or vertically oriented dihedral angles with a frontalparallel planar back ground The horizontally oriented dihedral angles were centered vertically against the background and the verti cally oriented dihedral angles were centered horizon tally The background was thus above and below the dihedral angle when the angle was horizontal and to the left and right of the dihedral angle when the angle was vertical The dihedral angle and the background plane each contained 500 bright green dots The dot density was uniform in the image and constant over time except for the rotating dihedral angle in Experi ment 3 Dot density in the image of the rotating angle increased by a maximum of 15 during rotation but remained uniform At a viewing distance of 114 m the display subtended a visual angle of lO gtltlO with the dihedral angle subtending 10 X5 when it was hori zontal and 5 X10 when it was vertical The dihedral angle magnitudes calculated for the perspective projec tions Experiments 1 3 and 5 are based on the ratio of the front edge speed to the dihedral edge speed and a visual angle of 5 for the entire dihedral angle upper front edge to lower front edge for a horizontally oriented angle using Eq I 22 Apparatus The stimuli were presented on a l9in 48 cm calli graphic display scope with a Tucker Davis sixchannel digitaltoanalog interface controlled by a Dell Pentium III computer The positioning accuracy of the dots was l6000gtltl6000 The frame rate was 30 Hz 23 Procedure Observers viewed the stimuli monocularly through a viewing tube and square mask The mask was located 175 cm from the eye and limited the field of view to a 10 X10 20 cmgtlt20 cm area on the display scope The dihedral angle always extended beyond the field of view so that its leading and trailing edges were not visi ble The viewing distance was 114 m The observer s task was to adjust a crosssection of the angle on a mon itor positioned at a 90 angle to the display scope using a mouse so that it matched the perceived magnitude of Fig 2 The response the dihedral angle in the stimulus Fig 2 The experi ment was selfpaced When the observer was satis ed with her adjustment she pushed the middle button to advance to the next trial 24 Statistical analyses We used analysis of variance for withinsubjects de signs to analyze the data In order to compensate for the violation of the homogeneity assumption Box s e adjustment Geisser Greenhouse adjusted procedure was used for factors with more than two levels as recom mended by Keppel 1991 and Mexwell and Delaney 1990 The results are reported with the unadjusted de grees of freedom the adjustment magnitude e and the corrected p values 3 Experiment 1 Experiment I was designed to examine the effect of the speed of the background plane on the judged magni tude of horizontally oriented dihedral angles when the background and the dihedral angle translated horizon tally in the same direction In Experiment la a set of coarser levels of background speed was investigated to obtain the general characteristics of the effect of back ground speed on angle size judgments In Experiment lb a set of finer levels of background speed close to the speed of the dihedral angle was employed to exam ine more closely the effect of background speed on angle size judgments when the speeds of the angle and back ground were similar 3 Stimuli The stimuli were perspective projections of a horizon tal dihedral angle translating horizontally against a frontal plane that was either stationary or translating in the same direction as the angle 32 Design Three variables were examined the background speed the ratio of the angle s front edge speed to its 2508 H Zheng ML Braunstein Vision Research 44 2004 2505 2513 dihedral edge speed and the direction of translation left or right The experiment was run in two parts 1a and lb There were six levels of background speed in Exper iment 1a 00 10 20 40 60 and 80 s and ve levels of background speed in Experiment lb 20 225 25 40 and 50 s There were two velocity ratios 1125 and 125 When presented with a visual angle separation of 5 between the top and bottom front edges ie a sep aration of 25 between one of the front edges and the dihedral edge these two velocity ratios correspond to dihedral angle magnitudes of 385 and 198 respec tively With the dihedral edge translating at 2 s the two velocity ratios corresponded to front edges speeds of 225 and 25 s see Fig 3 Overall there were 6gtlt2gtlt2 conditions in Experiment 1a and 5gtlt2gtlt2 condi tions in Experiment 1b There were ve trials for each condition In each experiment the trials were grouped into two blocks preceded by a practice block consisting of ve trials of each combination of background speed and dihedral angle size The order of the trials was rand omized 33 Observers Six observers participated in this experiment ZB CF HZ RN SL and DS HZ is the rst author and ZB CF RN were familiar with the purpose of the research SL and DS were naive to the purpose of the study 34 Results The angle magnitude was always overestimated indi cating that the depth was underestimated This is con sistent with previous studies of size judgments of an isolated translating dihedral angle Braunstein et al 1993 Separate threeway ANOVAs 6 or 5 background speedsgtlt2 angle sizesgtlt2 translation directions were con ducted for Experiments 1a and 1b The main effect of background speed was signi cant in both experiments F5256629 e 0331 plt001 in Experiment 1a and F4205114 e 0504 plt005 in Experiment 1b The main effect of angle size was also signi cant in both experiments F15 5213 plt001 in Experiment 1a and F153010 plt001 in Experiment 1b The order of the angle magnitude was preserved in the judg ments judgments for the larger simulated angle were larger than the judgments for the smaller simulated angle for all background speed conditions The main ef 225 sec 2osec lt 225 sec 39 angle 25 sec 20sec lt 25 sec 20 angle Fig 3 The front edge speed for different angles when the dihedral edge speed was 2 s 1 0390 Phase 1 Phase III Phase Ill 9 CI 39 4 GD 1 1 Judged angler size 3 U E in D 4e 1 20 225 125 40 50 60 80 Background speed 03 00 10 Fig 4 Average results in Experiment I The judged angle sizes when the background speed was 2 and 4 s are the averages from the two experiments For the 39 dihedral angle the mean judgments were 621 and 548 in Experiments la and lb respectively for the 2 s background speed and 897 and 799 for the 4 s background speed For the 20 angle the means judgments were 492 and 473 in Experiments la and lb respectively for the 2 s background speed and 590 and 546 for the 4 s background speed Error bars show 1 standard error fect of translation direction was not signi cant in either experiment The interaction between the angle size and background speed was signi cant in Experiment 1a F5257063 e 0474 plt001 There was a signi cant interaction between the angle size and translation direction F1513604 plt005 in Experiment 1b There were no other signi cant interactions in the two experiments The combined results of Experiments 1a and 1b are shown in Fig 4 The curve showing judged angle size as a function of background speed can be divided into three phases on the basis of the relationship between the background speed and the speed of the front edge of the angle In the rst phase the background speed is less than the front edge speed 225 s for the 385 angle and 25 s for the 198 angle The judged angle magnitude in this region decreased as the background speed increased In the second phase the background speed is equal to or greater than the front edge speed In this region judged angle size increased sharply with background speed In the third phase the background speed is much larger than the dihedral edge speed In this region the back ground speed no longer appears to affect the judged angle magnitude This seems to occur when the back ground speed exceeds 4 s 4 Experiment 2 In Experiment 1 there was a signi cant effect of back ground speed on the judged shape of the dihedral angle when both the target and background translated in the same direction In this experiment we investigated whether there was a similar effect when the background and angle translated in opposite directions H Zhang ML Braunstein Visian Research 44 2004 2505 2513 2509 m a Phase I Phase 11 Phase III C S 39 80 F 70 7 200 5 a a 2 39 a H H g 70 I39 20 g 0 i 2 g E I E gee 2 gso E g I agt j n 4 10 20 40 00 10 20 225 25 4 0 SD 60 SD Bachround speed quots Fig 5 Judged angle size as a function of background speed in Experiment 2 41 Stimuli and design The stimuli were similar to those in Experiment 1 ex cept that the angle and background translated in oppo site directions and only three background speeds were included 1 2 and 4 s The design was the same as in Experiment 1a except for the reduced number of back ground speeds 42 Observers The four knowledgeable observers who participated in Experiment 1 ZB CF HZ and RN participated in Experiment 2 43 Results and discussion A threeway ANOVA showed a signi cant main ef fect for angle size F1317524 plt001 There were no other signi cant main effects or interactions The lar ger angle was judged larger for all speed conditions The dihedral angle magnitude was always overestimated Fig 5 The background motion did not have a signif icant effect on the judged shape of the dihedral angle when the background and angle translated in opposite directions Angle magnitude judgments were consistent with judgments in the control experiment in which the angle translated at 2 s with no background Fig 8 5 Experiment 3 The purpose of this experiment was to determine whether the results for horizontal dihedral angles can be extended to vertical dihedral angles 5 Stimuli and design The stimuli were similar to those in Experiment 1 with the conditions in la and 1b combined except that Background speed s Fig 6 Results of Experiment 3 the dihedral angle was oriented vertically and the angle and background translated vertically The design was similar to that of Experiment 1 52 Observers The observers were the same as in Experiment 1 53 Results The results for vertical dihedral angles were very sim ilar to the results for horizontal dihedral angles Fig 6 The angle magnitude was always overestimated The order of the angle magnitude was preserved A three way ANOVA showed signi cant main effects for angle size F1514651 plt005 and background speed F8404666 amp0321 plt005 As in Experiment 1 the function relating judged angle size to background speed appears to divide into three phases with a de crease in judged angle size with increased background speed in the rst phase an increase in judged angle size with increased background speed in the second phase and a relatively at function in the third phase The main effect of translation direction was signi cant F1517837 plt001 Judged angle size was smaller and thus closer to the simulated size when the transla tion was downward than when it was upward This could be related to a downward motion preference N aito Kaneoke Osaka amp Kakigi 2000 WattamBell 2001 There were no signi cant interactions 6 Experiment 4 The purpose of this experiment was to deter mine whether the background speed exhibits the same effect on the perceived 3D shape of an object spec i ed by structurefrommotion In particular we wanted to determine whether the results for a translating dihedral angle could be extended to a rotating dihedral angle 2510 H Zhang ML Braurtstein Visiart Research 44 2004 2505 2513 61 Stimuli The stimuli were orthographic projections of hori zontal dihedral angles oscillating in depth about a verti cal axis Although orthographic projections do not occur in direct vision they are approximated when the viewing distance is very large relative to the depth within an object they allow us to isolate the effects of motion on perceived 3D structure that are not based on per spective The background was a frontal plane that was either stationary or translating horizontally in a cyclical motion in phase with the rotation of the angle There were nine background speeds 00 10 20 225 25 40 50 60 80 s The 3D rotation magnitude of the dihedral angle was i10 The dihedral edge was located at a simulated distance of 456 cm from the axis of rota tion This distance was chosen to match the projected front edge and dihedral edge speeds in the center of the dihedral angle to the projected speeds in the transla tion sequences in the previous experiments The 2D speed at the center of the dihedral edge was 2 s As in the preceding experiments the ratios of the front edge speed to the dihedral edge speed were 1125 and 125 These ratios corresponded to simulated angle magni tudes of 70 and 38 To keep the images of the rotating dihedral angles similar to those of the translating angle we matched the velocity ratios rather than the simulated angle magnitudes across experiments Matching the projected speeds and speed ratios to the previous experi ments resulted in simulated distances from the front edge to the axis of rotation of 528 cm for the 70 angle and 600 cm for the 38 angle The rotation was either clockwise or counterclockwise Although the rotation direction and the angle orientation is geometrically ambiguous in an orthographic rotation previous re search Braunstein et al 1993 has found that the when the dihedral edge is moving more slowly than the outer edges the angle is almost always perceived as concave relative to the observer s viewpoint 62 Design Overall there were 9 background speedsgtlt2 angle magnitudesgtlt2 initial motion directions conditions with ve trials for each condition The trials were grouped into two sessions by background speed with the two sessions run on separate days In the rst session the background speeds were the same as in Experiment la In the second session the background speeds were the same as in Experiment lb In each session the trials were grouped into two equal blocks The order of the trials was randomized For the knowledgeable observ ers a practice block of 24 trials was run prior to the rst session on the rst day For naive observers a practice block of 60 trials preceded the rst session The order of the trials was randomized On the second day nn Phase II Phase III Phase I 03 1 co 0 o 0 Judged angle size lt11 0 00 10 20 225 25 40750 60 80 Background speed 75 Fig 7 Results of Experiment 4 there were six practice trials prior to each block for all observers 63 Procedure The procedure was the same as in Experiment I 64 Observers The participants were the four knowledgeable observ ers who participated in all previous experiments ZB CF HZ RN and one naive subject SL who had par ticipated in Experiments 1 and 3 6 5 Results The results for rotating dihedral angles Fig 7 were similar to the results for translating dihedral angles ex cept that in some conditions the angle magnitude was underestimated whereas it was always overestimated in the rst experiment A threeway ANOVA showed signi cant main effects for angle size Fl466l9l p lt001 and background speed F832 5995 e 0308 lt005 As shown in Fig 7 these results also can be divided into three phases based on the relation ship between background speed and front edge speed The effect of rotation direction was not signi cant The interaction between the background speed and an gle size was signi cant F8325874 e 0289 p lt005 There were no other signi cant interactions 7 Control experiment In all of the previous experiments a dihedral angle moved against a translating background plane The pur pose of the control experiment was to compare these re sults to angle magnitude judgments for a dihedral angle translating under the same viewing condition without a background plane H Zhang ML Braunstein Visian Research 44 2004 2505 2513 2511 Phase I Phase II Phase III 3 7o 2 u 1 TEE g1 60 m 13 G g 50 E 3 00 10 20 225 25 40 60 8 0 Background speed 13 Fig 8 Judged angle size as a function of angle speed 71 Design The stimulus was a horizontal dihedral angle sub tending 10 X5 and translating at 5 levels of speed 1 2 4 6 8 s There were two simulated angle sizes 385 and 198quot The translation direction was either to wards the right or towards the left There were ve rep etitions for each condition 72 Participants There were three knowledgeable observers CF HZ and RN who had participated in the previous experi ments and an observer ML who was naive to the pur pose of the experiment and had no prior experience with the stimuli 73 Results The magnitude of the dihedral angle was overesti mated Fig 8 A threeway ANOVA indicated that there was a signi cant effect of simulated angle size F133963 plt001 with the larger angle judged to be larger The perceived angle size decreased signi cantly with an increase in angle speed F41211020 E0267 plt005 There were no other signi cant main effects or interactions The re sults were comparable to those obtained when the dihe dral angle was translating against a stationary background 8 Discussion The principal ndings in this set of experiments are the following 1 The perceived order of dihedral angle magnitude was preserved The smaller simulated angle was judged smaller in all conditions 2 The judged angle size was overestimated in all con ditions when the dihedral angle translated and underestimated for some of the conditions when the angle rotated 3 When the background and angle moved in the same direction there was a signi cant effect of back ground speed on the judged 3D shape of the angle The translation speed of a frontal plane in the back ground exerted a similar signi cant in uence on perceived shape for both translating and rotating dihedral angles Theoretically the slant of a plane can be computed from a perspective projection of a translation using the ratio of the maximum to minimum velocity and the vis ual angle subtended by the distance between the edges moving at these velocities The slant of a plane undergo ing rotation can be computed from an orthographic pro jection using the difference between the maximum and minimum velocity and the rotation angle However an gle size is typically overestimated with perspective trans lations and is sometimes underestimated with orthographic rotations These results are consistent with the compromise hypothesis Braunstein et al 1993 which states that even when a pure perspective transla tion or a pure orthographic rotation is simulated the perceived slant is based on a combination of the slants that would be computed from the velocity ratio velocity difference visual angle and perceived rotation for these two alternative motion projection combinations How ever the compromise hypothesis alone cannot account for the changing relationship between background speed and perceived angle magnitude that was found as the background speed approached and then exceeded the front edge speed of the dihedral angle We propose a model extending the compromise hypothesis to account for the background speed effect In this model when the background speed is less than the front edge speed Phase I the dihedral angle is seen moving against the background Under these conditions the velocities used by the visual system in computing the velocity ratio would not be the objective velocities of the dihedral edge and front edge but should be based on relative velocities between the background and the dihedral angle Dunc ker 1929 Loomis amp Nakayama 1973 Norman et al 1996 Tynan amp Sekuler 1975 For simplicity we used the difference between the objective velocities of the background and the dihedral angle in the model to esti mate the perceived velocities of the dihedral edge and of the front edges of the angle Subtracting a constant from the objective velocities increases the velocity ratio When the background speed is equal to or greater than the front edge speed Phase II the angle is no longer perceived as moving against the background In stead the background may be seen as adjacent to the front edge in depth When the background speed is the 2512 H Zhang ML Braunstein Visian Research 44 2004 2505 2513 same as the front edge speed a rigid relationship may be perceived between the background and the front edge As the background speed increases some of the velocity difference between the angle and the background would have to be processed as resulting from rotation of the angle in order to maintain the perception of a rigid rela tionship between the angle and the background This in creases the weight given to the rotation component in the compromise hypothesis As a result less depth is perceived and the judged angle magnitude increases When the background speed becomes much greater than the front edge speed Phase III the discrepancy between the ow fields of the target and the background is so great that the rigid perception cannot be main tained Therefore the background speed no longer in u ences the perceived angle magnitude Phase 111 We used the same basic model as Braunstein et al 1993 to fit the data jw t1W n 3 where j is the judged magnitude of the dihedral angle w is weight of the judged angle size from perspective trans lation t is the dihedral angle magnitude computed for translation and r is the dihedral angle magnitude com puted for rotation The computation of t and LL however differed from the previous model in the following ways A l V The velocity ratio used in t was computed from the edge velocities relative to the background rather than from the objective edge velocities 2 The rotation angle in r included an additional component 6V Thus 1 2tan 1 ri 1 tang 4 and r 2tan 1 h Sinltgzl 6m 5 where relative front edge speed 6 r 7 relative dihedral edge speed 7 lt h is the projected height of the dihedral angle d is the difference between the maximum and minimum veloci ties GC is a constant perceived rotation angle and 6Vk background speed front edge speed where k is a constant If 6Vlt0 then 6V0 1 For the smaller simulated angle the background speed of 225 s was between the dihedral edge speed 25 s and the front edge speed 2 s resulting in relative speeds for the front edge and background that were opposite in sign In this case a background speed of 2 s was used to compute the velocity ratio A Translating horizontal dihedral angle 90 3939 39 observed 80 39039 39 model I39 20 observed ll 20 model I 5 V 70 2 8 m 60 0 B U 50 W 3 40 0 1 2 225 25 4 Background speed s B Translating vertical dihedral angle 90 0 39 observed 80 390 39 model I 20 observed ll 20 model Judged Angle size 0 o 50 W 40 0 1 2 225 25 4 Background speed s C Rotating horizontal dihedral angle 90 039 70 observed 80 O 70 model I 38 observed U39 38 model Judged Angle size 0 o 0 1 2 225 25 4 Background speed s Fig 9 Comparison of the model to the observed results in three experiments In Phase I with the front edge speed faster than the background speed 6V is 0 In Phase II with the back ground speed equal to or greater than the front edge speed 6V is a linear function of the difference between the background speed and the front edge speed Fig 9 compares the model estimates to the observed judg ments These fits use three parameters w 6C and k for each of the two angle magnitudes The same para meters were used for all three experiments shown in Fig 9 The parameter values were 0282 3047 and 0236 for the smaller angle and 0323 2028 and 0878 for the larger angle The standard error of estimates H Zhong ML Braunstein Vision Research 44 2004 2505 2513 2513 for tting the six curves horizontal motion small angle horizontal motion large angle vertical motion small an gle vertical motion large angle rotation small angle rotation large angle were 284 ll6 432 184 429 and 121 respectively When the background plane and dihedral angle translated in opposite directions background speed did not signi cantly affect judged shape This may be re lated to the smoothness constraint in motion parallax When the difference in the velocity gradients is too large a motion parallax analysis based on rigidity is not ap plied across the entire con guration and multiple objects moving independently may be perceived eg Ono Steinbach 1990 Theoretically the slant of a plane moving rigidly can be recovered unambiguously under perspective projec tion from two distinct views in the presence of a second plane given the rst spatial derivatives of an optical ow eld Negahdaripour amp Lee 1992 Under ortho graphic projection the slant of a plane can be recovered from three views of two points with rigid planar motion Hoffman amp Flinchbaugh 1982 Our results demon strate however that information that is theoretically suf cient does not ensure a veridical shape judgment In stead perceived shape depended on factors unrelated to the information that speci ed the simulated shape This has implications for applying theoretical models that re cover shape from optic ow to human visual perception Acknowledgment We thank George J Andersen Zheng Bian Cary Feria and Rui Ni for helpful discussions This research was supported by NIH Grant lROlEY12437 References Braunstein M L amp Andersen G J 1981 Velocity gradients and relative depth perception Perception ampPsychophysics 29 145 155 Braunstein M L Liter J C amp Tittle J S 1993 Recovering three dimensional shape from perspective translations and orthographic rotation Journal of Experimental Psychology Human Perception and Performance 19 594 614 Duncker K 1929 Induced motion Psychologische forschung 12 180 259 Translated and extracted in WD Ellis Ed 1950 A source book of Gestalt psychology pp 161 172 London Routledge amp Kegan Paul Hoffman D D amp Flinchbaugh B 1982 The interpretation of biological motion Biological Cybernetics 42 197 204 Howard 1 amp Rogers B J 2002 Seeing in depth pp 411 445 Thornhill Ont I Porteous Keppel G 1991 Design and analysis a researcher s handbook pp 351 353 3rd ed Englewood Cliffs NJ Prentice Hal Liter J C amp Braunstein M L 1998 The relationship of vertical and horizontal velocity gradients in the perception of shape rotation and rigidity Journal ofExperimental Psychology Human Perception and Performance 24 1257 1272 Loomis J M amp Nakayama K 1973 A velocity analogue of brightness contrast Perception 2 425 428 Mexwell S E amp Delaney H D 1990 Designing experiments and analyzing data a model comparison perspective pp 475 476 Belmont CA Wadsworth Publishing Company Naito T Kaneoke Y Osaka N amp Kakigi R 2000 Asymmetry of the human visual eld in magnetic response to apparent motion Brain Research 865 221 226 Negahdaripour S amp Lee S 1992 Motion recovery from image quences using only rst order optical ow information Interna tional Journal of Computer Vision 9 163 184 Norman H F Norman J F Todd J T amp Lindsey D T 1996 Spatial interactions in perceived speed Perception 25 815 830 Ono H amp Steinbach M J 1990 Monocular stereopsis with and without head movement Perception amp Psychophysics 48 179 187 Rogers B amp Graham M E 1979 Motion parallax as an independent cue for depth perception Perception 8 125 134 Todd J T amp Norman J F 1995 The visual discrimination of relative surface orientation Perception 24 855 866 Todd J T amp Norman J F 2003 The visual perception of 3 D metric structure Perception amp Psychophysics 65 31 Todd J T amp Perotti V J 1999 The visual perception of surface orientation from optical ow Perception amp Psychophysics 61 1577 1589 Tynan P amp Sekuler R 1975 Simultaneous motion contrast velocity sensitivity and depth response Vision Research 15 1231 1238 Ullman S 1979 The interpretation ofvisualmotion Cambridge MA a sachusetts Inst of Technology Wallach H amp O Connell D N 1953 The kinetic depth effect Journal ofExperimental Psychology 45 205 217 Wattam Bell J 2001 The effect of contrast on vertical motion processing asymmetries in 11 week old infants Perception 30 159 166 Whitney D amp Cavanagh P 2002 Surrounding motion affects the perceived locations ofmoving stimuli Visual Cognition 9 139 152 VOL 63 No 3 MAY 1956 THE PSYCHOLOGICAL REVIEW OPERATIONISM AND THE CONCEPT OF PERCEPTION1 WENDELL R GARNER HAROLD W HAKE AND CHARLES W ERIKSEN The Johns Hopkins University The attitude of contemporary opera tionists toward perceptual research has been well characterized recently by All port He has described their attitude by stating that a perception can be re garded as nothing more nor less than a discriminatory response 1 p 53 In even simpler terms the reaction is the perception and thus the role of the re searcher is simply to determine the con ditions under which a discriminatory re sponse is obtained These conditions then de ne perception Unfortunately we have to agree that many psycholo gists who consider themselves operation ists do in fact accept this position to ward perception However this posi tion is not necessary from the tenets of operationism In fact we believe that this viewpoint is a perversion of the fundamentals of operationism as stated by its originators The essence of the above position is that a concept of perception is not distinguishable from the operations on which it is based and thus that percep tion is indistinguishable from the re sponses which indicate its existence and character This idea springs from a restricted interpretation of Bridgman s writings For example Bridgman states 1The preparation of this report was sup ported in part under Contract N50ri166 Task Order 1 between the Of ce of Naval Research and The Johns Hopkins University This is Report No 1661201 under that contract that The concept is synonymous with the corresponding set of operations 4 p 5 This widely quoted statement has been used by psychologists to justify their unwillingness to distinguish be tween perceptions and responses and to support their position that any set of responses leads to a concept about the properties of the perceptual system However to state that a concept is synonymous with a set of operations is not to state that any operation can pro duce a concept Furthermore psychologists have ig nored the fact that Bridgman is talking about a set of operations not a single experimental operation He later em phasizes this distinction stating that Operational de nitions in spite of their pre cision are in application without signi cance unless the situations to which they are ap plied are suf ciently developed so that at least two methods are known of getting to the terminus De nition of a phenomenon by the operations which produced it taken naked and without further quali cation has an en tirely specious precision because it is a de scription of a single isolated event 3 p 248 Many operationists accept the sterile point of View described by Allport and consider perception not to have any op erationally determinable properties other than discrimination It seems to us that the above quotations from Bridg man do not require such a narrow point of view It is true that if the only op 149
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