- Email: [email protected]
Scene-based and viewer-centered representations for comparing shapes
CognitioPl,30 (198$) l-35
viewer-centered (i.e., heod-
onses also regressedtowa
the
first author was supported by grant87-2-36Jromthe Alfred P. Sloan Foundation. The -xcond author P.B-;*;*,~Y q+n*n ..--MPTQc?%lQ for _gU‘“.” ._,.I ..M from A.F. Sitian Fciuii ational Institute of Health. We thank NRSA Fellowship F32 anonymous reviewer for he and, Steve Pinker, Roger should be addressedto: LawrenceM. Parsons,Departmentof Fsycholo Hell 330, The University of Texas at Austin, Austin, TX 78712, U.S.A.
sevier Science
2
GE. Hindonand L.
rsom
‘An alternative, but bss common, hypothesis is that spatial structure is encoded by complex relational features such as “contains three points that form a triangle with angles of 30,60,90 degrees” or contains “5 line endings.”
Scene-based and viewer-centered representations
3
resentation of an object is the easiest to vantage that it changes with ev ‘ect-based frames are both us
ects, some of which may ect-based frame for the
e v~ksal system ne
,
to store where ea
of objects, the stored e orientation, and size) ca
all errors to accu
4
GE. Hinton and L.
Scene-based and viewer-centered representations
5
sof~eu~ous for ea
1cortex is r&m-
re relative to variou
tion of the fixati ead-based (or scene-based) found such neurons in area
tated into alignment with
tion that is changing is relative to a scene-based ntation relative revity, we refer
‘When the relation of the viewer to the sceneis very rapidly changing,it is conceivablethat the overhead of updating the scene-basedframe would make it more practicalto use only two frames, the object-basedand viewer-basedframes.
6
at was near see
rientation that regre
each object to perceive each object with respect to a body-based
Scene-based and viewer-centered representations
e
of reference. en subjects
In
xperiment 5, we fou the same pattern of alignco aring objects with quite different of
S.
respect to the viewer-centered identical views of each obje
Figure 2.
7
line-drawing illustrations of the two experimental stimuli.
8
GE.
Scene-based and viewer-centered representations
of viewer-centered
9
scene-based a&aments when obdegrees apart. (a) left at 315 degrees, tered a~i~n~nt; and (c) scene-based
GE. Hinton and L.
rsons
rocedure
The was to entical or mirror were te mke
ing
a trial su c~~~a~is~n object
Scene-based and Gewcr-cewrred representations
ent no more
Yk
12
GE. Hinton and L.
le 1.
Eugene 1: son object
~ien~atio~ to
Direction of subjects’ rotation
Orientation of stan 315 degrees
Nora. Based on 12 subjects and a to in Figure 3.
observations. Degrees refer to compass directions
&cause the comparison object was never presented in perfect aiignment with the viewer-centered frame, when identical objects differed in orientation by 90 degrees, a clockwise rotation was always the shortest angle to turn the object to achieve alignment in the scene-based frame. As expected, subjects chose the shortest angle of rotation 83 percent of the time in thes:: cases.
Scene-based and viewer-centered representations
13
Scene-based and vietier-centered representations
Table 2.
v&ion oforientath
15
to which subjects
em angular difference Parallel
180
270
179.9 (4.05)
269.6 (2.90)
160
200
340
175.6 (8.16)
215.6 (23.43)
357.4 (10.45)
4§
135
225
315
67.91(26.31)
159.73 (7.71)
248.09 (19.71)
336.46 (16.03)
0
90 1.0 (2.52)
~~~-P~el
70 f!k
Sk
(7.32)
91.7 (2.19)
on 11 subjects. Degrees refer to the compass directions in F&we 3.
tatio
on s
.75 (2.13)
14.95 (11.63)
23.05 (14.59)
16
GE. Hinton mui L.
rsons
Scene-based and viewer-centered representWorn
clt
been
in any
related
ex
17
ents,
ent 2 that used
eanm difference
0.33 (2.40)
90.67 (2.11)
M.ll(2.33)
271.22 (2.82)
22 (11.25) 343.22(20.13) Skewed
Note. B
45
135
225
74.22 (28.83)
167.56 (14.25)
245.
on 9 subjects.
Of
ali
grees refer to the compass dkmtions in
315
3.
G.G3(2.31 j
23.83 (21.88>
Scene-based and viewer-centeredrepresentations
Table 4.
19
-based ~ig~~~t, perceived perfect scene&ued aligm dard &v&ion oforietzmion to which subjectsrotated ‘k-a!compa.r&m object Meananghr difference 0 0.1s (2.13) 70
45 58.11(8.86)
90 9-0.11(2.18)
180
270
180.67 (2.31)
270.79 (2.53)
160
0.42 (.7)
340
169.11(19.33)
223.00(13.15)
344.44 (22.11)
135
225
315
239.89 (12.66)
333.56 (8.47)
(13.34)
Nore. Based on 9 subjects. Degrees refer to the compass diiom
in Qure 3.
10.1%(18.05)
15.64 (11.07)
20
G. E. Hinton and L.
Scene-based and viewer-centered representations
tical to those i
21
t to objecrs i&ion of orientation to
ble 5.
hallel
0
.II.__ 1.33 (1.97)
1
270
181.0 (1.29)
271.67 (2.38)
.” ---
21.29 (14.80)
.33(17.1) 45 .5 (18.70) ased on 6 subjects.
1.33 (1.54)
135
22.5
162.83 (16.77)
235.17 (16.
315
gmes refer to the compass directions in Figure 3.
26.71(14.!8)
Scene-based an$ viewer-centered representations
23
t 4: IS&Degree Separation, observer’s fines ofsight to two objects rii devia~n of orientation to
Meanaqular difference IParallel
0
90 1.5 (1.89)
Skc&?&
92.17 (3.34)
--_
180
270
181.5 (.%)
271.0
(1.83)
70
160
200
340
93.67 (2: 5)
199.17 (19.36)
24567 (16.4)
385.667 (12.66)
45
!35
225
315
94.00 (24.93)
188.0 (17.36)
272.5 (32.54)
366.67 (29.97)
ased on 6 subjects. Degrees refer to the compass diions
in Figure 3.
l.s4(1.75)
38.54 (17.83;
X29(26.76)
24
rsoras
0
had not bee
in any
relate
Scene-based and viewer-centemdrepresentations
25
tzler & Shepard Objects. Mean and whichsubjects rotatedcomparisonob-
Mean angular difference Parallel
0
90 1.43 (2.60)
Nearly-Parallel
Skewed
90.75 (2.59)
d on 8 subj
270
181.38(2.99)
271.00(1.80)
70
160
200
340
$2.63 (6.87)
174.13(27.61)
232.88 (12.92)
356.50 (13.35)
45
135
225
315
69.13 (8.95) 159.00(18.65) py.^-NC&?.
180
refer to the corn
-_
1.19 (2.56)
19.03(20.65)
247.75 (5.Ei4) 343.38 (23.37) 24.G (iS.Gj __I___I_c____I__I_~-_.~..--.-“III__IIIW-.
and L.M. Parsons
nton
Table 8.
and standard devotion of orientation to n objecrs ean angular differeiice
Parallel
0
90 2.00 (2.92)
Nearly-Parallel
91.13(1.76)
180
270
181.00 (2.45)
272.50 (1.50) ___ ~-
70
160
200
340
75.75(11.20)
175.88(13.73)
231.13(21.77)
336.00(28.54)
45
135 ---_~-~
225
3325
----_ Skewed ~----------_-_
1.66 (2.31)
12.19 (23.81)
_---_-.
79.13(18.09) 156.25 (17.89) 249.75 (9.86) 332.63 (21.52) 24.44 (17.28) ^---Ix.-~..-_xII-“.~_l._l____ll-_-__~.-~_,lllllllll~ .DIxIII~__. _______--_ - _.-. ~~~I^--“_~ -___ ~“. Nofe. Based on 8 subjects. Degrees rcfcr to the compass directions in Figure 3.
Scene-based and viewer-centeredrepresentations
ali an
27
e discrimination of mirror i was less than .5 percent.
d to correct for the
a scene-based fra
ise between scenemere are three observations of reliable effects of absolute orientation on the extent of compromise between scent-based and viewer-centered alignments in the Nearly-Parallel and Skewed conditions. In two cases,this effect occurred in the replication of the Shape-Comparisontask from Experiment 2. An ANQVA of responsesin each condition was conductedon the data from all performancesof this task in Experiments 2-5. This analysisshoweda reliable effect of absoluteorientation only in the Neariy-Parallel condition (F(3.66) = 5.86, p < .oOl). The effect occurredbecausethe responsesin the 70 degreeorientation were relatively near scene-basedalignment and those in the 200 degreeorientation were relatively far from scene-basedalignment: the overall means were 10.85, 19.67,27.81, and 18.57 for the 70, 160,200, and 340 degree orientations. The only other effect of absoluteorientations was in the Nearly-Parallel condition in the Helix task (in Experiment 5). The range of compromiseobservedthere varied more widely than usualacrossall the absoluteorientations. It remains a mysterywhy these variations in compromisealignmentsoccurredfor different absoluteorienta. _-_ A :- ^.._ ru-P1a...r*rl .a,..:,... tions. ihcse effect5couid hnve ken due to uuc of the hiGiiiS iioi CGiiiiiMGihiCEu 418 VUI wbpuwr;wm wagu. far example, either the order of trials (all subjectssaw the samesequenceof trials) or the interaction between prefercncc at which it was presented(e utc 0 handed object shapeand necessaryto unde~t~nd thi her r he object from some an
28
igure 5.
Scene-based and viewer-centered representations
29
30
Scene-based and viewer-centeredrepremmtims
31
Andersen, R.A., Essick, G.K., Br Siegel, R.M. (1984). The role of eye position on the visual response of neurons in area 7a. So&~ for PleuroscienceAbstracts, 10.934. Anderson, R.A., Essick, G.K., & Siegel, R.M. (1985). The encoding of spatial location by posteriorparietal neurons. Science, 230,456-458. Arnold, V.I. (1984). crrsnophe ti@o9. Berlin: Springer-Veriag. . Triangles as ambiguous figures. American Journal of Psychology, 81,447-453. Representation of physicalspace. In A.W. Melton & E.J. Martin(Eds.), Codingprmesses in human nrcmory. Washington, DC: Winston. Attneave, F., & Arnoult, M.D. (1956). The quantitativestudy of shape and pattern perception. Psychological Bulletin, 53,452471.
Attneave, F., % Farrar,P. (lm).
The visual world behind the head. American Journal of Psychology, 90. Discriminabilityof stimuli varying in physical and retinal orientation. 74, M!H57. a pointer into perceived and imaginedspace.
chology,
Vo~unta~ control of frame of referenceand slope equivalence under head rrhre~l Fsychdogy, 78, 153-159. : Structureand function. The Behavioral and Brain sciemes, 9,67-120.
32
G.E. Hinton and L.
Rirsons
y tilt on apparentverticality,apparentbody position, and their relation. Bauermeister,M. (1964). Effect of Jowt& of fiperimed Psychology,67.142-147. Biederman, I. (19gl). On the semantics of a glance at a scene. In . lwovy UL J. Pomerantz (Eds.), Petwpawl Orgtw&ation. HilWe, NS: Erlbaum. Belation between cognitive and motor-oriented Bridgeman, B., Lewis, S., Heir, 8.. L Nagie, M. (1 Ps@to&gy: Human Perceptionand systems of visual position perception. Jo& of Pe@ormufKe,5.692-700. of IEEE hitmnatiod CaMan, J., & Weiss, Ii. (1985). A model
II W -
atadspace in vision.Psycldogicd Review,7.325-343.
H.L. Boitblat, T.G. 975). Meotal rotation of random
nsional shapes. Ci?gniiivePsydaokbgy,7,2W3.
ExpcrimrnralPsychology:Human R.N. (1973). Chrommextic studiesof the rotation of mental images. In W.G.
CO co
.C., Nagourney. B.A., Shetzer, L.I., & Stefanatos, 6. (1918). Mental rotation under head tiitz Factorsinfluencing the location of subjective reference frame. Pemption d Psychophyk~.~, 24,263273. tection of symmetryas a fun&on of angularorientation. loud ?erception& I, 221-m. C.E. (1976 in mentai rotation? Pemeptiomdt
Day, R.H., (StWade, NJ. (1969). Mechanismsinvolved in visualorientation constancy. J%ycMogicofBuWn, 71,33-42. Giiinsky, A. (1955). The effect of attitude on the perception of size. AmericanJownd of Psychol@~,68, 173-192. Girgus, J.S., Gellman, LH., & Ho&erg, J. (19gtJ).The effect of spatial order on piecemeal shape recognition: A developmentalstudy. Perception& Psychophysics, 2&133-138. Gross,C.G., Bocha randa, CE,, & Bender, D.B. (t972). Visual propertiesof neurons in inferotemporal cortex of the macaque.Jod of Aletmphysiofogy, 35.96-111. Hinton, GE. (1981a). A parallelcomputation that assignscanonical object-based frames of reference. Proceedingsof the 7thlntematiod Joint Conferenceon Artijkialhueliigence.Vancouver, BC. Hinton, G.E. (1981b). Shape representation in parallel systems. Proceedingsof the 7th ham&ma/ J&t Conferenceon Adfxial Intelligence.Vancouver, BC. Hinton, G.E., & Parsons, L.M. (1981). Frames of reference and mental imagery. In A.D. Baddeley and 1. Long (Eds.) Attentionand Perfomtance(Vol. 9, pp. 241-277). Hiiisdaie, NJ: Erlbaum. Hochberg, J. (i96g). in the mind’seye. in &ii. Haber (Ed, j, &nfemporasrjl &oq & ~smmh h ii&& perception.New York: Holt, Rinehart, & Winston. Hochberg, J. (1982). How big is a stimulus? In J. Beck (Ed.), Orguttizution and representation in perceptiot~ (pp. 191-217). Hillsdale, NJ: Erlbaum.
Scene-based and viewer-centeredrepresentations
33
Hock, H., & TromIey, CL. (1978). Mental rotation and perceptualuprightness.Perception & Psychophysics, 24.529-533.
Howard, I.P. (lM6). The perception of posture, self motion, and the visual ve&al. In K.R. Boff, L. Kaufman, & J.P. Thomas(Eds.), Hadbookofperceptionandhumanperfomance (Vol. I: sensory processes dpem@on). New Yorkz Wiley. Hub& D.H., & V&M, T.H. (1962). Receptive fields, binocular interaction, and functhal architectureiz the cat’s v&x! cortex. Journal of Physioiogj @atdon), 140,10&154. Hub& D.H., & Whel, T.H. (1974). Uniformity of monkey striate cortex: A parallel relationshipbetween field size, ~LWT, znd ma@ication factor. Journal of Gwnpadve Neurology, IS8,295-302. Just, MA.. & Carpcmter,P.A. (1985). Cognitive coordinate systems. Psychologicd Review, 92,137-17~1. KaH, P., B P~EXMU,L.M. (1981). optical informationand practicein the disuimhation of 3-D mirror-refhted objects. Percepiion, IO, 545-562. Keeml, J. 8~ M~are, R.E. (1979). Memory for images of concealed objects: A reexamination of Neisser aiid . Jouii of Expdimd Psychokqy: Hmazii Learning and Kemory, 5,374-W. KaedlilIk. J.J. (1984). m internal rrpnsentacion of solid shape and visual expIoration.In L. Spihan & RR. Woott--c??~ Sensory eqxrhce, udqtu&=, ~&pemeption (pp.132142). HiMale. NJ: Erlbaum. Koeoderink. J-J., 8t Doom, A.J. van (1976). Siies of the visual mapping. Bidogid Cybrmclicp, 24, 51-59. Kaenderink, I. J., dprIhmm, A.J. van (1979). The internal representationof solid shape with respectto vision. Biokqid Cybmetics, 32.211-216. Kosslyn. SM. (1980). hage and mind. Cambridge,EUIA: bard University Press. Lynch, J.C. (1.980).The MonaI organht~n of posterior parietalassociation cortex. 77~ Behuviorulcurd Brain Sciences, 3,~S34. Mach, E. (1897). ?%eMolysY of seamdons. English translation(1959), New York: Dover. Marr, D., & Nii, H.K. (1978). Representation and recagaition of the spatial organization of threedimensional shapes. procbcdingsof the Royal Society, Series B, 200,~294. McCroq. C. (1980). Profiru of su&ces. Covenuy: Uoiversity of Wtick. McDermott, D., & Davis, E. (1984). planning routes through uncertain territory. Ar@ci&ffnteUigence,22, 101-156. Met&r, J. (1973). Chgnihe anahgues of the m&don of thnr-dimmsionol objects. Unpublished doctoraI dissertation, Stanford University. Met&r, J., & Shepard, R.N. (1974). Transformationalstudies of the internal representationof thedimensional objects. In R. S&o (Ed.), llrrories in cognitivepsychok?~: The Loyofa Symposium (pp. 174201). Hills&k, NJ: Erlbaum. Mishkin, M., Ungcrleider, L.G., & a&o, K.A. (1983). object vi&u! ad spatia! vision: ‘TLvocortical pathways. Trrndrin Neuroscience%6,414417. Minsky, ML., & Papert, S. (1969). Percepfrons, Cambridge,MA: MIT Press. or-m, M-J., Findlay, J.M., & Watt, R.J. (1982). Aperture viewing: A review and a synthesis. Qtierly Journal of Experime~ Psychology, 34A, 211-233. Noda, II., & Warabi, T. (1986). Dies of Purkinjecells in monkey’s floaxdus duringpursuit eye movements and visual stimulus movements. wrimentul Neurofugy, 93,39O-i03. GIson, R.K., % Attaeave, F. (1970). What variables produce similarity grouping? American Jowl of &ycholo#y, 83, l-21. Palmer, S.E. (1975). Visual roeption and world knowledge: Notes on a model of sensory cognitive interaction. In D.A. Norman 8t D.E. Rumelhart (Eds.), Expio~tions in cognition. San Francisco: WM. Prec!. Palmer, S.E. (1977). Hiera&ical structurein perceptual represeMation.Cogdive Psycho@Y, %441--4% rr SE., BrBuchet, N. (1981). Configuraleffects in perceived pointing of ambiguoustria@as. Journal P ofi!lqmhenurl P8ydwlogy: Human Pemeptio+ad P6yformanm, 7,~114.
doweusevhal
Van lEssen,D.C. (1985).Functionalorgmixationof primate visual aster. In A. Peters 8 E.G. Jones, l7te iX&hilGXitTX
(Vd
3;. SW
Y&Z
Fi~iBiifti &SS.
Scene-hased
viewer-centeredrepresentations
35
viewer-centered (i.e., heod-
onses also regressedtowa
the
first author was supported by grant87-2-36Jromthe Alfred P. Sloan Foundation. The -xcond author P.B-;*;*,~Y q+n*n ..--MPTQc?%lQ for _gU‘“.” ._,.I ..M from A.F. Sitian Fciuii ational Institute of Health. We thank NRSA Fellowship F32 anonymous reviewer for he and, Steve Pinker, Roger should be addressedto: LawrenceM. Parsons,Departmentof Fsycholo Hell 330, The University of Texas at Austin, Austin, TX 78712, U.S.A.
sevier Science
2
GE. Hindonand L.
rsom
‘An alternative, but bss common, hypothesis is that spatial structure is encoded by complex relational features such as “contains three points that form a triangle with angles of 30,60,90 degrees” or contains “5 line endings.”
Scene-based and viewer-centered representations
3
resentation of an object is the easiest to vantage that it changes with ev ‘ect-based frames are both us
ects, some of which may ect-based frame for the
e v~ksal system ne
,
to store where ea
of objects, the stored e orientation, and size) ca
all errors to accu
4
GE. Hinton and L.
Scene-based and viewer-centered representations
5
sof~eu~ous for ea
1cortex is r&m-
re relative to variou
tion of the fixati ead-based (or scene-based) found such neurons in area
tated into alignment with
tion that is changing is relative to a scene-based ntation relative revity, we refer
‘When the relation of the viewer to the sceneis very rapidly changing,it is conceivablethat the overhead of updating the scene-basedframe would make it more practicalto use only two frames, the object-basedand viewer-basedframes.
6
at was near see
rientation that regre
each object to perceive each object with respect to a body-based
Scene-based and viewer-centered representations
e
of reference. en subjects
In
xperiment 5, we fou the same pattern of alignco aring objects with quite different of
S.
respect to the viewer-centered identical views of each obje
Figure 2.
7
line-drawing illustrations of the two experimental stimuli.
8
GE.
Scene-based and viewer-centered representations
of viewer-centered
9
scene-based a&aments when obdegrees apart. (a) left at 315 degrees, tered a~i~n~nt; and (c) scene-based
GE. Hinton and L.
rsons
rocedure
The was to entical or mirror were te mke
ing
a trial su c~~~a~is~n object
Scene-based and Gewcr-cewrred representations
ent no more
Yk
12
GE. Hinton and L.
le 1.
Eugene 1: son object
~ien~atio~ to
Direction of subjects’ rotation
Orientation of stan 315 degrees
Nora. Based on 12 subjects and a to in Figure 3.
observations. Degrees refer to compass directions
&cause the comparison object was never presented in perfect aiignment with the viewer-centered frame, when identical objects differed in orientation by 90 degrees, a clockwise rotation was always the shortest angle to turn the object to achieve alignment in the scene-based frame. As expected, subjects chose the shortest angle of rotation 83 percent of the time in thes:: cases.
Scene-based and viewer-centered representations
13
Scene-based and vietier-centered representations
Table 2.
v&ion oforientath
15
to which subjects
em angular difference Parallel
180
270
179.9 (4.05)
269.6 (2.90)
160
200
340
175.6 (8.16)
215.6 (23.43)
357.4 (10.45)
4§
135
225
315
67.91(26.31)
159.73 (7.71)
248.09 (19.71)
336.46 (16.03)
0
90 1.0 (2.52)
~~~-P~el
70 f!k
Sk
(7.32)
91.7 (2.19)
on 11 subjects. Degrees refer to the compass directions in F&we 3.
tatio
on s
.75 (2.13)
14.95 (11.63)
23.05 (14.59)
16
GE. Hinton mui L.
rsons
Scene-based and viewer-centered representWorn
clt
been
in any
related
ex
17
ents,
ent 2 that used
eanm difference
0.33 (2.40)
90.67 (2.11)
M.ll(2.33)
271.22 (2.82)
22 (11.25) 343.22(20.13) Skewed
Note. B
45
135
225
74.22 (28.83)
167.56 (14.25)
245.
on 9 subjects.
Of
ali
grees refer to the compass dkmtions in
315
3.
G.G3(2.31 j
23.83 (21.88>
Scene-based and viewer-centeredrepresentations
Table 4.
19
-based ~ig~~~t, perceived perfect scene&ued aligm dard &v&ion oforietzmion to which subjectsrotated ‘k-a!compa.r&m object Meananghr difference 0 0.1s (2.13) 70
45 58.11(8.86)
90 9-0.11(2.18)
180
270
180.67 (2.31)
270.79 (2.53)
160
0.42 (.7)
340
169.11(19.33)
223.00(13.15)
344.44 (22.11)
135
225
315
239.89 (12.66)
333.56 (8.47)
(13.34)
Nore. Based on 9 subjects. Degrees refer to the compass diiom
in Qure 3.
10.1%(18.05)
15.64 (11.07)
20
G. E. Hinton and L.
Scene-based and viewer-centered representations
tical to those i
21
t to objecrs i&ion of orientation to
ble 5.
hallel
0
.II.__ 1.33 (1.97)
1
270
181.0 (1.29)
271.67 (2.38)
.” ---
21.29 (14.80)
.33(17.1) 45 .5 (18.70) ased on 6 subjects.
1.33 (1.54)
135
22.5
162.83 (16.77)
235.17 (16.
315
gmes refer to the compass directions in Figure 3.
26.71(14.!8)
Scene-based an$ viewer-centered representations
23
t 4: IS&Degree Separation, observer’s fines ofsight to two objects rii devia~n of orientation to
Meanaqular difference IParallel
0
90 1.5 (1.89)
Skc&?&
92.17 (3.34)
--_
180
270
181.5 (.%)
271.0
(1.83)
70
160
200
340
93.67 (2: 5)
199.17 (19.36)
24567 (16.4)
385.667 (12.66)
45
!35
225
315
94.00 (24.93)
188.0 (17.36)
272.5 (32.54)
366.67 (29.97)
ased on 6 subjects. Degrees refer to the compass diions
in Figure 3.
l.s4(1.75)
38.54 (17.83;
X29(26.76)
24
rsoras
0
had not bee
in any
relate
Scene-based and viewer-centemdrepresentations
25
tzler & Shepard Objects. Mean and whichsubjects rotatedcomparisonob-
Mean angular difference Parallel
0
90 1.43 (2.60)
Nearly-Parallel
Skewed
90.75 (2.59)
d on 8 subj
270
181.38(2.99)
271.00(1.80)
70
160
200
340
$2.63 (6.87)
174.13(27.61)
232.88 (12.92)
356.50 (13.35)
45
135
225
315
69.13 (8.95) 159.00(18.65) py.^-NC&?.
180
refer to the corn
-_
1.19 (2.56)
19.03(20.65)
247.75 (5.Ei4) 343.38 (23.37) 24.G (iS.Gj __I___I_c____I__I_~-_.~..--.-“III__IIIW-.
and L.M. Parsons
nton
Table 8.
and standard devotion of orientation to n objecrs ean angular differeiice
Parallel
0
90 2.00 (2.92)
Nearly-Parallel
91.13(1.76)
180
270
181.00 (2.45)
272.50 (1.50) ___ ~-
70
160
200
340
75.75(11.20)
175.88(13.73)
231.13(21.77)
336.00(28.54)
45
135 ---_~-~
225
3325
----_ Skewed ~----------_-_
1.66 (2.31)
12.19 (23.81)
_---_-.
79.13(18.09) 156.25 (17.89) 249.75 (9.86) 332.63 (21.52) 24.44 (17.28) ^---Ix.-~..-_xII-“.~_l._l____ll-_-__~.-~_,lllllllll~ .DIxIII~__. _______--_ - _.-. ~~~I^--“_~ -___ ~“. Nofe. Based on 8 subjects. Degrees rcfcr to the compass directions in Figure 3.
Scene-based and viewer-centeredrepresentations
ali an
27
e discrimination of mirror i was less than .5 percent.
d to correct for the
a scene-based fra
ise between scenemere are three observations of reliable effects of absolute orientation on the extent of compromise between scent-based and viewer-centered alignments in the Nearly-Parallel and Skewed conditions. In two cases,this effect occurred in the replication of the Shape-Comparisontask from Experiment 2. An ANQVA of responsesin each condition was conductedon the data from all performancesof this task in Experiments 2-5. This analysisshoweda reliable effect of absoluteorientation only in the Neariy-Parallel condition (F(3.66) = 5.86, p < .oOl). The effect occurredbecausethe responsesin the 70 degreeorientation were relatively near scene-basedalignment and those in the 200 degreeorientation were relatively far from scene-basedalignment: the overall means were 10.85, 19.67,27.81, and 18.57 for the 70, 160,200, and 340 degree orientations. The only other effect of absoluteorientations was in the Nearly-Parallel condition in the Helix task (in Experiment 5). The range of compromiseobservedthere varied more widely than usualacrossall the absoluteorientations. It remains a mysterywhy these variations in compromisealignmentsoccurredfor different absoluteorienta. _-_ A :- ^.._ ru-P1a...r*rl .a,..:,... tions. ihcse effect5couid hnve ken due to uuc of the hiGiiiS iioi CGiiiiiMGihiCEu 418 VUI wbpuwr;wm wagu. far example, either the order of trials (all subjectssaw the samesequenceof trials) or the interaction between prefercncc at which it was presented(e utc 0 handed object shapeand necessaryto unde~t~nd thi her r he object from some an
28
igure 5.
Scene-based and viewer-centered representations
29
30
Scene-based and viewer-centeredrepremmtims
31
Andersen, R.A., Essick, G.K., Br Siegel, R.M. (1984). The role of eye position on the visual response of neurons in area 7a. So&~ for PleuroscienceAbstracts, 10.934. Anderson, R.A., Essick, G.K., & Siegel, R.M. (1985). The encoding of spatial location by posteriorparietal neurons. Science, 230,456-458. Arnold, V.I. (1984). crrsnophe ti@o9. Berlin: Springer-Veriag. . Triangles as ambiguous figures. American Journal of Psychology, 81,447-453. Representation of physicalspace. In A.W. Melton & E.J. Martin(Eds.), Codingprmesses in human nrcmory. Washington, DC: Winston. Attneave, F., & Arnoult, M.D. (1956). The quantitativestudy of shape and pattern perception. Psychological Bulletin, 53,452471.
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(Vd
3;. SW
Y&Z
Fi~iBiifti &SS.
Scene-hased
viewer-centeredrepresentations
35