# GEOMETRIJA VIZUELNOG PROSTORA

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```					VISUAL SPACE ANISOTROPY
IN FULL-CUE AND
REDUCED-CUE CONDITIONS
Oliver Tošković
Faculty of Philosophy, Kosovska Mitrovica;
Laboratory for Experimental Psychology, Belgrade, Serbia
VISUAL SPACE GEOMETRY
   Blumenfeld and Hillebrand:
   parallel alleys lie inside distance alleys
VISUAL SPACE GEOMETRY
   Luneburg – perceived                     x
space is Riemannian
space (with constant
Gaussian curvature)
   Points on a Vieth-Müller
circle are being perceived
as equidistant from the
observer

   Hyperbolae of Hillebrand     y   L       D

are being perceived as
direction
VISUAL SPACE GEOMETRY
   Luneburg – perceived
space is Riemannian                      x
space (with constant
Gaussian curvature)
   Points on a Vieth-Müller
circle are being perceived
as equidistant from the
observer

   Hyperbolae of Hillebrand
are being perceived as       y   L       D

direction
VISUAL SPACE GEOMETRY
   Luneburg – perceived
space is Riemannian                      x

space (with constant
Gaussian curvature)
   Points on a Vieth-Müller
circle are being perceived
as equidistant from the
observer

   Hyperbolae of Hillebrand
y   L       D
are being perceived as
direction
PHYSICAL vs PERCEIVED SPACE
   Herman von Helmoltz:
   Difference between physical and perceived horopter
   Change in perceived horopter with distance

horopter

L

R
PHYSICAL vs PERCEIVED SPACE
   Koenderink, J. Cuijpers, R.
perception of parallelism     distance perception

observer
MOON ILLUSION
   Ptolemy – apparent distance
   Alhazen – moon illusion as a
psychological phenomenon
   Rock and Kaufman
– apparent distance theory         physical dome

– flattened sky dome

perceived dome
Standing         Lying

y=0.69x
y≈ x

x
   Tošković (2004)            Indoor                                       x

   distance perception
   Elliptic model of                                        a                  b
visual space
y=0.73x
(anisotropy)                                                 y=0.74 x
   Phisically shorter
vertical distances =                                 x                      x
Outdoor
longer horizontal
   Vertical distances
are peceived as
c                  d
beeing longer
Standard distance
Estimate
Non-veridicality
Rock and Kaufman
standing              lying

eyes
   Tošković (2007)
   For near distances,
such as 1m, visual
space is isotropic
   For larger distances
space is anisotropic
   For distance estimates,
visual system uses
from:                        body
   Vestibular system
   Neck muscles
physical      perceived   deviation      perceived-
distance      distance                   physical size
TO RESUME:
   In a reduced cue-situation:
   For perceived distance, visual space is anisotropic
   It relies on additional vestibular and kinesthetic
information
   Anisotropy – an internal model of visual space
   In a full-cue situation:
   ?
AIM
   Does visual space anisotropy exist in full cue
situation, as in reduced cue situation?
   Does kinesthetic information influence distance
perception in full cue situation, as in reduced cue
situation?
   Does visual system relie on its internal model of
space even when visual information are present?
METHOD
   Two experiments were conducted, with participants
lying on their left side of the body
   Head moving does not change vestibular information
   Uniform distribution of depth cues in all directions
   Sample: 37 psychology undergraduates and high
school students
   Stimuli:
   three luminous objects
   rectangular in shape
   size: 7* 5 centimeters
EXPERIMENT 1: reduced-cue
   Procedure:
   Participants estimated distances
   In a dark room – reduced cue situation
   Lying on a floor, on left side of the body
   With special glasses on their eyes (with horizontal apertures 1mm wide)
   With rectangular frame around their head
   Three standard distances to estimate - 1, 3 i 5 meters
   Three directions of estimate
   horizontal (00)
   middle – tilted for 450 regarding to horizon
   vertical (900)
   Task – equalize the distances of three stimuli on a three different
directions
frame   glasses   stimuli
RESULTS
   DIRECTION: horizontal – middle
   NO significant effect of direction
   NO interaction between direction and distance
   DIRECTION: horizontal – vertical
   Significant effect of direction
   Significant interaction between direction and distance
   DIRECTION: middle – vertical
   Significant effect of direction
   Significant interaction between direction and distance
F(2, 24)=1.7337, p=.19803                                   F(2, 24)=8.3619, p=.00176                                    F(2, 24)=12.890, p=.00016
7                                                         7                                                            7

6                                                         6                                                            6

5                                                         5                                                            5
average match

average match
4                                         average match   4                                                            4

3                                                         3                                                            3

2                                                         2                                                            2

1                                                         1                                                            1

5m                                                          5m                                          5m
0                                                         0 3m                                                         03m                                          3m
0 degrees                45 degrees                          0 degrees                90 degrees                         45 degrees                90 degrees
1m                                                          1m                                          1m
DIRECTION                                                    DIRECTION                                                    DIRECTION
   Visual space is being
ELONGATED towards vertical
direction
   For the distances larger than 1m
   Effect is NOT measurable on 45o
tilt from horizontal direction

   In a reduced-cue situation
visual space is anisotropic:
   neck muscles information
influence distance perception
EXPERIMENT 2: full-cue
   Sample: 24 high school students
   Procedure:
   Participants estimated distances
   On an open field – full cue situation
   Lying on a ground, on left side of the body
   With special glasses on their eyes (with horizontal apertures 1mm wide)
   With rectangular frame around their head
   Three standard distances to estimate - 1, 3 i 5 meters
   Three directions of estimate
   horizontal (00)
   middle – tilted for 450 regarding to horizon
   vertical (900)
   Task – equalize the distances of three stimuli on a three different
directions
frame   glasses   stimuli
RESULTS
   DIRECTION: horizontal – middle
   No effect of direction
   No interaction between direction and distance
   DIRECTION: horizontal – vertical
   NO effect of direction
   No interaction between direction and distance
   DIRECTION: middle – vertical
   NO effect of direction
   No interaction between direction and distance
F(2, 46)=.23235, p=.79359                                  F(2, 46)=2.2548, p=.11637                                     F(2, 46)=.00378, p=.99623
6.0                                                        6.0                                                        6.0

5.5                                                        5.5                                                        5.5

5.0                                                        5.0                                                        5.0

4.5                                                        4.5                                                        4.5
average match

average match

average match
4.0                                                        4.0                                                        4.0

3.5                                                        3.5                                                        3.5

3.0                                                        3.0                                                        3.0

2.5                                                        2.5                                                        2.5

2.0                                                        2.0                                                        2.0

1.5                                                        1.5                                                        1.5

1.0                                                        1.0                                                        1.0

0.5                                                        0.5                                                        0.5
5m                                                            5m                                         5m
0.0                                                        0.0
3m                                                         0.03m                                         3m
0 degrees               45 degrees                         0 degrees               90 degrees                           45 degrees               90 degrees
1m                                                            1m                                         1m
DIRECTION                                                  DIRECTION                                                     DIRECTION
   Visual space is NOT being
ELONGATED towards vertical
direction
   Perceived distance does not
change with viewing direction

   In a full-cue situation visual
space is isotropic:
    neck muscles information
does NOT influence distance
perception
CONCLUSIONS
   In a reduced-cue situation:
   For near distances, such as 1m, visual space is isotropic
   For larger distances (3m and larger) head tilt ELONGATES space
towards vertical direction
   visual system uses additional kinesthetic information from neck
muscles
   In a full-cue situation:
   For all distances visual space is isotropic
   Head tilt does not change visual space towards vertical direction
   visual system does NOT use additional kinesthetic information from
neck muscles
   Presence of visual information reduces significance of
kinesthetic (non-visual) information for distance perception

```
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 views: 7 posted: 7/1/2012 language: pages: 25