Perspective!!!
Igor Juricevic & John M. Kennedy
Outline
• Basics of perspective
– What is perspective?
– Why study perspective?
– Why study perspective pictures?
• Experiments 1-4
– The ART theory
– Is the ART theory general across observer position?
– Is the ART theory general across eye-height?
– Is the ART theory general across object orientation?
What is perspective?
• Leonardo
– Perspective is nothing else than seeing a
place or objects behind a plane of glass, quite
transparent, on the surface of which the
objects behind the glass are to be drawn.
What is perspective?
from Taylor (1719)
What is perspective?
Why study perspective?
• Perspective is the basic geometry of the
visual system
– Determines the information available to the
visual system
Why study perspective pictures?
• Reason 1: explain picture perception
• Since the Renaissance… paradoxes
concerning picture perception have
plagued the consciousness of mankind
• Explanations by:
– Leonardo da Vinci
– Albert Einstein
– other guys…
– have all FAILED!!!
Reason 1: explain picture
perception
Reason 1: explain picture
perception
Reason 1: explain picture
perception
Reason 1: explain picture
perception
Why study perspective pictures?
• Reason 1: explain picture perception
• Reason 2: explain spatial perception
Reason 2: explain spatial
perception
• The assumption
– There is nothing special about picture
perception
– Picture Perception = Everyday Perception
• So, a theory that can account for picture
perception will account for everyday
perception as well
• But…
– Why not just study Everyday Perception?
Reason 2: explain spatial
perception
• Why not just study everyday perception?
• Newtonian Physics vs. Einstein’s Physics
Reason 2: explain spatial
perception
• Why not just study everyday perception?
• Everyday perception will give you a
“Newtonian Physics” theory of vision
• Picture perception may give you an
“Einstein’s Physics” theory of vision
– Why? Because you can put people in novel
situations
– i.e., you can have the observer at the wrong
vantage point
The ART theory
Experiment 1
Experiment 1
Experiment 1
Experiment 1
Experiment 1
Experiment 1
Experiment 1
Experiment 1
Observer is:
JUST RIGHT
Observer is: Observer is:
TOO FAR TOO CLOSE
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
The ART theory
• The “Angles and Ratios Together” theory
• Angles
– “Angle from the Normal”
• Ratios
– Visual Angle ratios
• Together
– Together
The ART theory
D
C
A B
O
The ART theory: Angle from the Normal
D
C
A B
O
The ART theory: Visual Angle Ratio (Side/Bottom)
D
C
A B
O
The ART theory
4.5
Elongated
4 Compressed
Square
3.5
Visual Angle Ratio
3
The “ART Theory Ranges”
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
Angle from Normal (radians)
The ART theory
• Able to account for Experiment 1…
• Can it generalize to other situations?
• Like…
The ART theory
• Changes in observer position?
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
Compressed (Average Response 110)
4.5
Experiment 1
Elongated
4
Square
Compressed
3.5
Visual Angle Ratio (Side/Bottom)
3
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
Angle from Normal (radians)
4.5
Experiment 2
Elongated
4
Square
Compressed
3.5
Visual Angle Ratio (Side/Bottom)
3
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
Angle from Normal (radians)
4.5
Experiments 1 & 2
Elongated 1
4
Square 1
Compressed 1
3.5
Elongated 2
Visual Angle Ratio (Side/Bottom)
3 Square 2
Compressed 2
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
Angle from Normal (radians)
The ART theory
• Changes in observer position?
The ART theory
• Changes in eye-height?
High
Mid
Low
3
Experiment 3
Elongated
2.5 Square
Compressed
Visual Angle Ratio (Side/Bottom)
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
Angle from Normal (radians)
4.5
Experiments 1 & 2
Elongated 1
4
Square 1
Compressed 1
3.5
Elongated 2
Visual Angle Ratio (Side/Bottom)
3 Square 2
Compressed 2
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
Angle from Normal (radians)
4.5
Experiments 1, 2, & 3
4
Elongated
3.5 Square
Visual Angle Ratio (Side/Bottom)
Compressed
3
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
Angle from Normal (radians)
The ART theory
• Changes in eye-height?
The ART theory
• Changes in orientation?
Experiments 1, 2, and 3 Experiment 4
Observer is:
TOO FAR
Observer is:
TOO FAR
Observer is:
TOO FAR
Observer is:
JUST RIGHT
Observer is:
TOO CLOSE
Observer is:
TOO CLOSE
Observer is:
TOO CLOSE
4
Experiment 4
3.5 Elongated
Square
Visual Angle Ratio (Side/Bottom)
Compressed
3
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
Angle from Normal (radians)
4.5
Experiments 1, 2, & 3
4
Elongated
3.5 Square
Visual Angle Ratio (Side/Bottom)
Compressed
3
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
Angle from Normal (radians)
4.5
4.5 Experiments 1, 2, & 3
Experiments 1, 2, 3, & 4
4
4 Elongated 1 Square 1 Compressed 1
Elongated
Elongated 2 Square 2 Compressed 2
3.53.5 Square
Visual Angle Ratio (Side/Bottom)
Elongated 4d Square 4d Compressed 4d
Visual Angle Ratio (Side/Bottom)
Compressed
Elongated 3 Square 3 Compressed 3
3 3
2.52.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
0 0.2 0.4 0.6 0.8 1 1.2
0 0.2 0.4 Angle from Normal (radians)
0.6 0.8 1 1.2
Angle from Normal (radians)
The ART theory
• Changes in orientation?
Experiments 1, 2, and 3 Experiment 4
Conclusions
• The ART theory begins to explain some of
the paradoxes of picture perception
• The ART theory can be applied to
perception of the real world (i.e.,
“Everyday Perception”)
• May need to add factors to ART theory to
deal with orientation
Thank you.