Perspective!!!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?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:TOO FAR

Observer is:TOO CLOSE

Observer is:JUST RIGHT

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Observer is:TOO FAR

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Observer is:TOO FAR

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Observer is:TOO FAR

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Observer is:JUST RIGHT

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Observer is:TOO CLOSE

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Observer is:TOO CLOSE

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Observer is:TOO CLOSE

The ART theory

• The “Angles and Ratios Together” theory

• Angles– “Angle from the Normal”

• Ratios– Visual Angle ratios

• Together– Together

The ART theoryDD

OO

CC

BBAA

The ART theory: Angle from the Normal

DD

OO

CC

BBAA

The ART theory: Visual Angle Ratio (Side/Bottom)

DD

OO

CC

BBAA

The ART theory

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ual

An

gle

Rat

io

ElongatedCompressedSquare

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ual

An

gle

Rat

io

ElongatedCompressedSquare

The “ART Theory Ranges”

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 <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Compressed (Average Response <90)

Perspective Constancy (Average Response 90-110)

Elongated (Average Response >110)

Experiment 1

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ual

An

gle

Rat

io (

Sid

e/B

ott

om

)

ElongatedSquareCompressed

Experiment 2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ual

An

gle

Rat

io (

Sid

e/B

ott

om

)

ElongatedSquareCompressed

Experiments 1 & 2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ua

l A

ng

le R

ati

o (

Sid

e/B

ott

om

)

Elongated 1

Square 1

Compressed 1

Elongated 2

Square 2

Compressed 2

The ART theory

• Changes in observer position?

YES

The ART theory

• Changes in eye-height?

High

Mid

Low

Experiment 3

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ua

l An

gle

Ra

tio

(S

ide

/Bo

tto

m)

ElongatedSquareCompressed

Experiments 1 & 2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ua

l A

ng

le R

ati

o (

Sid

e/B

ott

om

)

Elongated 1

Square 1

Compressed 1

Elongated 2

Square 2

Compressed 2

Experiments 1, 2, & 3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ua

l A

ng

le R

ati

o (

Sid

e/B

ott

om

)

ElongatedSquareCompressed

The ART theory

• Changes in eye-height?

YES

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

Experiment 4

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ual

An

gle

Rat

io (

Sid

e/B

ott

om

)

Elongated

Square

Compressed

Experiments 1, 2, & 3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ua

l A

ng

le R

ati

o (

Sid

e/B

ott

om

)

ElongatedSquareCompressed

Experiments 1, 2, 3, & 4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

Angle from Normal (radians)

Vis

ual

An

gle

Rat

io (

Sid

e/B

ott

om

)

Elongated 1 Square 1 Compressed 1

Elongated 2 Square 2 Compressed 2

Elongated 4d Square 4d Compressed 4d

Elongated 3 Square 3 Compressed 3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1 1.2

ElongatedSquareCompressed

The ART theory

• Changes in orientation?

Experiments 1, 2, and 3 Experiment 4

MAYBE

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.