Pose

from Vanishing Points

Z X Y

What is the camera po se

Z X Y

with respect to world f

rame?

s t n i o p g n i h s i n a v o w t m o r f d e r e v o c e r e b n a c e s o p

Z X Y

Z X Y

Z X Y

v Y1 Z X Y

v X1

v Y1

v X1

Z X Y

vX1 = Mint r1

r2

r3

t X1

Vanishing v = f d1 , v = f d2 1 2 d3 d3 Point

v

Vanishing v = f d1 , v = f d2 1 2 d3 d3 Point

v

r o t c e v n o i t c e r i d n o s d n e p e d y l n o vanishing point

v Y1

v X1

Z X Y

vX1 = Mint r1

r2

r3

t X1

v Y1

v X1

Z X Y

vX1 = Mint r1

r2

r3

= Mint r1

r2

r3

t X1 0 1 1 B0C C t B @0A 0

v Y1

v X1

Z X Y

vX1 = Mint r1

r2

r3

0 1 1 B0C C X t B @1 0A 0

v Y1

v X1

Z X Y

vX1 = Mint r1 = Mint r1

r2

r3

0 1 1 B0C C X t B @1 0A 0

v Y1

v X1

Z X Y

vX1 = Mint r1r1

r2

r3

t X1

v Y1

v X1

Z X Y

vX1 = Mint r1r1

vY1 = Mint r1

r2

r3

r2

r3

t Y1

t X1

v Y1

v X1

Z X Y

vX1 = Mint r1r1

vY1 = Mint r1

r2

r3

r2

r3

t Y1

t X1

v Y1

v X1

Z X Y

vX1 = Mint r1r1

vY1 = Mint r1 = Mint r2

r2

r3

r2

r3

t Y1

t X1

v Y1

v X1

Z X Y

vX1 = Mint r1r1

r2

r3

t X1

vY1 = Mint r2r1

r2

r3

t Y1

v Y1

v X1

Z X Y

vX1 = Mint r1r1

r2

r3

t X1

vY1 = Mint r2r1 r2 r3 assume camera intrins ics are known

t Y1

v Y1

v X1

Z X Y

r1 =

1 Mint vX1 1 kMint vX1 k

vX1 = Mint r1r1

r2

r3

t X1

vY1 = Mint r2r1

r2

r3

t Y1

v Y1

v X1

Z X Y

r1 =

1 Mint vX1 1 kMint vX1 k

vX1 = Mint r1r1

r2

r3

t X1

vY1 = Mint r2r1

r2

r3

t Y1

r2 =

1 Mint vY1 1 kMint vY1 k

v Y1

v X1

Z X Y

r1 =

1 Mint vX1 1 kMint vX1 k

vX1 = Mint r1r1

r2

r3

t X1

vY1 = Mint r2r1

r2

r3

t Y1

r2 =

1 Mint vY1 1 kMint vY1 k

r3 = r1 ⇥ r2

v Y1 Z X

v X1

Y

r1 =

1 Mint vX1 1 kMint vX1 k

r2 =

1 Mint vY1 1 kMint vY1 k

r3 = r1 ⇥ r2

v Y1

v X1

Z X Y

r1 =

1 Mint vX1 1 kMint vX1 k

r2 =

1 Mint vY1 1 kMint vY1 k

r3 = r1 ⇥ r2

d e r e v o c e r e b t o n n a c a r e m a c f o n translatio

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