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### Transcript of Lecture 8: Camera Calibration - Artificial · PDF file Fei-Fei Li Lecture 8 - 21 19-Oct-11...

• Lecture 8 -Fei-Fei Li

Lecture 8:

Camera Calibration

Professor Fei-Fei Li

Stanford Vision Lab

19-Oct-111

• Lecture 8 -Fei-Fei Li

What we will learn today?

• Review camera parameters

• Affine camera model (Problem Set 2 (Q4))

• Camera calibration

• Vanishing points and lines (Problem Set 2

(Q1))

19-Oct-112

• [FP] Chapter 3 • [HZ] Chapter 7, 8.6

• Lecture 8 -Fei-Fei Li

What we will learn today?

• Review camera parameters

• Affine camera model

• Camera calibration

• Vanishing points and lines

19-Oct-113

• [FP] Chapter 3 • [HZ] Chapter 7, 8.6

• Lecture 8 -Fei-Fei Li 19-Oct-114

Projective camera f

Oc

f = focal length

• Lecture 8 -Fei-Fei Li 19-Oct-115

Projective camera

x

y

xc

yc

C=[uo, vo]

f

Oc

f = focal length

uo, vo = offset

• Lecture 8 -Fei-Fei Li 19-Oct-116

Projective camera f

Oc

Units: k,l [pixel/m]

f [m]

[pixel],αααα ββββ Non-square pixels

f = focal length

uo, vo = offset

→ non-square pixels,αααα ββββ

• Lecture 8 -Fei-Fei Li 19-Oct-117

Projective camera

   

   

  

  

=

1 0100

00

0

z

y

x

v

us

P' o

o

β α

f

Oc

K has 5 degrees of freedom!

Pc

P’

f = focal length

uo, vo = offset

→ non-square pixels,αααα ββββ θ = skew angle

• Lecture 8 -Fei-Fei Li 19-Oct-118

Projective camera f

Oc

   

   

  

  

 −

=′

1

z

y

x

0100

0v0

0ucot

P o

o

sinθθθθ ββββ

θθθθαααααααα

Pc

P’

f = focal length

uo, vo = offset

→ non-square pixels,αααα ββββ θ = skew angle

K has 5 degrees of freedom!

• Lecture 8 -Fei-Fei Li 19-Oct-119

Projective camera f

Oc

Pc

Ow

iw

kw

jw R,T

P’

f = focal length

uo, vo = offset

→ non-square pixels,αααα ββββ θ = skew angle R,T = rotation, translation

wP TR

P 44

10 ×  

  

 =

cORT ~−=

• Lecture 8 -Fei-Fei Li 19-Oct-1110

Projective camera

f = focal length

uo, vo = offset

→ non-square pixels,αααα ββββ

f

Oc

P

Ow

iw

kw

jw

wPMP =′

[ ] wPTRK= Internal (intrinsic) parameters

External (extrinsic) parameters

θ = skew angle R,T = rotation, translation

P’

R,T

• Lecture 8 -Fei-Fei Li 19-Oct-1111

Projective camera

wPMP =′ [ ] wPTRK= Internal (intrinsic) parameters

External (extrinsic) parameters

• Lecture 8 -Fei-Fei Li 19-Oct-1112

Projective camera

wPMP =′ [ ] wPTRK=

  

  

 −

= 100

v0

ucot

K o

o

sinθθθθ ββββ

θθθθαααααααα

  

  

= T 3

T 2

T 1

R

r

r

r

  

  

=

z

y

x

t

t

t

T

43×

• Lecture 8 -Fei-Fei Li 19-Oct-1113

Goal of calibration

wPMP =′ [ ] wPTRK=

  

  

 −

= 100

v0

ucot

K o

o

sinθθθθ ββββ

θθθθαααααααα

  

  

= T 3

T 2

T 1

R

r

r

r

  

  

=

z

y

x

t

t

t

T

43×

Estimate intrinsic and extrinsic parameters

from 1 or multiple images

• Lecture 8 -Fei-Fei Li

What we will learn today?

• Review camera parameters

• Affine camera model (Problem Set 2 (Q4))

• Camera calibration

• Vanishing points and lines

19-Oct-1114

• [FP] Chapter 3 • [HZ] Chapter 7, 8.6

• Lecture 8 -Fei-Fei Li 19-Oct-1115

Weak perspective projection

Relative scene depth is small compared to its distance from the camera

= magnification   

−= −=

myy

mxx

'

'

0

' where

z

f m −=

• Lecture 8 -Fei-Fei Li 19-Oct-1116

Orthographic (affine) projection

Distance from center of projection to image plane is infinite

  

= =

y'y

x'x

• Lecture 8 -Fei-Fei Li 19-Oct-1117

Affine cameras

[ ] PTRKP ='

  

  

= 100

00

0s

K y

x

αααα αααα

 

  

  

  

= 10

TR

1000

0010

0001

KM

Affine case

Parallel projection matrix

 

  

  

  

= 10

TR

0100

0010

0001

KM

  

  

= 100

y0

xs

K oy

ox

αααα αααα

Projective caseCompared to

• Lecture 8 -Fei-Fei Li 19-Oct-1118

Remember….

Projectivities:   

  

=   

  

 

  

 =

  

  

1

y

x

H

1

y

x

bv

tA

1

'y

'x

p

Affinities:   

  

=   

  

 

  

 =

  

  

1

y

x

H

1

y

x

10

tA

1

'y

'x

a

• Lecture 8 -Fei-Fei Li 19-Oct-1119

[ ] PTRKP ='

  

  

= 100

00

00

y

x

K α α

 

  

  

  

= 10

TR

1000

0010

0001

KM

 

  

 =

  

  

=×   

  

×= 10

bA

1000

]affine44[

1000

0010

0001

]affine33[ 2232221

1131211

baaa

baaa

M

 

  

 =+=

  

 +   

  

 

  

 =

  

 =

1 '

2

1

232221

131211 PMP b

b

Z

Y

X

aaa

aaa

y

x P EucbA

[ ]bAMM Euc ==

We can obtain a more compact formulation than:

Affine cameras

• Lecture 8 -Fei-Fei Li 19-Oct-1120

Affine cameras

PP’

P’

; 1

'  

  

 =+=

  

 =

P bAP M

v

u P [ ]bAM =

M = camera matrix

[non-homogeneous image coordinates]

To recap:

This notation is useful when we’ll discuss affine structure from motion

• Lecture 8 -Fei-Fei Li 19-Oct-1121

Affine cameras

• Weak persp