Lecture 2 Camera Calibration

1

Lecture 2: Camera Calibration

Lecture 2Camera Calibration

Joaquim SalviUniversitat de Girona

Visual Perception

http://www.vibot.org/

http://www.vibot.org/

http://europa.eu.int/comm/education/programmes/mundus/index_en.html

http://europa.eu.int/comm/education/programmes/mundus/index_en.html

2


Contents

2. Camera Calibration2.1 Calibration introduction

2.2 The pinhole model

2.3 The method of Hall

2.4 The method of Faugeras-Toscani – Modelling

2.5 The method of Faugeras-Toscani – Calibration

2.6 The method of Faugeras-Toscani with distortion

2.7 Experimental comparison of methods

3


Contents








4


– Dense reconstruction – Visual inspection

– Object localization – Camera localization

2.1 Calibration Introduction

• Some applications of this capability include

5


Image courtesy of C. Taylor

“The Scholar of Athens,” Raphael, 1518

2.1 Calibration Introduction – Perspective Imaging

6


WZ

WY

WX

WO

wP

Image Plane

{ }W

uP

IY

IX

IO

{ }I

Focal Point

WZ

WY

WX

WO

wP

Image Plane

{ }W

uP

IY

IX

IO

{ }I

Focal Point

1

I

u

I I

u u

X

P Y

1

W

w

W

W w

w W

w

X

YP

Z

In pixels

In metrics?

wl

wl

0

W

w

W

W w

w W

w

X

Yl

Z


7


Modelling

G(X) X ?

Calibration

X !!!

Modelling:

• Determine the equation that approximates the camera behaviour.

• Define the set of unknowns in the equation (camera parameters).

• The camera model is an approximation of the physics & optics of the camera.

Calibration:

• Get the numeric value of every camera parameter.

G(X)


8


Contents








9


Contents








10


2.2 Pinhole Model

Camera

coordinate

system

World

coordinate

system

0 0,u v

fCY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

uP

dP

IY

IXIO{ }I

RY

RX{ }R

RO

Image

coordinate

system

11


2.2 Pinhole Model (Step 1: World to Camera)

Camera

coordinate

system

World

coordinate

system

CY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

C

WK

Step 1

12


2.2 Pinhole Model (Step 2: Projection)

Camera

coordinate

system

World

coordinate

system

CY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

uPf

Step 2

wX

wY

wZ

uX

uY

RY

RX{ }R

RO

13


2.2 Pinhole Model (Step 3: Lens Distortion)

Camera

coordinate

system

World

coordinate

system

fCY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

uP

RY

RX{ }R

RO

Step 3

dP

14



dP

uP dr

CY

CX

Observed position

Ideal

projection

dr: radial distortion

a

b

Radial distortion effect (a: negative, b: positive)

Radial Distortion

15



Axis with

maximum

radial

distortion

Axis with

minimum

tangential

distortion

CY

CX

Ideal

projection

Observed

position


dt: tangential distortion

dPuP

dr

CY

CX

dt

Radial and Tangential Distortion

Image with distortionImage without distortion

16


2.2 Pinhole Model (Step 4: Camera to Image)

Camera

coordinate

system

World

coordinate

system

0 0,u v

fCY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

uP

IY

IXIO{ }I

RY

RX{ }R

RO

Image

coordinate

system

Step 4

dP

17


Camera

coordinate

system

World

coordinate

system

0 0,u v

fCY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

uP

dP

IY

IXIO{ }I

RY

RX { }R

RO

C

WK

Image

coordinate

system

Step 1

Step 2Step 3

Step 4

2.2 Pinhole Model

18


2.2 Calibration Methods (I)

• Method of Hall– Lineal method

– Transformation matrix

• Method of Faugeras-Toscani– Lineal method

– Obtaining camera parameters

• Method of Faugeras-Toscani with distortion– Iterative method

– Radial distortion

• Method of Tsai– Iterative method


– Focal distance estimation

• Method of Weng– Iterative method

– Radial and tangential distortion

• … and many more

19


Contents








20


Contents








21


2.3 The Method of Hall













22


World

coordinate

system

WZ

WYWX

WO

wP

Image plane

{ }W

uP

IY

IXIO{ }IImage

coordinate

system

2.3 The Method of Hall - Modelling

23


11 12 13 14

21 22 23 24

31 32 33 341

W

I w

u W

I w

u W

w

Xs X A A A A

Ys Y A A A A

Zs A A A A

Assume light is captured on the image plane by a linear projection

The matrix is defined up to a scale factor Multiple Solutions

A component is fixed to the unity Unique Solution

11 12 13 14

21 22 23 24

31 32 33 11

W

I w

u W

I w

u W

w

Xs X A A A A

Ys Y A A A A

Zs A A A

2.3 The Method of Hall - Modelling

24


11 12 13 14

31 32 33

21 22 23 24

31 32 33

1

1

W W W

I w w w

u W W W

w w w

W W W

I w w w

u W W W

w w w

A X A Y A Z AX

A X A Y A Z

A X A Y A Z AY

A X A Y A Z

11 12 13 14

21 22 23 24

31 32 33 11

W

I w

u W

I w

u W

w

Xs X A A A A

Ys Y A A A A

Zs A A A

11 31 12 32 13 33 14

21 31 22 32 23 33 24

W I W W I W W I W I

w u w w u w w u w u

W I W W I W W I W I

w u w w u w w u w u

A X A X X A Y A X Y A Z A X Z A X

A X A Y X A Y A Y Y A Z A Y Z A Y

2.3 The Method of Hall - Calibration

25


2 1

2

1 0 0 0 0

0 0 0 0 1

W W W I W I W I W

i w w w u w u w u wi i i i i i i i i

W W W I W I W I W


Q X Y Z X X X Y X Z

Q X Y Z Y X Y Y Y Z

2 1

2

I

i u i

I

i u i

B X

B Y

T

11 12 13 14 21 22 23 24 31 32 33A A A A A A A A A A A A

1

t tA Q Q Q B

QA B

Pseudoinverse leads to a unique solution:

1A Q B

Obtaining 11 unknowns and each 2D point gives two equations

So, at least 6 points are needed. More points leads to a more accurate solution.

11 31 12 32 13 33 14

21 31 22 32 23 33 24

W I W W I W W I W I

w u w w u w w u w u

W I W W I W W I W I

w u w w u w w u w u

A X A X X A Y A X Y A Z A X Z A X

A X A Y X A Y A Y Y A Z A Y Z A Y


26


Camera

coordinate

system

CY

CX CZ

CO{ }C

IY

IXIO{ }I

RY

RX

RO

{ }R

World

coordinate

system

WZ

WYWX

WO{ }W

Reconstruction

Area

Image of the calibrating pattern

2 1

2

1 0 0 0 0

0 0 0 0 1

W W W I W I W I W


W W W I W I W I W


Q X Y Z X X X Y X Z

Q X Y Z Y X Y Y Y Z

2 1

2

I

i u i

I

i u i

B X

B Y

1t t

A Q Q Q B


27


Contents








28


Contents








29


2.4 The Method of Faugeras-Toscani













30


Camera

coordinate

system

World

coordinate

system

0 0,u v

fCY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

uP

IY

IXIO{ }I

RY

RX { }R

RO

C

WK

Image

coordinate

system

Step 1

Step 2Step 3

Step 4


31


• Extrinsic parameters: Model the situation and orientation of the camera with

respect to a world co-ordinate system.

• Intrinsic parameters: Model the behaviour of the internal geometry and the optical

characteristics of the camera.

u

w

v

Yc

Xc

Zc

Oc

Oi

(u0, v0)

Pu

P

image

co-ordinate

system

(píxels)

retinal

co-ordinate

system

(mm.)

Image plane

Retinal plane

Yr

Xr

Zr

w

World

co-ordinate

system

WZ

WY

WX

WO { }W

Camera

co-ordinate system


32


Yc

Xc

Zc

Zw

YwOc

Ow

Pw

Camera

co-ordinate

system World

co-ordinate system

Retinal Plane

K

Xw

X

C

W Y

Z

t

T t

t

11 12 13

21 22 23

31 32 33

, , ,C

W

C

W

R Rot X Rot Y Rot Z

r r r

R r r r

r r r

C W

w w

C C W C

w W w W

C W

w w

X X

Y R Y T

Z Z

1 1

C W

Cw w

W

P PK

3 3 3 1

1 30 1

C C

C W Wx x

W

x

R TK

2.4 Extrinsic Parameters

33


CPw

CPu

Yc

Xc

Zc

Oc C

f

PZc

Yu

PYc XuPXc

C

C w

u C

w

C

C w

u C

w

XX f

Z

YY f

Z

2.4 The Intrinsic Parameters: Ideal Projection

34


pixel

Retinal

plane

(0, 0)

Yr

Xr (0, 0)

(Xd, Yd)

Image

Plane

(Xp, Yp)

R C

d u u

R C

d v u

X k X

Y k Y

2.4 The Intrinsic Parameters: Pixel Conversion

35


Yr

Xr

V

U(0, 0)

Principal point

(u0,v0)

Computer image

co-ordinate

system

Camera

co-ordinate

system

0

0

I R

d d

I R

d d

X X u

Y Y v

2.4 The Intrinsic Parameters: Principal Point

36


Camera

coordinate

system

World

coordinate

system

0 0,u v

fCY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

uP

IY

IXIO{ }I

RY

RX { }R

RO

C

WK

Image

coordinate

system

Step 1

Step 2Step 3

Step 4


37


Real projection on the image plane (Xi, Yi)

(Xw, Yw, Zw) 3D object point with respect to world co-ordinate system

Affine transformation.

Modelled parameters: R, T

(Xc, Yc, Zc) 3D object point with respect to camera co-ordinate system

Perspective transformation.

Modelled parameter: f

(Xu, Yu) Ideal projection on the retinal plane

Pixel adjustment

Modelled parameters: ku, kv

(Xp, Yp) Real projection on the image plane

Adaptation to the computer image buffer

Modelled parameters: u0, v0


38


C

C w

u C

w

C

C w

u C

w

XX f

Z

YY f

Z

R C

d u u

R C

d v u

X k X

Y k Y

0

0

I R

d d

I R

d d

X X u

Y Y v

0

0

C

I w

u u C

w

C

I w

u v C

w

XX k f u

Z

YY k f v

Z

0

0

0 0

0 0

0 0 1 01

C

I w

u u C

I w

u v C

w

Xs X u

Ys Y v

Zs

vv

uu

fk

fk

2.4 The Method of Faugeras-Toscani - Modelling

39


11 12 13

0

21 22 23

0

31 32 33

0 0

0 0

0 0 1 00 0 0 1 1

W

xI w

u u W

yI w

u v W

z w

r r r t Xs X u

r r r t Ys Y v

r r r t Zs

1 0 3 0

2 0 3 0

3

u u x z

v v y z

z

r u r t u t

A r v r t v t

r t

Intrínsecs Extrínsecs

2.4 The Method of Faugeras-Toscani - Modelling

40


Contents








41


Contents








42


11 12 13

0

21 22 23

0

31 32 33

0 0

0 0

0 0 1 00 0 0 1 1

W

xI w

u u W

yI w

u v W

z w

r r r t Xs X u

r r r t Ys Y v

r r r t Zs

1 0 3 0

2 0 3 0

3

u u x z

v v y z

z

r u r t u t

A r v r t v t

r t

Intrínsecs Extrínsecs

2.5 The Method of Faugeras-Toscani – Modelling

43


1 14 3 34

2 24 3 34

0

0

W I W

w u w

W I W

w u w

A P A X A P A

A P A Y A P A

31 14

34 34 34

32 24

34 34 34

I W W I

u w w u

I W W I

u w w u

AA AX P P X

A A A

AA AY P P Y

A A A

1 1 2

3 2 2

I W W I

u w w u

I W W I

u w w u

X T P C T P X

Y T P C T P Y

v

z

y

v

zz

z

u

z

xu

zz

t

tvC

t

rv

t

rT

t

rT

t

tuC

t

ru

t

rT

022

03

3

32

011

03

1

2.5 The Method of Faugeras-Toscani – Calibration

1 0 3 0

2 0 3 0

3

u u x z

v v y z

z

r u r t u t

A r v r t v t

r t

343

242

141

AA

AA

AA

1343

242

141

w

W

u

I

u

I

P

AA

AA

AA

s

Ys

Xs

44


1

2

3

1

2

T

T

X T

C

C

B QX

1 3

1 3

0 1 0

0 0 1

t tW I W

w u w xi i i

t tI W W

x u w wi i i

P X PQ

Y P P

I

u i

I

u i

XB

Y

1

t tX Q Q Q B

2.5 The Method of Faugeras-Toscani – Calibration

1 1 2

3 2 2

I W W I

u w w u

I W W I

u w w u

X T P C T P X

Y T P C T P Y

11 unknowns

minimum 6 points

45


v

z

y

v

zz

z

u

z

xu

zz

t

tvC

t

rv

t

rT

t

rT

t

tuC

t

ru

t

rT

022

03

3

32

011

03

1

3 1r 2

1zt

T

2.5 The Method of Faugeras-Toscani – tz

𝑅 =

𝑟1𝑟2𝑟3

46


1 2 1 2

1 2 1 2

cos

sin

v v v v

v v v v

0

1

1

0

t

i j

t

i j

i j

i j

r r i j

r r i j

r r i j

r r i j

v

z

y

v

zz

z

u

z

xu

zz

t

tvC

t

rv

t

rT

t

rT

t

tuC

t

ru

t

rT

022

03

3

32

011

03

1

2.5 The Method of Faugeras-Toscani – Intrinsics

02

33130

33310

32121

·· u

t

rr

t

r

t

ru

t

r

t

r

t

r

t

ru

t

rTTTT

z

u

zzzzz

u

zz

t

2

1zt

T

2

2

210

T

TTu

t

47


1 2 1 2

1 2 1 2

cos

sin

v v v v

v v v v

0

1

1

0

t

i j

t

i j

i j

i j

r r i j

r r i j

r r i j

r r i j

v

z

y

v

zz

z

u

z

xu

zz

t

tvC

t

rv

t

rT

t

rT

t

tuC

t

ru

t

rT

022

03

3

32

011

03

1

2 31 2

0 02 2

2 2

1 2 2 3

2 2

2 2

tt

t t t t

u v

T TT Tu v

T T

T T T T

T T

2.5 The Method of Faugeras-Toscani – Intrinsics

48


1 2 1 2

1 2 1 2

cos

sin

v v v v

v v v v

0

1

1

0

t

i j

t

i j

i j

i j

r r i j

r r i j

r r i j

r r i j

v

z

y

v

zz

z

u

z

xu

zz

t

tvC

t

rv

t

rT

t

rT

t

tuC

t

ru

t

rT

022

03

3

32

011

03

1

2.5 The Method of Faugeras-Toscani – Extrinsics

tt

t

tt

t

u

z

z

u

zz

TT

T

T

TTTTr

TTT

T

T

TTTTr

tu

t

rTr

t

ru

t

rT

21

2

2

2

21211

221

2

2

2

2

212110

311

10

31

1

49


1 2 1 2

1 2 1 2

cos

sin

v v v v

v v v v

0

1

1

0

t

i j

t

i j

i j

i j

r r i j

r r i j

r r i j

r r i j

v

z

y

v

zz

z

u

z

xu

zz

t

tvC

t

rv

t

rT

t

rT

t

tuC

t

ru

t

rT

022

03

3

32

011

03

1

2 1 2

1 1 22

1 2 2

2 2 3

2 3 22

2 3 2

2

3

2

t

t t

t

t t

T T Tr T T

T T T

T T Tr T T

T T T

Tr

T

2 1 2

1 2

1 2 2

2 2 3

2 2

2 3 2

2

1

t

x t t

t

y t t

z

T T Tt C

T T T

T T Tt C

T T T

tT

2.5 The Method of Faugeras-Toscani – Extrinsics

50


Contents








51


Contents








52


2.6 The Method of Faugeras-Toscani with distortion













53


Camera

coordinate

system

World

coordinate

system

0 0,u v

fCY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

uP

dP

IY

IXIO{ }I

RY

RX { }R

RO

C

WK

Image

coordinate

system

Step 1

Step 2Step 3

Step 5

Step 4


54


Ideal

projection

Observed

position

drdt

Xr

Yr


dt: tangential distortion

PuPd

2.6 Lens Distortion

55


a

b

Radial distorsion effect Tangential distorsion effect

Xr

Axe of a

maximum

tangential

distortion

Axe of a

minimum

tangential

distortion

Radial distorsion is the most important and usually the only considered in

calibration.

2.6 Lens Distortion

56


X X Du d x Y Y Du d y

D X k rx d 1

2 D Y k ry d 1

2r X Yd d 2 2

2 4

1 2

2 4

1 2

2 2

C

x d

C

y d

C C

d d

D X k r k r

D Y k r k r

r X Y

k1 is the most important component

and usuallly sufficient in most

applications.

2.6 Lens Distortion

Model of Faugeras-Toscani with distortion:

57


u

w

v

Yc

Xc

Zc

Oc

Oi

(u0, v0)

Pu

P

Camera

co-ordinate system

image

co-ordinate

system

f Pd

retinal

co-ordinate

system

Image plane

Retinal plane

Yr

Xr

Zr

X

f

P

P

u Xc

Zc

Y

f

P

P

u Yc

Zc

X X Du d x Y Y Du d y

D X k rx d 1

2 D Y k ry d 1

2r X Yd d 2 2

X k Xp u d Y k Yp v d

X X ui p 0 Y Y vi p 0


58


Camera

coordinate

system

World

coordinate

system

0 0,u v

fCY

CX CZ

CO

WZ

WYWX

WO

wP

Image plane

{ }W

{ }C

uP

dP

IY

IXIO{ }I

RY

RX { }R

RO

C

WK

Image

coordinate

system

Step 1

Step 2Step 3

Step 5

Step 4


59


(Xw, Yw, Zw) 3D object point with respect to world co-ordinate system

Affine transformation.

Modelled parameters: R, T

(Xc, Yc, Zc) 3D object point with respect to camera co-ordinate system

Perspective transformation.

Modelled parameter: f

(Xu, Yu) Ideal projection on the retinal plane

Radial lens distortion.

Modelled parameter: k1

(Xd, Yd) Real projection on the retinal plane

Pixel adjustment

Modelled parameters: ku, kv

(Xp, Yp ) Real projection on the image plane

Adaptation to the computer image buffer

Modelled parameters: u0, v0

(Xi, Yi) Real projection on the image plane


60


2

1

2

1

C

C Cw

d dC

w

C

C Cw

d dC

w

Xf X k r X

Z

Yf Y k r Y

Z

0

0

I

dC

d

u

I

dC

d

v

X uX

k

Y vY

k

1 1

C W

w w

C W

Cw w

WC W

w w

X X

Y YK

Z Z

r X Yd d 2 2

The model is NON-LINEARIterative minimisation:

• Newton-Raphson

• Levenberg-Marquardt


61


Contents








62


Contents








63


Hall Faugeras Faugeras distorted

Tsai Weng

Transformation

matrix

Step 3Lens

Distortion

Step 2Projection

Step 1World2camera

Transformation

with , , , tx, ty and tz

Projection with f

Radial distortion with k1

UndistortedMultiple

distortion

k1, g1, g2, g3, g4

Transformation with

u0, v0 , ku and kv

Transformation

with u0, v0 and sx Transformation

with u0, v0,

ku and kv

Step 4Camera2image

C C W C

w W w WP P T R

,

C C

C Cw w

u uC C

w w

X YX f Y f

Z Z

C C

w uP P

C C

u dP P

C I

d dP P

C C

u dP P

0

0

I C

d u d

I C

d v d

X k X u

Y k Y v

2 2

1

2 2

1

C C C C C

u d u u u

C C C C C

u d u u u

X X k X X Y

Y Y k Y X Y

1'

0

1

0

I C

d x x d

I C

d y d

X s d X u

Y d Y v

=

W C

w wP P

I W

d wP P A

2.7 Experimental Comparison - Methods

64


wP

Optical Ray

3Dd

2.7 Experimental Comparison - Accuracy Evaluation

• 3D Measurement

– Distance with respect to the optical ray

– Normalized Stereo Calibration Error

• 2D Measurement

– Accuracy of distorted image coordinates

– Accuracy of undistorted image

coordinates

1 22 2

2 2 21

ˆ ˆ1

NSCEˆ 12

C C C Cn

w w w wi i i i

Ci w u vi

X X Y Y

n Z

Camera

coordinate

system

World

coordinate

system

fCY

CX

WZ

WX

WO

wP

Image plane

{ }W

uP

dP

IX{ }I

RX

{ }R

RO

Image

coordinate

system

ˆuP

ˆdP

0 0,u v

WYCZ

CO { }C

IY

IO

RY

uP

ˆuP

0 0,u v

dd

Observed Point

Linear Projection

- distortion

+ distortion

ud

ˆdP

dP

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2.7 Experimental Comparison: Synthetic Images (I)

2D distorted image (pix.) 2D undistorted image (pix.)

Mean Standard

desviation

Max Min Mean Standard

desviation

Max Min

1 Hall 0.2676 0.1979 1.2701 0.0213 0.2676 0.1979 1.2701 0.0213

2 Faugeras 0.2689 0.1997 1.2377 0.0075 0.2689 0.1997 1.2377 0.0075

3 Faugeras with distortion 0.0840 0.0458 0.2603 0.0081 0.0834 0.0454 0.2561 0.0080

4 Tsai 0.0838 0.0457 0.2426 0.0035 0.0832 0.0453 0.2386 0.0035

5 Weng 0.0845 0.0455 0.2608 0.0019 0.0843 0.0443 0.2584 0.0129

2D distorted

0

0,05

0,1

0,15

0,2

0,25

0,3

1 2 3 4 5

pix

.

Mean Standard deviation

2D undistorted

0

0,05

0,1

0,15

0,2

0,25

0,3

1 2 3 4 5p

ix.


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2.7 Experimental Comparison: Synthetic Images (II)

3D position (mm) NSCE

Mean Standard

desviation

Max Min

1 Hall 0.1615 0.1028 0.5634 0.0113 n/a

2 Faugeras 0.1811 0.1357 0.8707 0.0147 0.6555

3 Faugeras NR with distortion 0.0566 0.0307 0.1694 0.0055 0.2042

4 Tsai optimized 0.0565 0.0306 0.1578 0.0087 0.2037

5 Weng 0.0570 0.0305 0.1696 0.0088 0.2064

Normalized Stereo Calibration Error

Normalized Stereo Calibration Error

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

1 2 3 4 5

NSCE

3D position

0

0,05

0,1

0,15

0,2

1 2 3 4 5

mm

.


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Computing Time

160 punts 1800 punts

• Hall 1 ms 70 ms

• Faugeras 1 ms 70 ms

• Faugeras with distortion 10 ms 380 ms

• Tsai 10 ms 530 ms

• Weng 51 ms 4216 ms

Pentium III at 1 GHz.

2.7 Experimental Comparison: Synthetic Images (III)

68


2.7 Experimental Comparison: Real Images (I)

Camera

coordinate

system

CY

CX CZ

CO{ }C

IY

IXIO{ }I

RY

RX

RO

{ }R

World

coordinate

system

WZ

WYWX

WO{ }W

Reconstruction

Area

Image of the calibrating pattern


Mean Standard

desviation

Max Min

Hall 0.5219 0.2595 1.1370 0.0143 n/a

Faugeras 0.7782 0.4253 2.0210 0.0187 4.0649

Faugeras with distortion 0.4967 0.3367 1.5642 0.0094 2.5489

Tsai 0.4815 0.3023 1.4014 0.0093 2.4836

Weng 0.4740 0.2904 1.2669 0.0087 2.4556

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2.7 Experimental Comparison: Real Images (II)


Mean Standard

desviation

Max Min

Hall 1.5698 0.9842 8.9249 0.0247 n/a

Faugeras 1.6187 0.9856 8.8812 0.0302 2.0175

Faugeras with distortion 0.9930 0.5660 3.2386 0.0154 0.9909

Tsai 0.9927 0.5655 3.2311 0.0153 0.9908

Weng 0.9896 0.5724 3.3526 0.0149 0.9869

Image of the calibration patternStereo camera over a mobile robot

70


2.7 Experimental Comparison - Conclusions

• Implementation of 5 of the most used camera calibration

methods

– Notation was unified

– The methods were compared in terms of model and

calibration

• The accuracy of non-linear methods is better than linear

methods

• Modelling of radial distortion is quite sufficient when high

accuracy is required

• Accuracy measuring methods obtain similar results if they are

relatively compared

Additional bibliography:

J. Salvi, X. Armangué and J. Batlle. A Comparative Review of Camera Calibrating Methods with Accuracy Evaluation. Pattern Recognition, PR, pp. 1617-1635, Vol. 35, Issue 7, July 2002.

Lecture 2 Camera Calibration

Education

Transcript of Lecture 2 Camera Calibration