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

Click here to load reader

  • date post

    06-Jul-2020
  • Category

    Documents

  • view

    0
  • download

    0

Embed Size (px)

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

    Reading:

    • [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

    Reading:

    • [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

    Reading:

    • [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