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Camera calibration & Omnidirectional camera calibration. Ph.D. student Chang- Ryeol Lee November 26, 2013. Contents. Camera model What is camera calibration? Camera calibration Tsai’s and Zhang’s methods Omnidirectional camera Camera model

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slide1

Camera calibration &

Omnidirectional camera calibration

Ph.D. student

Chang-RyeolLee

November 26, 2013

contents
Contents
  • Camera model
  • What is camera calibration?
  • Camera calibration
    • Tsai’s and Zhang’s methods
  • Omnidirectional camera
    • Camera model
    • Calibration: A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion
camera model
Camera model

* Prof. Kuk-Jin Yoon’s slides on High-level Image Understanding and Processing

what is calibration
What is calibration?

* Prof. Kuk-Jin Yoon’s slides on High-level Image Understanding and Processing

camera model1
Camera model

* Prof. Kuk-Jin Yoon’s slides on High-level Image Understanding and Processing

camera calibration
Camera calibration
  • We know positions of pattern corners with respect to world and image coordinate

3D corners

2D corners

y

z

x

Grid size:3cm

{World}

{Image}

camera calibration1
Camera calibration
  • Camera parameters
    • Intrinsic parameter K
      • Focal length, skew, principal point
    • Extrinsic parameter P
      • Rotation, translation
tsai s and zhang s methods
Tsai’s and Zhang’s methods
  • Retrieve not only the intrinsic but also extrinsic parameters
  • Set their Z-coordinate to 0
    • because the 3D points on the object are coplanar.
  • A homography between m and M
tsai s and zhang s methods1
Tsai’s and Zhang’s methods
  • Solving for Homography
tsai s and zhang s methods2
Tsai’s and Zhang’s methods
  • Any rotation matrix is an orthonormal matrix
  • Define the symmetric matrix B as

- 6 unknown variable

=

=

tsai s and zhang s methods3
Tsai’s and Zhang’s methods
  • One image offers two linear equations in elements of B
  • We can get intrinsic parameter through 3 or more images
    • because unknown variable() is 6.

= ,

tsai s and zhang s methods4
Tsai’s and Zhang’s methods
  • Derive equations for the internal parameters of K

=

tsai s and zhang s methods5
Tsai’s and Zhang’s methods
  • After intrinsic parameters, the extrinsics readily follow
omnidirectional camera
Omnidirectional camera

Dioptric (fish-eye lens)

Catadioptric

(camera with mirror)

omnidirectional camera1
Omnidirectional camera
  • Camera model

Dioptric case

Catadioptric case

a flexible technique for accurate omnidirectional camera calibration and structure from motion
A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion
  • Don’t care whether catadioptric or dordioptric
  • General method even NASA use this currently
  • Key idea
    • Camera modeling by Taylor expansion
a flexible technique for accurate omnidirectional camera calibration and structure from motion1
A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion
  • No focal length, skew, principal point
  • Calibration parameters
    • Taylor expansion coefficients a
    • Rotation R
    • Translation t
a flexible technique for accurate omnidirectional camera calibration and structure from motion2
A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion
  • Set their Z-coordinate to 0 by planarity of pattern
a flexible technique for accurate omnidirectional camera calibration and structure from motion3
A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion
  • Cross product of a corner point

make three equations

a flexible technique for accurate omnidirectional camera calibration and structure from motion4
A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion
  • The 3rd equation can be linearly expressed on unknowns
    • We know
  • Homogeneous linear least square problem is solved by SVD
a flexible technique for accurate omnidirectional camera calibration and structure from motion5
A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion
  • is uniquely determined by
  • Extrinsic parameter is determined except for
  • The 1st, 2nd equations are used to determine

, where

a flexible technique for accurate omnidirectional camera calibration and structure from motion6
A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion
  • Equations stacked with K observations of pattern is expressed linearly

where

  • Unknown parameter are estimated

1st

Kth

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