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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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Camera calibration omnidirectional camera calibration

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


What is camera calibration

What is camera calibration?


What is camera calibration1

What is camera calibration?


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


Camera calibration omnidirectional camera calibration

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