Camera calibration & Omnidirectional camera calibration

1. Camera calibration & Omnidirectional camera calibration Ph.D. student Chang-RyeolLee November 26, 2013

2. 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

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

4. What is calibration? * Prof. Kuk-Jin Yoon’s slides on High-level Image Understanding and Processing

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

6. What is camera calibration?

7. What is camera calibration?

8. 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}

9. Camera calibration • Camera parameters • Intrinsic parameter K • Focal length, skew, principal point • Extrinsic parameter P • Rotation, translation

10. 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

11. Tsai’s and Zhang’s methods • Solving for Homography

12. Tsai’s and Zhang’s methods • Any rotation matrix is an orthonormal matrix • Define the symmetric matrix B as - 6 unknown variable = =

13. 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. = ,

14. Tsai’s and Zhang’s methods • Derive equations for the internal parameters of K =

15. Tsai’s and Zhang’s methods • After intrinsic parameters, the extrinsics readily follow

16. Omnidirectional camera Dioptric (fish-eye lens) Catadioptric (camera with mirror)

17. Omnidirectional camera • Camera model Dioptric case Catadioptric case

18. 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

19. 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

20. A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion • Set their Z-coordinate to 0 by planarity of pattern

21. A flexible Technique for Accurate Omnidirectional Camera Calibration and structure from motion • Cross product of a corner point make three equations

22. 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

23. 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

24. 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

25. Question or Comments ?