1. Camera Calibration Coordinate change Translation P’ = P – O
Rotation P’ = R P
General transformation P’ = R[P - O]
What is a rotation matrix

2. Perspective Projection
Projection to normal coordinates
A line from (0,0,0) to P
Z=1 plane: x = X/Z , y = Y/Z
p  P
Camera as a box.
A line from (0,0,0) to P
Z=1 plane: x = X/Z , y = Y/Z
Lenses

3. From normal coordinates to pixels
If focal length is f : x = fX/Z y = fY/Z

4. Internal calibration K External calibration O & R
Calibration options:
Full calibration M
Internal calibration K
External calibration O & R

5. Calibration Use linear methods to recover M Extract from them K, R , O
What to do about Radial distortion

6. Radial Distortion

7. Radial distortion
Define d as the distance from the center of the image on the normalized image plane

8. Radial distortion
Solve the whole thing in a non-linear fashion. Bad idea
Assume u0 and v0 are known (center of image).
Try to get rid of .
Solve what you can
Return to solve the rest in a non-linear fashion.

9. Calibration from checkers pattern

10. Calibration from checkers pattern

11. Planes
Planes have a one-to-one relationship from the world to the image
Planes have a one-to-one relationship from two images of the same plane

12. Vanishing points

13. Vanishing points

14. Special cases of 
If s = 0 then w(1,2)-w(2,1)=0. If fx=fy then w(1,1)=w(2,2).
Need less equations. Only two homographies.

18. Points and Lines

19. Points and Lines

20. 3 Points on a line

27. The fundamental matrix